Math

Problem 701

Solve the rational inequality $\frac{(x+7)(x-9)}{x-6}<0$ using the critical value method.

See Solution

Problem 702

Continuous function $f(x)$ has values $\{7, -9, 8, 2, -8\}$ at $x=\{0, 10, 20, 30, 40\}$ . Guarantee roots between $x=0$ and $x=10$ , $x=20$ and $x=30$ , $x=30$ and $x=40$ , but not between $x=10$ and $x=20$ .

See Solution

Problem 703

Multiply $(-9) \times 7$ and enter the answer.

See Solution

Problem 704

Solve the absolute value equation $2|a|-1=3$ .

See Solution

Problem 705

Find the product and ratio of $f(x)=x^{1/2}$ and $g(x)=\sqrt[3]{2x}+1$ , and rationalize the denominator of the ratio.

See Solution

Problem 706

Find the expression for the product of $(p-10 q)$ and $(p+10 q)$ .

See Solution

Problem 707

Find the value of $x$ where the ratios $(3x+2):(2x+5)$ and $7:5$ are equivalent. Provide the answer as an integer or simplified fraction.

See Solution

Problem 708

Convert the equation to standard form by completing the square on $x$ and $y$ . Graph the hyperbola, find the foci, and the equations of the asymptotes. $16 x^{2}-y^{2}-128 x-8 y+244=0$ The standard form of the equation is $\frac{(x-4)^2}{16}-\frac{y^2}{1}=1$ .

See Solution

Problem 709

Find the fraction equivalent of the repeating decimal $0.\overline{074}$ .

See Solution

Problem 710

Convert the repeating decimal $3.\overline{2}$ to a mixed number.

See Solution

Problem 711

Multiply $23.096$ and $90.300$ . Express the result in scientific notation with correct significant figures.

See Solution

Problem 712

Sell 21 tickets for a school play, with adult tickets at $6 and child tickets at$ 4. Solve for the number of adult and child tickets sold.
$a$ = number of adult tickets, $c$ = number of child tickets $a + c = 21$ $6a + 4c = 104$

See Solution

Problem 713

Solve the linear equation $15 + 6x = 45 + 8x$ for the unknown variable $x$ .

See Solution

Problem 714

Simplify the expression $3x(x+3)+x^2(x+3)$ .

See Solution

Problem 715

Factor the expression $6n^2 - n - 12$ . If it's not factorable, write "prime".

See Solution

Problem 716

Find the point of intersection of two linear equations: $4x - 2y = 1$ and $3x - 4y = 16$ .

See Solution

Problem 717

For a voltmeter with 0.1 V as the smallest division, estimate measurements to the nearest $100 \mathrm{mV}$ , $10 \mathrm{mV}$ , or $1 \mathrm{mV}$ .

See Solution

Problem 718

Create a division story problem about 7 feet of rope, modeled by the tape diagram: $\text{? halves}$

See Solution

Problem 719

Reflect the pre-image coordinates $A(-4,-11)$ , $B(6,-11)$ , and $C(-4,1)$ over the $x$ -axis.

See Solution

Problem 720

Find the quotient of $1.76 \div 0.9$ rounded to the nearest tenth.

See Solution

Problem 721

Harper knits a scarf 5 cm longer each night. Write an equation relating the number of nights $x$ and the scarf length $y$ (cm).
$y = 5x$

See Solution

Problem 722

Determine which numbers (721, 720, 372) are divisible by 10, 5, or 2.

See Solution

Problem 723

Translate the phrase into a variable expression using $p$ to represent the number of plants divided among 8 yards.

See Solution

Problem 724

Solve for the value of $x$ given the equation $y=5(x-a)$ .

See Solution

Problem 725

Find the cotangent of the negative of an angle x if the cotangent of x is 0.3.

See Solution

Problem 726

Find $\sec(-x)$ if $\sec(x)=2$ .

See Solution

Problem 727

Solve the equation using the Distributive Property: $\frac{1}{6}(p+24)=10$ , where $p=36$ .

