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IceJOKER [234]
3 years ago
9

Triangle STU is rotated 270 clockwise about the origin to create triangle S'T'U'. If point U of triangle STU is a (a,b), which a

lgebraic representation best describes point U' of triangle S'T'U'?
Mathematics
1 answer:
nadya68 [22]3 years ago
6 0

Answer:

(b, -a)

Step-by-step explanation:

First note that the rule for a rotation by 270° about the origin is (x,y)→(y,−x)

Note that the coordinates were swapped and the x coordinates negated. Similarly;

Given the coordinate of the point U as (a, b), if the triangle is rotated 270degrees clockwise, the resulting coordinate will  be (b, -a)

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Alex_Xolod [135]

Answer:

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Step-by-step explanation:

The formula of a distance between two points:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

A(-3, 0) , B(3, 2)

AB=\sqrt{(3-(-3))^2+(2-0)^2}=\sqrt{6^2+2^2}=\sqrt{36+4}=\sqrt{40}=\sqrt{4\cdot10}=\sqrt4\cdot\sqrt{10}=2\sqrt{10}

A(-3, 0), D(-2, -3)

AD=\sqrt{(-2-(-3))^2+(-3-0)^2}=\sqrt{1^2+(-3)^2}=\sqrt{1+9}=\sqrt{10}

AB = CD and AD = BC

The area of a rectangle:

A=(AB)(AD)

Substitute:

A=(2\sqrt{10})(\sqrt{10})=(2)(10)=20

The perimeter of a rectangle:

P=2(AB+AD)

Substitute:

P=2(2\sqrt{10}+\sqrt{10})=2(3\sqrt{10})=6\sqrt{10}

4 0
3 years ago
Suppose a sample of 80 with a sample proportion of 0.58 is taken from a
Anvisha [2.4K]

Answer:

99.7% confidence interval is [0.4162,0.7437]

Step-by-step explanation:

The formula for a confidence interval for a population proportion is CI=\hat{p}\pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} } where \hat{p} is the sample proportion, n is the sample size, and z^* is the critical score for the desired confidence level.

We are given a sample size of n=80 and a sample proportion of \hat{p}=0.58. Our critical score for a 99.7% confidence level would be z^*=normalcdf(0.9985,0,1)=2.9677

Therefore, the approximate 99.7% confidence interval for the population parameter is CI=\hat{p}\pm z^*\sqrt{\frac{\hat{p}(1-\hat{p})}{n} }=0.58\pm 2.9677\sqrt{\frac{0.58(1-0.58)}{80} }=[0.4162,0.7438]

So we are 99.7% confident that the true population proportion is contained within the interval [0.4162,0.7437]

3 0
3 years ago
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spayn [35]
I should think that this works just like the trapezoids
volume=base times height
so
base=pir^2
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V=49pix
1176pi=49pix
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