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1 year ago

Triangle \triangle A'B'C'△A

1 answer:

6 0

From the information given, the rotated triangle is same as the original triangle. This is because, vertices of the rotation remain at the origin - (0,0).

<h3>What is the proof the above?</h3>

Notice that the question states: △A'B'C' is the image of △ABC. Given that the △ without primes is the original and the one with primes depict the rotated triangle,

under a rotation about the origin, (0,0) (0,0) (0, 0), indicating no movement,

△A'B'C' is in the same position with △ABC.

Learn more about rotation at:
brainly.com/question/27915888
#SPJ1

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The length of a rectangle is twice its width. Given the length of the diagonal is $5\sqrt{5}$, find the area of the rectangle.

lianna [129]

Answer: Area of rectangle is 50 square units.

Step-by-step explanation:

Since we have given that

Diagonal of the rectangle = 5√5

Let the width of rectangle be 'x'

Let the length of rectangle be '2x'

As we know the formula for diagonal of rectangle:

$5\sqrt{5}=\sqrt{l^2+w^2}\\\\(5\sqrt{5}})^2=(2x)^2+x^2\\\\125=4x^2+x62\\\\125=5x^2\\\\\dfrac{125}{5}=x^2\\\\25=x^2\\\\x=\sqrt{25}\\\\x=5\ units$

So, Length of rectangle be 2x=2×5=10 units

And the area of the rectangle is given by

$Area=Length\times width\\\\Area=10\times 5\\\\Area=50\ sq.\ unit$

Hence, area of rectangle is 50 square units.

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2 years ago

Solve the system of equations.<br> y=5x-9<br> y=3x +7

ELEN [110]

Download photomath it really helps and solves the question for you and shows you the steps

7 0

2 years ago

Five-sixths of the boats in the marina are white, 2 5 of the remaining boats are blue, and the rest are red. If there are 12 red

Inga [223]

Answer: There are 120 boats in the marina.

Step-by-step explanation:

Let's suppose that there are N boats

We know that 5/6 of them are white, then we have: (5/6)*N white boats.

The remaining is: N - (5/6)*N = (1/6)*N

We know that 2/5 of the remaining are blue, then we have:

(2/5)*(1/6)*N blue boats

And the rest are red, the rest is:

(1/6)*N - (2/5)*(1/6)*N = (3/5)*(1/6)*N

Then we have (3/5)*(1/6)*N red boats.

And we know that there are 12 red boats, then:

(3/5)*(1/6)*N = 12

Now we can solve this for N, which is the total number of boats in the marina.

N = 12*(6)*(5/3) = 120

There are 120 boats in the marina.

4 0

2 years ago

The average systolic blood pressure was found to be 140 mm for people who have high responsibility jobs, specifically investment

defon

Answer:

t = -1.428

Step-by-step explanation:

Average blood pressure among people with high responsibility jobs = u = 140 mm

Number of people sampled for the study = n = 51

Average blood pressure of the sample = x = 139 mm

Standard deviation of the sample = s = 5 mm

The claim is that practicing yoga decreases the blood pressure. So we have to test that after practicing yoga, the average blood pressure will be lesser than 140. Based on this we can formulate the null and alternate hypothesis as:

Null Hypothesis: $\mu \geq 140$

Alternate Hypothesis: $\mu < 140$

Since population standard deviation is not known, we cannot use z-distribution for this test. We are given the value of sample standard deviation, so t-test will be used for this case.

Test statistic is calculated as:

$t=\frac{x-u}{\frac{s}{\sqrt{n} } }$

Using the values in this formula gives us:

$t=\frac{139-140}{\frac{5}{\sqrt{51}}}\\\\ t=-1.428$

Therefore, the value of test statistic is -1.428

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2 years ago

Emay ears $15 for each car she washes. Create an equation to represent the relationship between the number of cars

emmasim [6.3K]

Answer:

$25

Step-by-step explanation:

8 0

2 years ago