Browse Math problems in the Studdy Learning Bank!

Problem 3301

Find the number of associates and partners assigned to a case where the daily rate for associates is $500 and for partners is$ 1400, and the total daily charge to the client is $5800.

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Problem 3302

Find the missing addend in the equation $556 + \square = 1,046$ .

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Problem 3303

Write an equation to describe the proportional relationship between paint used (x quarts) and wall area (y sq. yards) given the table: $3x = 23 \frac{1}{2}y, 4x = 31 \frac{1}{3}y, 5x = 39 \frac{1}{6}y$ .

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Problem 3304

Find the value of $w$ if $16=2(2w+w-1)$ .

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Problem 3305

Évaluez l'expression fractionnaire $\frac{5}{9} \div \frac{4}{9}+\frac{1}{3}$ .

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Problem 3306

Find the quotient of $2,356 \div 27$ .

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Problem 3307

Find which values of the variable satisfy the given equations: $d+9=35$ with $d=16,22,26,36$ , and $14 n=35$ with $n=2,3,3.5,4$ .

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Problem 3308

Solve for the variable $j$ given the equation $4j=18.8$ .

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Problem 3309

What is the value of $12(8+9)$ ?

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Problem 3310

Find the value of $9b$ if $4-2b=b$ .

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Problem 3311

Solve the linear equation $-4x = -8$ for the unknown variable $x$ .

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Problem 3312

Determine if two independent samples from normal populations have equal means using a two-tailed test at $\alpha = 0.05$ . The test statistic is $t = -1.67$ , and the p-value is $\square$ .

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Problem 3313

Solve for $y$ in $3y=57$ . Simplify the solution to $y=19$ .

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Problem 3314

Simplify the expression $3(x-8)$ and show the step-by-step work.

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Problem 3315

Find the derivative of $\sec x \cos x$ .

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Problem 3316

Find the length of $Y X$ if $Y$ is between $X$ and $Z$ , $Y Z=4$ , and $X Z=12$ .

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Problem 3317

Find the y-intercept of the parabola $y=x^2 + 6x + \frac{19}{4}$ . Simplify the answer as a fraction or integer.

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Problem 3318

Leilani's sixteenth note is $\frac{3}{16}$ shorter than her classmate's note. Solve $n-\frac{1}{16}=\frac{3}{16}$ to determine the note her classmate is singing.

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Problem 3319

Valve regulates water pressure on 180 engines. Mean pressure is 6.2 lbs/square inch, variance is 0.25. Determine if there is sufficient evidence at 0.02 level that valve does not meet 6.3 lbs/square inch specification.
$H_0$ : $\mu = 6.3$ lbs/square inch $H_a$ : $\mu \neq 6.3$ lbs/square inch

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Problem 3320

Solve for the value of $w$ when $\frac{w}{3}=3.75$ .

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Problem 3321

Find the average of $x+15$ , $7x$ , and $x$ in terms of $x$ .

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Problem 3322

Find the value of $x$ where $\frac{x}{8}=4$ .

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Problem 3323

Calculate the range of the data set with $n=10$ observations: $\text{range} = \max(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9) - \min(63.6, 81.9, 74.5, 66.8, 53.5, 57.4, 69.6, 46.1, 81.9, 81.9)$ .

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Problem 3324

Solve the linear system and find the value of $q$ .

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Problem 3325

Solve the linear equation: $-86 = -8y + 2$

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Problem 3326

Find the quadratic equation with two $x$ -intercepts from the given options: $-2 x^{2}-5=0$ , $x^{2}-4 x+4=0$ , $-x^{2}-x=0$ , $x^{2}+12=0$ , $-x^{2}-12=0$ .

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Problem 3327

Find the value of the linear function $g(x) = 19.60 + 1.74x$ evaluated at $x = 30$ .

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Problem 3328

Simplify $(2 x+3)^{2}$ and subtract it from $2 x^{2}-4$ to get the result in standard polynomial form.

