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3 years ago

What is the common difference of the arithmetic sequence? −10x, −7x, −4x, −x, 2x, 5x, ... A) −3x B) −3 C) 3 D) 3x

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

3 0

Answer:

D) 3x

Step-by-step explanation:

The difference of adjacent terms is ...

(-7x) -(-10x) = (-7+10)x = 3x . . . . the common difference

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2. Carl needs 15 hours longer than Jennifer to paint a room. If they work together, they can complete the job in 4 hours. Explai

nasty-shy [4]

Answer:

Jennifer would complete the job on her own in 5 hours.

Step-by-step explanation:

Solving a quadratic equation:

Given a second order polynomial expressed by the following equation:

$ax^{2} + bx + c, a\neq0$ .

This polynomial has roots $x_{1}, x_{2}$ such that $ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})$ , given by the following formulas:

$x_{1} = \frac{-b + \sqrt{\Delta}}{2*a}$

$x_{2} = \frac{-b - \sqrt{\Delta}}{2*a}$

$\Delta = b^{2} - 4ac$

Rates

The together rate is the sum of their separates rate.

We have that:

Jennifer takes x hours to complete the job on her own, so her rate is 1/x.

Carl needs 15 hours longer than Jennifer, that is, 15 + x hours, so his rate is 1/(15+x).

The together rate is 1/4. So

$\frac{1}{4} = \frac{1}{x} + \frac{1}{15+x}$

$\frac{1}{4} = \frac{15 + x + x}{x(15+x)}$

$\frac{1}{4} = \frac{15 + 2x}{x(15+x)}$

Applying cross multiplication.

$x^2 + 15x = 4(15 + 2x)$

$x^2 + 15x = 60 + 8x$

$x^2 + 7x - 60 = 0$

Quadratic equation with $a = 1, b = 7, c = -60$ . So

$\Delta = 7^{2} - 4*1*60 = 289$

$x_{1} = \frac{-7 + \sqrt{289}}{2} = 5$

$x_{2} = \frac{-7 - \sqrt{289}}{2} = -12$

Since the time to complete the job has to be a positive value.

Jennifer would complete the job on her own in 5 hours.

4 0

2 years ago

Evaluate 23x + 4y when x=20 and y=23

never [62]

Answer:

552

Step-by-step explanation:

23x + 4y when x=20 and y=23

if x=20 and y=23 all you have to do is replace the numbers and solve

23(20) + 4(23)

Multiply 23*20 which is equal to 460

Then you multiply 4*23 which is equal to 92

The problem is now 460 + 92

add it, and you get 552.

Hope this helps!!

-Ketifa

3 0

3 years ago

1. Denise makes 21 quarts of ice cream. She stores the ice cream in containers

Alenkinab [10]

21 containers for the ice cream

4 0

3 years ago

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tara made a snack mix with 3/4 cup of rice crackers and 2/3 cup of pretzels. she then ate 5/8 cup of the mix for lunch. how much

grandymaker [24]

First you add 3/4 and 2/3 you but then do 3/4 2/3 you think what the both can go to is 12 the dominator is 12 then you time it by 3,4 because they both go to 12 then the 3 will be time 3 because 4 x 3 = 12 then you do it the top so 3x3 = 9 9/12 then you do the next one is2/3 do the same then will get 8/12 then you can subtract it 9/12 - 8/12 will gave you 1/12

8 0

3 years ago

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Rational numbers that are not integers are?

Vladimir [108]

Any number that can be writen as a fraction example: 0.75, -15, 0, 9

6 0

3 years ago