Browse Linearity problems Studdy Solved!

Problem 4401

Sketch the graph for the constraints: $x \geq 50$ , $y \geq 60$ , $x+y \leq 200$ , $4x+5y \leq 900$ . Find the feasible region and minimize $P=0.3x+0.5y$ .

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Problem 4402

Chang's trip to the mountains took 7 hours; the return took 5 hours at 18 mph faster. Find the distance to the mountains.

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Problem 4403

Two trains start 420 miles apart, one at 85 mph and the other at 65 mph. How long until they meet?

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Problem 4404

Solve the equation: $9y + 5 = 9(y + 5) - 46$ .

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Problem 4405

Two cars start 400 km apart, meet in 2 hours. One is 18 km/h slower. Find the speed of the slower car.

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Problem 4406

What percent $n$ of 20 equals 4? Find $n$ .

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Problem 4407

Find the ordered pair $(x, y)$ that satisfies the equation $5x + y = 8$ .

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Problem 4408

Find $b$ and $Y Z$ given $X Y=6b$ , $Y Z=8b$ , and $X Z=154$ with $Y$ between $X$ and $Z$ .

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Problem 4409

Find $Y$ and $Y Z$ given $X Y=11$ , $Y Z=4c$ , and $X Z=83$ .

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Problem 4410

Find three consecutive integers that add up to 339. Let the smallest be $n$ , then the integers are $n$ , $n+1$ , and $n+2$ .

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Problem 4411

Solve the linear equation: $\frac{6 z-4}{4}+\frac{13}{8}=\frac{12 z+1}{8}$ .

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Problem 4412

How many hours does Nisha need to make 64 pairs of ghungroos using the equation $y=4.75 x-2.5$ ?

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Problem 4413

Solve the linear equation: $6x + 5 = 6(x + 2) - 7$ .

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Problem 4414

Find $DE$ if $DF = 42$ , $DE = 7x + 1$ , $EF = 4x - 3$ , and $DF = DE + EF$ .

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Problem 4415

Solve the equation: $6(5x - 5) = -31(3 - x)$

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Problem 4416

Solve the equation: $6y + 8 = 6(y + 3) - 10$ .

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Problem 4417

Solve the linear equation: $6z + 4 = 6(z + 3) - 14$ .

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Problem 4418

Solve the equation: $\frac{2 y-6}{4}+\frac{9}{8}=\frac{4 y+4}{8}$ .

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Problem 4419

Solve the equation: $\frac{2y-3}{5} + \frac{9}{10} = \frac{4y+5}{10}$ .

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Problem 4420

Solve the linear equation: $6(3x - 3) = -19(3 - x)$ .

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Problem 4421

Solve the linear equation: $4t + 7 = 4(t + 4) - 16$ .

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Problem 4422

Find three consecutive integers that add up to 345. Let the smallest be $n$ , so the integers are $n$ , $n+1$ , $n+2$ .

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Problem 4423

Find the equation of the line through $(-1,-4)$ parallel to $3x+y=5$ . Choices: $y=3x+1$ , $y=-3x+7$ , $y=-3x-7$ , $y=3x-1$ .

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Problem 4424

Solve the compound inequality: $x-3 \leq 6$ and $x+2 \geq 4$ . Provide the solution set in interval and graph forms.

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Problem 4425

Solve the compound inequality: $-3x > 6$ and $x + 5 > 0$ . Provide the solution set in interval and graph forms.

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Problem 4426

Solve the compound inequality: $x \leq 5$ or $x \leq 11$ . Provide the solution set in interval and graph forms.

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Problem 4427

Solve the compound inequality $x > -5$ or $x \leq 4$ and express the solution in interval and graph form.

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Problem 4428

How many pitchers of lemonade does Molly need to serve 16 large glasses and 12 small glasses with none left over?

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Problem 4429

A truck driver is 150 miles from his exit, driving at 50 mph. Find his min and max driving hours before a rest stop within 30 miles.

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Problem 4430

Simplify the expression: $7s - 3s$ .

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Problem 4431

Simplify the expression by combining like terms: $-3x + 9x$ .

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Problem 4432

Solve the compound inequality $x+6>13$ or $-3x+3 \geq 6$ and provide the solution in interval and graph form.

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Problem 4433

Identify the first term in $6a + 6$ . Is it a variable or constant term? If variable, state the coefficient.

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Problem 4434

Solve the compound inequality $x < -2$ and $x > -6$ . Provide the solution set in interval and graph forms.

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Problem 4435

Solve the inequality $x<7$ or $x<-3$ . Provide the solution set in interval notation and graph form.

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Problem 4436

Solve the compound inequality: $x+1 \geq 5$ and $x-2 \leq 10$ . Provide the solution in interval and graph forms.

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Problem 4437

Find the equation of a line in point-slope form that passes through $(5,-3)$ with a slope of $-\frac{1}{2}$ .

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Problem 4438

Find the equation of a line in point-slope form with slope $\frac{1}{6}$ through the point $(10,2)$ .