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Problem 3329

Find the equation of the normal line to the curve $y=2x^2-4x+1$ at the point $(2,1)$ in the form $y=mx+c$ .

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Problem 3330

Solve the linear equation $-9x - g = -27g$ for $x$ and $g$ .

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Problem 3331

Find the solutions for the absolute value equation $|x| = 9$ .

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Problem 3332

Solve for the variable $y$ in the equation $-2=\frac{4}{3}y$ .

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Problem 3333

Find the composition of the functions $g(t) = t - 3$ and $f(t) = t^2 + 5t$ .

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Problem 3334

Find the simplified expression for $2x + 9 + 7x$ .

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Problem 3335

Find the location of $\sqrt{31}$ on the number line, between 5 and 6.

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Problem 3336

Find the simplified difference quotient $\frac{f(x+h)-f(x)}{h}$ and complete the table for $f(x)=x^2$ , $x=5$ , and various $h$ values.

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Problem 3337

A spinner has 6 slices: 2 blue, 1 yellow, 3 red. Find the probability the spinner stops on a non-blue slice. Write as a fraction or whole number.
$P(\text{non-blue slice}) = \frac{4}{6} = \frac{2}{3}$

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Problem 3338

Plot the complex number $-2$ on the complex plane.

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Problem 3339

Use long division to show $a-5$ is a factor of $a^3 - 5a^2 - 6a + 30$ .

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Problem 3340

Find the value of $x$ given the equation $x + 98^\circ + 48^\circ = 180^\circ$ .

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Problem 3341

Solve the linear equation $0=4+\frac{n}{5}$ for the unknown variable $n$ .

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Problem 3342

Plot the image of a triangle with vertices at $(-3,6)$ , $(6,0)$ , and $(-6,-9)$ dilated by a factor of $\frac{1}{3}$ centered at the origin.

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Problem 3343

Which number is a multiple of 4, 5, and 20? $10$ is a multiple of 4, 5, and 20.

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Problem 3344

Solve the exponential equation $3^{9x} = 3^{7x+8}$ for $x$ .

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Problem 3345

Laura's go-kart used 3.4 liters of fuel. The go-kart now has 4.91 liters of fuel. Write an equation to find the initial amount of fuel $A$ , then solve for $A$ . $A - 3.4 = 4.91$ $A = 8.31$ liters

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Problem 3346

Solve for the expression: $34 + 3 - 7$

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Problem 3347

Find the value of $x$ that satisfies the equation $2(x-3)=9-x$ .

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Problem 3348

Find the sum: $378.03+17.5$ . Find the difference: $18.398-4.37$ . Compute: $18 \cdot 348 - 437 = 61$ .

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Problem 3349

Evaluate the sine of 1.2 using a calculator.

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Problem 3350

Solve for the general solution of the differential equation $(x^2-xy+y^2)dx-xy\,dx=0$ . If homogeneous, use $y=vx$ .

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Problem 3351

Find the remaining distance for a linear function with slope -0.95 miles/minute, given 64 miles remaining after 37 minutes of driving. Determine the remaining distance after 57 minutes of driving.

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Problem 3352

Solve the linear equation $2(w+1)+4w=3(2w-1)+8$ for $w$ . The equation has no unique solution, and all real numbers are solutions.

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Problem 3353

Simplify the expression $(8+2) \cdot 4$ using the order of operations.

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Problem 3354

Find the value of $z$ that satisfies the equation $10(z-1)=50$ .

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Problem 3355

Evaluate the piecewise function $g(x)$ at different values in its domain: $g(-4), g(-2), g(0), g(3), g(4)$ .

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Problem 3356

Find $x$ that satisfies $5x - 3 = 12x + 11$ . The solution set is...

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Problem 3357

Find the zeros of the quadratic relation $y=-3(x-5)(x+7)$ and determine if the parabola opens upward or downward.

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Problem 3358

Solve the linear equation $-8(-x+7)=8(x-7)$ and determine the number of solutions.

