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Problem 2101

You earn \$5/hour as a cashier and \$8/hour as a lifeguard. You want to work ≤15 hours and earn ≥\$100 weekly.

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Problem 2102

A school play sold tickets for \$ 3 (student) and \$ 7 (adult). Total sales were \$ 2,001 with 467 tickets sold. Find counts.

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Problem 2103

Lisa bought 100 items: cups at \ $2 and bracelets at \$3, costing \$260. Find the number of cups using:$ $\left\{\begin{array}{l} c+b=100 \\ 2 c+3 b=260 \end{array}\right.$ $

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Problem 2104

A school needs 5 more desks in secondary classrooms than in elementary ones. With 20 elementary and 25 secondary classrooms totaling 1,115 desks, find the number of desks in each secondary classroom.

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Problem 2105

Find the solutions for the system: $2y=4x+12$ and $y=2x-6$ .

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Problem 2106

Solve the equations: 4x - 3y = 8 and 2x + y = 11. Find the value of $y$ . Choices: $-\frac{8}{3}$ , $-6$ , $14$ , $\frac{14}{5}$ .

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Problem 2107

A school play sold 500 tickets for \$1480. Student tickets are \$2, adult tickets are \$5. How many of each type?

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Problem 2108

Solve the equations: $-2x + 3y = 8$ and $5x - 2y = -9$ . Choose the correct solution from the options provided.

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Problem 2109

Solve the equations: $-3x + 4y = 13$ and $5x - 3y = -18$ . Choose the correct solution from the options provided.

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Problem 2110

At a party with 130 students, 35 speak French, 50 speak English, 28 speak only English, and 13 speak only French. Find the probability a randomly selected student speaks both languages.

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Problem 2111

Solve the system of linear equations by elimination. $\begin{array}{l} x+y=2 \\ 2 x+7 y=9 \end{array}$

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Problem 2112

5. A number $x$ is three less than twice $y$ . When you add $x$ multiplied by 4 and $y$ , the sum is six. What are the values of $x$ and $y$ ?
Equation 1: $\qquad$
Equation 2: $\qquad$

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Problem 2113

a) A factory makes 3types of products $P_{1}, P_{2}, P_{3}$ . The factory needs 5 units of volume to store one unit of $P_{1}, 3.5$ units of volume to store one unit of $P_{2}, 4.2$ units of volume to store one unit of $P_{3}$ . The factory uses 3 hours of manpower to make 1 unit of $P_{1}, 4$ hours of manpower to make 1 unit of $P_{2}, 6$ hours of manpower to make 1 unit of $P_{3}$ It sells 1 unit of $P_{1}$ at $450 \mathrm{~F}, 1$ unit of $P_{2}$ at $620 \mathrm{~F}, 1$ unit of $P_{3}$ at 780 F . The factory has only 40 units of stock volume, it cannot pay over 20 hours of manpower. Formulate it as the optimization LPP. b) What is difference between TRANSPORTATION PROBLEM and ASSIGNMENT PROBLEM? c) What are the steps in decision marking process? d) Find the maximum of $f(x, y)=17 x+15 y$ $\begin{array}{l} 80 \leq 4 x+2 y \\ y \leq 4+x \\ x \leq 8+y \\ x+y \leq 40 \\ x \geq 0 \\ y \geq 0 \end{array}$

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Problem 2114

Question Watch Video Show Examples
The perimeter of a rectangle is 204 centimeters. Find the length and width if the length is an even integer and the width is 3 times the next consecutive even integer.
Answer Attempt 1 out of 2
Length = $\square$ centimeters
Width = $\square$ centimeters Submit Answer

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Problem 2115

Solve by Graphing: $\left\{\begin{array}{l} y=\frac{1}{4} x-8 \\ y=x-5 \end{array}\right.$

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Problem 2116

35.16. Найти систему линейных уравнений, задающую систему векторов: а) $\langle(1,-1,1,0),(1,1,0,1),(2,0,1,1)\rangle$ ; б) $\langle(1,-1,1,-1,1),(1,1,0,0,3),(3,1,1,-1,7)\rangle$ .

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Problem 2117

^ Pretest: Unit 1
Question 1 of 29 What is the solution to the system of equations below? $\begin{array}{l} 2 x+y-3 z=-7 \\ 3 x-y+4 z=-17 \\ x+2 y+2 z=9 \end{array}$ A. $x=4, y=1, z=5$ B. $x=4, y=4, z=3$ C. $x=-5, y=6, z=1$ D. $x=-5, y=4, z=3$

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Problem 2118

8. A manufacturer makes two types of jet skis, single rider and multiple riders. The profit on a single-rider jet ski is $\$ 200$ and the profit on the multi-rider jet ski is $\$ 250$ . To meet customer demand, the company must manufacture at least 50 single-rider jet skis and 75 multi-rider jet skis per week. To maintain high quality, the total number of both models manufactured by the company should not exceed 150 models per week. How many of each model should the company produce to maximize the profit?

