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4 years ago

How to make an equation with numbers 0.25, 7.00, and 27

Mathematics

1 answer:

shepuryov [24]4 years ago

8 0

There are many ways to do this.

One way could be 0.25x+7.00=27

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1. Under a dilation, the points (-3, -4) is moved to (-15, -20). What is the scale factor of the dilation?

LuckyWell [14K]

Answer:

5 and 2

Step-by-step explanation:

-15 / -3 = 5

-20 / -4 = 5

6 / 3 = 2

10 / 5 = 2

8 0

3 years ago

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What is the value of y in the solution to this system of equations? 5x – 7y = 7 y = -5x + 3

zysi [14]

Answer:

y = -0.5

Step-by-step explanation:

given

5x – 7y = 7 ------- eq 1

y = -5x + 3 (we rearrange this so that the terms are in the same order as eq 1)

-5x – y = -3 ----- eq 2

by elimination, eq 1 + eq 2

(5x – 7y) + (-5x – y) = 7 + (-3)

5x - 7y -5x - y = 7-3

-8y = 4

y = 4/(-8)

y = -0.5

7 0

3 years ago

Convert the Cartesian equation x^2 + y^2 = 16 to a polar equation.

RideAnS [48]

Answer:

Problem 1: $r=4$

Problem 2: $r=-2\sin(\theta)$

Problem 3: $r\sin(\theta)=3$

Step-by-step explanation:

Problem 1:

So we are going to use the following to help us:

$x=r \cos(\theta)$

$y=r \sin(\theta)$

$\frac{y}{x}=\tan(\theta)$

So if we make those substitution into the first equation we get:

$x^2+y^2=16$

$(r\cos(\theta))^2+r\sin(\theta))^2=16$

$r^2\cos^2(\theta)+r^2\sin^2(\theta)=16$

Factor the $r^2$ out:

$r^2(\cos^2(\theta)+\sin^2(\theta))=16$

The following is a Pythagorean Identity: $\cos^2(\theta)+\sin^2(\theta)=1$ .

We will apply this identity now:

$r^2=16$

This implies:

$r=4 \text{ or } r=-4$

We don't need both because both of include points with radius 4.

Problem 2:

$x^2+y^2+2y=0$

$(r\cos(\theta))^2+(r\sin(\theta))^2+2(r\sin(\theta))=0$

$r^2\cos^2(\theta)+r^2\sin^2(\theta)+2r\sin(theta)=0$

Factoring out $r^2$ from first two terms:

$r^2(\cos^2(\theta)+\sin^2(\theta))+2r\sin(\theta)=0$

Apply the Pythagorean Identity I mentioned above from problem 1:

$r^2(1)+2r\sin(\theta)=0$

$r^2+2r\sin(\theta)=0$

or if we factor out r:

$r(r+2\sin(\theta))=0$

$r=0 \text{ or } r=-2\sin(\theta)$

r=0 is actually included in the other equation since when theta=0, r=0.

Problem 3:

$y=3$

$r\sin(\theta)=3$

8 0

4 years ago

Question 3 of 10 What is 9C6? O A. 96 OB. 10 O C. 56 O D. 84

koban [17]

The answer is d because

3 0

3 years ago

in a history class, the girl to boy ratio is 9 to 5. if there is a total of 70 students how many boys is there

DedPeter [7]

Answer:

25 boys.

Step-by-step explanation:

To solve this problem, first add the two parts of the ratio. 9 + 5 = 14. Then divide 70 by 14 to get 5. Since the total is 5 times the ratio total, multiply both sides of the ratio by 5. The result is 45 : 25. If you add them together, you get a total of 70. Therefore, there are 25 boys in the class.

7 0

4 years ago

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