Emily cut a triangle with a height of 4 inches and a base of 6 inches out of a square piece of wood measuring 18 inches by 18 inches. He keeps the leftover wood for other projects. What is the area of the wood he will have left over

Answers

Answer 1

Answer: This is definitely one of those kinds of problems that's hard to do without visualizing the slab of wood.

Step one is to find the total area of the slab of wood before any cuts are made. What's the formula to find the area of a rectangle? base*height. The square is 18 long and 18 high, so to find the area you'd need to do 18*18, and you should get 324 inches^2 as the area of the square.
Step two is to find the area of a triangle. How can you find the area of a triangle? Well, think of it this way... What do you get when you cut a square in half, diagonally? A triangle! So if the formula for the area of a square is A=bh (base*height), then wouldn't the formula of a triangle be 1/2(bh), since a triangle is half of a square? Yep! So what would be the area of this triangle? It would be 1/2(6*4), because the base is 6 and the height is 4. 6*4 is 24, so now you have 1/2*24. One half of 24 is 12, so the area of the triangle he uses is 12.
Step 3: If he uses that wood, doesn't that mean he's taking it away? What's another word for "take away"? Subtract! That means you subtract the triangle he uses from the square he cut it out from! If the area of the square slab of wood is 324, and you subtract 12, 324 -12 is 312! That means that the area of wood he will have left over is 312 inches ^2! I hope this was helpful!

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Answers

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add the original 13 miles
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Y = (x - 1)2 – 6
y = 4x + 10
Answer As Corrdinates

PLEASE HELP

Answers

Answer:

(-9, -26)

Step-by-step explanation:

y = (x - 1)2 - 6 and y = 4x + 10

Since they are both y =, you can set the two equations equal to each other:

(x - 1)2 - 6 = 4x + 10

2x - 2 - 6 = 4x + 10

-2 - 6 = 2x + 10

-8 = 2x + 10

2x = -18

x = -9

Check:

y = (x - 1)2 - 6

y = (-9 - 1)2 - 6

y = -18 - 2 - 6

y = -26

y = 4x + 10

y = 4 (-9) + 10

y = -36 + 10

y = -26

The answer to these equations is (-9, - 26). If you graph this, this is the point where the two graphs intersect.

PLEASE HELP! THANKS! The measures, in degrees, of the 3 angles of a triangle are given by 2x +1, 3x - 3, and 9x. What is the measure of the smallest angle? A.) 13 degrees B.) 23 degrees C.) 29 degrees D.) 40 degrees please show how to solve this I GIVE THANKS!!!

Answers

So all of the internal angles of a triangle will add up to 180 degrees. So if we add all of the expressions given and set them equal to 180, we can solve for x, then solve for each angle...

(2x + 1) + (3x - 3) + 9x = 180
2x + 3x + 9x + 1 - 3 = 180
14x - 2 = 180
14x = 182
x = 13

Now we can substitute 13 into each expression to find the value of each angle...

2x + 1 =
2(13) + 1 =
26 + 1 = 27 degrees

3x - 3 =
3(13) - 3 =
39 - 3 = 36 degrees

9x =
9(13) = 117 degrees

So the 3 angles are 27 degrees, 36 degrees, and 117 degrees.

The smallest is 27 degrees

** Note-- I don't see 27 degrees in the answer choices you gave, so I double checked my math (I didn't find any mistakes). Please check to see that the question is written correctly (pay close attention to plus and minus signs).

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Answers

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Answers

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Answers

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