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Problem 2119

(4.8) Using the determinant's method solve the following systems: $x+2 y+3 z=3$ a) $\begin{array}{l} 2 x-y+z=6 \\ 3 x+y-z=4 \end{array}$

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Problem 2120

```latex Sejam os planos: $\pi:\left\{\begin{array}{c} x=1+h-t \\ y=-h+2 t \quad \text { e } \\ z=1+h \end{array} \quad \alpha: x+y-z+1=0\right.$
Encontre a interseção entre os planos $\pi$ e $\alpha$ .

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Problem 2121

The graph below shows the amount of money charged by two electricity providers per month, depending on the amount of electricity used. a) Alexander uses 240 kWh of electricity per month. Which provider would be cheaper for Alexander? b) Lawrence pays the same price for electricity whether he uses provider A or provider B. How much electricity does Lawrence use per month?

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Problem 2122

5) The senior classes at High School A and High School B planned separate trips to New York City. The senior class at High School A and High School B planned separes with 814 students. High School B rented School A rented and filled 13 vans and 14 buses willed 14 vans and 12 buses with 732 students. Each van and each bus carried the same num and filled 14 vans and 12 buses with 732 students. Each van and each bus.

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Problem 2123

PRACTISING
4. Determine the point(s) of intersection of each pair of functions. $\mathbf{K}_{\text {a) }} f(x)=-2 x^{2}-5 x+20, g(x)=6 x-1$ b) $f(x)=3 x^{2}-2, g(x)=x+7$ c) $f(x)=5 x^{2}+x-2, g(x)=-3 x-6$ d) $f(x)=-4 x^{2}-2 x+3, g(x)=5 x+4$

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Problem 2124

Solve for $a$ : $3a + 2 > \frac{3a - 6}{3}$ , $a > -2$ , $a < 0$ , $a > 0$ , $a < -2$ .

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Problem 2125

Fill in the missing values in the table given that 47 prefer bike, 103 prefer bus, and 150 total employees.

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Problem 2126

Complete the table and find students who neither go to the beach nor the mountains. Total students = 49.

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Problem 2127

Solve for $a$ : $3a + 2 > \frac{3a - 6}{3}$ , $a > -2$ , $a < 0$ , $a > 0$ , $a < -2$ .

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Problem 2128

Is the statement true or false? Justify: Does the augmented matrix $\left[\begin{array}{llll}a_{1} & a_{2} & a_{3} & b\end{array}\right]$ imply $b$ is in Span $\{a_{1}, a_{2}, a_{3}\}$ ?

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Problem 2129

Is the statement true or false? The linear system from $\left[\begin{array}{llll}a_{1} & a_{2} & a_{3} & b\end{array}\right]$ has a solution if $b$ is in Span $\{a_{1}, a_{2}, a_{3}\}$ . Choose A, B, C, or D.

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Problem 2130

The side of an equilateral triangle is 6 inches longer than a square's side, with a perimeter difference of 13 inches. Find the triangle's side.

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Problem 2131

Ryan walked 8 dogs for a total of \$ 55, earning \$ 5 for small dogs and \$ 8 for large. How many small dogs did he walk?

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Problem 2132

4. A teacher is creating a test for his Algebra 1 students. The test is made up of multiple-choice and free response questions. Each mutliple-choice question is worth 7 points and each free response question is worth 8 points. If the test has 48 questions and is worth a total of 374 points, which equations can be used to find $x$ , the number of multiple-choice questions and $y$ , the number of free response questions on the test? Choose TWO correct answers.

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Problem 2133

Solve the following system of equations for all three variables. $\begin{array}{r} 4 x+3 y-z=10 \\ 8 x+y-z=6 \\ 6 x+y+z=4 \end{array}$

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Problem 2134

Une $f$ \begin{tabular}{|c|c|} \hline $x$ & $y$ \\ \hline 2 & 7 \\ \hline 4 & 10.5 \\ \hline 7 & 15.75 \\ \hline 11 & 22.75 \\ \hline \end{tabular}
