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2 years ago

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If trapezoid JKLM with vertices) (3, 4), K (6,4), L (8, 1) and M (1,1) is rotated 270 degrees counterclockwise, what are the

1 answer:

Stels [109]2 years ago

7 0

Answer:

$J' = (4,-3)$

Step-by-step explanation:

Given

$J = (3, 4)$

$K =(6,4)$

$L = (8, 1)$

$M = (1,1)$

$Rotation = 270CCW$

Required

Determine the new coordinate of J

From rules of rotation,

When a point (x,y) is rotated 270 degrees CCW;

The new point becomes (y,-x)

Considering point J

$J = (3, 4)$

This means

$(x,y) = (3,4)$

Where $x = 3$ and $y = 4$

Using the above rotation rule of

$(x,y) -> (y,-x)$

The coordinates of J' becomes

$J' = (4,-3)$

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Adam must fly home to city A from a business meeting in city B. One flight option flies directly to city A from B, a distance o

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Answer:

The value is $k =109.6 \ miles$

Step-by-step explanation:

The diagram illustrating the question is shown on the first uploaded image

From the question we are told that

The distance from city A to B is AB = 467.3 miles

The bearing from B to C is $\theta_{BC} = N 28.7E$

The bearing from B to A is $\theta_{BA} = N 60.7E$

The bearing from A to B is $\theta_{AB} = S60.7W$

The bearing from A to C is $\theta_{AC} = S79.1W$

Generally from the diagram

$\theta_A = 180 - 60.7 -79.1$

=> $\theta_A = 40.2 ^o$

Also

$\theta_B = 32^o$

and

$\theta_C = 180 - (\theta_A +\theta_B )$

=> $\theta_C = 180 - (40.2 + 32 )$

=> $\theta_C = 107.8 ^o$

Generally according to Sine Rule

$\frac{BC}{sin (\theta_A)} = \frac{CA}{sin (\theta_B)} =\frac{AB}{sin (\theta_C)}$

=> $\frac{BC}{sin (40.2)} = \frac{CA}{sin (32)} =\frac{467.3 }{sin (107.8)}$

So

$\frac{BC}{sin (40.2)} = \frac{467.3 }{sin (107.8)}$

=> $BC = 316.8 \ miles$

Also

$\frac{CA}{sin (32)} = \frac{467.3 }{sin (107.8)}$

$CA = 260 .1 \ miles$

Generally the additional flyer miles that Adam will receive if he takes the connecting flight rather than the direct flight is mathematically represented as

$k = [CA +BC] - AB$

=> $k = [260 .1 +316.8]- 467.3$

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2 years ago

Elise does not like sorbet, so she omits that ingredient and adds 5 percent of each of the other ingredients. How many cups of p

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Answer:

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Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If Elise adds 5 percent of each of the other ingredients

then

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Orange Juice=25%+5%=30%

Pineapple Juice=20%+5%=25%

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Find out how many cups of punch will she have if she uses 6 cups of orange juice, using proportion

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x ----> the total cups of punch

$\frac{6}{30\%}=\frac{x}{100\%}\\\\x=6(100)/30\\\\x=20\ cups\ of\ punch$

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