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Problem 4439

Find the equation of a line in point-slope form with slope -4 through the point $(-3,8)$ . Simplify all fractions.

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Problem 4440

Find the equation of a line with slope 6 that passes through the point $(6,8)$ in point-slope form.

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Problem 4441

Find the equation of the line in point-slope form with point $(-9,9)$ and slope $\frac{1}{6}$ .

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Problem 4442

Determine the range of the function $f(x)=3x+2$ for the domain $\{0,2,4,6\}$ .

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Problem 4443

Solve the equation: $4 x - 5 = 8 - 2 x$ .

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Problem 4444

Find $x$ such that $y=5x+4$ is within 0.003 of 7. What values of $x$ satisfy this?

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Problem 4445

Solve for $x$ in the equation $2 x = 9 - 7 x$ .

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Problem 4446

Solve the equations: (b) $8x + 5 = 3(2x - 11)$ and (e) $\frac{1 - 4x}{8} = \frac{3x - 7}{4}$ .

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Problem 4447

mb A block of mass 3 m can move without friction on a horizontal table. This block is attached to another block of mass $m$ by a cord that passes over a frictionless pulley, as shown above. If the masses of the cord and the pulley are negligible, what is the magnitude of the acceleration of the descending block? (A) $g / 4$ (B) $g / 3$ (C) $2 g / 3$ (D) g

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Problem 4448

Question 4 (2 points) Happy Belly Restaurant solls to items: turkey sandwiches and hamburgers. The turkey sandwich accounts for $30 \%$ of their sales revenue, whereas the hamburger accounts for $70 \%$ of their sales revenue. Happy Belly also knows that the margin(\%) of the turkey sandwich is much higher than that of the hamburger: whereas the hamburger's margin(\%) is 20\%, the margin(\%) of the turkey sandwich is $50 \%$ .
Based on this information, Happy Belly wants to understand their break-even revenue. Given that their fixed operating costs per month is $\$ 58,000$ ; how much revenue should the company be making per month to break even? \$200,000 \$290,000 \$150,000 \$100,000

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Problem 4449

Give the equation of the line graphed below.

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Problem 4450

Write a system of linear equations represented by the augmented matrix. Give your answer in standard form using the variables $x$ and $y$ . The equations in the system should be in the same order as the rows in the given'augmented matrix. $\left[\begin{array}{cc:c} -4 & 8 & 3 \\ -1 & 5 & 9 \end{array}\right]$
System of Equations:

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Problem 4451

8 Which of the following equations represents a line without a $y$ -intercept? (a) $y=4$ (b) $x=-4$ (c) $x+y=2$ (d) $y=3 x$

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Problem 4452

12 Which line is parallel to the line $y=-2 x-3$ ? (a) $y=-2 x+2$ c. $y=2 x+2$ (b) $y=2 x-2$ (d) $y=-0.5 x-2$

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Problem 4453

Write the sentence as an equation. the product of 189 and $h$ equals $m$
Type a slash ( / ) if you want to use a division sign. $\square$ Submit

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Problem 4454

Solve the formula for the given variable. $\begin{array}{l} T=f m-g m ; m \quad \text { (Engineering) } \\ m=\square \end{array}$
Need Help? Read It Watch It

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Problem 4455

$5(3 x+4)+2=37$

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Problem 4456

Solve for $x$ . $2(3 x-6)=12$
Simplify your answer as much as possible. $x=$

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Problem 4457

Soient les vecteurs: $\vec{U}=2 \vec{i}+6 \vec{k}, \vec{V}=8 \vec{i}+y \vec{j}+z \vec{k}, \vec{P}=3 \vec{i}-4 \vec{j}+2 \vec{k}, \vec{Q}=-2 \vec{i}+y \vec{j}+12 \vec{k}$ 1) Déterminer yet $z$ pour que les vecteurs $\vec{U}$ et $\vec{V}$ soient colinéaires: 2) Déterminer la valeur de y potur que les vecteurs $\vec{p}$ et $\vec{Q}$ soient perpendiculaires:

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Problem 4458

Soient les vecteurs: $\vec{U}=2 \vec{i}+6 \vec{k}, \vec{V}=8 \vec{i}+y \vec{j}+z \vec{k}, \vec{P}=3 \vec{i}-4 \vec{j}+2 \vec{k}, \vec{Q}=-2 \vec{i}+y \vec{j}+12 \vec{k}$ 1) Déterminer yet $z$ pour que les vecteurs $\vec{U}$ et $\vec{V}$ soient colinéaires: 2) Déterminer la valeur de y potur que les vecteurs $\vec{p}$ et $\vec{Q}$ soient perpendiculaires:

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Problem 4459

3. Хоёр тооны яи. .ихр 5-тай тэнцуу бөгөөд эдгээр тоонууд $\frac{1}{3}: \frac{1}{4}$ г. ларьцдаг бол бага тоог ол. A. 20 B. 16 C. 24 D. 18 E. 15