Line $g$ \begin{tabular}{|r|r|} \hline $x$ & \multicolumn{1}{|c|}{ $y$ } \\ \hline-3 & 4 \\ \hline-2 & 0 \\ \hline 1 & -12 \\ \hline 4 & -24 \\ \hline \end{tabular}
Write a system of equations that represents lines fand $g$ . (work space below)

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Problem 2135

$6 x+1>5 x+4$ or $1-x>-4$

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Problem 2136

Determine if the equations are parallel, perpendicular, or neither.

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Problem 2137

Find the inverse of each function. 1) $y=\log _{3} \frac{3^{x}}{-4}$ 2) $y=\log _{4}\left(2^{x}+7\right)$ 3) $y=\frac{5^{x}+7}{-2}$ 4) $y=\left(\frac{\left(\frac{1}{5}\right)^{x}}{-4}\right)^{\frac{1}{3}}$ 5) $y=5 \log _{6} x^{3}$ 6) $y=\log _{3}(4 x+8)$ 7) $y=\log _{6} x^{5}+8$ 8) $y=\log _{4}\left(4 x^{3}\right)$ 9) $y=\log _{3}\left(-4 \cdot 2^{x}\right)$

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Problem 2138

A party rental company has chairs and tables for rent. The total cost to rent 2 chairs and 6 tables is $\$ 42$ . The total cost to rent 5 chairs and 3 tables is $\$ 30$ . What is the cost to rent each chair and each table?
Cost to rent each chair: $\$$ $\square$ Cost to rent each table: $\$$ $\square$

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Problem 2139

14 Solve the system using substitution: $\left\{\begin{array}{l} 2 x-y=3 \\ x=-2 y-1 \end{array}\right.$
Solution - write as an ordered pair, $(x, y)$

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Problem 2140

32500 صندوق، 2000 دئر 2000 بنك ، 525 نور وميار، 875 عمولة وكلاء الشراء، 2500 جمارك مشتريات، 3500 مردود المبيعات، 2000 ايجار، 625 خصم مسموح به، 32500 مصاريف نتل مبيعات، 1250 عمولة وكلاء البيع، 14000 أنات، 175000 عملاء، 1750 مردود مشتريات، 4000 مسحوبات، 13635 خصم مكتسب، 1125 فواند داننة، 6000 أوراق مالية ، 8750أوراق دفع، 1300 مصروف دعاية وإعلان ، 13625 موردون، 127500 راس المال. إذا علمت أن بضاعة أخر المدة قدرت ب 35875 المطلوب: 1. إعداد قائمة الدخل (قَائمة نتيجة الاعمال) عن السنة المنتهية في 2018/12/31

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Problem 2141

10. Use simplex method to solve $\begin{aligned} \text { Maximize } z & =7 x_{1}+5 x_{2} \\ \text { Subjected to } & 2 x_{1}+x_{2} \leq 10 \\ & 4 x_{1}+3 x_{2} \leq 24 \\ & x_{1} \geq 0, x_{2} \geq 0 \end{aligned}$

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Problem 2142

9. For which values of the parameter $c \in \mathbb{R}$ is the vector $(1,1, c)$ a linear combination of the vectors $(2,1,3),(1,2,4),(3,0,2),(2,-2,-2)$ ?

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Problem 2143

sider the curve defined by the equations: $\left\{\begin{array}{l} x=t^{2}-t \\ y=t^{3}-3 t^{2} \end{array}\right.$
Find all points $(x, y)$ where the tangent line to the path is Horizontal.
Find $\frac{d^{2} y}{d x^{2}}$ . You do not need to simplify your answer.

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Problem 2144

Part A: Isolate $y$ and Graph
1. $3 x+2 y=6$
2. $4 x-y=8$
3. $-2 x+y=-3$
4. $5 x+3 y=15$
5. $6 x-2 y=12$
Part B: $y$ is Already Isolated
6. $y=2 x+1$
7. $y=-\frac{3}{4} x+5$
8. $y=\frac{1}{2} x-2$
9. $y=-2 x+4$
10. $y=3-x$

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Problem 2145

metrobüs $3 x-4 y-10=0$ kanalizasyon $3 x-4 y+c=0$
Şekilde birbirine paralel doğrultuda inșa edilmiş metrobüs metro ve kanalizasyon hatları ve denklemleri gösterilmiștir.
Metro-metrobūs arasındaki mesafe metro-kanalizasyon hattı arasındaki mesafenin yarısı ise c nin pozitif değeri kaçtır? A) 100 B) 110 C) 120 D) 130 E) 140

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Problem 2146

g system of equations graphically on the set $\begin{array}{c} y=x-2 \\ y=-3 x-6 \end{array}$

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Problem 2147

* Problem 2
Groundwater well is known to begin pumping sand once it becomes exploited (old), and this may damage the subsequent water treatment processes. To solve this problem, two alternatives are proposed: - A new well can be drilled at a capital cost of $\$ 580,000$ with minimal operating and maintenance expenses of $\$ 11,500$ per year. - A settling tank can be constructed ahead of the treatment processes which will cost $\$ 230,000$ to build and $\$ 42,400$ per year to operate and maintain.
The salvage value of either option at EOY 20 is $10 \%$ of the capital investment. Using a MARR of $5 \%$ .

