All Questions ⁺⁰230723 Questions

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Algebra

Solve the inequality -4(x + 4) > x + 7 + 8x + 21.

siIviajendeukie Apr 15, 2024

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+158

Algebra

I own a large truck, and my neighbor owns four small trucks that are all identical. My truck can carry a load of at least $500$ pounds more than each of her trucks, but no more than $\frac{1}{4}$ of the total load her four trucks combined can carry. read more ..

siIviajendeukie Apr 15, 2024

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+158

Algebra

Solve the inequality 2x - 5 <= -x + 12 - 7x + 18.

siIviajendeukie Apr 15, 2024

Apr 14, 2024

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+158

Algebra

Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $15$ days earlier. If the job needs to be completed $40$ days earlier, how many additional workers should be hired?

siIviajendeukie Apr 14, 2024

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+158

Algebra

Three runners, Dirk, Edith, and Foley all start at the same time for a $24$ km race, and each of them runs at a constant speed. When Dirk finishes the race, Edith is $10$ km behind, and Foley is $15$ km behind. When Edith finishes the race, how far read more ..

siIviajendeukie Apr 14, 2024

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+158

Algebra

For a certain value of $k$, the system
x + y + 3z = 10,
x - 2y + 8z = 7,
kx + 5z = 3
has no solutions. What is this value of k?

siIviajendeukie Apr 14, 2024

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+24

help pls

Determine the smallest positive integer n such that 5^n equivalent n^5 mod 3.

MEMEGOD Apr 14, 2024

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1

+158

Algebra

Our badminton team has finished $75\%$ of its season. So far, we have won $35\%$ of the games we played. What percent of the remainder of our games must we win in order to finish the season with the same number of wins as losses?

siIviajendeukie Apr 14, 2024

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+158

Algebra

The function f(x) is defined for 1 \le x \le 5 as follows:
f(x) = 2x + 8 if 1 \le x \le 2
f(x) = 13 - 5x if 2 < x \le 3
f(x) = 20 - 14x if 3 < x \le 4 read more ..

siIviajendeukie Apr 14, 2024

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+158

Algebra

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

siIviajendeukie Apr 14, 2024

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+158

Algebra

Let f(x) = \left \lfloor \frac{2 - 3x}{x + 3} + x^2 \right \rfloor.
Find f(1) + f(2) + f(3) + ... + f(999) + f(1000).

siIviajendeukie Apr 14, 2024

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+158

Algebra

Find the minimum value of \frac{x^2}{x - 1 + x^3} for x > 1

siIviajendeukie Apr 14, 2024

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+158

Algebra

Let
f(x) = \sqrt{x - \sqrt{x}}
Find the largest three-digit value of x such that f(x) is an integer.

siIviajendeukie Apr 14, 2024

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+733

Algebra

Evaluate the infinite geometric series
0.4 + 0.016 +...
Express your answer as a fraction with integer numerator and denominator.

LiIIiam0216 Apr 14, 2024

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+1117

Geometry

Points $A,$ $B,$ and $C$ are given in the coordinate plane. There exists a point $Q$ and a constant $k$ such that for any point $P$,
PA^2 + PB^2 + PC^2 = 3PQ^2 + k.
If $A = (2,4),$ $B = (-3,1),$ and $C = (1,7)$, then find the constant read more ..

parmen Apr 14, 2024

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+1117

Geometry

A rectangle in the coordinate plane is shown below. A line with slope $\frac{1}{3}$ splits this rectangle into two regions with equal area. What is the $y$-intercept of this line?
The rectangle has coordinates (-1,-1), (-1,1), read more ..

parmen Apr 14, 2024

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+1117

Geometry

Let $O$ be the origin. Points $P$ and $Q$ lie in the first quadrant. The slope of line segment $\overline{OP}$ is $11,$ and the slope of line segment $\overline{OQ}$ is $13.$ If $OP = OQ,$ then compute the slope of line segment $\overline{PQ}.$
Note: read more ..

parmen Apr 14, 2024

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+1117

Geometry

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The circle is x^2 + y^2 = 1, and the line is y = x.

parmen Apr 14, 2024

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+1565

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes $4$ hours and 20 minutes, but when there is a wind blowing from Penthaven to Jackson at $50$ miles per hour, the trip takes $4$ hours and read more ..

bader Apr 14, 2024

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+64

Find the ordered quintuplet that satisfies the system of equations

Find the ordered quintuplet that satisfies the system of equations

SilviaJendeukie Apr 14, 2024

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+1565

Algebra

For a certain value of k, the system
x + y + 3z = 10,
x - 2y + 8z = 7,
kx + 5z = 3
has no solutions. What is this value of k?

bader Apr 14, 2024

0

4

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+1565

Algebra

Will and Grace are canoeing on a lake. Will rows at $50$ meters per minute and Grace rows at $25$ meters per minute. Will starts rowing at $2$ p.m. from the west end of the lake, and Grace starts rowing from the east end of the lake at $2{:}15$ p.m. read more ..

bader Apr 14, 2024

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+733

help counting

The grid below is made up of line segments, like the line segment in red. There are a number of paths that go from A to B in the grid, where every step goes to the right or up. If we choose a line segment at random, then what is the expected number of squares read more ..

LiIIiam0216 Apr 14, 2024

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+733

help me

Let PQR be an equilateral triangle, centered at O. A point X is chosen at random inside the triangle. Find the probability that X is closer to O than to any of the sides. (In other words, find the probability that XO is read more ..

LiIIiam0216 Apr 14, 2024

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+733

need help

The numbers $x_1,$ $x_2,$ $x_3,$ $x_4$ are chosen at random in the interval $[0,1].$ Let $I$ be the interval between $x_1$ and $x_2,$ and let $J$ be the interval between $x_3$ and $x_4.$ Find the probability that intervals $I$ and $J$ both contain read more ..

LiIIiam0216 Apr 14, 2024

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