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Problem 4460

$4 a=5 b, 9 c=7 a$ бол $\frac{b}{c}=?$

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Problem 4461

DEPARTMEN: OF M in ( 7 PO
UESTIONS 1-7: In the following 7 QUESTIONS, choose the correct answers Q1) What is the slope of a line which passes through the points $(-4,3)$ and $(-2,-5)$ ? A) 1 B) -4 C) 4 D) $-\frac{1}{3}$ 22) The equation of a line passes through the point $(2,0)$ and has a slope of -5 is A) $y=5 x+10$ B) $y=-5 x+10$ C) $y=-5 x-10$ D) $y=-5 x$ 3) The $y$ -intercept of a line $4 x-2 y+8=0$ is A) 2 B) 4 C) -2 D) 8 4) A system of two linear equations has only one solution if its equations have A) the same slope B) different slope B) the same $x$ -intercept D) the same y-intercept 5) Which of the following linear systems has no solution? A) $y=4 x-5, \quad y=-\frac{1}{4} x+5$ B) $y+4 x=-2, \quad y=-4 x+5$ C) $y+4 x=-2, \quad 2 y+8 x=-4$ D) None of the above
Solve the linear system: $\quad 2 x-y=6, \quad-x+3 y=2$ $x=1, y=2$ B) $x=4, y=2$ C) $x=2, y=2$ D) $x=2, y=4$
The following diagram shows the demand (D) and supply (S) lines for a product. he equilibrium quantity for this product? B) 30

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Problem 4462

Question 25: The intercept on $x$ -axis of the line $4 x-3 y=16$ is
Single-digit integer (-9 to 9)
Type your answer here

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Problem 4463

Question 28: If lines whose equation are $y=2 x-5$ and $2 y+p x=3$ are perpendicular to each other, then the value of $p$ is
Single-digit integer (-9 to 9)
Type your answer here

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Problem 4464

Find the slope-intercept equation of the line that has the given characteristics. Slope 9.5 and $y$ -intercept $(0,-5)$
The slope-intercept equation $y=$ $\square$ (Use integers or decimals for any numbers in the expression.)

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Problem 4465

Solve the following system of equations by the elimination method. $\begin{array}{l} \frac{1}{3} x+\frac{1}{5} y=6 \\ \frac{1}{3} x-\frac{3}{5} y=-6 \end{array}$
What is the solution of the system? Select the correct choice below, and fill in the answer box if necessary. A. The solution is $\square$ (Type an ordered pair. Use integers or fractions for any numbers in the expression.) B. There are infinitely many solutions. C. There is no solution.

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Problem 4466

Fully simplify $9 x+5 y+5+2 y-3 x$

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Problem 4467

Find an equation of the line having the given slope and containing the given point. $m=-5,(6,0)$
The equation of the line is $y=$ $\square$ (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.)

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Problem 4468

Solve by the elimination method. $\begin{array}{l} 2 x+3 y=1 \\ 4 x+6 y=2 \end{array}$

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Problem 4469

Solve the given system by the substitution method. $\begin{array}{r} 2 x+y=6 \\ 7 x-4 y=6 \end{array}$

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Problem 4470

UESTIONS 1-7: ( 7 PO
In the following 7 QUESTIONS, choose the correct answers Q1) What is the slope of a line which passes through the points $(-4,3)$ and $(-2,-5)$ ? A) 1 B) -4 C) 4 D) $-\frac{1}{3}$ 22) The equation of a line passes through the point $(2,0)$ and has a slope of -5 is A) $y=5 x+10$ B) $y=-5 x+10$ C) $y=-5 x-10$ D) $y=-5 x$ 3) The $y$ -intercept of a line $4 x-2 y+8=0$ is A) 2 B) 4 C) -2 D) 8 4) A system of two linear equations has only one solution if its equations have A) the same slope B) different slope B) the same x -intercept D) the same $y$ -intercept 5) Which of the following linear systems has no solution? A) $y=4 x-5, \quad y=-\frac{1}{4} x+5$ B) $y+4 x=-2, \quad y=-4 x+5$ C) $y+4 x=-2, \quad 2 y+8 x=-4$ D) None of the above
Solve the linear system: $\quad 2 x-y=6, \quad-x+3 y=2$ $x=1, y=2$ B) $x=4, y=2$ C) $x=2, y=2$ D) $x=2, y=4$
The following diagram shows the demand (D) and supply (S) lines for a product. he equilibrium quantity for this product?

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Problem 4471

Fill in the gaps to factorise this expression. $16 m+8=8(-\square)$

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Problem 4472

Lines Finding slope given the graph of a line in quadrant 1 that models a real-...
Keisha makes house calls. For each, she is paid a base amount and makes additional money for each hour she works. The graph below. shows her pay (i dollars) versus the number of hours worked.
Use the graph to answer the questions. (a) How much does her pay increase for each hour worked? \\square$ (h) What is the slone of the line?

