All Questions ⁺⁰234620 Questions

Nov 22, 2023

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40

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+1678

hyperbola

The equation of a hyperbola is
\[\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1,\]
where $a > b > 0.$ The angle between the asymptotes is $45^\circ$ Find $\frac{a}{b}.$

wiseowl Nov 22, 2023

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29

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+1678

ellipse

Below is the graph of an ellipse. (Assume that tick marks are placed every $1$ unit along the axes.) Compute the coordinates of the focus of the ellipse with the greater $x$-coordinate. read more ..

wiseowl Nov 22, 2023

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47

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+1678

ellipse

The equation of an ellipse is
\[\frac{x^2}{4} + y^2 = 1.\]
Let $C$ be a point that varies on this ellipse, and let $H$ be the orthocenter of triangle $ABC,$ where $A = (-4,0)$ and $B = (4,0).$ Then $H$ traces a closed curve as $C$ varies read more ..

wiseowl Nov 22, 2023

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43

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+1678

help with quadratic

Find all real values of $p$ such that
(x+1)(x-2p)
has a minimum value of 0 over all real values of $x$.

wiseowl Nov 22, 2023

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41

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+1678

graphing question

Let $c$ be a real number. What is the maximum value of $c$ such that the graph of the parabola $y = -6x^2$ has at most one point of intersection with the line $y = 5x+c?$

wiseowl Nov 22, 2023

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46

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+1678

maximum

Let $x$ and $y$ be real numbers. If $x^2 + 3y^2 = 18$, then find the maximum value of $x + y$.

wiseowl Nov 22, 2023

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28

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+1678

minimum

Let $x$ and $y$ be nonnegative real numbers. If $x + y = 25$, then find the minimum value of $6x + 3y.$

wiseowl Nov 22, 2023

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28

1

+1678

algebra

If $t$ is a real number, what is the maximum possible value of the expression $-t^2 + 8t -4 +5t^2 - 4t + 18$?

wiseowl Nov 22, 2023

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42

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+1678

help with quadratic

If $s$ is a real number, then what is the smallest possible value of $2s^2 - 8s + 19 - 7s^2 - 8s + 20$?

wiseowl Nov 22, 2023

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27

0

+1678

quadratic

What real value of $t$ produces the smallest value of the quadratic $t^2 -9t - 36 + 13t - 60$?

wiseowl Nov 22, 2023

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21

1

+36

Just checking

Let be the inradius of where . Find .
I got , can you guys check my answer?
Thanks!

JovenlyCosmo Nov 22, 2023

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50

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+1348

plz help

In triangle $ABC,$ $D$ is on side $\overline {AB}.$ We know $\triangle ABC \sim \triangle ACD$. If $BC = BD,$ what is $\angle B$ in degrees?

sandwich Nov 22, 2023

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21

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+1348

help geometry

In quadrilateral $BCED$, sides $\overline{BD}$ and $\overline{CE}$ are extended past $B$ and $C$, respectively, to meet at point $A$. If $BD = 8$, $BC = 3$, $CE = 1$, $AC = 19$ and $AB = 13$, then what is $DE$?

sandwich Nov 22, 2023

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43

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+1348

need help

In triangle $ABC$, points $D$ and $F$ are on $\overline{AB},$ and $E$ is on $\overline{AC}$ such that $\overline{DE}\parallel \overline{BC}$ and $\overline{EF}\parallel \overline{CD}$. If $CE =3$ and $DF = 3$, then what is $BD$?

sandwich Nov 22, 2023

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48

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+1348

right triangles

Points $X$, $Y$, and $Z$ are on the sides $\overline{QR}$, $\overline{PR}$, and $\overline{PQ}$, respectively, of right triangle $PQR$ such that $PZXY$ is a square. If $PQ = 1$ and $PR = 1$, then what is the side length of the square?

sandwich Nov 22, 2023

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28

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+1348

help geometry

In the figure, angles $\angle ABC$ and $\angle AST$ are right angles. If $AC = 35,$ then what is $AS$?

sandwich Nov 22, 2023

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23

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+1348

help me

In the diagram below, we have $\overline{BC}\parallel\overline{DE}$ and $AE = 20$. Find $AC$.

sandwich Nov 22, 2023

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44

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+1348

similar triangles

In the diagram below, we have $\overline{AB}\parallel\overline{DE}$ and $BD = 24$. Find $CD$.

sandwich Nov 22, 2023

Nov 21, 2023

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41

1

+1678

algebra

Find all real values of $x$ such that
\frac{x^2 + 2x + 5}{3x^2 - x - 4} + \frac{x^2 + 4x + 8}{x^2 - 4x - 5} \ge 0.
Note: Your solution should be thorough, and explain why all your values are the only values that satisfy the inequalit read more ..

wiseowl Nov 21, 2023

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41

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+1678

inequality

Solve the inequality $x^3 + 4x > 5x^2 + 2x - x^3 + 7x^2 - 36$. Write your answer in interval notation.

wiseowl Nov 21, 2023

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48

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+1678

inequality

Solve the inequality x^3 + 4x > 5x^2 - 17x - x^4 + 3. Write your answer in interval notation.

wiseowl Nov 21, 2023

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27

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+1678

quadratic inequality

For an integer $n$, the inequality
\[x^2 + nx + 15 < -21 - x^2 - 150 \]
has no real solutions in $x$. Find the number of different possible values of $n$.

wiseowl Nov 21, 2023

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