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Problem 2148

(42) Find the smallest positive integer which leaves the remainder 1 when divided by $2,3,4,5,6$ , and the remainder 0 when divided by 7 .

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Problem 2149

each system of equations and state its solution. 1. $\begin{array}{l|l} x-2 y=11 \\ y=x=7 & \text { 2. } y=3 x+12 \\ x+3 y=6 \end{array}$ $\begin{array}{l} y=x-7 \\ x=3+\frac{1}{3} y \\ y=\frac{5}{2} x-8 \end{array}$
3. $y=x+8$ $x-y=-8$ 5. $\begin{array}{l} x=\frac{3}{2} y+\frac{17}{2} \\ x-3 y=13 \end{array}$ 6. $\begin{array}{l} 3 x-4 y=-7 \\ -8 x=28-6 y \end{array}$ $y=\frac{5}{3} x-3$ 8. $y=\frac{1}{2} x-\frac{3}{2}$
9. $x=1 y+6$ $5 x-4 y=12$ $12 y=-21+3 x$ $x-y=6$ $5 x-y=-11$ $3 x=-10+4 y$ 11. $\begin{array}{l} \frac{x-y}{3}=\frac{2}{3} \\ x-y=2 \end{array}$ 12. $\begin{array}{l} x-2 y=10 \\ 4 x-3 y=15 \end{array}$

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Problem 2150

21 Solve each equation.

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Problem 2151

Solve the system with elimination. $\left\{\begin{array}{l} 2 x-5 y=-2 \\ 3 x+y=31 \end{array}\right.$

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Problem 2152

\begin{tabular}{c|c|} PROBLEM & SOLUTION \\ $-3 x+y=14$ \\ $-2 x-y=16$ & \\ & \end{tabular}

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Problem 2153

The equations of three lines are given below. Line 1: $4 y=3 x+7$ Line $2: 6 x+8 y=6$ Line $3: y=\frac{4}{3} x-6$ For each pair of lines, determine whether they are parallel, perpendicular, or neither.
Line 1 and Line 2: Parallel Perpendicular Neither Line 1 and Line 3: Parallel Perpendicular Neither Line 2 and Line 3: Parallel Perpendicular Neither

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Problem 2154

For three food shelters, model food costs $F$ based on people served $N$ and receipts $R$ . Predict $F$ for $N=3500$ , $R=\$ 13,500$ .

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Problem 2155

Solve the system:
-25x - 33y - z = 20 -40x - 55y - 2z = 37 30x + 33y + z = -5
Choose: A. One solution (exact form) B. Infinitely many $(\square, \square, z)$ C. No solution.

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Problem 2156

Solve the system using Gaussian elimination and backward substitution. Find the ordered triple for $x$ , $y$ , $z$ :
$\begin{array}{rr} x+2y+4z= & 14 \\ -x+3y+4z= & 8 \\ x+y-5z= & -20 \end{array}$
Choose A, B, or C based on the solution type.

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Problem 2157

To eliminate $x$ in the system below, if you multiply the first equation by 8, what should you multiply the second by?
$\begin{array}{l} -6 x+8 y=-5 \\ -8 x-13 y=0 \end{array}$

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Problem 2158

2) A 0.3 kg ball is tied to a 1 m piece of string and spun so that it is moving in a horizontal circle as shown below. The angle measured between the vertical dashed line and the string is $20^{\circ}$ . Determine angular speed of the ball and tension in the string. $\left[\omega=3.2 \mathrm{rad} \mathrm{~s}^{-1} \text { and } T=3.1 \mathrm{~N}\right]$

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Problem 2159

$\begin{array}{l}6(w+1)-3 w=3(w+4 \\ 2(3 a-1)=4 a+10 \\ 7 b-3(b+2)=4 b-11 \\ 5(c-2)+3 c=4(2 c+1\end{array}$

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Problem 2160

The perimeter of a triangle is 107 m . The second side is three times as long as the first side. The third side is 5 m shorter than than the second side. How long is each side.
Determine the length of each side of the triangle. The first side is $\square$ m
The second side is $\square$ m.
The third side is $\square$ m

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Problem 2161

Joanna has a total of 50 coins in her purse. • The coins are either nickels or quarters. ■ The total value of the coins is $7.10. Which system of equations can be used to determine the number of nickels, n, and quarters, q, that Joanna has in her purse? O n+q= 50 0.05n+ 0.25q = 7.10 n+q=7.10 50n+50q = 7.10 0.05n+ 0.25q = 50 n+q= 7.10 0.05n+ 0.25q = 7.10 50n+ 50q = 7.10

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Problem 2162

5. $\begin{aligned} y & =-2 x+2 \\ & y=7 x+11\end{aligned}$