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Problem 3359

The red car is $150$ feet up a straight road from a police car $50$ feet to the side. The police radar reads the distance between the cars is decreasing at $90$ feet/second. Find the red car's actual speed along the road in feet/second.

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Problem 3360

Evaluate the following expressions: $-10(-8.874)$ and $0.2 \cdot (-3.2)$ .

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Problem 3361

Find if $\triangle ABC$ with slopes $\frac{3}{4}$ and $-\frac{4}{3}$ is isosceles, right-angled, parallel, or equilateral.

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Problem 3362

Find the side length of a square with a diagonal of $8\mathrm{~cm}$ .

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Problem 3363

Simplify the expression $\left(\frac{3}{8}\right)^{-\frac{1}{2}} \times (2 \sqrt{3})^{3}$ .

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Problem 3364

Solve the linear equation $p - 5 = \frac{7}{2}(t - 4)$ for the variable $p$ .

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Problem 3365

Find the limit of $\sqrt{x+4}$ as $x$ approaches 0.

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Problem 3366

Find the minimum monthly savings needed to cover the remaining cost of a $\$ 26,750$ per year private college after a $60\%$ academic scholarship and $\$ 1,500$ Pell grant, over 24 months.

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Problem 3367

Multiply $(8-y)(8+y)$ and simplify the result.

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Problem 3368

Find the cosecant of $\frac{5 \pi}{3}$ .

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Problem 3369

Solve for the value of $x$ in the equation $20 = 5x$ .

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Problem 3370

Find the surface area of a box with length $l=27$ feet, width $w=7$ feet, and height $h=9$ feet.

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Problem 3371

Find equations with the same solution as $x^2 - 16x - 8 = -7$ .

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Problem 3372

Find the two integers between which $x$ lies when $2^{x} = 50$ .

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Problem 3373

Solve the linear equation $84x + 6 = 2(2x + 43)$ for $x$ .

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Problem 3374

Find the products of $0.009 \times 10$ , $3.1 \times 10^{3}$ , $0.062 \times 10^{2}$ , and $1.24 \times 10^{4}$ .

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Problem 3375

Solve the equation $-6u-13=3-8u$ . The solution set is $\{u\}$ .

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Problem 3376

Simplify the expression $\left(\frac{4}{25}\right)^{2} \times 2^{4} \div\left(\frac{15}{2}\right)$ .

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Problem 3377

Solve the equation $-3(3y+8)=48$ and express the solution as an integer or simplified fraction.

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Problem 3378

Solve the quadratic equation $7(5 x-4)^{2}+7=350$ for $x$ .

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Problem 3379

Humpback whale ( $3 \cdot 10^{4} \mathrm{~kg}$ ) vs. tiger shark ( $5.9 \cdot 10^{3} \mathrm{~kg}$ ). Basheera or Elena - which claim is correct?

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Problem 3380

Solve the linear equation $3.25(x-2)=19.5$ for the unknown variable $x$ .

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Problem 3381

Identify which statements about the polynomial function $y=(x-5)^{2}(x+3)$ are true: $x$ -intercepts, degree, domain, range.

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Problem 3382

Solve the linear inequality $5x/8 \geq 30$ . Graph the solution set.

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Problem 3383

Determine the correct product of $(-4 \times 10^{2})$ and $(2 \times 10^{-8})$ . The coefficient may be rounded.

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Problem 3384

Find the time $t$ when the ball reaches the ground, given the height function $H = -5(t - 3)(t + 5)$ .

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Problem 3385

Find the relative maximum point of $f(x) = -x^3 + 3x^2 - 4$ using $f'(x)$ and $f''(x)$ .

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Problem 3386

Evaluate $2^{x}$ for (a) $x=-2$ and (b) $x=3$

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Problem 3387

Find the algebraic expression for "Eight divided by the difference of $x$ and $m$ ". Options: A) $\frac{8}{m}-x$ , B) $8-\frac{x}{m}$ , C) $\frac{x-m}{8}$ , D) $\frac{8}{x-m}$

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Problem 3388

Find two numbers whose sum is -12 and difference is -4. $x=$ $y=$

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Problem 3389

Simplify $\sqrt{24 p^{13} q^{6}}$ , assuming all variables are positive. Express exponents as positive values.

