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kiruha [24]
3 years ago
11

In 2010, there were 13,300 students at college A, with a projected enrollment increase of 1000 students per year. In the same ye

ar, there were 26,800 students at college B, with a projected enrollment decline of 500 students per year. According to these projections, when will the colleges have the same enrollment? What will be the enrollment in each college at that time?
Mathematics
1 answer:
Galina-37 [17]3 years ago
4 0

Answer:

89gtij

Step-by-step explanation:

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A bakery will make 5,400 graham crackers. The graham crackers are packaged in boxes of 60. How many boxes of graham crackers wil
inna [77]

Answer:

90 boxes

Step-by-step explanation:

If you divide 5,400 by 60 you get 90. Hope this helps, let me know if correct, and have a great day!!

8 0
3 years ago
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<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx....%7D%20%7D%20%7D%20%7D%20%20%3D%20%
andrey2020 [161]

First observe that if a+b>0,

(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}

Let a=0 and b=x. It follows that

a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}

Now let b=1, so a^2+a=4x. Solving for a,

a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2

which means

a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}

Now solve for x.

x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2

(note that we assume 2x-1\ge0)

4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}

(we omit x=0 since 2\cdot0-1=-1\ge0 is not true)

3 0
1 year ago
seven pounds of potatoes were used to make a potato soup. the cook served all of the soup in sixteen equal servings. how many po
marshall27 [118]

Answer:

0.4375

Step-by-step explanation:

7/16=0.4375

If you have any additional questions let me know. :)

8 0
3 years ago
HELP PLEASE ITS DUE TODAY!!! Express 14 hours in 2 weeks as a unit rate
user100 [1]

Answer:

14/336 ----------> 0.41

Step-by-step explanation:

you substituto 2 week to 336 cause there are 336 hours in 2 weeks therefore 14/336 = 0.41

the unit rate is 14/336

7 0
3 years ago
Which of the following describes the correct process for solving the equation 2x − 4 = 20 and arrives at the correct solution?
Alexxandr [17]

Answer:

a) Add 4 to both sides, and then divide by 2. The solution is x=12.

Step-by-step explanation:

Question:

Which of the following describes the correct process for solving the equation 2x − 4 = 20 and arrives at the correct solution?

a) Add 4 to both sides, and then divide by 2. The solution is x = 12.

b) Divide both sides by −4, and then subtract 2. The solution is x = −7.

c) Subtract 4 from both sides, and then divide by 2. The solution is x = −12.

d) Multiply both sides by −4, and then divide by 2. The solution is x = −40.

Solution:

Given equation:

2x-4=20

We need to determine the steps in order to solve for x.

Solving for x.

Step 1: Adding 4 both sides.

2x-4+4=20+4

2x=24

Step 2: Dividing both sides by 2.

\frac{2x}{2}=\frac{24}{2}

∴ x=12

Thus, we added 4 both sides and then divided both sides by 2 to get solution = 12

7 0
3 years ago
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