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Problem 2163

A. B. C. $x \leq-3$ and $x \geq 5$ D. $x<-3$ and $x>5$ F. $(-\infty,-3] \cup[5, \infty)$ E. $\mathbb{R}$ G. $(-\infty,-3) \cup(5, \infty)$ H. All real numbers I. No solutions
The questions in this level are taken directly from the Units 3 and 4 Review in "Activity: Review by Unit." Only proceed if you have completed that section of the activity.
Solve the compound inequality $4 x+1 \leq-11$ and $-3 x+1<-14$ . Which of the options shown accurately represent(s) the solutions?

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Problem 2164

Jeffrey has a plot of land where he would like to build three fenced areas for his horses. He wants two areas to be congruent in size and a third area to have side lengths 2 times the length of the sides of the other two An image is shown with rectangles $W N Y F$ and $R B Y F$ representing the congruent fenced areas and rectangle $L B N K$ representing the larger similar area.
Given that $W N Y F \cong R B Y F, R B Y F \sim L B N K, W N=F Y, F W=Y N, F R=7 x+7.8, W N=13 y-25.4, L B=17 y+1.4$ , and $K L=21 x-16.6$ , what is the perimeter of the entire plot of land, rectangle $W K L R$ ? $\square$ feet

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Problem 2165

Liana is putting tile behind the stove in her kitchen. The base pattern of the tile, polygon $R W M K T$ , is made up of two congruent rhombi, RHLY and $K T Y L$ , and a similar rhombus, HWMK, that has side lengths that are $\frac{3}{2}$ times the side lengths of the smaller rhombi. A partial image of the tile pattern is shown
Given that $R H L Y \cong K T Y L, R H L Y \sim H W M K, R H=Y L, Y L=T K, W H=M K, H L=(y+0.5)$ inches (in.), $L Y=(3 x-0.2)$ in., $W M=(3 y-1.5)$ in., $M K=(5 x-0.7)$ in., and $R Y=(5 x)$ in., what is the perimeter of one base pattern, $R W M K T$ ? $\square$ inches

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Problem 2166

Equation 2 $\begin{array}{l} 2 \quad 8 x+20 y=-03 \\ 0=-91 \end{array}$ c $16 x=-91$
41c This system of equations is: Dependent - there are an Independent - there is only Inconsistent - there are no infinite number of solutions one solution solutions Submit step $\curvearrowright$ View next step

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Problem 2167

$5 \quad 5 x-7=2(x+1)$ $63(x-2)=9(x+2)$ $73 x-4=2 x+8-5 x$ $83(8-4 x)=34-11 x$

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Problem 2168

1) $\begin{array}{l} -x+y=-1 \\ x+3 y=-11 \end{array}$ 2) $\begin{array}{l} x+3 y=3 \\ 3 x-2 y=-2 \end{array}$ 3) $\begin{array}{l} -x-2 y=-5 \\ 2 x-3 y=-18 \end{array}$ 4) $\begin{array}{l} y=6 x-11 \\ -2 x-3 y=-7 \end{array}$ 5) $\begin{array}{l} x=3 y+1 \\ 2 x+4 y=12 \end{array}$

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Problem 2169

7.) $a x=b y=c z=\frac{3}{5} \quad a b+b c+c a=75 a b c \quad x+y+z=$ ?

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Problem 2170

Solve the system using Gaussian elimination: $\begin{array}{rr} x+2y+4z= & 14 \\ -x+3y+4z= & 8 \\ x+y-5z= & -20 \end{array}$ Find the solution as an ordered triple.

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Problem 2171

Solve the system using Gaussian elimination and backward substitution:
$\begin{array}{rr} x+2y+4z= & 11 \\ -x+3y+3z= & -2 \\ x+y-5z= & -6 \end{array}$
Is the solution unique, infinite, or nonexistent?

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Problem 2172

Solve the system: -25x - 33y - z = 28 -40x - 55y - 2z = 52 30x + 33y + z = -8 Choose A (one solution), B (infinitely many), or C (no solution).

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Problem 2173

Elsa, Chau, and Manuel served 105 orders total. Elsa served 5 more than Chau, and Manuel served 3 times Chau. Find their orders.

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Problem 2174

解不等式 $2x - 6 > -16$ 和 $3x - 10 \leq 8$ 。

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Problem 2175

Find prices $p_{1}$ and $p_{2}$ for Ultra Mini and Big Stack such that $q_{1}=0$ and $q_{2}=0$ using given demand functions.

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Problem 2176

(16) A $90 \%$ antifreeze solution is to be mixed with a $75 \%$ solution to make 120 liters of a $78 \%$ solution. How many liters of the $90 \%$ and $75 \%$ solutions will be used?