See Solution

Problem 728

Compute the correlation coefficient $r$ given $\sum x=5,811, \sum x^{2}=5,632,643, \sum y=578, \sum y^{2}=65,292$ and $\sum x y=553,170$ . Does $r$ imply that $y$ should tend to increase, decrease, or remain constant as $x$ increases?

See Solution

Problem 729

Find the value of $x$ that satisfies the equation $7x - 7 = 28$ . Verify the solution.

See Solution

Problem 730

Determine if Rolle's Theorem applies to $f(x) = \sin 7x$ on $[\pi/7, 2\pi/7]$ . If so, find the point(s) guaranteed to exist. Select A and fill in the answer if Rolle's Theorem applies, otherwise select B.

See Solution

Problem 731

Find the inverse function $f^{-1}(x)$ if $f(x) = e^{x+1} - 2$ .

See Solution

Problem 732

Solve for $t$ in the equation $\frac{7}{4} + \frac{1}{3}t = 5$ .

See Solution

Problem 733

Find the range of values for $x$ given the inequality $0 < 2x + 4 < 40$ .

See Solution

Problem 734

Find the equation of a line with slope 0.5.

See Solution

Problem 735

Find the mean of a dataset with $S^{2}=10$ , $n=30$ , and $\sum x^{2}=3290$ .

See Solution

Problem 736

Multiply $(4x + 1/2)(2x + 1/2)$ using the FOIL method.

See Solution

Problem 737

Solve for x in the linear equation $3(x-4)=-9$ .

See Solution

Problem 738

Calculate the arc length of $y=\frac{1}{4} x^{2}-\frac{1}{2} \ln x$ on $[1,3 e]$ .

See Solution

Problem 739

Solve the linear equation $7x + 4 = 2x + 5$ for $x$ . The solution is $x = \square$ .

See Solution

Problem 740

Find the percent change in the weight Jake can lift, from 25 lbs on Monday to 45 lbs one month later.

See Solution

Problem 741

Find the length of the curve $y = \log\left(\frac{e^{x} - 1}{e^{x} + 1}\right)$ from $x = 1$ to $x = 2$ .

See Solution

Problem 742

Find parabola equation $y=ax^2+bx+c$ through 3 points: a) $A(-1,7)$ , $B(0,4)$ , $C(2,10)$ b) $A(-1,-6)$ , $B(1,0)$ , $C(3,-2)$ .

See Solution

Problem 743

Solve the equation $z^{2} + 9 = 10z$ .

See Solution

Problem 744

Solve for $u$ where $4^{u}=1024$ .

See Solution

Problem 745

Determine the constant $k$ that makes the given density function $f(x)$ a valid probability density function for the measurement error $X$ .

See Solution

Problem 746

Identify the real number property shown in the equation $4 \cdot 0 = 0$ .

See Solution

Problem 747

Find the value of $c$ if the vectors $v_1 = [1, 0, 0]$ , $v_2 = [1, 1, 0]$ , and $v_3 = [1, -1, c]$ are linearly dependent.

See Solution

Problem 748

Find the degree of the monomial $7 a^{5} b^{9}$ . The degree of the monomial is $14$ .

See Solution

Problem 749

Find the values of y that satisfy the equation $-2=4y^2-6y$ . Round the solutions to the nearest hundredth.

See Solution

Problem 750

Find the value of $y$ when $x=7$ , given the equation $y=x^{2}-7$ .

See Solution

Problem 751

5. Each question refers to geometric progressions: a) $a_{2}=2, a_{5}=\frac{1}{4}$ . Calculate $r, S_{6}$ and $S$ . b) $r=3, a_{3}=9$ . Determine $a_{n}, a_{7}$ and $P_{7}$ . c) $a_{1}=-6, r=\frac{2}{3}$ . Calculate $S_{4}$ and $S$ . d) $a_{n}=(-2)^{n-1}$ . Determine $S_{5}$ and $P_{5}$ .

See Solution

Problem 752

Evaluate $x^{2}-3y^{2}+2xy$ when $x=3$ and $y=-9$ .

See Solution

Problem 753

Sketch an angle $\theta$ such that $(6,-8)$ is on the terminal side and $\theta$ has the least positive measure. Find the exact values of the six trigonometric functions for $\theta$ .

