When it comes to finding the value of a variable, the process usually involves making sure the variable is alone on one side of an equation. This may necessitate the use of various mathematical techniques such as multiplication, division, addition, or subtraction. The ultimate aim is to identify the exact value that will validate the equation when it replaces the variable.
| Topic | Problem | Solution |
|---|---|---|
| None | 3. A rectangle has length $(3 x+7) \mathrm{cm}$ a… | Find the area by multiplying the length and width: \((3x + 7)(2x - 1)\) |
| 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 | $\left(4 x^{5}\right) \times\left(2 x^{3}\right)$ | 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 $63 \mathrm{yd}^{2}$, … | 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 $=\frac{4}{3} \pi r^{3}$, 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… | \(M = kr^2\) |
| None | 2 Resolva as equações a) $\frac{3 x}{4}-\frac{2 x… | Find a common denominator for the fractions: \(\text{lcm}(4, 3) = 12\) |
| 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 \(u\): \(uv = st\) |
| None | Solve for $V$ in terms of $P, n, R$, and $T$. \[ … | Divide both sides of the equation by P: \(V = \frac{nRT}{P}\) |
| 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… | \( T = 2B \) |
| 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… | \( ext{Total Earnings} = \text{Hourly Earnings} + \text{Commission} \) |
| None | Find the values of \( x \) and \( y \) in paralle… | PT = TS, \(y = 3x + 9\) |
| None | Let \( \mathcal{X} \) represent the original pric… | \( \textrm{Let } \mathcal{X} \textrm{ represent the original price} \) |
| 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 $y = kx$. |
| 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 \(2n\) people si… |
| None | $\begin{array}{l}\frac{\text { th }}{3(3 x-6)=18}… | Solve the equation: \(3x - 6 = 18\) |
| None | Which expression is equivalent to \( (7 a+7)- \) … | \( (7a+7)-(-4a+6) \) |
| None | Which expression is equivalent to \( (4 g-4)- \) … | \( (4 g-4)-(7 g+9) = 4g - 4 - 7g - 9 \) |
| None | (.) https://www.ixl.com/math/grade-7/identify-equ… | Distribute the 5 through the parentheses: \( 5(6f + 9) \) = \( 30f + 45 \) |
| 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 \(h(x) = 2x^3 - 17x^2 + 40x\) 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 \(P(x) = x^4 - 2x^3 + ax + b\), 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 \( 75 x-25 x \)… | \( 75x - 25x \) |
| 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: \(-ab \cdot -ab = a^2b^2\) |
| None | The length of a rectangle is \( 3 \mathrm{ft} \) … | Let width be \(w\mathrm{ft}\) and length be \(l\mathrm{ft}\). 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… | \( V = \pi r^2 h \) |
| 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 \(p=-0.15x+450\), 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: \(6(2a-4c)-6(6a-4b)+3(4b-8c) = -24a + 36b - 48c\) |
| 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… | \(D = rt\) |
| None | The length of a rectangle is \( 3 \mathrm{~m} \) … | 1. Let width of rectangle be \( w \mathrm{~m} \), so length \( = (2w - 3) \mathrm{~m} \). |
| None | Which of the following equations is equivalent to… | Isolate h in the given equation $S=\pi r^{2} h$: $h=\frac{S}{\pi r^{2}}$ |
| None | \( 128 \pi=\frac{1}{3} \pi x^{2}(24) \) | \( 128 \pi = \frac{1}{3} \pi x^{2} (24) \) |
| 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… | \[ \frac{1}{2}(10s + 14d) \] |
| 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… | \( 3n \) |
| 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 \(V = lwh\), 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 $3 \mathrm{~m}$ 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 $5t^{2} = 36$ |
| None | When six times a number is decreased by 4 , the r… | Translate the problem into a mathematical equation: \(6x - 4 = 50\) |
| 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 \(4x+3\) 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 $\frac{x}{2}-3=4$ \[ x=\ldots \] | 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 \(p+0.002x=50\). |
| 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: \(\left(4^{x}\right)^{3}=4^{36}\) |
| None | The length of a rectangle is five times its width… | Let the width of the rectangle be \(w\) and the length be \(5w\). |
| 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 $n^{\text {th }}$ term of a sequence is given… | Given the formula for the nth term of a sequence: \(T(n) = 8n + 9\) |
| 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 \(f(x)=7x-1\), 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 \((30-2x)\) … |
| 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. \(\text{Price of Ken's sandwich} = x \) |
| 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 \((15 - 2x)\) met… |
| None | A coffee shop creates its house brand by mixing $… | Let's find the total amount of coffee in the house brand: \(\frac{80}{8/13} = 130\text{ kg}\) |
| 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… | \(a^3 + b^3 + c^3 - 3abc = (a + b + c)((a + b + c)^2 - 3(ab + bc + ca))\) |
| 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{… | \(\left(\frac{d^{6}}{d^{-7}}\right)^{\frac{4}{39}} = \left(d^{(6 + 7)}\right)^{\frac{4}{39}}\) |
| None | 4) Stacy is thinking of a number, which she calls… | \(3n+10 = 3(12) + 10\) |
| 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: \(2C = f(q+b)\) |
| 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: \( (v1 + 2) * 24 = 400 \), \( (v2 - 2) * 24 = 400 \), 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 \(BSA = \sqrt{\frac{w \times h}{3600}}\)… |
| 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 $8 \mathrm{~m}$ 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 \(48\mathrm{~g}\) 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: \(P = IV\) |
| 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: \((x-1) cdot f(x)=3 x^{4}+x^{3}-25 x^{2}+38 x-17\) |
| 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 $1 \mathrm{yd}$ 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 … | \(\text{Total cost} = s \times C_s + p \times C_p - 18 \) |
| 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: \(f(x) - g(x) = (x^2 + 3x - 70) - (x - 7)\) |
| 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… | \(d = k \cdot t\) |