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Problem 3390

Determine if the equation $7x(y+2) = 3 - 7y(10-x)$ is linear or not linear.

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Problem 3391

Solve the system of linear equations $-4x - 8y = 8$ and $3x - 5y = 16$ using the elimination method.

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Problem 3392

Simplify $5x^2 + 7x - 2x^2 + 9y + 8y^2 - 3x$ .

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Problem 3393

Find the domain, limits, and graph of the piecewise function $f(x) = \sqrt{25 - x^2}$ for $0 \leq x < 5$ , $f(x) = 5$ for $5 \leq x < 10$ , and $f(x) = 10$ for $x = 10$ .

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Problem 3394

Find the inverse function of $y=\sqrt{x-1}+3$

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Problem 3395

Solve the absolute value equation $|h-4|=7$ . Rewrite as a compound statement, solve for $h$ , and write the solution set.

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Problem 3396

Find the $x$ that satisfies the equation $\frac{1}{3x+5} \cdot 25^{4x-1} = \sqrt[8]{625}$ .

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Problem 3397

Find the value of $x$ that makes the exponent of $f(x)=2^{x-1}$ zero.

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Problem 3398

a) How many $1$ -L paint cans needed to cover a $5.2 \times 5.2 \mathrm{~m}$ ceiling if $1$ can covers $11 \mathrm{~m}^{2}$ ? b) What are the max dimensions of a square ceiling that can be painted with $4 \mathrm{L}$ of paint if $1$ can covers $11 \mathrm{~m}^{2}$ ? (to nearest $0.1 \mathrm{~m}$ )

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Problem 3399

Simplify the expression $6x^{2} - 24x$ .

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Problem 3400

Find the limit of $\frac{\sin 2x}{x^2 \cot 4x}$ as $x$ approaches 0.

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Math

Problem 3301

Find the number of associates and partners assigned to a case where the daily rate for associates is 500andforpartnersis500 and for partners is 500andforpartnersis1400, and the total daily charge to the client is $5800.

Problem 3302

Find the missing addend in the equation 556+□=1,046556 + \square = 1,046556+□=1,046.

Problem 3303

Write an equation to describe the proportional relationship between paint used (x quarts) and wall area (y sq. yards) given the table: 3x=2312y,4x=3113y,5x=3916y3x = 23 \frac{1}{2}y, 4x = 31 \frac{1}{3}y, 5x = 39 \frac{1}{6}y3x=2321​y,4x=3131​y,5x=3961​y.

Problem 3304

Find the value of www if 16=2(2w+w−1)16=2(2w+w-1)16=2(2w+w−1).

Problem 3305

Évaluez l'expression fractionnaire 59÷49+13\frac{5}{9} \div \frac{4}{9}+\frac{1}{3}95​÷94​+31​.

Problem 3306

Find the quotient of 2,356÷272,356 \div 272,356÷27.

Problem 3307

Find which values of the variable satisfy the given equations: d+9=35d+9=35d+9=35 with d=16,22,26,36d=16,22,26,36d=16,22,26,36, and 14n=3514 n=3514n=35 with n=2,3,3.5,4n=2,3,3.5,4n=2,3,3.5,4.

Problem 3308

Solve for the variable jjj given the equation 4j=18.84j=18.84j=18.8.

Problem 3309

What is the value of 12(8+9)12(8+9)12(8+9)?

Problem 3310

Find the value of 9b9b9b if 4−2b=b4-2b=b4−2b=b.

Problem 3311

Solve the linear equation −4x=−8-4x = -8−4x=−8 for the unknown variable xxx.

Problem 3312

Determine if two independent samples from normal populations have equal means using a two-tailed test at α=0.05\alpha = 0.05α=0.05. The test statistic is t=−1.67t = -1.67t=−1.67, and the p-value is □\square□.