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Problem 4473

$\left\{\begin{array}{l}2 x=4 y-2 \\ 1+x=3 y\end{array}\right.$

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Problem 4474

Moira solved a problem on the board. What error did Moira make and how can she correct it? $\begin{aligned} 12 x+10 & =54-10 x \\ 12 x+10-10 & =54-10 x-10 \\ 12 x & =44-10 x \\ 12 x-10 x & =44-10 x+10 x \\ 2 x & =44 \\ x & =22 \end{aligned}$ On the left side of the equation, Moira should have subtracted 10x and on the right side of the equation, Moira should have added 10x. On the left side of the equation, Moira should have added $10 x$ , and on the right side of the equation, Moira should have subtracted $10 x$ . On the left side of the equation, Moira should have added 10x, and on the right side of the equation, Moira should have also added 10x. On the left side of the equation, Moira should have subtracted $10 x$ , and on the right side of the equation, Moira should have also subtracted $10 x$ .

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Problem 4475

b) $\left\{\begin{array}{l} \{x-2 y=1 \\ x=2 \end{array}\right.$

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Problem 4476

d) $\frac{x}{5}+1=2$

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Problem 4477

$-4 x<5 x-[-3(x-2)+18]$

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Problem 4478

Is 2 a solution of $4 x+12=4$ ? Complete the statement.
The equation is $\square$ ? when $x=2$ , so 2 $\square$ a solution.

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Problem 4479

Solve for $x$ : $7 x-9=3 x-5$

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Problem 4480

Sunland Industries incurs unit costs of \ $8 (\$5 variable and \$3 fixed) in making an assembly part for its finished product. A supplier offers to make 10,300 of the assembly part at$ \ $6$ per unit. If the offer is accepted, Sunland will save all variable costs but no fixed costs. Prepare an analysis showing the total cost saving, if any, that Sunland will realize by buying the part. (Enter negative amounts using either a negative sign preceding the number e.g. -45 or parentheses e.g. (45).) \begin{tabular}{|c|c|c|c|c|c|} \hline & & & Buy & & \begin{tabular}{l} Net Income \\ Increase (Decrease) \end{tabular} \\ \hline Variable manufacturing costs & \$ & \$ & & \$ & \\ \hline Fixed manufacturing costs & & & & & \\ \hline Purchase price & & & & & \\ \hline Total annual cost & \$ & \$ & & \$ & \\ \hline \end{tabular}
The decision should be to $\square$ the part.

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Problem 4481

A 6000-seat theater has tickets for sale at $\$ 24$ and $\$ 40$ . How many tickets should be sold it each price for a sellout performance to generate a total revenue of $\$ 171,200$ ?
The number of tickets for sale at $\$ 24$ should be $\square$ The number of tickets for sale at $\$ 40$ should be $\square$

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Problem 4482

Solve the given system of equations. $\begin{array}{lr} 3 x+2 y-3 z= & 5 \\ 2 x-3 y+2 z= & -8 \\ 4 x-2 y+4 z= & -24 \end{array}$
Select the correct choice below and fill in any answer boxes within your choice. A. There is one solution. The solution set is $\square$ 影 $\square$ \}. (Simplify your answers.) B. There are infinitely many solutions. C. There is no solution.

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Problem 4483

13. Last year Conner paid $15 \%$ of his earmings in federal taxes. He paid $\$ 3000$ . Jose also paid $15 \%$ of his earnings in federal taxes, but he paid $\$ 3600$ . How much more did lose earn than Conner? (A) $\$ 4000$ (c) $\$ 20,000$ (B) $\$ 6000$ (D) $\$ 24,000$
14. The tahle shows the price of a bus ticket based on the number of miles traveled. Which equation represents the relationship between the ticket price $p$ and the number of miles traveled $m$ ? (F) $p=2 m$ \begin{tabular}{|c|c|} \hline Miles & Price \\ \hline 100 & $\$ 50$ \\ \hline 150 & $\$ 70$ \\ \hline 200 & $\$ 90$ \\ \hline 250 & $\$ 110$ \\ \hline \\ \hline \end{tabular} (6) $p=0.5 m$ (H) $p=2 \pi+10$ (I) $p=0.4 m+10$
15. During a trip, Josh recorded the amount of time it took him to travel the distances shown in the table below. \begin{tabular}{|l|c|c|c|c|} \hline Time (hours) & 2 & 5 & 7 & 8 \\ \hline Distance (miles) & 60 & 150 & 210 & 240 \\ \hline \end{tabular}
Which equation represents the relationship between distance $d$ and time $t$ ? (A) $d=30 t$ (C) $d=30+t$ (B) $t=30 d$ (D) $t=d+30$
16. A stepped-out solution is shown below. $\begin{aligned} 3(3 x-1)-3(5 x-3) & =4 \\ 9 x-3-15 x+9 & =4 \\ -6 x+6 & =4 \\ -6 x+6-6 & =4-6 \\ -6 x & =-2 \\ \frac{-6 x}{-6} & =\frac{-2}{-6} \\ x & =\frac{1}{3} \end{aligned}$ $\begin{array}{lr} \text { Step } 1 & 9 x-3-15 x+9=4 \\ \text { Step } 2 & -6 x+6=4 \end{array}$
Step 3 Step 4 Step 5 Step 6 Which property justifies Step 1? (F) Division Property of Equality (G) Suburaction Property of Equality (H) Commutative Property (I) Distributive Property

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Problem 4484

Solve the equation $13 d+8=-1$ $d=$

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Problem 4485

3 A thermocouple consists of two junctions between two metals; when one junction is at a higher temperature than the other, an emf is generated.
The hot junction and the cold junction of a thermocouple are at 373 K and 273 K , respectively. The emf generated is 1.0 mV . Show that the emf changes to 0.85 mV when the hot junction is moved to a water bath at 358 K , if the emf generated varies linearly with the temperature difference between the junctions.

