Solving for a Variable Introduction,Examples with Step-by-Step Explanations

The problems about Solving for a Variable

Topic	Problem	Solution
None	3. A rectangle has length $(3 x + 7) cm$ a…	Find the area by multiplying the length and width: $(3 x + 7) (2 x - 1)$
None	A person invested $$ 6100$ for 1 year, part at $…	Let's denote the amount invested at 5% as $x$ , the amount invested at 11% as $y$ , and the amoun…
None	Ms. Suzuki invested $$ 22, 000$ in two accounts, …	Let's denote the amount invested at 4% as x and the amount invested at 8% as y.
None	$(4 x^{5}) \times (2 x^{3})$	Multiply the coefficients: $4 \times 2 = 8$
None	You are volunteering to help with the soccer team…	Bob suggests mixing equal amounts of the 50/50 nuts and the 80% chocolate-covered nuts. This would …
None	The width of a rectangle is $\sqrt[3]{8^{4}} \mat…	The width of the rectangle is given as $\sqrt[3]{8^{4}}$ feet.
None	Determine the original amount if $63 %$ of the a…	$0.63 * x = 63.5$
None	The area of a rectangle is $63 {yd}^{2}$ , …	Let's denote the width of the rectangle as $w$ and the length as $l$ . We know that the area \(A…
None	1 point Flying to Riyadh with a tailwind a plane …	Let's denote the plane's speed as p and the wind's speed as w. We then have the following two equat…
None	volume of a sphere $= \frac{4}{3} π r^{3}$ , wher…	We are given the volume of the sphere and we need to find the radius. We can use the formula for th…
None	$M$ is directly proportional to $r^{2}$ When $r=2…	$M = k r^{2}$
None	2 Resolva as equações a) $\frac{3 x}{4}-\frac{2 x…	Find a common denominator for the fractions: $lcm (4, 3) = 12$
None	12. Ashlley was asked by her Math teacher to find…	Let the two numbers be x and y, such that y - x = 8.
None	$y$ is inversely proportional to $x$ . When $y=7, …	Since $y$ is inversely proportional to $x$ , we have $y = \frac{k}{x}$ for some constant $k$ .
None	Solve for $w$ in terms of $x$ and $y$ . \[ \begin{…	Divide both sides of the equation by $x^{2}$ to isolate $w$ : $w = \frac{y}{x^{2}}$
None	Solve for $t$ in terms of $s, u$ , and $v$ . \[ \be…	Multiply both sides of the equation by $u$ : $u v = s t$
None	Solve for $V$ in terms of $P, n, R$ , and $T$ . \[ …	Divide both sides of the equation by P: $V = \frac{n R T}{P}$
None	A washer and a dryer cost $$ 600$ combined. …	Let the cost of the dryer be x. Then the cost of the washer is 3x.
None	A garden table and a bench cost $$ 750$ comb…	$T = 2 B$
None	Gabrielle is 7 years younger than Mikhail. The su…	Let Gabrielle's age be $g$ and Mikhail's age be $m$ .
None	A local hamburger shop sold a combined total of 5…	hamburgers = x
None	You earn $$ 13$ per hour plus a commission e…	$e x t T o t a l E a r n i n g s = Hourly Earnings + Commission$
None	Find the values of $x$ and $y$ in paralle…	PT = TS, $y = 3 x + 9$
None	Let $X$ represent the original pric…	$Let X represent the original price$
None	Find the sum $\sum_{n = 11}^{80} 3 n =$	First, we identify the first term $a_{1}$ as $3 * 11 = 33$ , the last term $a_{n}$ as $3 * 80 = 240$ …
None	Suppose that $y$ is directly proportional to $x$ .…	Given that $y$ is directly proportional to $x$ , we can write the equation as $y = k x$ .
None	The container that holds the water for the footba…	The problem is asking for the total capacity of the container. We know that the difference between …
None	1. Write a proportion that represents the problem…	Given that it takes a copy machine 3 minutes to make 80 copies, we are asked to find out how long i…
None	Find the value of $x$ if the area of the rectangl…	Let's find the value of $x$ if the area of the rectangle is 78 with the dimensions $x + 7$ and $x$ .
None	3. Match the problem with one of the following eq…	Match the problem with one of the following equations where $x$ represents the unknown in the probl…
None	3. Solve, then choose the interval that contains …	Solve the equation 221-7x=185 for x. Subtract 221 from both sides of the equation to isolate the te…
None	HW Score: $14 %, 7$ of 50 points Save Legend has…	Given the problem, we are asked to find the sum of the first 310 counting numbers. We can use the m…
None	Solve each word problem algebraically. 13. The su…	Let the two consecutive integers be x and x + 1.
