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3 years ago

Point G(−7, 4) is translated using the rule (x+10, y−6). What is the x-coordinate of G′ ?

Mathematics

1 answer:

den301095 [7]3 years ago

6 0

Answer:

x = 3

Step-by-step explanation:

The translation rule (x + 10, y - 6) means add 10 to the original x- coordinate and subtract 6 from the original y- coordinate, that is

G(- 7, 4) → G'(- 7 + 10, 4 - 6) → G'(3, - 2)

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Convert the Cartesian equation (x 2 + y 2)2 = 4(x 2 - y 2) to a polar equation.

SashulF [63]

<u>ANSWER</u>

${r}^{2} = 4 \cos2\theta$

<u>EXPLANATION</u>

The Cartesian equation is

${( {x}^{2} + {y}^{2} )}^{2} = 4( {x}^{2} - {y}^{2} )$

We substitute

$x = r \cos( \theta)$

$y = r \sin( \theta)$

and

${x}^{2} + {y}^{2} = {r}^{2}$

This implies that

${( {r}^{2} )}^{2} = 4(( { r \cos\theta) }^{2} - {(r \sin\theta) }^{2} )$

Let us evaluate the exponents to get:

${r}^{4} = 4({ {r}^{2} \cos^{2}\theta } - {r}^{2} \sin^{2}\theta)$

Factor the RHS to get:

${r}^{4} = 4{r}^{2} ({ \cos^{2}\theta } - \sin^{2}\theta)$

Divide through by r²

${r}^{2} = 4 ({ \cos^{2}\theta } - \sin^{2}\theta)$

Apply the double angle identity

$\cos^{2}\theta -\sin^{2}\theta= \cos(2 \theta)$

The polar equation then becomes:

${r}^{2} = 4 \cos2\theta$

7 0

3 years ago

For the figure above: Assume that <ABD has a mesure of 105° ANSWER ASAP WILL GIVE 15 POINTS AND BRAINLIEST

kykrilka [37]

Answer:

DBC = 75

Step-by-step explanation:

ABD and DBC are supplementary angles. They add to 180 degrees.

ABD + DBC = 180

105 + DBC = 180

Subtract 105 from each side

105-105 + DBC = 180-105

DBC = 75

4 0

2 years ago

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A 3-meter roll of red ribbon costs $1.89. What is the unit price?

Elan Coil [88]

Answer:

The price of ribbon is $0.63 per meter.

Step-by-step explanation:

It is given that:

Cost of 3 meter ribbon = $1.89

Unit price per meter = $\frac{1.89}{3}$

Unit price per meter = $0.63 per meter

Therefore,

The price of ribbon is $0.63 per meter.

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3 years ago

The ratio of passenger cars to cargo cars in

gayaneshka [121]

Answer:

126

Step-by-step explanation:

the number of cargo cars is represented by the 35 part of the ratio , then

105 ÷ 35 = 3 ← value of 1 part of the ratio , then

passenger cars = 7 × 3 = 21

total cars = 105 + 21 = 126

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2 years ago

A small plant is 212 inches tall. How tall will it be in 3 weeks if it grows 34 inch each week? Which method will NOT give the c

Neporo4naja [7]

34*3=102 hope this helps so 102 is the answer please give me brainliest

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3 years ago

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