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2 years ago

Matthew drove 189 miles in 7 hours. If he continued at the same rate, how long would it take to travel 297 miles

Mathematics

1 answer:

zzz [600]2 years ago

8 0

Answer:

11 hours

Step-by-step explanation:

27 miles per hour. 297/27 equals 11. to double check 11 times 27 equals 297.

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30 PTS!!!!! Cole needs to include at least 11 mg and at most 22 mg of iron in his diet each day. Cole plans to eat multiple ba

ser-zykov [4K]

Answer:

See explanation

Step-by-step explanation:

<u>Part A:</u> If Cole eats 3 bananas each day. These 3 bananas contain $3\cdot 0.3=0.9$ mg of iron.

Let x be the number of vitamins Cole takes. Each whole vitamin contains 4 mg of iron, then x vitamins contain 4x mg of iron.

The total amount of iron Cole takes is

$0.9+4x\ mg$

Cole needs to include at least 11 mg and at most 22 mg of iron in his diet each day, so

$11\le 0.9+4x\le 22$

Solve it:

$11-0.9\le 4x\le 22-0.9\\ \\10.1\le 4x\le 21.1\\ \\2.525\le x\le 5.275$

The smallest number of vitamins - 3, the greatest number of vitamins - 5.

<u>Part B: </u>Cole continues to eat 3 bananas each day. He pays $\$2\cdot 7=\$14$ for bananas per week.

If Cole spends a total of $20 on bananas and vitamins this week, then he spent $20 - $14 = $6 on vitamins.

Let x be the number of vitamins Cole takes this week.

First 10 vitamins are free, then x - 10 vitamins each cost $0.50 (he pays an additional dollar for every 2 additional vitamins he purchases) and they cost

$\$0.50(x-10)$

This amount of money is exactly $6, so

$0.50(x-10)=6\\ \\5(x-10)=60\\ \\x-10=12\\ \\x=22$

This means Cole takes 3 vitamins per day (the whole number) and he is able to meet his iron requirement every day this week, based on answer in Part A.

5 0

2 years ago

Read 2 more answers

Given ΔMNO, find the measure of ∠LMN.

Novay_Z [31]

Answer:

104°

Step-by-step explanation:

If segments NO and NM are congruent, then angles NMO and NOM are congruent. So, their supplements, angles NML and NOP are congruent. That is ...

∠NML ≅ ∠NOP = 104°

∠NML = 104°

3 0

1 year ago

Read 2 more answers

How many terms in the arithmetic sequence(2,4,6,8....) will give sum of 600

andriy [413]

Answer:

24 terms

Step-by-step explanation:

The sum of an arithmetic sequence is the average of the first and last terms, multiplied by the number of terms. The last term is given by ...

an = a1 + (n-1)d

We have a sequence with first term a1 = 2 and common difference d = 2. So the last term is ...

an = 2+ 2(n -1) = 2n

Then the average of first and last terms times the number of terms is ...

Sn = 600 = n(2 + 2n)/2 = n(n+1) . . . . . . close to n²

We can solve the quadratic in n, or we can estimate the value of n as the integer just below the square root of 600.

√600 ≈ 24.5

so we believe n = 24.

_____

<em>Check</em>

S24 = 24·25 = 600 . . . . . . as required.

8 0

1 year ago

Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. L

lesya692 [45]

Answer: $A(t)=-8t+52$

Step-by-step explanation:

<h3> The missing question is: "What is the Functions formula A(t)=?"</h3><h2 />

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

According to the data given in the exercise, you know that:

- $A(t)$ represents the area to paint the Hiros' romm as a function of time.

- The rate he painted the room was 8 square meters per hour.

- The area left to paint after 3 hours was 28 m².

Therefore, based on this, you can idenfity that:

1. The slope of the line is:

$m=-8$

2. One of the point on the line is:

$(3,28)$

So you must substitute the slope and the coordinates of that point into $y=mx+b$ and then solve for "b" in order to find its value:

$28=-8(3)+b\\\\28+24=b\\\\b=52$

Therefore, you can determine that the function $A(t)$ is:

$A(t)=-8t+52$

4 0

1 year ago

If 10a+10b=35, what is the average (arithmetic mean) of a and b?

worty [1.4K]

Answer:

1.75

Step-by-step explanation:

If a and b are two numbers, then their arithmetic mean is

$\dfrac{a+b}{2}$

Given:

$10a+10b=35$

Divide this equation by 10:

$a+b=3.5$

Now, divide it by 2:

$\dfrac{a+b}{2}=\dfrac{3.5}{2}\\ \\\dfrac{a+b}{2}=1.75$

6 0

2 years ago