None	2) Com 8 eletricistas podemos fazer a instalação …	Primeiro, vamos representar o trabalho feito por 1 eletricista em 1 dia como W. Então, o trabalho f…
None	$w \propto d$ When $d = 35$ , the value of $w$ i…	Given that $w \propto d$ , which means $w = k \times d$ , where $k$ is a constant of proportion…
None	$- 5 = - \frac{1}{x - 1}$	$- 5 = - \frac{1}{x - 1}$
None	13 Sakira invested $£ 3550$ in a savings account …	Let's first calculate the amount in Sakira's account after the first 2 years with 2.6% compound int…
None	Question 2 Flag this question. In a park, there a…	There are n benches with a maximum of 2 people sitting on each bench, so there are $2 n$ people si…
None	$\begin{array}{l}\frac{\text { th }}{3(3 x-6)=18}…	Solve the equation: $3 x - 6 = 18$
None	Which expression is equivalent to $(7 a + 7) -$ …	$(7 a + 7) - (- 4 a + 6)$
None	Which expression is equivalent to $(4 g - 4) -$ …	$(4 g - 4) - (7 g + 9) = 4 g - 4 - 7 g - 9$
None	(.) https://www.ixl.com/math/grade-7/identify-equ…	Distribute the 5 through the parentheses: $5 (6 f + 9)$ = $30 f + 45$
None	Pi-Ready Area of Triangles and Other Polygons - I…	Let the base be $b$ , then the height is $b + 11$ .
None	8itheody Solive Problems wich Pertent - linoturti…	$\frac{180}{t} = \frac{75}{100}$
None	A recipe for baba ghanoush calls for twice as muc…	j = 4
None	4) The school is planning a field trip to the sci…	t(28-8)=24(28-8)
None	5. Tickets to a school dance cost $$ 4$ and the …	Let x be the number of $0.10$ increases in ticket price, and let y be the number of people attendin…
None	3. Find three consecutive integers such that the …	Let the three consecutive integers be x, x+1, and x+2.
None	If $\frac{x^{a}}{x^{b}} = x^{8}$ and $a + b = 7$ , what …	We are given the equation $\frac{x^{a}}{x^{b}} = x^{8}$ and the condition that $a + b = 7$ .
None	5. The Valley High School student council is plan…	The Valley High School student council is planning a dance. The school has 135 students. The lowest…
None	Question 13 of 60 The velocity of water in a pipe…	The velocity of water in a pipe is given by $v = \frac{121}{4 + x^{2}}$ , where $x$ is the distance …
None	Question list Question 1 Question 2 If the cost t…	First, we need to convert the weight from grams to ounces since the cost is given in ounces. There …
None	2. The height of a small glider is described by t…	We are given the function $h (x) = 2 x^{3} - 17 x^{2} + 40 x$ which describes the height of a glider in h…
None	The start of an arithmetic sequence is shown. Wha…	Identify the common difference: $d$
None	Paul thinks of a number $n$ . He divides $n$ by 2 …	Divide $n$ by 2: $\frac{n}{2}$
None	A bedroom suite costs Town \& Country Furniture $…	Let the original cost of the bedroom suite be $c$ .
