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grin007 [14]
3 years ago
6

∆ABC is translated 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at (1, 5), then vert

ex A' is at
Mathematics
2 answers:
Paladinen [302]3 years ago
4 0
<span>So we want to know the new coordinates for the vertex A'(x,y) if we know that the vertex A is at A(-1,2) and vertex B is at B(1,5) and that the triangle ABC is translated 6 units up and 3 units left. So the method is simply to add units 6 to x and 3 to y of A to get A'. Going left means we need to go to negative x direction and going up means we need to go to positive y direction. So: A'(-1-3,2+6) and that is: A'(-4,8). </span>
sineoko [7]3 years ago
3 0

Answer: (-4,8)

Step-by-step explanation:

The translation rule for translating a point h units left  is given by :-

(x,y)\to (x-h,k)

The translation rule for translating a point k units up is given by :-

(x,y)\to (x,y+k)

Given : ∆ABC is translated 6 units up and 3 units left to create ∆A'B'C'. If vertex A is at (-1, 2) and vertex B is at (1, 5).

Then, the vertex A'  will be :-

A(-1,2)\to(-1-3,\ 2+6)=(-4,\ 8)

Hence, the vertex A' is at (-4,8).

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Answer:

The answer is true.

Step-by-step explanation:

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The area of the rectangle shown is 24 square inches. how much longer is its length than its width?
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What is the volume of a square pyramids
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Answer:

\large\boxed{V=75\ in^3}

Step-by-step explanation:

The formula ogf a volume of  a pyramid:

V=\dfrac{1}{3}BH

B - area of a base

H - height

We have a base length a = 5 in and a height H = 9 in.

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3 years ago
⦁ In a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football. Construct a 95% confiden
fomenos

Answer:

95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].

Step-by-step explanation:

We are given that in a simple random sample of 1219 US adults, 354 said that their favorite sport to watch is football.

Firstly, the pivotal quantity for 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is given by;

        P.Q. = \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } ~ N(0,1)

where, \hat p = proportion of adults in the United States whose favorite sport to watch is football in a sample of 1219 adults = \frac{354}{1219}

           n = sample of US adults  = 1291

           p = population proportion of adults

<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5%

                                                    significance level are -1.96 & 1.96}

P(-1.96 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 1.96) = 0.95

P( -1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } < {\hat p-p} < 1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } ) = 0.95

P( \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } < p < \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } ) = 0.95

<u>95% confidence interval for p</u> = [ \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } , \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } ]

                         = [ \frac{354}{1219}-1.96 \times {\sqrt{\frac{\frac{354}{1219}(1-\frac{354}{1219})}{1219} } , \frac{354}{1219}+1.96 \times {\sqrt{\frac{\frac{354}{1219}(1-\frac{354}{1219})}{1219} } ]

                         = [0.265 , 0.316]

Therefore, 95% confidence interval for the proportion of adults in the United States whose favorite sport to watch is football is [0.265 , 0.316].

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