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oee [108]
3 years ago
5

A rectangle has vertices located at (–4, 4), (2, 4), (2, –4) and (–4, –4). What is the length of a diagonal of the rectangle?

Mathematics
1 answer:
Allisa [31]3 years ago
5 0

Answer:

A diagonal of this rectangle has length 10.

Step-by-step explanation:

The vertices (-4, 4) and (-4, -4) have the same x-coordinate (-4) and different y-coordinates (4 and -4).  These two points are the endpoints of a vertical side of the rectangle which has length 4 - (-4) = 8.

Similarly, the vertices (2, -4) and (-4, -4) have the same y-coordinate (-4) but different x-coordinates (2 and -4).  To find the horizontal dimension of the rectangle, we calculate 2 - (-4), which comes out to 6.

Thus, the width of the rectangle is 6 and the length is 8.

Using the Pythagorean Theorem, we find the length of a diagonal as follows:

d = √(6^2 + 8^2) = √(36 + 64) = √100 = 10.

A diagonal of this rectangle has length 10.

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Tyler and Han are trying to solve this system by substitution: x+3y=-5 9x+3y=3 Tyler's first step is to isolate x in the first e
Lelechka [254]

Answer:

Yes, they can both be solved and get the same answer.

Step-by-step explanation:

<u>Tyler's way:</u>

Since Tyler solved first by isolating x, resulting in x=-5-3y, he can then go and look at the second equation and solve for y there. In the second equation you're going to want to subtract 9x from the right side and left side to then get 3y=3-9x. Now you're going to divide by 3 on both sides to isolate y. You'll get y=1-3x. Now we know what y equals. Plug that back into the first equation and you'll get x=-5-3(1-3x). Use the distributive property to simplify that and you'll get x=-5-3+9x. That simplified is x=-8+9x. Add 8 on both sides and you'll get 8+x=9x. Subtract x from the both sides and you'll get 8=8x. Divide by 8 on both sides and you'll get the final answer: 1=x, or x=1.

<u>Han's way:</u>

Since Han solved first by isolating 3y, resulting in 3y=-5-x, he can then go and look at the second equation and solve for y there. In the second equation you're going to want to subtract 9x from the right side and left side to then get 3y=3-9x. Now you're going to divide by 3 on both sides to isolate y. You'll get y=1-3x. Now we know what y equals. Plug that back into the first equation and you'll get 3(1-3x)=-5-x. Use the distributive property to simplify that and you'll get 3-9x=-5-x. Add 9x to both sides and you'll get 3=-5+8x. Add 5 to both sides to isolate 8x and you'll get 8=8x. Divide by 8 on both sides and you'll get the final answer: 1=x, or x=1.

3 0
3 years ago
Aniyah spent $36 on snacks for Super Bowl Sunday and had $12 left. What percent of her money did she spend?
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She spent about 33% of her money
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4 years ago
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Line a: 3y - x= 6
Darya [45]
Line a and b are parallel
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3 years ago
How is this written in an expanded version?
Yuri [45]

Powers distribute over multiplications:

(ab)^c = a^c\cdot b^c

So, you have

(3k^5)^2 = 3^2 \cdot (k^5)^2

Now, 3^2 is simply 9.

As for (k^5)^2, we have to use the rule

(a^b)^c = a^{bc}

to get

(k^5)^2=k^{5\cdot 2}=k^{10}

So, the final answer is

(3k^5)^2 =9k^{10}

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Step-by-step explanation:

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