All Questions ⁺⁰235615 Questions

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Graphing question

The parabola $y = ax^2 + bx + c$ is graphed below. Find $a + b + c$. (The grid lines are one unit apart.)

tomtom Dec 9, 2023

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39

1

+1911

Parabola

Find the vertex of the graph of the equation $x - y^2 + 8y = 13 + 2y + y^2 - 7y - 14$.

tomtom Dec 9, 2023

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38

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+1911

Algebra

Let $a$ and $b$ be real numbers, where $a < b$, and let $A = (a,a^2)$ and $B = (b,b^2)$. The line $\overline{AB}$ (meaning the unique line that contains the point $A$ and the point $B$) has $x$-intercept $(10,0)$ and $y$-intercept $(0,-2)$. Find read more ..

tomtom Dec 9, 2023

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41

1

+1911

Help with algebra

What are the coordinates of the points where the graphs of $f(x)=x^3 + x^2 - 3x + 5$ and $g(x)=x^4-7x^3+5x^2-18x+17$ intersect?
Give your answer as a list of points separated by commas, with the points ordered such that read more ..

tomtom Dec 9, 2023

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46

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+1911

graph question

The graph of $y=f(x)$ is shown below in red. Given that $f$ is invertible, find $f^{-1}(4)$. (Assume grid lines are spaced $1$ unit apart.)

tomtom Dec 9, 2023

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37

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+1348

Algebra

Compute $\log_{1/2} (16(-5))$.

sandwich Dec 9, 2023

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61

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+1348

help with logs

Suppose $a\neq 0$. Compute $\log_{8a} b$ in terms of $a$ and $b$.

sandwich Dec 9, 2023

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53

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+1348

logarithm problem

Find $x$ if $\log_2 (\log_3 x) = \log_3 (\log_2 x).$

sandwich Dec 9, 2023

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38

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+1348

Equation

Find all $c$ such that $|c + 5| - 3|c + 7| = 10 + 2|c - 8|.$ Enter all the solutions, separated by commas.

sandwich Dec 9, 2023

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39

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+1348

Algebra

Let $x$, $y$, and $z$ be nonzero real numbers. Find all possible values of
\frac{x}{|x|} + \frac{y}{|y|} + \frac{z}{|z|} + \frac{x + y + z}{|x + y + z|}

sandwich Dec 9, 2023

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55

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+1348

help with logs

Solve the system of equations
y = \log_2 (2x)
y = log_4 (16 + x)

sandwich Dec 9, 2023

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55

1

+44

Help pls

Thanks for your help btw!
fill in the blank so that the resulting exxpression can be factored as the product of the two linear equations

omgitsme Dec 9, 2023

-1

55

1

+1427

coordinates

Find all points $(x,y)$ that are $5$ units away from the point $(2,7)$ and that lie on the line $y = 5x - 28.$

blackpanther Dec 9, 2023

-1

28

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+1427

Counting

Find the number of positive integers that satisfy both the following conditions:
- Each digit is a 1 or a 3 or a 5
- The sum of the digits is 6

blackpanther Dec 9, 2023

-1

52

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+1427

need help

Let $x \mathbin{\spadesuit} y = \frac{x^2}{y}$ for all $x$ and $y$ such that $y\neq 0$. Find all values of $a$ such that $a \mathbin{\spadesuit} (a + 1) = 9$. Write your answer as a list separated by commas.

blackpanther Dec 9, 2023

-1

53

1

+1427

help plz

Let
\[f(x) = \frac{2x + 5}{x - 4} + \frac{x^2 + 1}{4x - 3}.\]
Find the inverse $f^{-1}(x)$.

blackpanther Dec 9, 2023

-1

33

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+1427

Functions

Let $f(x) = 3x - 8 + 4x^2$ and $g(x) = 15x + c - 3x^2$. Find $c$ if $(f \circ g)(x) = (g \circ f)(x)$ for all $x$.

blackpanther Dec 9, 2023

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34

1

+4

Algebra 2 question

Given a, b, and c are positive integers greater than 2 what are all the possible values of a*b*c given a*b*c=5(a-2)(b-2)(c-2).

SHIBIDI Dec 9, 2023

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55

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+1911

Arithmetic series

Let $a_1,$ $a_2,$ $a_3,$ $\dots$ be an arithmetic sequence. Let $S_n$ denote the sum of the first $n$ terms. If $S_{20} = \frac{1}{5}$ and $S_{10} = 0,$ then find $S_{70}.$

tomtom Dec 9, 2023

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40

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+4

describe the possible values for X

I need to find the possible values of X

iouihjghvnbmn Dec 9, 2023

0

24

1

+1911

Arithmetic series

Laverne starts counting out loud by ${}5$'s. She starts with $2$. As Laverne counts, Shirley sums the numbers Laverne says. When the sum finally exceeds $20,$ Shirley runs screaming from the room. What number does Laverne say that read more ..

tomtom Dec 9, 2023

0

37

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+1911

arithmetic

Let $a_1,$ $a_2,$ $a_3,$ $\dots,$ $a_{10},$ $a_{11},$ $a_{12}$ be an arithmetic sequence. If $a_1 + a_3 + a_5 + a_7 + a_9 + a_{11} = 0$ and $a_2 + a_4 + a_6 + a_8 + a_{10} + a_{12} = 0$, then find $a_1$.

tomtom Dec 9, 2023

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44

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+1911

geometric sequence

When the same constant is added to the numbers $60,$ $120,$ and $160,$ a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

tomtom Dec 9, 2023

0

23

1

+1911

Arithmetic series

Find the sum of all positive integers less than $1000$ ending in $3$ or $4$ or $5$.

tomtom Dec 9, 2023

+2

25

1

+180

Let theta be an acute angle such that sin2theta=sin3theta What is the measure of theta in degrees?

Let theta be an acute angle such that sin2theta=sin3theta What is the measure of theta in degrees?

itsash Dec 9, 2023

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