All Questions ⁺⁰230866 Questions

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38

1

polynomials

Let $f(x)$ be a polynomial with integer coefficients. There exist distinct integers $p,$ $q,$ $r,$ $s,$ $t$ such that
\[f(p) = f(q) = f(r) = f(s) = 1\]
and $f(t) > 1.$ What is the smallest possible value of $f(t)?$

Guest Aug 29, 2023

0

29

5

right triangles

Find the number of non-congruent right triangles, where all the sides are positive integers, and one of the legs is $6$.

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Guest Aug 29, 2023

0

29

1

+4

Algebra 1 question

over the last three evenings, susan received a total of 97 phone calls at the call center. the first evening, she received 7 more calls than the third evening. the second evening, she received 4 times as many calls as the third evening. how many phone calls read more ..

BugBrain Aug 29, 2023

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26

1

help with quadratic

Let $a$ and $b$ be the roots of the quadratic equation $x^2-25x+80=-28x+75$. Compute $\frac{a^2}{b} + \frac{b^2}{a}$.

Guest Aug 29, 2023

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35

1

real numbers

The real numbers $x$ and $y$ satisfy the equation $x^2+y^2=14x+48y-8x-26y+16$. What is the minimum value of $y$?

Guest Aug 29, 2023

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37

0

confidence interval

A special bumper was installed on selected vehicles in a large fleet. The dollar cost of body repairs was recorded for all vehicles that were involved in accidents over a 1-year period. Those with the special bumper are the test group and the other vehicles read more ..

Guest Aug 29, 2023

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33

0

coordinates

Let $P = (x,y)$ be a point in the coordinate plane. The point $P$ has a distance of $12$ units from the $x$-axis, and it has a distance of $10$ units from the point $(2,5)$. If $P$ has a distance of $n$ units from the origin, and $x > 1$, read more ..

Guest Aug 29, 2023

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30

1

help algebra

Ruth has a beaker containing a solution of 800 mL of acid and 200 mL of water. She thinks the solution is a little strong, so she drains 150 mL from the beaker, adds 150 mL of water, and stirs the solution. Ruth thinks the solution is still too strong, read more ..

Guest Aug 29, 2023

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40

1

Solve the following equation: /4y + 8 = 14

Solve the following equation: /4y + 8 = 14

Guest Aug 29, 2023

0

31

1

help plz

Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $8$ days earlier. If the job needs to completed $28$ days earlier, how many additional workers should be hired?

Guest Aug 29, 2023

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35

0

help

The nth term of the sequence 6,14,24,36... is of the form an^2 + bn + c for some constants a b and c. What is a b and c, and what is the 100th term of this sequence?

Guest Aug 29, 2023

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28

1

-2(-4x+5)+6x

Guest Aug 29, 2023

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36

0

geometry question

Let $AC$ be a diameter of a circle $\omega$ of radius $1$, and let $D$ be the point on $AC$ such that $CD = \frac{1}{5}$. Let $B$ be the point on $\omega$ such that $DB$ is perpendicular to $AC$, and let $E$ be the midpoint of $DB$. Compute length $AE$ read more ..

Guest Aug 29, 2023

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35

1

help quadratic

The quadratic equation $x^2-5x+t =3x$ has only positive integer roots. Find the average of all distinct possible values of $t$.

Guest Aug 29, 2023

0

32

1

+4

Help pls

A 4'' x 6'' x 8'' rectangular solid is cut by slicing through the midpoints of three adjacent sides. Find the volume of the shaded piece that is cut off.

zhouxia004 Aug 29, 2023

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29

3

coordinates

Triangle $ABC$ has vertices $A(2, 3),$ $B(1, -8)$ and $C(-3, 2).$ The line containing the altitude through $A$ intersects the point $(0, y).$ What is the value of $y$?

Guest Aug 29, 2023

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23

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function

If $y = \frac{x + 1}{x^2 + 1 - x},$ and $x$ is any real number, then what is the sum of the maximum and minimum possible values of $y \, ?$

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Guest Aug 29, 2023

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33

6

need help

In the three-dimensional figure shown, all edges meet at right angles. The surface area of the figure is $164 \text{ in}^{2}$ and the volume is $140\text{ in}^{3}.$ What is the value of $x,$ in inches? Express your answer as a decimal to the nearest hu read more ..

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Guest Aug 29, 2023

Aug 28, 2023

-3

33

5

+819

graph of rational function

The graph of $y = \frac{p(x)}{q(x)}$ is shown below, where $p(x)$ and $q(x)$ are quadratic. (Assume that the grid lines are at integers.)
The horizontal asymptote is $y = 2,$ and the only vertical asymptote is $x = -2.$ read more ..

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maximum Aug 28, 2023

-3

34

0

+819

asymptotes

For what values of the constant $c$ does the graph of $f(x) = \frac{x^2-x+c}{x^2+8x-50}$ have exactly one vertical asymptote?
Enter all possible values, separated by commas.

maximum Aug 28, 2023

-3

31

1

+819

asymptotes

How many vertical asymptotes does the graph of $y = \frac{1}{x^3-3x^2+7x-15}$ have?

maximum Aug 28, 2023

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