None	of $a^{3} - 5 a$ para $a = - 2$ b) $x^{2} - 2 y$ para $x…	$a^{3} - 5 a$ when $a = - 2$ is $(- 2)^{3} - 5 (- 2)$
None	Question 1 The polynomial $P(x)=x^{4}-2 x^{3}+a x…	Given the polynomial $P (x) = x^{4} - 2 x^{3} + a x + b$ , we know that it has a remainder of 3 when divi…
None	PART II QUESTIONS: **Use A LET statement for each…	Let the first integer be $x$ , the second integer be $x + 1$ , and the third integer be $x + 2$
None	Which expression is equivalent to $75 x - 25 x$ …	$75 x - 25 x$
None	16. After 9 weeks Mikayla has an average mark of …	Find the total marks Mikayla has currently: Total marks = average * number of weeks = 5 * 9
None	Record: $0 / 2$ Score: 0 Penalty: 1 off Complete:…	Condense the expression: $- a b \cdot - a b = a^{2} b^{2}$
None	The length of a rectangle is $3 ft$ …	Let width be $w ft$ and length be $l ft$ . We are given that \(l = w + 3\mathrm{…
None	The formula $W = 0.86 g^{2} - 0.01 g + 5.9$ models …	$W = 0.86 (3)^{2} - 0.01 (3) + 5.9$
None	Hawa models a can of ground coffee as a right cyl…	$V = π r^{2} h$
None	1. $a, b, c, d$ , and $N$ are positive whole numbe…	First, we rewrite the given equation in terms of exponents: $a^{b/x} c^{1/x} c^{d}=a c a^{5/4} c^{1…
None	3. (a) A father is 28 years older than the son. I…	Let the father's age be F and the son's age be S. We have two equations:
None	The volume of a pyramid varies jointly with the b…	The volume of a pyramid is given by the formula $V = \frac{1}{3} * B * h$ , where $B$ is the bas…
None	The price $p$ and the quantity $x$ sold of a smal…	Given the demand equation $p = - 0.15 x + 450$ , we are asked to find the price that should be charged f…
None	WHEN x^4+kx^2+2x+9 IS DIVIDED BY x-1, THE REMAIND…	The remainder theorem states that the remainder of a polynomial f(x) divided by (x-a) is f(a). So, …
None	$- (x - 1) = 1 - x$	Multiply the entire equation by -1 to remove the negative sign from the left side of the equation: …
None	Let $f (x) = 2 x^{2} - 7 x + 5$ and $g (x) = x^{2} + 16$ . Fin…	First, we need to find the sum of the functions $f$ and $g$ . This is done by adding the correspondi…
None	$$ 17, 818$ is invested, part at $11 %$ and the …	Let's denote the amount invested at 11% as x and the amount invested at 6% as y. We know that the t…
None	to calculate a seller's rating, $R$ , based on the…	1. Start with the given equation for the seller's rating: $R = \frac{F}{F + N}$
None	Together, teammates Pedro and Ricky got 2669 base…	Let's denote the number of hits Pedro got as P and the number of hits Ricky got as R.
None	If you are traveling in your car at an average ra…	To solve the formula for $t$ , we need to isolate $t$ on one side of the equation. We can do this by…
None	The sum of three consecutive even integers is 54.…	Let's denote the smallest of these integers as x. Because the integers are consecutive and even, th…
None	By himself, a person can mow his lawn in 48 minut…	Let x be the time it takes for the daughter to mow the lawn by herself.
None	Complete the simplification below by finding the …	First, simplify the numerator of the fraction: $6 (2 a - 4 c) - 6 (6 a - 4 b) + 3 (4 b - 8 c) = - 24 a + 36 b - 48 c$
None	3. Shoji invested $$ 7000$ , part at $9 %$ inter…	Let the amount invested at 9% be $x$ and the amount invested at 6% be $y$ .
None	Find a polynomial function of degree 3 with real …	Given the zeros of the polynomial function: $- 1, 2, - 5$
None	2. In rhombus $\mathrm{JKLM}, \mathrm{JK}=3 \math…	Set up the equation: 3x + 9 = 11x - 7
None	James covers a distance of 8 meters in the first …	James covers a distance of $8$ meters in the first second and then sprints at a speed of $9$ me…
None	The number of diagonals in a polygon, $d$ , in ter…	Given the equation for the number of diagonals in terms of the number of sides: \(d=\frac{n(n-3)}{2…
None	Two trains leave the station at the same time, on…	$D = r t$
None	The length of a rectangle is $3 m$ …	1. Let width of rectangle be $w m$ , so length $= (2 w - 3) m$ .
None	Which of the following equations is equivalent to…	Isolate h in the given equation $S = π r^{2} h$ : $h = \frac{S}{π r^{2}}$
None	$128 π = \frac{1}{3} π x^{2} (24)$	$128 π = \frac{1}{3} π x^{2} (24)$
None	Review What You Learned You wrote expressions wit…	12h + 20
None	4) Ty runs his own landscaping business. He earns…	30p + 25r + 20c
None	(1) Eric works at the deli on weekends to earn ex…	$\frac{1}{2} (10 s + 14 d)$
None	(1) The school is planning a field trip to the sc…	t(28-8) = t(20)
None	4) Stacy is thinking of a number, which she calls…	$3 n$
None	Use the formula for the general term (the nth ter…	Given the first term, $a_{1} = - 40$ , and common difference, $d = 5$ , of an arithmetic sequence, we are …
None	Salma's penny bank is $\frac{3}{10}$ full. After …	Set up the equation: $\frac{3}{10} x + 240 = \frac{4}{5} x$
None	A rectangular box has dimensions 2 in by 4 in by …	The volume of a rectangular box is given by the formula $V = l w h$ , where $l$ , $w$ , and $h$ …
None	A 6 in thick slice is cut off the top of a cube, …	Let's denote the side length of the original cube as $s$ . The volume of the cube is $s^{3}$ .
