All Questions ⁺⁰237808 Questions

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help geometry

In triangle $ABC$, let the perpendicular bisector of $BC$ intersect $BC$ and $AC$ at $D$ and $E$, respectively. If $BC = 20$ and $\angle C = 15^\circ$, then find the length of $BE$.

Akhain1 Mar 28, 2024

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80

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+1271

Geometry

In triangle $ABC$, $\angle ABC = 90^\circ$, and $D$ is on side $\overline{BC}$ such that $\overline{AD}$ bisects $\angle BAC$. If $AB = 4,$ $BC = 3$, and $AC = 5,$ then find the area of $\triangle ADC$. Round your answer to the nearest integer.

Akhain1 Mar 28, 2024

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59

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+1271

help geometry

Point D is the midpoint of median AM of triangle ABC. Point E is the midpoint of AB, and point T is the intersection of BD and ME. Find the area of triangle BEC if [ABC] = 14.

Akhain1 Mar 28, 2024

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44

10

+85

Geometry

Not so hard problems
1.

2.
<#> 3.<#> read more ..

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Akhaim1 Mar 28, 2024

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77

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+2730

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 ..

LiIIiam0216 Mar 28, 2024

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69

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+2730

Rate question

Five workers have been hired to complete a job. If one additional worker is hired, they could complete the job $4$ days earlier. If the job needs to be completed $20$ days earlier, how many additional workers should be hired?

LiIIiam0216 Mar 28, 2024

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74

0

+1271

Polynomial

Find $t$ if the expansion of the product of $x^3$ and $x^2 + tx$ has no $x^2$ term.

Akhain1 Mar 28, 2024

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72

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+1271

Polynomial

There exists a polynomial $f(x)$ and a constant $k$ such that
(x^2 - 2x - 5) f(x) = 2x^4 + 19x^3 + kx^2 - 15x - 1.
What is $k?$

Akhain1 Mar 28, 2024

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73

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+1271

Coefficient

What is the coefficient of $x$ in $(x^3 + x^2 + x + 1)(x^4 - 8x^3 + 17x^2 - 23x + 14)$?

Akhain1 Mar 28, 2024

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74

1

+2730

Quadratic

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

LiIIiam0216 Mar 28, 2024

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58

1

+1271

Sum

Find the sum of all positive integers less than $1000$ ending in $3$ or $4$ or $5$.

Akhain1 Mar 28, 2024

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66

1

+2730

I need help

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

LiIIiam0216 Mar 28, 2024

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58

1

+2730

help me

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

LiIIiam0216 Mar 28, 2024

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69

0

+1271

Series

When the same constant is added to the numbers $60,$ $120,$ and $160,$ a three-term geometric sequence arises. What is the common ratio of the resulting sequence?

Akhain1 Mar 28, 2024

0

73

0

+1271

Series

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 $a_1$.

Akhain1 Mar 28, 2024

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58

2

+363

I checked the other posts and they all didn't work.

Jeri finds a pile of money with at least 200. If she puts 50of the pile in her left pocket, gives away 2/3 of the rest of the pile, and then puts the rest in her right pocket, she'll have more money than if she instead gave away 200 of the original read more ..

Lilliam0216 Mar 28, 2024

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68

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+1271

Algebra

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 ..

Akhain1 Mar 28, 2024

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52

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+1271

Series

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 $S_{70}.$

Akhain1 Mar 28, 2024

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80

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+1271

Function

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 $x$.

Akhain1 Mar 28, 2024

0

73

1

+1271

Coordinates

Find all points $(x,y)$ that are $5$ units away from the point $(2,7)$ and that lie on the line $y = 5x - 28.$

Akhain1 Mar 28, 2024

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52

1

+1271

Logarithm

Solve the system of equations
y = \log_2 (2x)
y = log_4 (16 + x)

Akhain1 Mar 28, 2024

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55

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+869

Probability

In Ms. Q's deck of cards, every card is one of four colors (red, green, blue, and yellow), and is labeled with one of seven numbers ($1,$ $2,$ $3,$ $4,$ $5,$ $6,$ and $7$). Among all the cards of each color, there is exactly one card labeled with each number. read more ..

cooIcooIcooI17 Mar 28, 2024

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79

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+869

help with counting

You are given the 4 x 4 grid below.
(a) Find the number of ways of placing 8 counters in the squares (at most one counter per square), so that each row contains exactly two counters.
(b) Find the number of ways read more ..

cooIcooIcooI17 Mar 28, 2024

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62

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+869

need help

In how many ways can three pairs of siblings from different families be seated in two rows of three chairs, if siblings may sit next to each other in the same row, but no child may sit directly in front of their sibling?

cooIcooIcooI17 Mar 28, 2024

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73

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+869

Counting question

Find the number of positive integers that satisfy both the following conditions:
Each digit is a $1$ or a $2$ or a $3$
The sum of the digits is $5$

cooIcooIcooI17 Mar 28, 2024

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