Problem 3313

Solve for yyy in 3y=573y=573y=57. Simplify the solution to y=19y=19y=19.

Problem 3314

Simplify the expression 3(x−8)3(x-8)3(x−8) and show the step-by-step work.

Problem 3315

Find the derivative of sec⁡xcos⁡x\sec x \cos xsecxcosx.

Problem 3316

Find the length of YXY XYX if YYY is between XXX and ZZZ, YZ=4Y Z=4YZ=4, and XZ=12X Z=12XZ=12.

Problem 3317

Find the y-intercept of the parabola y=x2+6x+194y=x^2 + 6x + \frac{19}{4}y=x2+6x+419​. Simplify the answer as a fraction or integer.

Problem 3318

Leilani's sixteenth note is 316\frac{3}{16}163​ shorter than her classmate's note. Solve n−116=316n-\frac{1}{16}=\frac{3}{16}n−161​=163​ to determine the note her classmate is singing.

Problem 3319

Problem 3320

Solve for the value of www when w3=3.75\frac{w}{3}=3.753w​=3.75.

Problem 3321

Find the average of x+15x+15x+15, 7x7x7x, and xxx in terms of xxx.

Problem 3322

Find the value of xxx where x8=4\frac{x}{8}=48x​=4.

Problem 3323

Problem 3324

Solve the linear system and find the value of qqq.

Problem 3325

Solve the linear equation: −86=−8y+2-86 = -8y + 2−86=−8y+2

Problem 3326

Find the quadratic equation with two xxx-intercepts from the given options: −2x2−5=0-2 x^{2}-5=0−2x2−5=0, x2−4x+4=0x^{2}-4 x+4=0x2−4x+4=0, −x2−x=0-x^{2}-x=0−x2−x=0, x2+12=0x^{2}+12=0x2+12=0, −x2−12=0-x^{2}-12=0−x2−12=0.

Problem 3327

Find the value of the linear function g(x)=19.60+1.74xg(x) = 19.60 + 1.74xg(x)=19.60+1.74x evaluated at x=30x = 30x=30.

Problem 3328

Simplify (2x+3)2(2 x+3)^{2}(2x+3)2 and subtract it from 2x2−42 x^{2}-42x2−4 to get the result in standard polynomial form.

Problem 3329

Find the equation of the normal line to the curve y=2x2−4x+1y=2x^2-4x+1y=2x2−4x+1 at the point (2,1)(2,1)(2,1) in the form y=mx+cy=mx+cy=mx+c.

Problem 3330

Solve the linear equation −9x−g=−27g-9x - g = -27g−9x−g=−27g for xxx and ggg.

Problem 3331

Find the solutions for the absolute value equation ∣x∣=9|x| = 9∣x∣=9.

Problem 3332

Solve for the variable yyy in the equation −2=43y-2=\frac{4}{3}y−2=34​y.

Problem 3333

Find the composition of the functions g(t)=t−3g(t) = t - 3g(t)=t−3 and f(t)=t2+5tf(t) = t^2 + 5tf(t)=t2+5t.

Problem 3334

Find the simplified expression for 2x+9+7x2x + 9 + 7x2x+9+7x.

Problem 3335

Find the location of 31\sqrt{31}31​ on the number line, between 5 and 6.

Problem 3336

Find the simplified difference quotient f(x+h)−f(x)h\frac{f(x+h)-f(x)}{h}hf(x+h)−f(x)​ and complete the table for f(x)=x2f(x)=x^2f(x)=x2, x=5x=5x=5, and various hhh values.

Problem 3337

A spinner has 6 slices: 2 blue, 1 yellow, 3 red. Find the probability the spinner stops on a non-blue slice. Write as a fraction or whole number.P(non-blue slice)=46=23P(\text{non-blue slice}) = \frac{4}{6} = \frac{2}{3}P(non-blue slice)=64​=32​

Problem 3338

Plot the complex number −2-2−2 on the complex plane.