See Solution

Problem 754

Simplify the expression $-[-(-3)-(-(-8))] \cdot\left(-2^{4}\right)$ .

See Solution

Problem 755

Write an interval notation for the set of all real numbers greater than 7.

See Solution

Problem 756

Evaluate the expression $(-3)^{3}$ .

See Solution

Problem 757

Find the exponent that makes the equation $2^{?} = 4$ true. The possible answers are $\frac{1}{2}, 1, 2, -2$ .

See Solution

Problem 758

Expand the expression $(x+6)(x+5)$ and illustrate the resulting product as a rectangle.

See Solution

Problem 759

Solve the linear equation $w + 3 = 3$ for the unknown variable $w$ .

See Solution

Problem 760

Solve the absolute value equation $2.5|x+4|=0.5|x+4|+10$ and classify the solution(s).

See Solution

Problem 761

Find the least possible value of integer constant $k$ in the equation $x(k x-56)=-16$ with no real solution.

See Solution

Problem 762

Divide polynomials using long division: a. $\left(k^{3}-k^{2}-k-2\right) \div(k-2)$ b. $\left(6 a^{3}+20 a^{2}-15 a+9\right) \div(a+4)$ c. $\left(n^{4}+10 n^{3}+21 n^{2}+6 n-8\right) \div(n+2)$ d. $\left(8 v^{5}+32 v^{4}+5 v+20\right) \div(v+4)$

See Solution

Problem 763

Explore the Subtracting Blocks eManipulative and solve the problem $52-17$ . Which action is required? A. Take away 7 cubes B. Take away 1 long C. Convert 1 long into 10 cubes D. All of the above

See Solution

Problem 764

Solve $15(5c-7) = 9c-9$ using addition and multiplication. Find the correct value from the options: $\frac{114}{11}, \frac{16}{11}, \frac{4}{21}$ .

See Solution

Problem 765

Find the missing value in the proportion $3 \frac{1}{2} : 7 \frac{3}{5} = x : \text{Blank\#1} \frac{\text{Blank\#2}}{\text{Blank\#3}}$ .

See Solution

Problem 766

Classify the polynomial $x^{2} - 6x + 9$ as a monomial, binomial, trinomial, or none of these.

See Solution

Problem 767

Solve the linear equation $-5u + 6 = -12u + 62$ for $u$ .

See Solution

Problem 768

Find the value of the expression $28.6-35+12.7-(-5.2)$ .

See Solution

Problem 769

Find the vertical asymptotes and holes of the rational function $f(x) = \frac{x-7}{x^{2}-9 x+14}$ . B. Vertical asymptote(s) at $x=3, 5$ and hole(s) at $x=7$ .

See Solution

Problem 770

Find the least common denominator (LCD) of the rational expressions $\frac{2}{x} + \frac{3}{x^{2}}$ .

See Solution

Problem 771

Find the sum of $\frac{3}{10}$ , $\frac{41}{100}$ , and $\frac{22}{100}$ .

See Solution

Problem 772

Given constraints and optimal solution $(x, y) = (25, 0)$ , find the values of the slack variables $s_1$ and $s_2$ .

See Solution

Problem 773

Isolate $y$ in the equation $10 x - y = 1$ .

See Solution

Problem 774

Solve $8c^2 - 41c = 42$ for $c$ . Provide exact solution(s).

See Solution

Problem 775

Resolver para $x$ , donde $-\frac{15}{4}=-3x$ . Simplificar la respuesta tanto como sea posible.

See Solution

Problem 776

Find the value of c in the equation: $28 \text{qt} = c$

See Solution

Problem 777

Determine if $\int_{0}^{\infty} 6 e^{-2 x} d x$ converges or diverges. If convergent, calculate its value.

See Solution

Problem 778

Find the missing value in the equations: $10+\square=16$ and $12=\square+2$ .

See Solution

Problem 779

Find $\sin(\alpha/2), \cos(\alpha/2), \tan(\alpha/2)$ given $\tan\alpha=21/20$ and $0^{\circ}<\alpha<90^{\circ}$ .