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Problem 4486

41.0 kg of water per second flows through the cooling system of a diesel engine. The difference between the temperatures of the incoming and outgoing water is 5.0 K . How much energy is being removed each second?

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Problem 4487

d a $y$ -intercept of -0.75 and a gradient of 0.75 (e) a $y$ -intercept of -2 and a gradient of 0 f a gradient of 0 and a $y$ -intercept of 4 . 5 Find the equation (in the form $a x+b y=c$ ) of a line which has: a a gradient of $-\frac{3}{2}$ and a $y$ -intercept at $(0,-0.5)$ b a $y$ -intercept of 2 and a gradient of $-\frac{3}{4}$ c a $y$ -intercept of -3 and a gradient of $\frac{4}{8}$ .

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Problem 4488

I) $36 a *-6 b+c=6$ II) $4 a-2 b+c=-2$ III) $1 a+b+c=2,5$

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Problem 4489

$(-2,4)\left\{\begin{array}{l}3 x+2 y=2 \\ x-7 y=-30\end{array}\right.$

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Problem 4490

The price of an adult's ticket is $\$$ $\square$ .
Traffic signs are regulated by the Manual on Uniform Traffic Control Devices (MUTCD). The perimeter of a rectangular traffic sign is 128 inches. Also, its length is 12 inches longer than its width. Find the dimensions of this sign.
What is the length of the sign?
The length of the sign is $\square$ (1) $\qquad$
What is the width of the sign?
The width of the sign is $\square$ (2) $\qquad$ (1) $0 \mathrm{in}^{2}$ . (2) in . $i n^{3}$ . in. in. $i n^{3}$

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Problem 4491

THIS IS A PRACTICE TEST $2 \square$ Mark for Review (45)
A line in the $x y$ -plane has a slope of $\frac{1}{9}$ and passes through the point $(0,14)$ . Which equation represents this line? (A) $y=-\frac{1}{9} x-14$ (B) $y=-\frac{1}{9} x+14$ (C) $y=\frac{1}{9} x-14$
D $y=\frac{1}{9} x+14$

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Problem 4492

Bookwork code: 3E Calculator not allowed
A pair of simultaneous equations are shown below. (1) $6 x-9 y=15$ (2) $2 x+5 y=-3$ a) What is the highest common factor of the terms in equation (1)? b) Write an equation equivalent to (1) by dividing it by $y$ answer to part a). c) Solve the simultaneous equations.

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Problem 4493

What pressure of carbon dioxide is needed to maintain a $\mathrm{CO}_{2}$ concentration of 0.67 M in a can of grape soda if the constant for $\mathrm{CO}_{2}$ is $1.3 \times 10^{-3} \mathrm{M} /$ atm at $25^{\circ} \mathrm{C}$ ?
Give your answer in atm to the nearest tenth. Do not put units in the answer space.

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Problem 4494

Question 10 Find the solution to the following system of linea equations by using the substitution method. $\begin{array}{l} x=-6 y+7 \\ 2 x+y=3 \end{array}$

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Problem 4495

Pseudocode: Output ana Malak Nomaka Order and Output
FIRST LINE OF CODE : input NUMI : input NUM2 : calculate SUM = NUMI + NUM2 : calculate RESULT = SUM / 2 : display RESULT
LAST LINE OF CODE
The code is written to find the average between two numbers. The lines of code are currently out of order. Well done, the code is in the correct order! Determine the codes output if the first number entered is 5 and the second number entered is 10 .
I will let you know when your response is correct.

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Problem 4496

a) $(-5 \vec{\imath}-2 \vec{\jmath})+(3 \vec{\imath}+6 \vec{\jmath})$ $-2 \vec{\imath}+4 \vec{\jmath} \quad$ Same as $\langle-2,4\rangle$

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Problem 4497

ALEKS - 2024 Fall - College Alga A ALEKS-Alden Scott-Knowled www-awa.aleks.com/alekscgi//x/lsl.exe/10_u-lgNsIkr7j8P3jH-IQgKSJS_J3Lykq19bMqn3Sx1kuBwVjDD2XFImfpifl. C. K12 Bookmarks 品 Mall - Scott, Aiden E. Sioux Falls SD 49-5 e-hallpass Dashboard Knowledge C Question 3 Aiden
The credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 34 Españot minutes of calls is $\$ 25.24$ , and the remaining credit after 58 minutes of calls is $\$ 21.88$ . What is the remaining credit after 76 minutes of calls? s! $\square$ $\times$ 5 IDon't Know SNopmit

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Problem 4498

Noor wants to spend less than $\$ 20$ on condiments. Each kilogram of salt costs $\$ 1.50$ , and each kilogram of pepper costs \$2.50.
Write an inequality that represents the number of kilograms of salt $(S)$ and pepper $(P)$ Noor can buy on her budget.

