All Questions ⁺⁰235690 Questions

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+1678

help 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 $k$?

wiseowl Nov 13, 2023

0

47

1

+1678

runners

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 ..

wiseowl Nov 13, 2023

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48

1

+1678

help 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?

wiseowl Nov 13, 2023

0

57

1

+4

Pls help cphill

The vertices of triangle $ABC$ lie on the sides of equilateral triangle $DEF$, as shown. If $CD = 5$, $CE = BD = 2$, and $\angle ACB = 90^\circ$, then find $AE$.

ewewfeffebntn Nov 13, 2023

Nov 12, 2023

+5

46

1

+180

Help

Let G be the center of equilateral triangle ABC A dilation centered at G with scale factor -3/5 is applied to triangle ABC to obtain triangle A'B'C' Let K be the area of the region that is contained in both triangles ABC and A'B'C' Find K/[ABC] read more ..

itsash Nov 12, 2023

-1

33

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+1443

Algebra

The real numbers $a$ and $b$ satisfy $a - b = 1$ and $a^3 - b^3 = 1.$
(a) Find all possible values of $ab.$
(b) Find all possible values of $a + b.$
(c) Find all possible values of $a$ and $b.$

blackpanther Nov 12, 2023

-1

33

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+1443

Roots

Let $a$ and $b$ be the roots of the quadratic $2x^2 - 8x + 7 = -3x^2 + 5x + 11.$ Compute $a^3/b^2 + b^3/a^2.$

blackpanther Nov 12, 2023

-1

46

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+1443

need help with this

Let c be a real number, and consider the system of quadratic equations
y = 6x^2 - 9x + c - 3x^2 + 17x
y = 5x^2 - 3x - 2x^2 + 10x - 18

For which values of c does this system have:
(a) Exactly one real read more ..

blackpanther Nov 12, 2023

-1

58

0

+1443

help plz

Let $a$ and $b$ be the roots of the quadratic $x^2 - 5x + 3 = 4x^2 - 8x + 23$ Find the quadratic whose roots are $a^2$ and $b^2.$

blackpanther Nov 12, 2023

-1

61

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+1443

Solutions

Let a and b be the solutions to 7x^2 + x - 5 = 2x^2 - 3x + 1. Compute (a - 4) + (b - 4).

blackpanther Nov 12, 2023

-1

45

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+1443

Algebra

Let $u$ and $v$ be the solutions to $3x^2 + 5x + 7 = x^2 - 6x + 8$ Find $1/u + 1/v$.

blackpanther Nov 12, 2023

-1

55

0

+1443

help algebra

Let a and b be the solutions to 5x^2 - 11x + 4 = 2x^2 - 7x + 9 + 7x^2 - 14x - 11. Find 1/a + 1/b.

blackpanther Nov 12, 2023

-1

55

0

+1443

Need help

Expand (a + 2)(3a^2 - 2a - 12)(a^2 - 2a + 1).

blackpanther Nov 12, 2023

-1

48

1

+1443

help solve

Fill in the blanks to make a quadratic whose roots are $1$ and $-1.$
x^2 + ___ x + ___

blackpanther Nov 12, 2023

-1

19

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+1443

quadratic

Find the largest value of $x$ such that $3x^2 + 17x + 15 = 2x^2 + 21x + 12 - 5x^2 + 17x + 34.$

blackpanther Nov 12, 2023

-1

32

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+1443

Algebra

Compute (1 + i)/(2 - i)(3 + i).

blackpanther Nov 12, 2023

-1

32

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+1443

plz help

Simplify the expression
\frac{1}{\sqrt{36}} - \sqrt{27} - \frac{1}{\sqrt{27}} - \sqrt{18} + \frac{1}{\sqrt{18}} - \sqrt{9}

blackpanther Nov 12, 2023

-1

38

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+1443

triangle inequality

All the sides of a triangle have integer length. The perimeter of the triangle is 5 and the triangle is isosceles. How many such non-congruent triangles are there?

blackpanther Nov 12, 2023

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59

2

+4

please help thank you

In triangle ABC, we have angle B = 60, angle C = 90, and AB = 2.
Let P be a point chosen uniformly at random inside triangle ABC . Extend ray BP to hit side AC at D. What is the probability that BD>sqrt2?
<read more ..

euniwong Nov 12, 2023

0

47

0

+1533

need help

Solve for $c$ in $(c - 7)^2 = 81 + 5c$.

parmen Nov 12, 2023

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42

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+1533

help plz

Find all real values of $t$ that satisfy the equation
(t^2 - 13)*2 = 144.

parmen Nov 12, 2023

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44

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+1533

square

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

parmen Nov 12, 2023

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44

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+1533

square

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

parmen Nov 12, 2023

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45

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+1533

solutions

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

parmen Nov 12, 2023

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