See Solution

Problem 780

Find the value of $y_0(2)$ where $y_0$ is the solution to the ODE $xy' + 2y = 2x$ with $y(1) = 3$ .

See Solution

Problem 781

Find the number of solutions to $4x^2 - 2x + 7 = 0$ using the discriminant.

See Solution

Problem 782

Solve for $x$ in the equation $7^{x} = \frac{1}{7}$ . Express the answer as an integer or a simplified fraction.

See Solution

Problem 783

Convert 1973.1 cubic miles to cubic kilometers using the conversion ratio: $1.61 \mathrm{~km} = 1$ mile.

See Solution

Problem 784

Simplificar la expresión $\sqrt{\frac{81}{16}}$ y escribir la respuesta en forma reducida.

See Solution

Problem 785

Evaluate the expression $6x + 5y - 1$ at $x=3, y=3$ and simplify.

See Solution

Problem 786

Solve for $z$ in the equation $5(2z-1)=-(3z-21)$ .

See Solution

Problem 787

If the linear correlation between two variables is negative, the slope of the regression line is \negative.

See Solution

Problem 788

Find the direct proportion model for $V$ and $I$ using the constant of proportion $k$ , where $V = k \cdot I$ .

See Solution

Problem 789

Find the probability that the complement of event $E$ occurs if the probability of $E$ is $0.21$ .

See Solution

Problem 790

Solve for $x$ in the equation: 6(x+4) = 12(x-20)

See Solution

Problem 791

Find the probability of 2 girls and 1 boy in a 3-child family, assuming equal chances for boys/girls. (A) $1/3$ (B) $3/8$ (C) $2/3$ (D) $1/4$

See Solution

Problem 792

A system of 2 linear equations has positive slopes, but different slopes. Which statement is true? The equations are $\text{independent}$ , $\text{dependent}$ , or the lines are $\perp$ to each other.

See Solution

Problem 793

Find the transformation properties of the quadratic function $g(x) = 3(x-2)^{2}$ , including its vertex, domain, range, and axis of symmetry.

See Solution

Problem 794

Determine the base of $-(-5)^{3}$ and evaluate $6^{5}$ .

See Solution

Problem 795

Convert $8$ grams to centigrams.

See Solution

Problem 796

Solve the linear equation $3(-9a-21)+11=8(a-1)-9$ for the variable $a$ .

See Solution

Problem 797

Calculate the 2nd and 3rd order Taylor polynomials for $f(x) = 8 \tan(x)$ centered at $a = 0$ . Express the polynomials using symbolic notation and fractions.

See Solution

Problem 798

Find the coordinates of point $Z'$ given that point $Z$ has coordinates $(-3,5)$ and is translated left 2 units and down 2 units.

See Solution

Problem 799

Evaluate the function $y = (\frac{1}{4})^{x}$ for $x = 3$ .

See Solution

Problem 800

Solve the linear equation $-\frac{1}{4}(-16b-20)=-7b-16$ for the variable $b$ .

See Solution

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Math

Problem 701

Solve the rational inequality (x+7)(x−9)x−6<0\frac{(x+7)(x-9)}{x-6}<0x−6(x+7)(x−9)​<0 using the critical value method.

Problem 702

Problem 703

Multiply (−9)×7(-9) \times 7(−9)×7 and enter the answer.

Problem 704

Solve the absolute value equation 2∣a∣−1=32|a|-1=32∣a∣−1=3.

Problem 705

Find the product and ratio of f(x)=x1/2f(x)=x^{1/2}f(x)=x1/2 and g(x)=2x3+1g(x)=\sqrt[3]{2x}+1g(x)=32x​+1, and rationalize the denominator of the ratio.

Problem 706

Find the expression for the product of (p−10q)(p-10 q)(p−10q) and (p+10q)(p+10 q)(p+10q).

Problem 707

Find the value of xxx where the ratios (3x+2):(2x+5)(3x+2):(2x+5)(3x+2):(2x+5) and 7:57:57:5 are equivalent. Provide the answer as an integer or simplified fraction.

Problem 708

Problem 709

Find the fraction equivalent of the repeating decimal 0.074‾0.\overline{074}0.074.

