MATHEMATICS HIGH SCHOOL

294 miles every 14 gallons find the unit rate

Answers

Answer 1

Answer:

21miles

Step-by-step explanation:

If there are 24miles for every 14gallons,

294miles = 14gallons... 1)

To find the unit rate means finding the number of miles for just 1 gallon

xmiles = 1gallon ... (2)

Cross multiplying equation 1 and 2, we have!

294× 1 = 14x

x = 294/14

x = 21miles

The unit rate is 21miles

Answer 2

Answer:

When you are asked o find the unit rate, you have to take note of the ratio the problem is given to you. In here, you have 294 miles every 14 gallons. All you need to do is to divide it. 294/14 = 21 miles per gallon.

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There are two boards, a and b. The total length of both is 28 feet. Board b is at least 5 feet longer than board a, but the difference is not more than 12 feet. What are the possible lengths of the two boards?

Answers

Answer:

Step-by-step explanation:

Let a represent the length of board a.

Let y represent the length of board b.

The total length of both is 28 feet. This means that

a + b = 28

Board b is at least 5 feet longer than board a. This means that

b ≥ a + 5

The difference between both boards is not more than 12 feet. This means that

b - a < 12

Substituting a = 28 - b into b ≥ a + 5, it becomes.

b ≥ 28 - b + 5

2b ≥ 28

b ≥33/2

b ≥ 16.5

16.5 - a < 12

4.5 < a

a > 4.5

The possible lengths of board a is

8 to 11.5 feet

The possible lengths of board b is

16.5 to 20 feet

Which polynomial is factored completely? a) g^5 - g
b) 4g^3 + 18g^2 + 20g
c) 24g^2 - 6g^4
d) 2g^2 + 5g + 4

Answers

d) 2g² + 5g + 4 is the polynomial that is factored completely.
This is because the terms in the polynomial do not have any common factors.

a) g⁵ - g can be factored into g(g⁴ - 1)
b) 4g³ + 18g² + 20g can be factored into 2g(2g² + 9g + 10)
c) 24g² - 6g⁴ cab be factored into 6g²(4-g²)

Answer: D

Step-by-step explanation:

Water boils at different temperatures at different elevations. The boiling temperature of water is 212 degrees * F sea level (0 feet ) but drops about 1.72 degrees * F for every 1,000 feet of elevation. Write a formula for the boiling point at a given elevation. Then solve the formula for the elevation when the boiling point for water is 190 degrees F.

Answers

Answer:

The elevation when the boiling point of water is $190$ ° $F$ is 12790.70 feet

Step-by-step explanation:

Let every 1,000 feet of elevation be $x$ . Hence, we can write

$T = 212$ $- 1.72x$

Where $T$ is the boiling temperature of water at different elevations

Now, to the determine the elevation when the boiling point of water is $190$ ° $F$ .

We will determine $x$ by putting $T = 190$ ° $F$ .

Hence,

$T = 212$ $- 1.72x$

$190$ $= 212$ $- 1.72x$

$190 - 212$ $= - 1.72x$

$- 22$ $= - 1.72x$

$22 = 1.72x\nx = (22)/(1.72) \nx = 12.79070$

Since $x$ represents every 1,000 feet of elevation, then the elevation when the boiling point of water is $190$ ° $F$

$12.79070$ × $1000\n$ $= 12790.70$ feet

Hence, the elevation when the boiling point of water is $190$ ° $F$ is 12790.70 feet

What is the 10th term of the sequence 64, 16, 4,...?a. 1/1024

b. 1/256

c. 1/4096

d. 1/496

Answers

Each time we are dividing by 4.
Essentially, multiplying by 1/4.
Since we're multiplying, that makes this a geometric sequence!

So: Our first term is 64, and the common ratio is 1/4.
Let's plug that into the geometric sequence formula.

$a_n=a_1(r)^(n-1)$

Where a_n = the value of the nth term
a_1 = the first term, and r = the common ratio

$a_n=64(\frac14)^(n-1)$

Now that we have our equation, let's plug in 10 for n.
That way, we can solve to find $a_(10)$ , the value of the 10th term.

$a_(10)=64(\frac14)^(10-1)=\boxed{(1)/(4096)}$

the answer is C. 1/4096

Need to see how you divide 247÷100

Answers

It's very easy to divide 100 into a number because although it might be a decimal, there is no really difficult dividing going on.

100 goes into 247
2 times and then there is .47 remaining. This means 100 cannot be divided equally into this number but it will be a decimal.

Your answer would look like this:

2.47

*15 points* any help would be appreciated

Answers

Answer:

Step-by-step explanation:

this is what i think it might not be right but i tried my best ;3

can i please have brainly

Answer:

1, 4, 6 those are correct

Step-by-step explanation:

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