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Hatshy [7]
3 years ago
7

Carmela is growing her hair to donate to a charity. The hair must be a minimum length of 10 inches. Her hair is already 4 inches

long. If hair grows at the rate of 6 inches a year, write and solve an inequality to find the minimum number of years she must grow her hair to be able to make a donation.

Mathematics
1 answer:
mojhsa [17]3 years ago
5 0
It's kind of important to know how long it's been since her last cut but...
y=years
6y+4=10
I think that would work.
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Given that x and y are positive integers, solve the equation x² - 4y² = 13​
zvonat [6]
<h3>Answer:  x = 7 and y = 3</h3>

=====================================================

Explanation:

Apply the difference of squares rule

x² - 4y² = 13

x² - (2y)² = 13

(x - 2y)(x + 2y) = 13

Since x and y are positive integers, this means x-2y and x+2y are both integers as well.

The value 13 is prime. Its only factors are 1 and 13

Since the above equation shows 13 factoring into x-2y and x+2y, then we have two cases:

  • A) x-2y = 1 and x+2y = 13
  • B) x-2y = 13 and x+2y = 1

----------------

Let's consider case A

We have this system of equations

\begin{cases}x-2y = 1\\x+2y = 13\end{cases}

Add the equations straight down

  • x+x becomes 2x
  • -2y+2y becomes 0y = 0 which goes away
  • 1+13 becomes 14

Therefore we have 2x = 14 solve to x = 7

From here, plug this into either equation to solve for y

x-2y = 1

7 - 2y = 1

-2y = 1-7

-2y = -6

y = -6/(-2)

y = 3

You should get the same result if you used x+2y = 13

----------------

Since we've found that x = 7 and y = 3, notice how case B is not possible

Example:  x-2y = 13 becomes 7-2(3) = 13 which is false.

Also, x+2y = 1 would turn into 7+2(3) = 1 which is also false.

-----------------

Let's check those x and y values in the original equation

x² - 4y² = 13

7² - 4*(3)² = 13

49 - 4(9) = 13

49 - 36 = 13

13 = 13

The answer is confirmed.

4 0
2 years ago
An organic farm has been growing an heirloom variety of summer squash. A sample of the weights of 40 summer squash revealed that
natta225 [31]

Answer:

b. 0.0228

Step-by-step explanation:

We are given that

n=40

Mean,\mu=402.7 g

Standard deviation, \sigma=8.8g

We have to find the probability hat the mean weight for a sample of 40 summer squash exceeds 405.5 grams.

P(x>405.5)=P(\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}>\frac{405.5-402.7}{\frac{8.8}{\sqrt{40}}})

P(x>405.5)=P(Z>\frac{2.8}{\frac{8.8}{\sqrt{40}}})

P(x>405.5)=P(Z>2.01)

P(x>405.5)=1-P(Z\leq 2.01)

P(x>405.5)=1-0.977784

P(x>405.5)=0.022216

Hence, option b is correct.

5 0
2 years ago
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