Problem 710

Convert the repeating decimal 3.2‾3.\overline{2}3.2 to a mixed number.

Problem 711

Multiply 23.09623.09623.096 and 90.30090.30090.300. Express the result in scientific notation with correct significant figures.

Problem 712

Sell 21 tickets for a school play, with adult tickets at 6andchildticketsat6 and child tickets at 6andchildticketsat4. Solve for the number of adult and child tickets sold.aaa = number of adult tickets, ccc = number of child tickets a+c=21a + c = 21a+c=21 6a+4c=1046a + 4c = 1046a+4c=104

Problem 713

Solve the linear equation 15+6x=45+8x15 + 6x = 45 + 8x15+6x=45+8x for the unknown variable xxx.

Problem 714

Simplify the expression 3x(x+3)+x2(x+3)3x(x+3)+x^2(x+3)3x(x+3)+x2(x+3).

Problem 715

Factor the expression 6n2−n−126n^2 - n - 126n2−n−12. If it's not factorable, write "prime".

Problem 716

Find the point of intersection of two linear equations: 4x−2y=14x - 2y = 14x−2y=1 and 3x−4y=163x - 4y = 163x−4y=16.

Problem 717

For a voltmeter with 0.1 V as the smallest division, estimate measurements to the nearest 100mV100 \mathrm{mV}100mV, 10mV10 \mathrm{mV}10mV, or 1mV1 \mathrm{mV}1mV.

Problem 718

Create a division story problem about 7 feet of rope, modeled by the tape diagram: ? halves\text{? halves}? halves

Problem 719

Reflect the pre-image coordinates A(−4,−11)A(-4,-11)A(−4,−11), B(6,−11)B(6,-11)B(6,−11), and C(−4,1)C(-4,1)C(−4,1) over the xxx-axis.

Problem 720

Find the quotient of 1.76÷0.91.76 \div 0.91.76÷0.9 rounded to the nearest tenth.

Problem 721

Harper knits a scarf 5 cm longer each night. Write an equation relating the number of nights xxx and the scarf length yyy (cm).y=5xy = 5xy=5x

Problem 722

Determine which numbers (721, 720, 372) are divisible by 10, 5, or 2.

Problem 723

Translate the phrase into a variable expression using ppp to represent the number of plants divided among 8 yards.

Problem 724

Solve for the value of xxx given the equation y=5(x−a)y=5(x-a)y=5(x−a).

Problem 725

Find the cotangent of the negative of an angle x if the cotangent of x is 0.3.

Problem 726

Find sec⁡(−x)\sec(-x)sec(−x) if sec⁡(x)=2\sec(x)=2sec(x)=2.

Problem 727

Solve the equation using the Distributive Property: 16(p+24)=10\frac{1}{6}(p+24)=1061​(p+24)=10, where p=36p=36p=36.

Problem 728

Problem 729

Find the value of xxx that satisfies the equation 7x−7=287x - 7 = 287x−7=28. Verify the solution.

Problem 730

Determine if Rolle's Theorem applies to f(x)=sin⁡7xf(x) = \sin 7xf(x)=sin7x on [π/7,2π/7][\pi/7, 2\pi/7][π/7,2π/7]. If so, find the point(s) guaranteed to exist. Select A and fill in the answer if Rolle's Theorem applies, otherwise select B.

Problem 731

Find the inverse function f−1(x)f^{-1}(x)f−1(x) if f(x)=ex+1−2f(x) = e^{x+1} - 2f(x)=ex+1−2.

Problem 732

Solve for ttt in the equation 74+13t=5\frac{7}{4} + \frac{1}{3}t = 547​+31​t=5.

Problem 733

Find the range of values for xxx given the inequality 0<2x+4<400 < 2x + 4 < 400<2x+4<40.

Problem 734

Find the equation of a line with slope 0.5.

Problem 735

Find the mean of a dataset with S2=10S^{2}=10S2=10, n=30n=30n=30, and ∑x2=3290\sum x^{2}=3290∑x2=3290.

Problem 736

Multiply (4x+1/2)(2x+1/2)(4x + 1/2)(2x + 1/2)(4x+1/2)(2x+1/2) using the FOIL method.

