All Questions ⁺⁰236027 Questions

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help plz

Solve the inequality $x(x + 6) > 16 - 5x + 33.$ Write your answer in interval notation.

blackpanther Dec 12, 2023

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32

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need help

Solve the inequality $4t^2 \le -9t + 12 - 14t + 36.$ Write your answer in interval notation.

blackpanther Dec 12, 2023

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46

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help inequality

Solve the inequality
\[\frac{3-z}{z+1} \ge 2 + 7z.\]
Write your answer in interval notation.

blackpanther Dec 12, 2023

+1

47

3

+19

Help with an inequality

Any help is appreciated :) I don't know how to start this problem!
For an integer y, the inequality x^2+yx+36<0 has no real solutions in x. Find the number of different possible values of y.

breadysetgo Dec 12, 2023

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25

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+13

Suppose a line is tangent to a circle at A. Another line through A intersects the circle again at B; if the shorter arc AB is 50∘ of the

Suppose a line is tangent to a circle at A. Another line through A intersects the circle again at B; if the shorter arc AB is 50∘ of the circle, what is the acute angle between the lines? read more ..

rb2919 Dec 12, 2023

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53

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Geometry

In triangle $PQR$, let $M$ be the midpoint of $\overline{PQ}$, let $N$ be the midpoint of $\overline{PR}$, and let $O$ be the intersection of $\overline{QN}$ and $\overline{RM}$, as shown. If $\overline{QN}\perp\overline{PR}$, $QN = 1$, and $PR =1$, read more ..

sandwich Dec 12, 2023

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51

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+1348

Geometry

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$, read more ..

sandwich Dec 12, 2023

Dec 11, 2023

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61

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+1348

Equation

Find all values of $c$ such that $3^{2c+1} = 28\cdot 3^c - 9 + 4 \cdot 3^c - 25$. If you find more than one value of $c$, then list your values in increasing order, separated by commas.

sandwich Dec 11, 2023

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55

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+1348

Algebra

Each graph below is the graph of an exponential function of the form $ka^x$ (where $a > 0$). Match each graph with the correct option.

sandwich Dec 11, 2023

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51

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+1348

Algebra

Select all the correct statements. (For this problem, we assume that an exponential function is of the form ka^x where a > 0)
(A) The following function is exponential: y = 2^x
(B) The following function is exponential: read more ..

sandwich Dec 11, 2023

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35

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+1678

help me

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 $a_1$.

wiseowl Dec 11, 2023

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32

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need help

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 ..

wiseowl Dec 11, 2023

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40

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+1678

Algebra

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 $S_{70}.$

wiseowl Dec 11, 2023

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52

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+1678

Need help

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 $x$.

wiseowl Dec 11, 2023

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47

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+1678

Inverse functions

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

wiseowl Dec 11, 2023

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48

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Operations

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.

wiseowl Dec 11, 2023

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25

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+660

Coefficients

a) Fill in the blanks with positive integers:
= __+ __
b) Find the coefficient of in the expansion of

Keihaku Dec 11, 2023

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57

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+1911

Angles

In triangle ABC, angle A = p + 2q degrees, angle B = 6p - 5q degrees, and angle C = 14p + 8q degrees. Find p (in degrees) in terms of q.

tomtom Dec 11, 2023

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52

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+1911

geometry

Altitudes $\overline{AD}$ and $\overline{BE}$ of acute triangle $ABC$ intersect at point $H$. If $\angle AHB = 144^\circ$ and $\angle BAH = 66^\circ$, then what is $\angle HCA$ in degrees?

tomtom Dec 11, 2023

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56

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+1911

geometry

Let $M$, $N$, and $P$ be the midpoints of sides $\overline{TU}$, $\overline{US}$, and $\overline{ST}$ of triangle $STU$, respectively. Let $\overline{UZ}$ be an altitude of the triangle. If $\angle TSU = 60^\circ$ and $\angle STU = 45^\circ$, read more ..

tomtom Dec 11, 2023

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47

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+1911

Probability

A member of the junior varsity swim team will be elected as President. Each member is equally likely to be elected. The probability that a sophomore is elected is $\frac{1}{1}$ times the probability that a freshman is elected. Everyone on the junior varsity read more ..

tomtom Dec 11, 2023

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counting

Syd chooses two different primes, both of which are greater than 20, and multiplies them. The resulting product is less than 800. How many different products could Syd have ended up with?

blackpanther Dec 11, 2023

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62

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help with geometry

In square ABCD, P is on BC such that BP = 5 and PC = 2, and Q is on CD such that DQ = 4 and QC = 3. Find sin angle PAQ.

blackpanther Dec 11, 2023

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numbers

Arrange the following numbers in increasing order (smallest first, biggest last)
A = 2^(1/2)*4^(1/6)
B = (128)^(1/12)/64^(1/3)
C = (8^(1/5))^(2^2) read more ..

blackpanther Dec 11, 2023

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