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kondor19780726 [428]
3 years ago
9

31-inch piece of steel is cut into three pieces so that the second piece is twice as long as the first piece and the third piece

is one inch more than seven times the length of the first piece, find the lengths of the pieces
Mathematics
1 answer:
pychu [463]3 years ago
4 0

"31-inch piece of steel is cut into three pieces"

Call the pieces a,b,c

a + b + c = 31

"second piece is twice as long as the first piece"

b = 2a

"third piece is one inch more than seven times the length of the first piece"

c = 1 + 7a

Ok, we have our equations, let's substitute the second and third into the first.

a + 2a + 1 + 7a = 31

10a + 1 = 31

10a = 30

a = 30/10 = 3

b = 2a = 6

c = 1 + 7a = 22

Check: 3 + 6 + 22 = 31, good

Answer: 3 inches, 6 inches, 22 inches


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for an art project you make a square print with a side length of 8 inches. You make a frame using strip of wood 1 1/4 inch wide.
lord [1]

Given that square print has side length = 8 inches

Given that you make a frame using strip of wood 1 1/4 inch wide. Since frame is on both sides of the square print so new side length after adding the frame =1 \frac{1}{4} + 8 + 1 \frac{1}{4} = 10 + \frac{2}{4} = 10 + \frac{1}{2} = 10.5 inches


Area of the square is given by formula = x^2where x is the side of square

Shape of the frame including print will also be square so

Area of the frame including print = 10.5^2 = 110.25 square inches

Area of the print = 8^2 = 64 square inches


We have to find the area of frame only so we can subtract area of print from the total area


Area of frame = [Area of frame including print] - [Area of print]

Area of frame = 110.25-64 = 46.25


Hence final answer is 46.25 square inches


7 0
3 years ago
Select the three true statements about parallelograms
quester [9]
Opposite sides are congruent, Consecutive angels are complementary, and Opposite sides are parallel

Hope this helps!
7 0
3 years ago
Read 2 more answers
A line passes through (–1, 5) and (1, 3). Which is the equation of the line?
fredd [130]

Answer:

Use the slope formula and slope-intercept form  y = m x + b  to find the equation.  y = − x + 4

7 0
3 years ago
I HAVE30 min left help
frez [133]

Answer:

I think 10.5 would be the unit price and 10lbs of potatoes and 2lbs of tomatoes would cost less

Step-by-step explanation:

since tomatoes cost 2 times more I decided to act as he only bought potatoes and in that case he would have bought 22lbs of potatoes so I divided 16.50 by 22 and got .75 then I multiplied it by 10 and got 7.5 as well as multiplied .75 by two to get the price of the tomatoes then I added 7.5+3 to get 10.5

3 0
3 years ago
Given the line 2x - 3y - 5 = 0, find the slope of a line that is perpendicular to this line. ​
sweet [91]

Answer:

The slope of the line would be -3/2.

Step-by-step explanation:

Let's get this equation into the proper slope form:

2x - 3y - 5 = 0

2x - 3y + 3y - 5 = 0 + 3y

2x - 5 = 3y

(1/3)(2x - 5) = 3y * 1/3

2/3x - 5/3 = y

Since the slope is 2/3, we need to find the negative reciprocal of that number, which is -3/2.

8 0
2 years ago
Read 2 more answers
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