All Questions ⁺⁰235737 Questions

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35

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+2669

Floor

Find all values of t such that \lfloor t\rfloor = 3t + 4 - \lfloor 2t \rfloor. If you find more than one value, then list the values you find in increasing order, separated by commas.

LiIIiam0216 Mar 21, 2024

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24

0

+2669

help with function

The function f(x) is defined for 1 \le x \le 5 as follows:
-2x + 4 & \text{if }1 \le x \le 2, \\
5 - x & \text{if }2 < x \le 3, \\
9 - 2x & \text{if }3 < x \le 4, \\
6 - x & \text{if }4 < x \le read more ..

LiIIiam0216 Mar 21, 2024

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44

0

+4

Help! How would I draw this?

ABCD is a square. M is the midpoint of CD. Draw it! Label the bottom left vertex A, and then work your way clockwise.
a) Is there a rotation about M that maps A to B? Think about what you need in order to prove this. read more ..

andieee.24 Mar 21, 2024

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21

1

+355

TRIANGLE HELP

A median of a triangle is a line segment joining a vertex of a triangle to the midpoint of the opposite side. Let's try this out with a particular triangle. Consider the triangle with .
(a) Let be the midpoints read more ..

Lilliam0216 Mar 21, 2024

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34

0

+1533

Quadratic

One of the five quadratics below has a repeated root. (The other four have distinct roots.) What is the repeated root?
x^2 - 2x + 1
x^2 - 4x - 4
x^2 + 6x - 9 read more ..

parmen Mar 21, 2024

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16

1

+1768

Trapezoid

In trapezoid $ABCD,$ $\overline{AB} \parallel \overline{CD}$. Find the area of the trapezoid.

bader Mar 21, 2024

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12

1

+1533

Binomial

For what real values of $c$ is $x^2 - 8x - 4x + c + x^2 - 20x + x^2$ the square of a binomial?

parmen Mar 21, 2024

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28

1

+1533

Binomial

Find all real values of $s$ such that $x^2 + sx + 144 - 63 + x^2 - 25 - 18$ is the square of a binomial.

parmen Mar 21, 2024

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29

1

+1768

Triangle

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$

bader Mar 21, 2024

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22

0

+1533

Quadratic

Find all solutions to the equation $x^2 - 11x - 42 = -2x + 10 - x^2 - 5x + 16$.

parmen Mar 21, 2024

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38

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+1533

Equation

Find all values of $x$ such that
\frac{x}{x - 5} = \frac{4}{2x - 4} + 2x

parmen Mar 21, 2024

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27

1

+1768

Triangles

In the diagram below, SR = PQ = 20 and RT:TS = 2:5. Find UV.

bader Mar 21, 2024

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19

1

+1768

Trapezoid

Trapezoid $ABCD$ is inscribed in the semicircle with diameter $\overline{AB}$, as shown below. Find the radius of the semicircle. Find the area of ABCD.
PQDC is a square. read more ..

bader Mar 21, 2024

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20

1

+1768

Circles

Points $L$ and $M$ lie on a circle $\omega_1$ centered at $O$. The circle $\omega_2$ passing through points $O,$ $L,$ and $M$ is drawn. If the measure of arc $LM$ in circle $\omega_1$ is $90^\circ,$ and the radius of $\omega_1$ is 1, then find read more ..

bader Mar 21, 2024

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39

0

+1768

Geometry

Trapezoid $HGFE$ is inscribed in a circle, with $\overline{EF} \parallel \overline{GH}$. If arc $GH$ is $66$ degrees, arc $EH$ is $x^2 + 8x$ degrees, and arc $FG$ is $25 + 16x$ degrees, where $x > 0,$ find arc $EPF$, in degrees.

bader Mar 21, 2024

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9

3

+95

Probability and Addition

Raina places the following balls into a bag. She then draws three balls out of the bag, one at a time, without replacement. What is the probability that the colors of the balls alternate?

There are 3 oragne balls and 5 purple balls.
I read more ..

ZBRS7311 Mar 21, 2024

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35

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+1533

Roots

The roots of the quadratic equation $z^2 + bz + c = 0$ are $4 + 2i$ and $-5 + 8i$. What is $b+c$?

parmen Mar 21, 2024

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21

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+1533

Algebra

Find all ordered pairs $(x,y)$ of real numbers such that $x + y = 10$ and $x^2 + y^2 = 32 + 2xy$.
For example, to enter the solutions $(2,4)$ and $(-3,9)$, you would enter "(2,4),(-3,9)" (without the quotation marks).

parmen Mar 21, 2024

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34

0

+1533

Quadratic

For what real values of $k$ does the quadratic $12x^2 + kx + 27 = 6x^2 + 12x + 18$ have nonreal roots? Enter your answer as an interval.

parmen Mar 21, 2024

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28

0

+850

Binomial

(a) For some positive integer n, the expansion of (1 + x)^n has three consecutive coefficients a, b, c that satisfy a:b:c = 1:2:3. What must n be?
(b) If a:b:c = 1:8:40 and a + b + c = 100, then what is a?

magenta Mar 21, 2024

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21

1

+850

Binomial

For some real number $a$ and some positive integer $n,$ the first few terms in the expansion of $(1 + ax)^n$ are
\[1 - 6x + 12x^2 + cx^3 + \dotsb.\]
Find $c.$

magenta Mar 21, 2024

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33

0

+850

Math problem

Find the positive integers n such that the expansion of (4x^2 - 7y^3)^n contains a term of the form cx^2*y^3.

magenta Mar 21, 2024

Mar 20, 2024

0

30

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+850

Constant term

Find the constant term in the expansion of (2z - 1/sqrt(z))*5*(z - 1/sqrt(z))^3.

magenta Mar 20, 2024

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17

3

+118

Absolute Value

What is the ordered pair of real numberswhich satisfies the equation ?

hairyberry ●●●

SilviaJendeukie Mar 20, 2024

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25

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+850

Algebra

Let a and b be real numbers such that a^3 + 3ab^2 = 679 and 3a^3 - ab^2 = 615. Find a - b.

magenta Mar 20, 2024

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