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Problem 2177

2. (35)Risolvere le seguenti equazioni e disequazioni logaritmiche:() a) $3-\log _{2}\left(x^{2}-2 x\right)=0$ d) $\log _{\frac{1}{2}}(3 x)-\log _{\frac{1}{2}}(x+1)>1$ b) $\log (1+x)+2 \log \sqrt{1-x}=\log (9-6 x)$ c) $2 \cdot 3^{x+2}=2^{x+1}$ e) $\frac{\log (x-3) \cdot \log x}{\log (x-4)} \leq 0$ f) $\left(\log _{2} x\right)^{3}-9 \log _{2} x \leq 0$ g) $\log _{\frac{1}{2}}\left(x^{2}-4\right)+\log _{2} 2 x-1>0$

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Problem 2178

Determine the number of solutions of the system. $\begin{array}{l} y=-4 x+5 \\ y=-2 x+5 \end{array}$ The systom has no solution. The systom has one solution. The system has infinitely many solutions.

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Problem 2179

Listen
There are three integers. The sums of each distinct pair of integers are $-16,-9$ , and -1 . What is the greatest integer?
Greatest Integer: $\square$ Previous 5 6 7 8 9 10 11 12 13 14 Next

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Problem 2180

$f(x)=5 x+1 \quad g(x)=2 x+6$
1. Find $f(g(x))$

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Problem 2181

In a jar, $\frac{2}{5}$ are blue, $\frac{1}{3}$ are red, and the rest (126) are green and yellow. Green = $\frac{3}{4}$ yellow. Find yellow beads.

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Problem 2182

ب) جد المعادلة الديكارتبة للمعادللتين البار امتريتين : $0 \leq t \leq 2 ، x=\sqrt{4-t^{2}}$ ،

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Problem 2183

Downstream sales of inventory
When parents co, sells inventory to subsidiary co its referred to downstream sales, and when subsidiary co sells inventory to parentseb it is called upstream sales. P Company acquired 100 percent ownership of S Corporation in 2017, at book value. S Co purchased inventory from $P$ for $\$ 90,000$ on August 20, 2018, and resold 70 percent of the inventory to unaffiliated companies on December 1, 2018, for $\$ 100,000$ . P produced the inventory sold to $S$ for $\$ 67,000$ . The companies had no other transactions during 2008 Record the elimination entries , and consolidation income statement?

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Problem 2184

Exercice 3 ( 06 points) 3 kg d'air à la température de $20^{\circ} \mathrm{C}$ et sous une pression de 2 bar sont comprimes pusqua las pression de 10 bar.
Déterminer la variation de l'énergie interne, le travail de compression et la quantité de chaleur échangée au cours de l'évolution, pour les trois cas suivants :
1. Compression isotherme.
2. Compression adiabatique.
التمرين
3. Compression polytropique ( $n=1,3$ ).
صنة دة د.إلهام بن عمر On suppose que l'air est un gaz parfait. ( $C_{\mathrm{v}}=714 \mathrm{~J} \cdot \mathrm{~kg}^{-1} \cdot \mathrm{~K}^{-1}$ et $\left.\mathrm{R}=0,287 \mathrm{~kJ}^{-} \cdot \mathrm{kg}^{-1} \cdot \mathrm{~K}^{-1}\right)$
Réponses 3 \begin{tabular}{|c|c|c|} \hline & Expressions littérales & Résultats numériques \\ \hline \multirow{3}{}{Compression isotherme} & $\Delta U=$ & $\Delta \mathrm{U}=$ \\ \hline & & W = \\ \hline & $\mathrm{Q}=$ & $Q=.!$ \\ \hline \multirow{3}{}{Compression adiabatique} & $\Delta \mathrm{U}=-$ & $\Delta \mathrm{U}=$ \\ \hline & & $\mathrm{W}=$ \\ \hline & $Q=$ & $\mathrm{Q}=$ \\ \hline \multirow{3}{*}{Compression polytropique} & $\Delta \mathrm{U}=$ & $\Delta \mathrm{U}=$ \\ \hline & $\mathrm{W}=$ & w = \\ \hline & $\mathrm{Q}=$ & $\mathrm{Q}=$ \\ \hline \end{tabular}

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Problem 2185

Дана пирамида EABCD. Её основание - параллелограмм, диагонали которого пересекаются в точке $O$ . Определи, справедливо ли равенство: $1.2 \overrightarrow{O D}-\overrightarrow{A D}+\overrightarrow{A C}=\overrightarrow{B E}$ $\square$
2. $\overrightarrow{O D}+\overrightarrow{O E}-\overrightarrow{C E}+0,5 \overrightarrow{C A}=\overrightarrow{O B}$ . $\square$
3. $\overrightarrow{A E}-\overrightarrow{O E}+0,5 \overrightarrow{B D}=\overrightarrow{D A}$ . $\square$

See Solution

Problem 2186

得分
4. (15) Determine IBQ, ICQ and Vo CEQ. 6kQ 2ΚΩ www www Q16V 1kQ B=200 VCEQ IBQ 2ΚΩ

See Solution

Problem 2187

