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3 years ago

2 Solve the equation for x: 3x – 5 = 5x + 2x. Show your work.

Mathematics

1 answer:

Galina-37 [17]3 years ago

8 0

Answer:

—5/4 or —1 1/4

Step-by-step explanation:

3x – 5 = 5x + 2x

Collect like terms

—5 = 5x + 2x — 3x

—5 = 4x

Divide both side by the coefficient of x i.e 4

x = —5/4 or —1 1/4

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A home owner wants to purchase two different chairs for the living room, one for in front of the fire place and one for in front

Ipatiy [6.2K]

Using the combination formula, it is found that photos of 9 different chairs were shown to the home owner.

The order in which the chairs are chosen is important, hence, the <em>permutation formula </em>is used to solve this question.

<h3>What is the permutation formula?</h3>

$P_{n,x}$ is the number of different permutations of x objects from a set of n elements, given by:

$P_{n,x} = \frac{n!}{(n-x)!}$

In this problem, two chairs are chosen from a set of n, and there are 72 different outcomes, hence:

$P_{n,x} = 72, x = 2$

$P_{n,x} = \frac{n!}{(n-x)!}$

$72 = \frac{n!}{(n-2)!}$

$72 = \frac{n(n - 1)(n - 2)!}{(n-2)!}$

$n^2 - n = 72$

$n^2 - n - 72 = 0$

Which is a quadratic function with coefficients $a = 1, b = -1, c = -72$ , hence:

$\Delta = b^2 - 4ac = (-1)^2 - 4(1)(-72) = 289$

Taking the positive root:

$x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{1 + \sqrt{289}}{2} = 9$

Photos of 9 different chairs were shown to the home owner.

You can learn more about the permutation formula at brainly.com/question/25925367

3 0

2 years ago

Are these triangles congruent?

sashaice [31]

Answer:

The answer is D because the angles ABC are not corresponding to DEF

3 0

2 years ago

Rewrite the function y=3x+8

frozen [14]

Answer:

3x-y= -8

Step-by-step explanation:

i believe this answer is correct

3 0

3 years ago

Find the measure of x. Line PU has points R and S between points P and U, lines QR and ST are parallel, line QR intersects line

Genrish500 [490]

The value of x is 1.

* Let's explain how to solve the problem

- Line PU has points R and S between points P and U

- Line QR intersects line PU at point R

- Line ST intersects line PU at point S

- Lines QR and ST are parallel

- Look to the attached figure

∵ QR // ST

∴ m∠TSU = m∠QRU ⇒ corresponding angles

∵ m∠TSU = 15(x + 2)°

∴ m∠QRU = 15(x + 2)

∵ Points P, R, S lie on the same line

∵ RQ intersects PS at R

∵ m∠PRQ + m∠QRU = 180° ⇒ straight angle

∵ m∠PRQ = 135°

∵ m∠QRU = 15(x + 2)°

∴ 135 + 15(x + 2) = 180

∴ 135 + 15x + 30 = 180

- Add like terms

∴ 15x + 165 = 180

- Subtract 165 from both sides

∴ 15x = 15

- Divide both sides by 15

∴ x = 1

∴ The value of x is 1

In geometry, parallel lines are coplanar instantly traces that do not intersect at any factor. Parallel planes are planes in identical three-dimensional space that in no way meet. Parallel curves are curves that do not touch every different or intersect and hold a set minimal distance

In mathematics, the intersection of or more gadgets is any other item that includes the whole thing that is contained in all the items simultaneously.

Learn more about parallel lines here : brainly.com/question/24756209

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4 0

2 years ago

Write down the next term in each following sequence <br> 83,77,71,65...

rosijanka [135]

Answer:

59,53,47,41,35 and many more

Step-by-step explanation:

substract 6

3 0

3 years ago

Read 2 more answers