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Problem 4499

$\text{Given:} \\ \text{Final velocity } v_f = 0.635 \, \text{m/s} \\ \text{Initial velocity } v_i = 0 \, \text{m/s} \\ \text{Mass } m = 132 \, \text{g} = 0.132 \, \text{kg} \\ \text{Change in distance } \Delta d = 98 \, \text{cm} = 0.98 \, \text{m} \\
\text{Solve for the force of friction } F_f \text{ in two different ways:} \\
\text{1. Using motion:} \\ \text{Use the kinematic equation:} \\ v_f^2 = v_i^2 + 2a\Delta d \\ \text{Solve for acceleration } a \text{ and use } F = ma \text{ to find } F_f. \\
\text{2. Using work/energy/power:} \\ \text{Use the work-energy principle:} \\ \text{Work done by friction } = \Delta \text{Kinetic Energy} \\ \text{Calculate the change in kinetic energy and equate it to the work done by friction to find } F_f.$

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Problem 4500

Graph the solution set of the following system of inequalities. $\begin{array}{r} 4 x+8 y \leq 8 \\ 3 x+y \leq 9 \end{array}$
Use the graphing tool to graph the system of inequalities.

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Linearity

Problem 4401

Sketch the graph for the constraints: x≥50x \geq 50x≥50, y≥60y \geq 60y≥60, x+y≤200x+y \leq 200x+y≤200, 4x+5y≤9004x+5y \leq 9004x+5y≤900. Find the feasible region and minimize P=0.3x+0.5yP=0.3x+0.5yP=0.3x+0.5y.

Problem 4402

Chang's trip to the mountains took 7 hours; the return took 5 hours at 18 mph faster. Find the distance to the mountains.

Problem 4403

Two trains start 420 miles apart, one at 85 mph and the other at 65 mph. How long until they meet?

Problem 4404

Solve the equation: 9y+5=9(y+5)−469y + 5 = 9(y + 5) - 469y+5=9(y+5)−46.

Problem 4405

Two cars start 400 km apart, meet in 2 hours. One is 18 km/h slower. Find the speed of the slower car.

Problem 4406

What percent nnn of 20 equals 4? Find nnn.

Problem 4407

Find the ordered pair (x,y)(x, y)(x,y) that satisfies the equation 5x+y=85x + y = 85x+y=8.

Problem 4408

Find bbb and YZY ZYZ given XY=6bX Y=6bXY=6b, YZ=8bY Z=8bYZ=8b, and XZ=154X Z=154XZ=154 with YYY between XXX and ZZZ.

Problem 4409

Find YYY and YZY ZYZ given XY=11X Y=11XY=11, YZ=4cY Z=4cYZ=4c, and XZ=83X Z=83XZ=83.

Problem 4410

Find three consecutive integers that add up to 339. Let the smallest be nnn, then the integers are nnn, n+1n+1n+1, and n+2n+2n+2.

Problem 4411

Solve the linear equation: 6z−44+138=12z+18\frac{6 z-4}{4}+\frac{13}{8}=\frac{12 z+1}{8}46z−4​+813​=812z+1​.

Problem 4412

How many hours does Nisha need to make 64 pairs of ghungroos using the equation y=4.75x−2.5y=4.75 x-2.5y=4.75x−2.5?

Problem 4413

Solve the linear equation: 6x+5=6(x+2)−76x + 5 = 6(x + 2) - 76x+5=6(x+2)−7.

Problem 4414

Find DEDEDE if DF=42DF = 42DF=42, DE=7x+1DE = 7x + 1DE=7x+1, EF=4x−3EF = 4x - 3EF=4x−3, and DF=DE+EFDF = DE + EFDF=DE+EF.

Problem 4415

Solve the equation: 6(5x−5)=−31(3−x)6(5x - 5) = -31(3 - x)6(5x−5)=−31(3−x)

Problem 4416

Solve the equation: 6y+8=6(y+3)−106y + 8 = 6(y + 3) - 106y+8=6(y+3)−10.

Problem 4417

Solve the linear equation: 6z+4=6(z+3)−146z + 4 = 6(z + 3) - 146z+4=6(z+3)−14.

Problem 4418

Solve the equation: 2y−64+98=4y+48\frac{2 y-6}{4}+\frac{9}{8}=\frac{4 y+4}{8}42y−6​+89​=84y+4​.

Problem 4419

Solve the equation: 2y−35+910=4y+510\frac{2y-3}{5} + \frac{9}{10} = \frac{4y+5}{10}52y−3​+109​=104y+5​.

Problem 4420

Solve the linear equation: 6(3x−3)=−19(3−x)6(3x - 3) = -19(3 - x)6(3x−3)=−19(3−x).