Problem 737

Solve for x in the linear equation 3(x−4)=−93(x-4)=-93(x−4)=−9.

Problem 738

Calculate the arc length of y=14x2−12ln⁡xy=\frac{1}{4} x^{2}-\frac{1}{2} \ln xy=41​x2−21​lnx on [1,3e][1,3 e][1,3e].

Problem 739

Solve the linear equation 7x+4=2x+57x + 4 = 2x + 57x+4=2x+5 for xxx. The solution is x=□x = \squarex=□.

Problem 740

Find the percent change in the weight Jake can lift, from 25 lbs on Monday to 45 lbs one month later.

Problem 741

Find the length of the curve y=log⁡(ex−1ex+1)y = \log\left(\frac{e^{x} - 1}{e^{x} + 1}\right)y=log(ex+1ex−1​) from x=1x = 1x=1 to x=2x = 2x=2.

Solve the rational inequality $\frac{(x+7)(x-9)}{x-6}<0$ using the critical value method.

Multiply $(-9) \times 7$ and enter the answer.

Solve the absolute value equation $2|a|-1=3$ .

Find the product and ratio of $f(x)=x^{1/2}$ and $g(x)=\sqrt[3]{2x}+1$ , and rationalize the denominator of the ratio.

Find the expression for the product of $(p-10 q)$ and $(p+10 q)$ .

Find the value of $x$ where the ratios $(3x+2):(2x+5)$ and $7:5$ are equivalent. Provide the answer as an integer or simplified fraction.

Find the fraction equivalent of the repeating decimal $0.\overline{074}$ .

Convert the repeating decimal $3.\overline{2}$ to a mixed number.

Multiply $23.096$ and $90.300$ . Express the result in scientific notation with correct significant figures.

Sell 21 tickets for a school play, with adult tickets at $6 and child tickets at$ 4. Solve for the number of adult and child tickets sold.
$a$ = number of adult tickets, $c$ = number of child tickets $a + c = 21$ $6a + 4c = 104$

Solve the linear equation $15 + 6x = 45 + 8x$ for the unknown variable $x$ .

Simplify the expression $3x(x+3)+x^2(x+3)$ .

Factor the expression $6n^2 - n - 12$ . If it's not factorable, write "prime".

Find the point of intersection of two linear equations: $4x - 2y = 1$ and $3x - 4y = 16$ .

For a voltmeter with 0.1 V as the smallest division, estimate measurements to the nearest $100 \mathrm{mV}$ , $10 \mathrm{mV}$ , or $1 \mathrm{mV}$ .

Create a division story problem about 7 feet of rope, modeled by the tape diagram: $\text{? halves}$

Reflect the pre-image coordinates $A(-4,-11)$ , $B(6,-11)$ , and $C(-4,1)$ over the $x$ -axis.

Find the quotient of $1.76 \div 0.9$ rounded to the nearest tenth.

Harper knits a scarf 5 cm longer each night. Write an equation relating the number of nights $x$ and the scarf length $y$ (cm).
$y = 5x$

Translate the phrase into a variable expression using $p$ to represent the number of plants divided among 8 yards.

Solve for the value of $x$ given the equation $y=5(x-a)$ .

Find $\sec(-x)$ if $\sec(x)=2$ .

Solve the equation using the Distributive Property: $\frac{1}{6}(p+24)=10$ , where $p=36$ .

Find the value of $x$ that satisfies the equation $7x - 7 = 28$ . Verify the solution.

Determine if Rolle's Theorem applies to $f(x) = \sin 7x$ on $[\pi/7, 2\pi/7]$ . If so, find the point(s) guaranteed to exist. Select A and fill in the answer if Rolle's Theorem applies, otherwise select B.

Find the inverse function $f^{-1}(x)$ if $f(x) = e^{x+1} - 2$ .

Solve for $t$ in the equation $\frac{7}{4} + \frac{1}{3}t = 5$ .

Find the range of values for $x$ given the inequality $0 < 2x + 4 < 40$ .

Find the mean of a dataset with $S^{2}=10$ , $n=30$ , and $\sum x^{2}=3290$ .