None	Use an algebraic equation to find the measures of…	Let $x$ represent the degree measure of the angle's complement. The measure of the angle is 80 degr…
None	The length of a rectangle is $3 m$ less…	We are given that the length of a rectangle is 3m less than twice the width, and the area of the re…
None	Use a calculator to evaluate the formula for $x=1…	Substitute the value of x into the equation: P = 0.37 * 105 - 158
None	$3 t^{2} + 2 t^{2} = 6^{2}$	Simplify the equation $3 t^{2} + 2 t^{2} = 6^{2}$ to $5 t^{2} = 36$
None	When six times a number is decreased by 4 , the r…	Translate the problem into a mathematical equation: $6 x - 4 = 50$
None	$27^{2} + x^{2} = 54^{2}$	$x^{2} = 54^{2} - 27^{2}$
None	\( \frac{\frac{a^{2}-b^{2}}{a^{2}-25}}{\frac{b-a}…	$= \frac{a^{2} - b^{2}}{a^{2} - 25} \cdot \frac{a + 5}{b - a}$
None	Simplify the expression $\frac{x^{1 / 3}}{x^{-5 /…	Given the expression $\frac{x^{1 / 3}}{x^{- 5 / 4}}$ , we can simplify it by using the rule of expo…
None	$(x y + 24) \cdot (1 y - 2) = 0$	$x y + 24 = 0$ or $1 y - 2 = 0$
None	Evaluate the given expression for $x = 11$ . \[ 4 x+…	The problem is asking to evaluate the expression $4 x + 3$ for $x = 11$ . This means we need to subst…
None	To borrow money, you pawn your guitar. Based on t…	Calculate the interest paid by subtracting the loan amount from the amount paid back: \(1472 - 600 …
None	Date: Answer question 8. Show your work and expla…	$500 - 140 = 360$
None	$(x - 7)^{2} =$	Expand the given expression: $(x - 7)^{2} = (x - 7) (x - 7)$
None	Determine the value of $y$ , if $x$ is 5 . \[ y=x^…	Substitute x with 5: y = 5^2 - 7
None	Solve $\frac{x}{2} - 3 = 4$ $x = \dots$	Add 3 to both sides of the equation: $\frac{x}{2} - 3 + 3 = 4 + 3$
None	Directions: Type your answer in the box. Quadrila…	Given: Perimeter of Quadrilateral ABCD = 34 ft, AD = 12 ft
None	In a certain country people own a total of about …	Let's denote the number of fish as F, the number of cats as C, and the number of dogs as D. We know…
None	You have 700 feet of fencing to enclose a rectang…	Let's denote the length of the rectangle as $x$ and the width as $y$ . The total length of the f…
None	13. Mark bought 8 boxes. A week later, half of al…	Let b represent the initial number of boxes. After buying 8 more boxes, Mark had (b + 8) boxes. Hal…
None	15. On Tuesday, Shanice bought 5 new pens. On Wed…	Let p represent the number of pens Shanice had on Monday. After buying 5 new pens on Tuesday, she h…
None	4. The amount of time, $m$ , it takes for an i…	1. $m = \frac{k}{a}$
None	The length of one side of a golden rectangle is 7…	The golden ratio, often denoted by the Greek letter φ (phi), is an irrational mathematical constant…
None	Answer the following questions for the price-dema…	The given price-demand equation is $p + 0.002 x = 50$ .
None	Solve for $V$ in terms of $C$ and $Q$ . \[ \begin{…	Given the equation: $C = \frac{Q}{V}$
None	Solve the proportion. \[ \frac{99}{v}=\frac{11}{2…	Cross-multiply: $99 \times 2 = v \times 11$
None	Write an equation that expresses the following re…	The question is asking for an equation that expresses a relationship where $p$ varies directly with…
None	What is the value of $x$ in $\left(4^{x}\right)^{…	Given the equation: ${(4^{x})}^{3} = 4^{36}$
None	The length of a rectangle is five times its width…	Let the width of the rectangle be $w$ and the length be $5 w$ .