Problem 4421

Solve the linear equation: 4t+7=4(t+4)−164t + 7 = 4(t + 4) - 164t+7=4(t+4)−16.

Problem 4422

Find three consecutive integers that add up to 345. Let the smallest be nnn, so the integers are nnn, n+1n+1n+1, n+2n+2n+2.

Problem 4423

Find the equation of the line through (−1,−4)(-1,-4)(−1,−4) parallel to 3x+y=53x+y=53x+y=5. Choices: y=3x+1y=3x+1y=3x+1, y=−3x+7y=-3x+7y=−3x+7, y=−3x−7y=-3x-7y=−3x−7, y=3x−1y=3x-1y=3x−1.

Problem 4424

Solve the compound inequality: x−3≤6x-3 \leq 6x−3≤6 and x+2≥4x+2 \geq 4x+2≥4. Provide the solution set in interval and graph forms.

Problem 4425

Solve the compound inequality: −3x>6-3x > 6−3x>6 and x+5>0x + 5 > 0x+5>0. Provide the solution set in interval and graph forms.

Problem 4426

Solve the compound inequality: x≤5x \leq 5x≤5 or x≤11x \leq 11x≤11. Provide the solution set in interval and graph forms.

Problem 4427

Solve the compound inequality x>−5x > -5x>−5 or x≤4x \leq 4x≤4 and express the solution in interval and graph form.

Problem 4428

How many pitchers of lemonade does Molly need to serve 16 large glasses and 12 small glasses with none left over?

Problem 4429

A truck driver is 150 miles from his exit, driving at 50 mph. Find his min and max driving hours before a rest stop within 30 miles.

Problem 4430

Simplify the expression: 7s−3s7s - 3s7s−3s.

Problem 4431

Simplify the expression by combining like terms: −3x+9x-3x + 9x−3x+9x.

Problem 4432

Solve the compound inequality x+6>13x+6>13x+6>13 or −3x+3≥6-3x+3 \geq 6−3x+3≥6 and provide the solution in interval and graph form.

Problem 4433

Identify the first term in 6a+66a + 66a+6. Is it a variable or constant term? If variable, state the coefficient.

Problem 4434

Solve the compound inequality x<−2x < -2x<−2 and x>−6x > -6x>−6. Provide the solution set in interval and graph forms.

Problem 4435

Solve the inequality x<7x<7x<7 or x<−3x<-3x<−3. Provide the solution set in interval notation and graph form.

Problem 4436

Solve the compound inequality: x+1≥5x+1 \geq 5x+1≥5 and x−2≤10x-2 \leq 10x−2≤10. Provide the solution in interval and graph forms.

Problem 4437

Find the equation of a line in point-slope form that passes through (5,−3)(5,-3)(5,−3) with a slope of −12-\frac{1}{2}−21​.

Problem 4438

Find the equation of a line in point-slope form with slope 16\frac{1}{6}61​ through the point (10,2)(10,2)(10,2).

Problem 4439

Find the equation of a line in point-slope form with slope -4 through the point (−3,8)(-3,8)(−3,8). Simplify all fractions.

Problem 4440

Sketch the graph for the constraints: $x \geq 50$ , $y \geq 60$ , $x+y \leq 200$ , $4x+5y \leq 900$ . Find the feasible region and minimize $P=0.3x+0.5y$ .

Solve the equation: $9y + 5 = 9(y + 5) - 46$ .

What percent $n$ of 20 equals 4? Find $n$ .

Find the ordered pair $(x, y)$ that satisfies the equation $5x + y = 8$ .

Find $b$ and $Y Z$ given $X Y=6b$ , $Y Z=8b$ , and $X Z=154$ with $Y$ between $X$ and $Z$ .

Find $Y$ and $Y Z$ given $X Y=11$ , $Y Z=4c$ , and $X Z=83$ .

Find three consecutive integers that add up to 339. Let the smallest be $n$ , then the integers are $n$ , $n+1$ , and $n+2$ .

Solve the linear equation: $\frac{6 z-4}{4}+\frac{13}{8}=\frac{12 z+1}{8}$ .

How many hours does Nisha need to make 64 pairs of ghungroos using the equation $y=4.75 x-2.5$ ?

Solve the linear equation: $6x + 5 = 6(x + 2) - 7$ .

Find $DE$ if $DF = 42$ , $DE = 7x + 1$ , $EF = 4x - 3$ , and $DF = DE + EF$ .

Solve the equation: $6(5x - 5) = -31(3 - x)$

Solve the equation: $6y + 8 = 6(y + 3) - 10$ .

Solve the linear equation: $6z + 4 = 6(z + 3) - 14$ .

Solve the equation: $\frac{2 y-6}{4}+\frac{9}{8}=\frac{4 y+4}{8}$ .

Solve the equation: $\frac{2y-3}{5} + \frac{9}{10} = \frac{4y+5}{10}$ .

Solve the linear equation: $6(3x - 3) = -19(3 - x)$ .

Solve the linear equation: $4t + 7 = 4(t + 4) - 16$ .