Problem 3339

Use long division to show a−5a-5a−5 is a factor of a3−5a2−6a+30a^3 - 5a^2 - 6a + 30a3−5a2−6a+30.

Problem 3340

Find the value of xxx given the equation x+98∘+48∘=180∘x + 98^\circ + 48^\circ = 180^\circx+98∘+48∘=180∘.

Problem 3341

Find the number of associates and partners assigned to a case where the daily rate for associates is $500 and for partners is$ 1400, and the total daily charge to the client is $5800.

Find the missing addend in the equation $556 + \square = 1,046$ .

Write an equation to describe the proportional relationship between paint used (x quarts) and wall area (y sq. yards) given the table: $3x = 23 \frac{1}{2}y, 4x = 31 \frac{1}{3}y, 5x = 39 \frac{1}{6}y$ .

Find the value of $w$ if $16=2(2w+w-1)$ .

Évaluez l'expression fractionnaire $\frac{5}{9} \div \frac{4}{9}+\frac{1}{3}$ .

Find the quotient of $2,356 \div 27$ .

Find which values of the variable satisfy the given equations: $d+9=35$ with $d=16,22,26,36$ , and $14 n=35$ with $n=2,3,3.5,4$ .

Solve for the variable $j$ given the equation $4j=18.8$ .

What is the value of $12(8+9)$ ?

Find the value of $9b$ if $4-2b=b$ .

Solve the linear equation $-4x = -8$ for the unknown variable $x$ .

Determine if two independent samples from normal populations have equal means using a two-tailed test at $\alpha = 0.05$ . The test statistic is $t = -1.67$ , and the p-value is $\square$ .

Solve for $y$ in $3y=57$ . Simplify the solution to $y=19$ .

Simplify the expression $3(x-8)$ and show the step-by-step work.

Find the derivative of $\sec x \cos x$ .

Find the length of $Y X$ if $Y$ is between $X$ and $Z$ , $Y Z=4$ , and $X Z=12$ .

Find the y-intercept of the parabola $y=x^2 + 6x + \frac{19}{4}$ . Simplify the answer as a fraction or integer.

Leilani's sixteenth note is $\frac{3}{16}$ shorter than her classmate's note. Solve $n-\frac{1}{16}=\frac{3}{16}$ to determine the note her classmate is singing.

Solve for the value of $w$ when $\frac{w}{3}=3.75$ .

Find the average of $x+15$ , $7x$ , and $x$ in terms of $x$ .

Find the value of $x$ where $\frac{x}{8}=4$ .

Solve the linear system and find the value of $q$ .

Solve the linear equation: $-86 = -8y + 2$

Find the quadratic equation with two $x$ -intercepts from the given options: $-2 x^{2}-5=0$ , $x^{2}-4 x+4=0$ , $-x^{2}-x=0$ , $x^{2}+12=0$ , $-x^{2}-12=0$ .

Find the value of the linear function $g(x) = 19.60 + 1.74x$ evaluated at $x = 30$ .

Simplify $(2 x+3)^{2}$ and subtract it from $2 x^{2}-4$ to get the result in standard polynomial form.

Find the equation of the normal line to the curve $y=2x^2-4x+1$ at the point $(2,1)$ in the form $y=mx+c$ .

Solve the linear equation $-9x - g = -27g$ for $x$ and $g$ .

Find the solutions for the absolute value equation $|x| = 9$ .

Solve for the variable $y$ in the equation $-2=\frac{4}{3}y$ .

Find the composition of the functions $g(t) = t - 3$ and $f(t) = t^2 + 5t$ .

Find the simplified expression for $2x + 9 + 7x$ .

Find the location of $\sqrt{31}$ on the number line, between 5 and 6.

Find the simplified difference quotient $\frac{f(x+h)-f(x)}{h}$ and complete the table for $f(x)=x^2$ , $x=5$ , and various $h$ values.

