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Leviafan [203]
3 years ago
10

In the figure above AB = 4x + 6 and BC = 7x + 15. If AC = 120, find the length of segment AB.

Mathematics
1 answer:
Mrac [35]3 years ago
7 0

Answer:

x = 9

Step-by-step explanation:

AB = 4x + 6 and BC = 7x + 15  AC is the sum of AB and BC

so 4x + 6 + 7x + 15 = 120 add like terms

11x + 21 = 120 subtract 21 from both sides

11x = 99 divide both sides by 11

x = 9

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The sum of the areas of two circles is 80 pi
katovenus [111]
The area of a circle is A = πr^2. We let A1 And A2 the areas of the circles and r1 and r2 the radius of each, respectivley.

A1 + A2 = 80π
Substitute the formula for the area,
π(r1)^2 + π (r2)^2 = 80π

From the statement, we know that r2=2(r1).

<span>π(r1)^2 + π (2 x r1)^2 = 80π
</span>We can cancel π, we will have

5 x (r1)^2 = 80
Thus,

r1 = 4 and r2 = 8
5 0
3 years ago
Solve the equation, keeping the value for x as an improper fraction. 23x = − 12x + 5 1.Isolate the variable by adding 12x to bot
kogti [31]

Answer:

x=\frac{30}{7}

Step-by-step explanation:

We have been given an equation \frac{2}{3}x=-\frac{1}{2}x+5. We are asked to solve our given equation.

First of all, we will add \frac{1}{2}x on both sides of equation to separate x variable on one side of equation.

\frac{2}{3}x+\frac{1}{2}x=-\frac{1}{2}x+\frac{1}{2}x+5

\frac{2}{3}x+\frac{1}{2}x=5

Now, we will make a common denominator.

\frac{2*2}{3*2}x+\frac{1*3}{2*3}x=5

\frac{4}{6}x+\frac{3}{6}x=5

Add numerators:

\frac{4+3}{6}x=5

\frac{7}{6}x=5

Upon multiply both sides of our equation by \frac{6}{7}, we will get:

\frac{6}{7}*\frac{7}{6}x=5*\frac{6}{7}

x=\frac{5*6}{7}

x=\frac{30}{7}

Therefore, the solution for our given equation is x=\frac{30}{7}.

5 0
3 years ago
Read 2 more answers
Which statements about 12 ÷ 7 are true? Use the array to answer the question. Check all that apply.
AURORKA [14]

Answer:

The remainder is 5

Step-by-step explanation:

12 Divided by 7 equals 12 over 7 or 1.714285. 7 can only go into 12, one time. if we subtract 7 from 12 we get 5 which is the remainder. There is no way it can be 2 because 7 plus 2 equals 9. 1 x 7 + 5 equals 12 which isn't 1.714285. 2 x 7 + 4 equals 18 which also isn't 1.714285. Same with 2 x 5 + 5. That equals 15 which isn't 1.714285.

5 0
3 years ago
Lainey is sliding down a water slide that is 376 feet long at a rate of 47 feet per second. How long will it take Lainey to trav
chubhunter [2.5K]

Answer:

8 seconds

Step-by-step explanation:

The length of the water slide is 376 feet and Lainey is sliding down at a rate of 47 feet per second. That is her speed.

Speed is given as distance divided by time or the time rate of displacement.

Therefore, time is:

Time = distance / speed

Therefore, the time it will take Lainey to get from the top to the bottom is:

Time = 376 / 47 = 8 seconds

It will take her 8 seconds to get from the top to the bottom.

8 0
3 years ago
Which twos ratios represent quantities that are proportional?
Inessa05 [86]

Answer: it’s 10/15 and 14/21 ;)

Step-by-step explanation:

8 0
3 years ago
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