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2 years ago

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A projectile is launched from a hole in the ground one foot deep. It’s height follows the equation h= -16^2+7t-1. Use factoring

by perfect-squares to find the time when the projectile lands back on the ground. (Hint: Landing on the ground means projectial height is zero.)

1 answer:

3241004551 [841]2 years ago

5 0

16x16 = 256+7t-1
= 255+7t

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The average heights of x number of girls and 15 boys is 123. if the average heights of boys is 125 and that of girls is 120.find

mamaluj [8]

Answer:

$x = 10$ . In other words, there number of girls is $10$ .

Step-by-step explanation:

The average of a number of measurements is equal to the sum of these measurements over the number of measurements.

$\displaystyle \text{Average} = \frac{\text{Sum of measurements}}{\text{Number of measurements}}$ .

Rewrite to obtain:

$\begin{aligned}& \text{Sum of measurements}= (\text{Number of measurements}) \times (\text{Average}) \end{aligned}$ .

For this question:

$\begin{aligned}& \text{Sum of heights of boys} \\ &= (\text{Number of boys}) \times (\text{Average height of boys}) \\ &= 15 \times 125 = 1875\end{aligned}$ .

$\begin{aligned}& \text{Sum of heights of girls} \\ &= (\text{Number of girls}) \times (\text{Average height of girls}) \\ &= x \times 120 = 120\, x\end{aligned}$ .

Therefore:

$\begin{aligned}& \text{Sum of boys and girls} \\ &= \text{Sum of heights of boys} + \text{Sum of heights of girls}\\ &= 1875 + 120\, x\end{aligned}$ .

On the other hand, there are $(15 + x)$ boys and girls in total. Using the formula for average:

$\begin{aligned}& \text{Average height of boys and girls} \\ &= \frac{\text{Sum of heights of boys and girls}}{\text{Number of boys and girls}} \\ &= \frac{1875 + 120\, x}{15 + x}\end{aligned}$ .

From the question, this average should be equal to $123$ . In other words:

$\displaystyle \frac{1875 + 120\, x}{15 + x} = 123$ .

Solve this equation for $x$ to obtain:

$1875 + 120\, x= 123\, (15 + x)$ .

$(123 - 120)\, x = 1875 - 123 \times 15$ .

$x = 10$ .

In other words, the number of girls here is $10$ .

5 0

2 years ago

Use the distributive property to remove the parentheses.<br> (w-4)7

ella [17]

Answer: 7w - 28

7*w - 7*4

7w - 28

Brainliest pwease if the answer is correct! <3

4 0

2 years ago

-3(5)^2-(-2)(-8) simplify

avanturin [10]

To do this, we're going to use the order of operations (PEMDAS):

P - Parentheses

E - Exponents

M - Multiplication

D - Division

A - Addition

S - Subtraction

First let's do parentheses, there isn't anythig in parentheses we need to simplify, so we can skip this step.

Next let's look for exponents. I see we have a $5^2$ so let's replace that with $5^2=25$ :

$-3(25)-(-2)(-8)$

Now let's look for multiplcation. We know that things that are right next to eachother in parentheses represent multiplcation, so let's simply this more:

$-3(25)=-75$

$(-2)(-8)=16$

$-75-16$

And now we're left with a simple problem we know how to solve.

Answer: $-91$

Hope this helps!

3 0

3 years ago

The question is Stephen read for 34 minutes on Monday and 45 minutes on Tuesday. Use breaking apart to find how many minutes Ste

user100 [1]

Breaking apart means that you just take the tens from each number, and the ones from each number, then add them up.

The tens from your numbers are:
30 from 34
40 from 45

The ones from your numbers are:
4 from 34
5 from 45

Now, you have to add up the tens and ones separately.
30 + 40 = 70
4 + 5 = 9

Finally, you add up those 2 numbers that you got- 70 and 9

The answer: Stephen read for 79 minutes total.

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3 years ago

brenda and her bestfriend went on a vacation together. They both paid for a flight, and brenda had a fancy room for $150 per nig

AURORKA [14]

Answer:

What is the question?

Step-by-step explanation:

1. Write all of the question to receive a correct answer.

7 0

2 years ago