Find three consecutive integers that add up to 345. Let the smallest be $n$ , so the integers are $n$ , $n+1$ , $n+2$ .

Find the equation of the line through $(-1,-4)$ parallel to $3x+y=5$ . Choices: $y=3x+1$ , $y=-3x+7$ , $y=-3x-7$ , $y=3x-1$ .

Solve the compound inequality: $x-3 \leq 6$ and $x+2 \geq 4$ . Provide the solution set in interval and graph forms.

Solve the compound inequality: $-3x > 6$ and $x + 5 > 0$ . Provide the solution set in interval and graph forms.

Solve the compound inequality: $x \leq 5$ or $x \leq 11$ . Provide the solution set in interval and graph forms.

Solve the compound inequality $x > -5$ or $x \leq 4$ and express the solution in interval and graph form.

Simplify the expression: $7s - 3s$ .

Simplify the expression by combining like terms: $-3x + 9x$ .

Solve the compound inequality $x+6>13$ or $-3x+3 \geq 6$ and provide the solution in interval and graph form.

Identify the first term in $6a + 6$ . Is it a variable or constant term? If variable, state the coefficient.

Solve the compound inequality $x < -2$ and $x > -6$ . Provide the solution set in interval and graph forms.

Solve the inequality $x<7$ or $x<-3$ . Provide the solution set in interval notation and graph form.

Solve the compound inequality: $x+1 \geq 5$ and $x-2 \leq 10$ . Provide the solution in interval and graph forms.

Find the equation of a line in point-slope form that passes through $(5,-3)$ with a slope of $-\frac{1}{2}$ .

Find the equation of a line in point-slope form with slope $\frac{1}{6}$ through the point $(10,2)$ .

Find the equation of a line in point-slope form with slope -4 through the point $(-3,8)$ . Simplify all fractions.

Find the equation of a line with slope 6 that passes through the point $(6,8)$ in point-slope form.

Find the equation of the line in point-slope form with point $(-9,9)$ and slope $\frac{1}{6}$ .

Determine the range of the function $f(x)=3x+2$ for the domain $\{0,2,4,6\}$ .

Solve the equation: $4 x - 5 = 8 - 2 x$ .

Find $x$ such that $y=5x+4$ is within 0.003 of 7. What values of $x$ satisfy this?

Solve for $x$ in the equation $2 x = 9 - 7 x$ .

Solve the equations: (b) $8x + 5 = 3(2x - 11)$ and (e) $\frac{1 - 4x}{8} = \frac{3x - 7}{4}$ .

8 Which of the following equations represents a line without a $y$ -intercept? (a) $y=4$ (b) $x=-4$ (c) $x+y=2$ (d) $y=3 x$

12 Which line is parallel to the line $y=-2 x-3$ ? (a) $y=-2 x+2$ c. $y=2 x+2$ (b) $y=2 x-2$ (d) $y=-0.5 x-2$

Write the sentence as an equation. the product of 189 and $h$ equals $m$
Type a slash ( / ) if you want to use a division sign. $\square$ Submit

Solve the formula for the given variable. $\begin{array}{l} T=f m-g m ; m \quad \text { (Engineering) } \\ m=\square \end{array}$
Need Help? Read It Watch It

$5(3 x+4)+2=37$

Solve for $x$ . $2(3 x-6)=12$
Simplify your answer as much as possible. $x=$

3. Хоёр тооны яи. .ихр 5-тай тэнцуу бөгөөд эдгээр тоонууд $\frac{1}{3}: \frac{1}{4}$ г. ларьцдаг бол бага тоог ол. A. 20 B. 16 C. 24 D. 18 E. 15

$4 a=5 b, 9 c=7 a$ бол $\frac{b}{c}=?$

Question 25: The intercept on $x$ -axis of the line $4 x-3 y=16$ is
Single-digit integer (-9 to 9)
Type your answer here

Question 28: If lines whose equation are $y=2 x-5$ and $2 y+p x=3$ are perpendicular to each other, then the value of $p$ is
Single-digit integer (-9 to 9)
Type your answer here

Find the slope-intercept equation of the line that has the given characteristics. Slope 9.5 and $y$ -intercept $(0,-5)$
The slope-intercept equation $y=$ $\square$ (Use integers or decimals for any numbers in the expression.)

Fully simplify $9 x+5 y+5+2 y-3 x$

Find an equation of the line having the given slope and containing the given point. $m=-5,(6,0)$
The equation of the line is $y=$ $\square$ (Simplify your answer. Type your answer in slope-intercept form. Use integers or fractions for any numbers in the expression.)

Solve by the elimination method. $\begin{array}{l} 2 x+3 y=1 \\ 4 x+6 y=2 \end{array}$

Solve the given system by the substitution method. $\begin{array}{r} 2 x+y=6 \\ 7 x-4 y=6 \end{array}$

Fill in the gaps to factorise this expression. $16 m+8=8(-\square)$

$\left\{\begin{array}{l}2 x=4 y-2 \\ 1+x=3 y\end{array}\right.$