All Questions ⁺⁰237313 Questions

0

15

3

+789

Algebra

Pearl writes down seven consecutive integers, and adds them up. The sum of the integers is equal to 28/9 times the largest of the seven integers. What is the smallest integer that Pearl wrote down?

bingboy Aug 6, 2024

0

33

2

+1517

Algebra

Seven years ago, Grogg's dad was $9$ times as old as Grogg. Four years ago, Grogg's dad was $6$ times as old as Grogg. How old is Grogg's dad currently?

learnmgcat Aug 6, 2024

0

24

3

+54

Number theory...

Let x be an integer such that . Find the value of . Express your answer as a residue between 0 and the modulus.

AUnVerifiedTaxPayer Aug 6, 2024

0

27

0

+864

Geometry

Point $D$ is the midpoint of median $\overline{AM}$ of triangle $ABC$. Point $E$ is the midpoint of $\overline{AB}$, and point $T$ is the intersection of $\overline{BD}$ and $\overline{ME}$. Find the area of triangle $BET$ if $AB = 20$, $AC = 20$, read more ..

RedDragonl Aug 6, 2024

0

17

1

+750

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $100$ square foot wall in $10$ minutes, then how long would it take the $15$ members to paint a $100$ square foot wall, in minutes?

siIviajendeukie Aug 6, 2024

0

13

1

+750

Algebra

All members of our painting team paint at the same rate. If $10$ members can paint a $1000$ square foot wall in $10$ minutes, then how long would it take for $5$ members to paint a $1000$ square foot wall, in minutes?

siIviajendeukie Aug 6, 2024

Aug 5, 2024

+1

17

1

+582

Algebra

A plane flies from Penthaven to Jackson and then back to Penthaven. When there is no wind, the round trip takes 3 hours and 36 minutes, but when there is a wind blowing from Penthaven to Jackson at 30 miles per hour, the trip takes 3 hours and 45 read more ..

onyuIee Aug 5, 2024

+1

29

1

+582

Algebra

In physics, Ohm's law says that current through a wire, $I$, is directly proportional to voltage, $V$, and inversely proportional to resistance, $R$:
I = V/R
It's also true that resistance is directly proportional to the length of the wire. read more ..

onyuIee Aug 5, 2024

0

36

0

+1208

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 ..

AnswerscorrectIy Aug 5, 2024

0

25

0

+1208

Algebra

Let $a$ and $b$ be complex numbers. If $a + b = 4$ and $a^2 + b^2 = 6,$ then what is $a^3 + b^3?$

AnswerscorrectIy Aug 5, 2024

0

32

1

+1855

Geometry

A line and a circle intersect at $A$ and $B,$ as shown below. Find the distance between $A$ and $B$.
The line is x = 4, and the equation of the circle is x^2 + y^2 = 25.

ABJeIIy Aug 5, 2024

0

27

0

+1855

Geometry

Let $k$ be a positive real number. The line $x + y = 3 + k$ and the circle $x^2 + y^2 = k$ are drawn. Find $k$ so that the line is tangent to the circle.

ABJeIIy Aug 5, 2024

0

43

0

+864

Algebra

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

RedDragonl Aug 5, 2024

0

27

0

+750

Algebra

Find all ordered pairs x, y of real numbers such that x+y=10 and x^3+y^3=300.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

siIviajendeukie Aug 5, 2024

0

34

0

+864

Algebra

For an integer n, the inequality
x^2 + nx + 15 < -89 - 3x^2
has no real solutions in $x$. Find the number of different possible values of $n$.

RedDragonl Aug 5, 2024

0

27

1

+750

Counting

Catherine rolls a standard 6-sided die six times. If the product of her rolls is 60 then how many different sequences of rolls could there have been? (The order of the rolls matters.)

siIviajendeukie Aug 5, 2024

0

48

0

+279

Algebra

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

fjeihqoO Aug 5, 2024

0

39

0

+4

Algebra

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 $k?$

justarandornperson Aug 5, 2024

0

20

1

+359

Algebra

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

falafronk Aug 5, 2024

0

36

0

+1266

Algebra

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

Akhain1 Aug 5, 2024

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