None	If the 5 th term of a geometric sequence is 1875 …	Given that the common ratio is $r$ , we have $r^{2} = \frac{46875}{1875} = 25 = 5^{2}$ . Therefore, \…
None	The $n^{th}$ term of a sequence is given…	Given the formula for the nth term of a sequence: $T (n) = 8 n + 9$
None	Solve the following problem using the formula $V=…	We are given the volume of the sphere and we need to find the radius. We can rearrange the formula …
None	Find the difference quotient $\frac{f(x+h)-f(x)}{…	Given the function $f (x) = 7 x - 1$ , we are asked to find the difference quotient \(\frac{f(x+h)-f(x)}…
None	10) A rectangular building is to be placed on a l…	Let's denote the width of the lawn as x. Then, the dimensions of the building would be $(30 - 2 x)$ …
None	The area of a rectangular wall of a barn is 154 s…	We are given that the area of a rectangular wall of a barn is 154 square feet. Its length is 8 feet…
None	You need a 20\% alcohol solution. On hand, you ha…	We are given a 385 mL of a 15% alcohol mixture and we want to add some amount of a 75% alcohol mixt…
None	Find the numerical answer to the summation given …	The given expression is an arithmetic series with first term $6 * 1 + 7 = 13$ , last term $6 * 65 + 7 = 397$ …
None	When $x = 2$ , which expression can be completel…	Substitute $x = 2$ into each expression
None	Ken and Paul each ordered a sandwich at a restaur…	1. $Price of Ken's sandwich = x$
None	\( -\frac{6}{5}-\frac{2}{3} v+\frac{4}{15}+\frac{…	$(- \frac{6}{5}) + (\frac{4}{15})$
None	14 The regular price of an item at a store is \( …	\text{Sale price} = p - (0.2 \times p)
None	A hotel is in the shape of a cylinder, with a cir…	The problem provides that the circumference of the foundation is 4 times the radius, increased by 1…
None	7. A mural is to be painted on a wall that is $15…	Let the width of the border be x meters. Then the dimensions of the mural will be $(15 - 2 x)$ met…
None	A coffee shop creates its house brand by mixing $…	Let's find the total amount of coffee in the house brand: $\frac{80}{8 / 13} = 130 kg$
None	$\frac{10}{20} = \frac{x}{24}$	1. Cross-multiply: $10 \times 24 = 20 \times x$
None	The first three terms of a geometric sequence are…	$r = \frac{20}{- 5} = - 4$
None	If $a_{n} = \frac{1}{1024}$ for the geometric s…	1. Identify the common ratio: $r = - \frac{1}{2}$
None	\( \begin{array}{l}a+b+c=4 \ a^{2}+b^{2}+c^{2}=1…	$a^{3} + b^{3} + c^{3} - 3 a b c = (a + b + c) ((a + b + c)^{2} - 3 (a b + b c + c a))$
None	$R = \frac{F}{N + F}$ A website uses the formula …	$R = \frac{F}{N + F}$
None	The average, or mean, D, of three exam grades, $v…	Given the formula for the average, or mean, D, of three exam grades, $v, r$ , and $w$ , is \(D=\frac{…
None	Select the equivalent expression. \[ \left(\frac{…	${(\frac{d^{6}}{d^{- 7}})}^{\frac{4}{39}} = {(d^{(6 + 7)})}^{\frac{4}{39}}$
None	4) Stacy is thinking of a number, which she calls…	$3 n + 10 = 3 (12) + 10$
None	4)) A group of neighborhood families are planning…	Substitute a=5 and c=9 into the expression: 25(5)+10(9)-5
None	The temperature $T (d)$ in degrees Fahrenheit in t…	We are given two formulas, one that converts Celsius to Fahrenheit and another that converts Kelvin…
None	Evaluate the given expression for $x = 9$ . \[ x^{2}…	Substitute $x = 9$ into the expression $x^{2} + 4 x - 1$ .