be Л. (此 10 分) $R_{1}=2 \mathrm{k} \Omega, \mathrm{R}_{2}=3 \mathrm{k} \Omega, \mathrm{R}_{3}=4 \mathrm{k} \Omega, \mathrm{R}_{4}=12 \mathrm{k} \Omega$ . Determine the reldionship of $\mathrm{V}_{0}$ and $\mathrm{V}_{1}, \mathrm{~V}_{2}, \mathrm{~V}_{3}$ .

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System

Problem 2101

You earn \$5/hour as a cashier and \$8/hour as a lifeguard. You want to work ≤15 hours and earn ≥\$100 weekly.

Problem 2102

A school play sold tickets for \$ 3 (student) and \$ 7 (adult). Total sales were \$ 2,001 with 467 tickets sold. Find counts.

Problem 2103

Problem 2104

A school needs 5 more desks in secondary classrooms than in elementary ones. With 20 elementary and 25 secondary classrooms totaling 1,115 desks, find the number of desks in each secondary classroom.

Problem 2105

Find the solutions for the system: 2y=4x+122y=4x+122y=4x+12 and y=2x−6y=2x-6y=2x−6.

Problem 2106

Solve the equations: 4x - 3y = 8 and 2x + y = 11. Find the value of yyy. Choices: −83-\frac{8}{3}−38​, −6-6−6, 141414, 145\frac{14}{5}514​.

Problem 2107

A school play sold 500 tickets for \$1480. Student tickets are \$2, adult tickets are \$5. How many of each type?

Problem 2108

Solve the equations: −2x+3y=8-2x + 3y = 8−2x+3y=8 and 5x−2y=−95x - 2y = -95x−2y=−9. Choose the correct solution from the options provided.

Problem 2109

Solve the equations: −3x+4y=13-3x + 4y = 13−3x+4y=13 and 5x−3y=−185x - 3y = -185x−3y=−18. Choose the correct solution from the options provided.

Problem 2110

At a party with 130 students, 35 speak French, 50 speak English, 28 speak only English, and 13 speak only French. Find the probability a randomly selected student speaks both languages.

Problem 2111

Solve the system of linear equations by elimination. x+y=22x+7y=9\begin{array}{l} x+y=2 \\ 2 x+7 y=9 \end{array}x+y=22x+7y=9​

Problem 2112

5. A number xxx is three less than twice yyy. When you add xxx multiplied by 4 and yyy, the sum is six. What are the values of xxx and yyy ?Equation 1: \qquadEquation 2: \qquad

Problem 2113

Problem 2114

Problem 2115

Solve by Graphing: {y=14x−8y=x−5\left\{\begin{array}{l} y=\frac{1}{4} x-8 \\ y=x-5 \end{array}\right.{y=41​x−8y=x−5​

Problem 2116

Problem 2117

Problem 2118

Problem 2119

(4.8) Using the determinant's method solve the following systems: x+2y+3z=3x+2 y+3 z=3x+2y+3z=3 a) 2x−y+z=63x+y−z=4\begin{array}{l} 2 x-y+z=6 \\ 3 x+y-z=4 \end{array}2x−y+z=63x+y−z=4​

Problem 2120

Problem 2121

Problem 2122

Problem 2123

Problem 2124

Solve for aaa: 3a+2>3a−633a + 2 > \frac{3a - 6}{3}3a+2>33a−6​, a>−2a > -2a>−2, a<0a < 0a<0, a>0a > 0a>0, a<−2a < -2a<−2.

Problem 2125

Fill in the missing values in the table given that 47 prefer bike, 103 prefer bus, and 150 total employees.

Problem 2126

Complete the table and find students who neither go to the beach nor the mountains. Total students = 49.

Problem 2127

Solve for aaa: 3a+2>3a−633a + 2 > \frac{3a - 6}{3}3a+2>33a−6​, a>−2a > -2a>−2, a<0a < 0a<0, a>0a > 0a>0, a<−2a < -2a<−2.

Problem 2128

Is the statement true or false? Justify: Does the augmented matrix [a1a2a3b]\left[\begin{array}{llll}a_{1} & a_{2} & a_{3} & b\end{array}\right][a1​​a2​​a3​​b​] imply bbb is in Span {a1,a2,a3}\{a_{1}, a_{2}, a_{3}\}{a1​,a2​,a3​}?

Problem 2129

Is the statement true or false? The linear system from [a1a2a3b]\left[\begin{array}{llll}a_{1} & a_{2} & a_{3} & b\end{array}\right][a1​​a2​​a3​​b​] has a solution if bbb is in Span {a1,a2,a3}\{a_{1}, a_{2}, a_{3}\}{a1​,a2​,a3​}. Choose A, B, C, or D.

Problem 2130

The side of an equilateral triangle is 6 inches longer than a square's side, with a perimeter difference of 13 inches. Find the triangle's side.

Problem 2131

Ryan walked 8 dogs for a total of \$ 55, earning \$ 5 for small dogs and \$ 8 for large. How many small dogs did he walk?

Problem 2132

Problem 2133

Solve the following system of equations for all three variables. 4x+3y−z=108x+y−z=66x+y+z=4\begin{array}{r} 4 x+3 y-z=10 \\ 8 x+y-z=6 \\ 6 x+y+z=4 \end{array}4x+3y−z=108x+y−z=66x+y+z=4​

Problem 2134

Problem 2135

6x+1>5x+46 x+1>5 x+46x+1>5x+4 or 1−x>−41-x>-41−x>−4

Problem 2136

Determine if the equations are parallel, perpendicular, or neither.

Problem 2137

Problem 2138

Problem 2139

14 Solve the system using substitution: {2x−y=3x=−2y−1\left\{\begin{array}{l} 2 x-y=3 \\ x=-2 y-1 \end{array}\right.{2x−y=3x=−2y−1​Solution - write as an ordered pair, (x,y)(x, y)(x,y)