A spinner has 6 slices: 2 blue, 1 yellow, 3 red. Find the probability the spinner stops on a non-blue slice. Write as a fraction or whole number.
$P(\text{non-blue slice}) = \frac{4}{6} = \frac{2}{3}$

Plot the complex number $-2$ on the complex plane.

Use long division to show $a-5$ is a factor of $a^3 - 5a^2 - 6a + 30$ .

Find the value of $x$ given the equation $x + 98^\circ + 48^\circ = 180^\circ$ .

Solve the linear equation $0=4+\frac{n}{5}$ for the unknown variable $n$ .

Plot the image of a triangle with vertices at $(-3,6)$ , $(6,0)$ , and $(-6,-9)$ dilated by a factor of $\frac{1}{3}$ centered at the origin.

Which number is a multiple of 4, 5, and 20? $10$ is a multiple of 4, 5, and 20.

Solve the exponential equation $3^{9x} = 3^{7x+8}$ for $x$ .

Laura's go-kart used 3.4 liters of fuel. The go-kart now has 4.91 liters of fuel. Write an equation to find the initial amount of fuel $A$ , then solve for $A$ . $A - 3.4 = 4.91$ $A = 8.31$ liters

Solve for the expression: $34 + 3 - 7$

Find the value of $x$ that satisfies the equation $2(x-3)=9-x$ .

Find the sum: $378.03+17.5$ . Find the difference: $18.398-4.37$ . Compute: $18 \cdot 348 - 437 = 61$ .

Solve for the general solution of the differential equation $(x^2-xy+y^2)dx-xy\,dx=0$ . If homogeneous, use $y=vx$ .

Solve the linear equation $2(w+1)+4w=3(2w-1)+8$ for $w$ . The equation has no unique solution, and all real numbers are solutions.

Simplify the expression $(8+2) \cdot 4$ using the order of operations.

Find the value of $z$ that satisfies the equation $10(z-1)=50$ .

Evaluate the piecewise function $g(x)$ at different values in its domain: $g(-4), g(-2), g(0), g(3), g(4)$ .

Find $x$ that satisfies $5x - 3 = 12x + 11$ . The solution set is...

Find the zeros of the quadratic relation $y=-3(x-5)(x+7)$ and determine if the parabola opens upward or downward.

Solve the linear equation $-8(-x+7)=8(x-7)$ and determine the number of solutions.

The red car is $150$ feet up a straight road from a police car $50$ feet to the side. The police radar reads the distance between the cars is decreasing at $90$ feet/second. Find the red car's actual speed along the road in feet/second.

Evaluate the following expressions: $-10(-8.874)$ and $0.2 \cdot (-3.2)$ .

Find if $\triangle ABC$ with slopes $\frac{3}{4}$ and $-\frac{4}{3}$ is isosceles, right-angled, parallel, or equilateral.

Find the side length of a square with a diagonal of $8\mathrm{~cm}$ .

Simplify the expression $\left(\frac{3}{8}\right)^{-\frac{1}{2}} \times (2 \sqrt{3})^{3}$ .

Solve the linear equation $p - 5 = \frac{7}{2}(t - 4)$ for the variable $p$ .

Find the limit of $\sqrt{x+4}$ as $x$ approaches 0.

Find the minimum monthly savings needed to cover the remaining cost of a $\$ 26,750$ per year private college after a $60\%$ academic scholarship and $\$ 1,500$ Pell grant, over 24 months.

Multiply $(8-y)(8+y)$ and simplify the result.

Find the cosecant of $\frac{5 \pi}{3}$ .

Solve for the value of $x$ in the equation $20 = 5x$ .

Find the surface area of a box with length $l=27$ feet, width $w=7$ feet, and height $h=9$ feet.

Find equations with the same solution as $x^2 - 16x - 8 = -7$ .

Find the two integers between which $x$ lies when $2^{x} = 50$ .

Solve the linear equation $84x + 6 = 2(2x + 43)$ for $x$ .

Find the products of $0.009 \times 10$ , $3.1 \times 10^{3}$ , $0.062 \times 10^{2}$ , and $1.24 \times 10^{4}$ .