None	A rectangle has a width of 54 centimeters and a p…	We are given a rectangle with a width of 54 centimeters and a perimeter of 228 centimeters. We are …
None	Solve the following formula for the specified var…	Multiply both sides of the equation by 2 to get rid of the fraction: $2 C = f (q + b)$
None	If $X^{3} - Y^{3} = 26, X - Y = 2$ then \( X^{2}+X Y+…	1. X=Y+2
None	20.甲、乙两人沿400米环形跑道练习跑步，两人同时从跑道的同一地点向相反方向跑去。相遇后甲比原来…	1. Set up the equations: $(v 1 + 2) * 24 = 400$ , $(v 2 - 2) * 24 = 400$ , and \( v1 * t1 = v2 …
None	6. a) Write an expression in simplest form for th…	Write the expression for the perimeter: P = a + b + c
None	Use a model for body surface area, BSA, such that…	We are given a model for body surface area (BSA) such that $B S A = \sqrt{\frac{w \times h}{3600}}$ …
None	The difference of 2 polynomial expressions is sho…	(-2x^2+wx-4)-(x^2+5x+6)=-3x^2-10
None	6. A rectangular lawn measuring $8 m$ b…	Let the width of the flower bed be denoted as x. The dimensions of the lawn and flower bed combined…
None	In a park, there are $n$ benches. A maximum of 2 …	In a park, there are $n$ benches.
None	14. The length of a rectangular picture is 5 inch…	Let the width be denoted as $w$ and the length as $l$ .
None	A small country emits 70,000 kilotons of carbon d…	This problem can be solved using the formula for the sum of a geometric series, which is \(S = a \f…
None	An apple farm yields an average of 34 bushels of …	The problem is asking for the maximum yield, which is the product of the number of trees and the yi…
None	10. 有七个排成一列的数, 它们的平均数是 30 , 前三个数的平均数是 28 , 后五个数的平…	Find the sum of the first 7 numbers, the sum of the first 3 numbers, and the sum of the last 5 numb…
None	An alloy contains tin, copper and silver in the r…	Given the ratio of tin, copper, and silver as $7 : 5 : 3$ and there are $48 g$ of copper.
None	The polynomial of degree $5, P (x)$ , has leading c…	The polynomial of degree 5, P(x), has leading coefficient 1, has roots of multiplicity 2 at x=1 and…
None	Use the distributive property to remove the paren…	9y^2(2y) + 9y^2(3y^6)
None	The number of seconds that it takes for a kettle …	Given that the number of seconds to boil, $n$ , is inversely proportional to the power in kilowatts,…
None	The length of a rectangle is 23 centimeters less …	Let's denote the width of the rectangle as $w$ and the length as $l$ . According to the problem,…
None	Solve for $I$ in terms of $P$ and $V$ . \[ \begin{…	Given the equation: $P = I V$
None	Fill in the missing number. \[ 50 \% \text { of }…	$50 % = \frac{1}{2}$
None	Evaluate the algebraic expression for the given v…	The question is asking to substitute the value of x in the given algebraic expression and then simp…
None	问题 Suppose that $f$ is a polynomial such that \[ …	Given the equation: $(x - 1) c d o t f (x) = 3 x^{4} + x^{3} - 25 x^{2} + 38 x - 17$
None	10. The temperature on the surface of Mars was re…	문제는 24시간 동안 화성 표면의 가장 높은 온도를 화씨로 찾는 것입니다. 주어진 가장 높은 온도는 -30도 섭씨입니다. 주어진 공식 $C = \frac{5}{9} (F - 32)$ 를 사…
None	Solve for $x$ : \[ 2^{3}\left(\frac{3}{4}+x\r…	2^{3}(\frac{3}{4}+x)+12=2
None	The length of a rectangle is $1 yd$ more…	Given that the length (L) is 1 more than twice the width (W), and the area (A) is 45 square yards, …
None	i-Ready Write and Evaluate Algebraic Expressions …	$Total cost = s \times C_{s} + p \times C_{p} - 18$
None	The average, or mean, $T$ , of three exam grades, …	(a) To solve the formula for $y$ , we start with the given formula $T = \frac{r + s + y}{3}$ . Multiply bot…
None	Given that $f (x) = x^{2} + 3 x - 70$ and $g (x) = x - 7$ , fi…	Subtract g(x) from f(x) term by term: $f (x) - g (x) = (x^{2} + 3 x - 70) - (x - 7)$
None	If $a_{1} = 7$ and $a_{n} = a_{n - 1} + 1$ then f…	$a_{1} = 7$
None	Define a Variable: Solution \& Interpretation: An…	Define a variable x to represent the number of video game rentals.
None	4. After 3 weeks, a plant is 8 centimeters tall.…	The plant's growth follows an arithmetic sequence. This means that the difference between the heigh…
None	Find an nth-degree polynomial function with real …	We are given that the polynomial is of degree 3 and has roots 2, 4i, and -4i. The general form of a…
None	For a car moving at a constant speed, the distanc…	$d = k \cdot t$