Multiply $(4x + 1/2)(2x + 1/2)$ using the FOIL method.

Solve for x in the linear equation $3(x-4)=-9$ .

Calculate the arc length of $y=\frac{1}{4} x^{2}-\frac{1}{2} \ln x$ on $[1,3 e]$ .

Solve the linear equation $7x + 4 = 2x + 5$ for $x$ . The solution is $x = \square$ .

Find the length of the curve $y = \log\left(\frac{e^{x} - 1}{e^{x} + 1}\right)$ from $x = 1$ to $x = 2$ .

Find parabola equation $y=ax^2+bx+c$ through 3 points: a) $A(-1,7)$ , $B(0,4)$ , $C(2,10)$ b) $A(-1,-6)$ , $B(1,0)$ , $C(3,-2)$ .

Solve the equation $z^{2} + 9 = 10z$ .

Solve for $u$ where $4^{u}=1024$ .

Determine the constant $k$ that makes the given density function $f(x)$ a valid probability density function for the measurement error $X$ .

Identify the real number property shown in the equation $4 \cdot 0 = 0$ .

Find the value of $c$ if the vectors $v_1 = [1, 0, 0]$ , $v_2 = [1, 1, 0]$ , and $v_3 = [1, -1, c]$ are linearly dependent.

Find the degree of the monomial $7 a^{5} b^{9}$ . The degree of the monomial is $14$ .

Find the values of y that satisfy the equation $-2=4y^2-6y$ . Round the solutions to the nearest hundredth.

Find the value of $y$ when $x=7$ , given the equation $y=x^{2}-7$ .

Evaluate $x^{2}-3y^{2}+2xy$ when $x=3$ and $y=-9$ .

Sketch an angle $\theta$ such that $(6,-8)$ is on the terminal side and $\theta$ has the least positive measure. Find the exact values of the six trigonometric functions for $\theta$ .

Simplify the expression $-[-(-3)-(-(-8))] \cdot\left(-2^{4}\right)$ .

Evaluate the expression $(-3)^{3}$ .

Find the exponent that makes the equation $2^{?} = 4$ true. The possible answers are $\frac{1}{2}, 1, 2, -2$ .

Expand the expression $(x+6)(x+5)$ and illustrate the resulting product as a rectangle.

Solve the linear equation $w + 3 = 3$ for the unknown variable $w$ .

Solve the absolute value equation $2.5|x+4|=0.5|x+4|+10$ and classify the solution(s).

Find the least possible value of integer constant $k$ in the equation $x(k x-56)=-16$ with no real solution.

Explore the Subtracting Blocks eManipulative and solve the problem $52-17$ . Which action is required? A. Take away 7 cubes B. Take away 1 long C. Convert 1 long into 10 cubes D. All of the above

Solve $15(5c-7) = 9c-9$ using addition and multiplication. Find the correct value from the options: $\frac{114}{11}, \frac{16}{11}, \frac{4}{21}$ .

Find the missing value in the proportion $3 \frac{1}{2} : 7 \frac{3}{5} = x : \text{Blank\#1} \frac{\text{Blank\#2}}{\text{Blank\#3}}$ .

Classify the polynomial $x^{2} - 6x + 9$ as a monomial, binomial, trinomial, or none of these.

Solve the linear equation $-5u + 6 = -12u + 62$ for $u$ .

Find the value of the expression $28.6-35+12.7-(-5.2)$ .

Find the vertical asymptotes and holes of the rational function $f(x) = \frac{x-7}{x^{2}-9 x+14}$ . B. Vertical asymptote(s) at $x=3, 5$ and hole(s) at $x=7$ .

Find the least common denominator (LCD) of the rational expressions $\frac{2}{x} + \frac{3}{x^{2}}$ .

Find the sum of $\frac{3}{10}$ , $\frac{41}{100}$ , and $\frac{22}{100}$ .

Given constraints and optimal solution $(x, y) = (25, 0)$ , find the values of the slack variables $s_1$ and $s_2$ .

Isolate $y$ in the equation $10 x - y = 1$ .

Solve $8c^2 - 41c = 42$ for $c$ . Provide exact solution(s).