Problem 2140

Problem 2141

Problem 2142

9. For which values of the parameter c∈Rc \in \mathbb{R}c∈R is the vector (1,1,c)(1,1, c)(1,1,c) a linear combination of the vectors (2,1,3),(1,2,4),(3,0,2),(2,−2,−2)(2,1,3),(1,2,4),(3,0,2),(2,-2,-2)(2,1,3),(1,2,4),(3,0,2),(2,−2,−2) ?

Problem 2143

Problem 2144

Problem 2145

Problem 2146

g system of equations graphically on the set y=x−2y=−3x−6\begin{array}{c} y=x-2 \\ y=-3 x-6 \end{array}y=x−2y=−3x−6​

Problem 2147

Problem 2148

(42) Find the smallest positive integer which leaves the remainder 1 when divided by 2,3,4,5,62,3,4,5,62,3,4,5,6, and the remainder 0 when divided by 7 .

Problem 2149

Problem 2150

21 Solve each equation.

Find the solutions for the system: $2y=4x+12$ and $y=2x-6$ .

Solve the equations: 4x - 3y = 8 and 2x + y = 11. Find the value of $y$ . Choices: $-\frac{8}{3}$ , $-6$ , $14$ , $\frac{14}{5}$ .

Solve the equations: $-2x + 3y = 8$ and $5x - 2y = -9$ . Choose the correct solution from the options provided.

Solve the equations: $-3x + 4y = 13$ and $5x - 3y = -18$ . Choose the correct solution from the options provided.

Solve the system of linear equations by elimination. $\begin{array}{l} x+y=2 \\ 2 x+7 y=9 \end{array}$

5. A number $x$ is three less than twice $y$ . When you add $x$ multiplied by 4 and $y$ , the sum is six. What are the values of $x$ and $y$ ?
Equation 1: $\qquad$
Equation 2: $\qquad$

Solve by Graphing: $\left\{\begin{array}{l} y=\frac{1}{4} x-8 \\ y=x-5 \end{array}\right.$

(4.8) Using the determinant's method solve the following systems: $x+2 y+3 z=3$ a) $\begin{array}{l} 2 x-y+z=6 \\ 3 x+y-z=4 \end{array}$

Solve for $a$ : $3a + 2 > \frac{3a - 6}{3}$ , $a > -2$ , $a < 0$ , $a > 0$ , $a < -2$ .

Solve for $a$ : $3a + 2 > \frac{3a - 6}{3}$ , $a > -2$ , $a < 0$ , $a > 0$ , $a < -2$ .

Is the statement true or false? Justify: Does the augmented matrix $\left[\begin{array}{llll}a_{1} & a_{2} & a_{3} & b\end{array}\right]$ imply $b$ is in Span $\{a_{1}, a_{2}, a_{3}\}$ ?

Is the statement true or false? The linear system from $\left[\begin{array}{llll}a_{1} & a_{2} & a_{3} & b\end{array}\right]$ has a solution if $b$ is in Span $\{a_{1}, a_{2}, a_{3}\}$ . Choose A, B, C, or D.

Solve the following system of equations for all three variables. $\begin{array}{r} 4 x+3 y-z=10 \\ 8 x+y-z=6 \\ 6 x+y+z=4 \end{array}$

$6 x+1>5 x+4$ or $1-x>-4$

14 Solve the system using substitution: $\left\{\begin{array}{l} 2 x-y=3 \\ x=-2 y-1 \end{array}\right.$
Solution - write as an ordered pair, $(x, y)$

9. For which values of the parameter $c \in \mathbb{R}$ is the vector $(1,1, c)$ a linear combination of the vectors $(2,1,3),(1,2,4),(3,0,2),(2,-2,-2)$ ?

g system of equations graphically on the set $\begin{array}{c} y=x-2 \\ y=-3 x-6 \end{array}$

(42) Find the smallest positive integer which leaves the remainder 1 when divided by $2,3,4,5,6$ , and the remainder 0 when divided by 7 .

Solve the system with elimination. $\left\{\begin{array}{l} 2 x-5 y=-2 \\ 3 x+y=31 \end{array}\right.$

\begin{tabular}{c|c|} PROBLEM & SOLUTION \\ $-3 x+y=14$ \\ $-2 x-y=16$ & \\ & \end{tabular}

For three food shelters, model food costs $F$ based on people served $N$ and receipts $R$ . Predict $F$ for $N=3500$ , $R=\$ 13,500$ .

Solve the system:
-25x - 33y - z = 20 -40x - 55y - 2z = 37 30x + 33y + z = -5
Choose: A. One solution (exact form) B. Infinitely many $(\square, \square, z)$ C. No solution.

To eliminate $x$ in the system below, if you multiply the first equation by 8, what should you multiply the second by?
$\begin{array}{l} -6 x+8 y=-5 \\ -8 x-13 y=0 \end{array}$

$\begin{array}{l}6(w+1)-3 w=3(w+4 \\ 2(3 a-1)=4 a+10 \\ 7 b-3(b+2)=4 b-11 \\ 5(c-2)+3 c=4(2 c+1\end{array}$

5. $\begin{aligned} y & =-2 x+2 \\ & y=7 x+11\end{aligned}$

$5 \quad 5 x-7=2(x+1)$ $63(x-2)=9(x+2)$ $73 x-4=2 x+8-5 x$ $83(8-4 x)=34-11 x$

7.) $a x=b y=c z=\frac{3}{5} \quad a b+b c+c a=75 a b c \quad x+y+z=$ ?

Solve the system using Gaussian elimination: $\begin{array}{rr} x+2y+4z= & 14 \\ -x+3y+4z= & 8 \\ x+y-5z= & -20 \end{array}$ Find the solution as an ordered triple.

Solve the system using Gaussian elimination and backward substitution:
$\begin{array}{rr} x+2y+4z= & 11 \\ -x+3y+3z= & -2 \\ x+y-5z= & -6 \end{array}$
Is the solution unique, infinite, or nonexistent?

解不等式 $2x - 6 > -16$ 和 $3x - 10 \leq 8$ 。