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Helga [31]
3 years ago
12

Two congruent squares are shown in figures 1 and 2 below

Mathematics
1 answer:
BabaBlast [244]3 years ago
6 0

Answer:

I will answer everithing in terms of a and b.

The area of a square is equal to L*L = L^2

where L is the lenght of the side of a square.

The area of a triangle is equal to b*h/2

where b is the base of the triangle and h is the heigth.

1) Area of the triangles in the first image.

The area of one triangle is: a*b/2

then for the 4 triangles we have 4 times that amount:

Area = 4*(a*b/2) = 2*a*b

2) For the triangles in the second image we have the same situation the base is a and the heigth is b, so the area for the 4 triangles is:

Area = 4*(a*b/2) = 2*a*b

3)  The unshaded area in the first image is:

Area = c*c = c^2

And, by the Pythagorean theorem we have that:

b^2 + a^2 = c^2

Then the area of the square is:

Area = c^2 = a^2 + b^2

4) the combined areas from the two squares in image 2 are:

Area of the big one = b*b = b^2

Area of the small one = a*a = a^2

total area: a^2 + b^2

5) The total area for the two images will be:

Total area for both images = a^2 + b^2 + a^2 + b2 = 2*(a^2 + b^2)

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dybincka [34]

Answer:

$427,500 dollars

Step-by-step explanation:

Given the following question:
Initial price = 450,000
5% discount

In order to find the answer, we simply find 5% of 450,000.

\frac{5\times450000}{100} =5\times450000=2250000\div100=22500
450000-22500=427500
r=427500

The radio (after a 5% discount) costs "$427,500 dollars."

Hope this helps.

6 0
3 years ago
5.2 + 3 + (-1.5) + (-3.3)+ (-3.8) + (-9.2)<br><br> A. 96.1<br> B. -96.1<br> C. -9.6<br> D. 9.6
morpeh [17]

The answer is -9.6. Hope that helps

8 0
3 years ago
A salesperson had 240,000 dollars in sales last year, which is 60% of the sales she had this year. Which equation could be used
8_murik_8 [283]
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7 0
3 years ago
Read 2 more answers
In order to set​ rates, an insurance company is trying to estimate the number of sick days that full time workers at an auto rep
son4ous [18]

Answer:

D. 31

Step-by-step explanation:

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.025 = 0.975, so Z = 1.96.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

A previous study indicated that the population standard deviation is 2.8 days.

This means that \sigma = 2.8

How large a sample must be selected if the company wants to be​ 95% confident that the true mean differs from the sample mean by no more than 1​ day?

This is n for which M = 1. So

M = z\frac{\sigma}{\sqrt{n}}

1 = 1.96\frac{2.8}{\sqrt{n}}

\sqrt{n} = 1.96*2.8

(\sqrt{n})^2 = (1.96*2.8)^2

n = 30.12

Rounding up, at least 31 people are needed, and the correct answer is given by option D.

5 0
3 years ago
Alexandra has 4 bags of beads. Some of the bags contain 3 purple beads and the rest contain 6 indigo beads. If Alexandra has 21
Sedbober [7]

Answer:

1 bag of 3 purple beads and 3 bags of 6 indigo beads

Step-by-step explanation:

3 + 18 = 21

5 0
3 years ago
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