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miskamm [114]
3 years ago
9

Joseph weighs 120 pounds and is gaining ten pounds each month. Keith weighs 150 pounds and is gaining 4 pounds each month. How m

any months, m, will it take for Joseph to weigh the same as Keith?
Mathematics
1 answer:
svp [43]3 years ago
3 0

Answer:

Step-by-step explanation:

Let J = Joseph, K = Keith, m = number of months

We are told that Joseph weighs 120pounds and gains 10 pound each month.

From this we can write the following equation:

J = 120 + 10m

We also know Keith weights 150 pounds and gains 4 pounds each month, so:

K = 150 + 4m

Since we are trying to find how many months it will take for Joseph to weigh the same as Keith, this means we can say J = K

120 + 10m = 150 + 4m

Subtract 120 from both sides:

10m = 150 + 4m - 120

10m  = 30 +4m

Subtract 4m from both sides:

10m - 4m = 30

6m = 30

Divide both sides by 6 to find "m".

m = 30/6 = 5

Therefore, it will take 5 months for Joseph and Keith to be equal weight.

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3 years ago
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Given the equation of a circle below, find the diameter of the circle. Use only the digits 0-9 to enter the diameter.
kogti [31]

Answer:

10

Step-by-step explanation:

Standard form for a circle is

(x - h)² + (y - k)² = r²

where (h, k) is the center and r is the radius

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x² + y² - 18x + 24y = -200

Rearrange

(x² - 18x) + (y² + 24y) = -200

Complete the square for x

(x - 9)² + (y² + 24y) = -200 + (-9)²

Complete the sqaure for y

(x - 9)² + (y + 12)² = -200 + (-9)² + 12²

(x - 9)² + (y + 12)² =  25

Now the equation is in standard form

r² = 25

r = 5

Therefor Diameter = 10

4 0
3 years ago
The sum of two numbers is 2. The sum of three times the larger and twice the smaller is 14. Find the numbers.
anzhelika [568]

For this case we have to:

x: Be the variable that represents the largest number

y: Be the variable that represents the smallest number

We propose a system of equations:

x + y = 2\\3x + 2y = 14

From the first equation we have to:

x = 2-y

Substituting in the second equation:

3 (2-y) + 2y = 14\\6-3y + 2y = 14\\6-y = 14\\-y = 14-6\\-y = 8\\y = -8

We look for the value of "x":

x = 2 - (- 8)\\x = 2 + 8\\x = 10

Answer:x = 10\\y = -8

8 0
3 years ago
Leah claims that these figures are not similar. When she compared the heights, she wrote 2/7. Then she compared the bases and 21
antiseptic1488 [7]

Answer:

The two figures are similar and hey are not solid.

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

<em>Leah claims that these figures are not similar. When she compared the heights, she wrote 2/7. Then she compared the bases and 21/6. Why is Leah having trouble? Explain completely</em>

(Please have a look at the attached photo)

My answer:

In the first ratio, she compared the small figure's height to the large figure's height that is: 2/7

In the second ratio, she compared the large figure's base to the small figure's base that is: 21/6

=> She is wrong in this step, the ratio must be 6/21

Hence she needs to compare bases and heights thorugh division because the ratio between heights and the ratio between bases must be equal

\frac{21}{6}=3.5\\\frac{7}{2}=3.5

The scales are equal

=> Therefore, those rectangles are congruent.

8 0
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zloy xaker [14]

Answer:

Rounding it to the nearest foot, the length of the main span of the Akashi Kaikyo Bridge is 5,020 feet.

Step-by-step explanation:

Given that the Verrazano Narrows Bridge has a main span of 3,260 feet, while the Akashi Kaikyo Bridge has a main span that is about 54% longer, to determine the length of the main span of this last bridge, the following calculation must be performed:

3,260 x 1.54 = X

5,020.4 = X

Thus, rounding it to the nearest foot, the length of the main span of the Akashi Kaikyo Bridge is 5,020 feet.

7 0
3 years ago
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