What is the image of (-6, -2) after a dilation by a scale factor of 4 centered at the origin?

Answers

Answer 1

Answer:

The image of the point (-6, -2) after dilation by a scalefactor of 4 centered at the origin is (-24, -8).

What is a scale factor?

A scalefactor is defined as the ratio between the scale of a given original object and a new object,

We have,

To find the image of the point (-6, -2) after dilation by a scale factor of 4 centered at the origin, we can use the following formula:

(x', y') = (kx, ky)

where (x, y) are the coordinates of the original point, (x', y') are the coordinates of the image after dilation, k is the scale factor, and (0, 0) is the center of dilation.

Substituting the values given in the problem, we get:

(x', y') = (4*(-6), 4*(-2))

Simplifying,

(x', y') = (-24, -8)

Therefore,

The image of the point (-6, -2) after dilation by a scalefactor of 4 centered at the origin is (-24, -8).

Learn more about scalefactors here:

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In a group of 20 there are 7 boys what is the ratio of girls to boys?

Answers

Step-by-step explanation:

given,

total membersin grp =20

no.of boys =7

no.of girls=20-7=13

so,

the ratioof girlsto boys is =13:7

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An automobile engineer is redesigning a conical chamber that was originally specified to be 12 inches long with a circular base of diameter 5.7 inches. In the new design, the chamber is scaled by a factor of 1.5. The volume of the original chamber is a.)102.02 b.)248.04 c.)306.06 d.)412.08 cubic inches. This is a.)242.47 b.)344.49 c.)432.16 d.)448.21 cubic inches less than the volume of the new chamber.

Answers

The answers are:
a.)102.02
a.)242.47

The volume of the cone can be expressed as:
$V = (1)/(3) \pi r^(2) h$
where:
V - the volume of the cone,
r - the radius of the cone,
h - the height of the cone.

It is given:
h = 12 in
R = 2r = 5.7 in ⇒ r = 5.7 in ÷ 2 = 2.85 in
π = 3.14

Therefore, the volume of the original conical chamber (V₁)
$V = (1)/(3) *3.14*(2.85) ^(2) *12 = 3.14*8.1225*4 = 102.02 in^(3)$

Further, the new chamber is scaled by a factor of 1.5. That means that radius and height of the original chamber are increased 1.5 times:
r₁ = r · 1.5 = 2.85 in · 1.5 = 4.275 in
h₁ = h · 1.5 = 12 in · 1.5 = 18 in

The volume of the new chamber is:
$V_1= (1)/(3) *3.14*(4.275) ^(2) *18 = 3.14*18.28*6=344.49 in ^(3)$

The difference between two chambers is:
V₁ - V = 344.49 - 102.02 = 242.47

Answer:

a and a

Step-by-step explanation:

If the 1600m race is 4 laps, what is the path length raced?

Answers

it is 400 because you have to divide

you are standing, on the horizontal ground, __ feet from the base of a cliff. Admiring your surroundings, you nite that the angle of elevation to the top of the cliff to be __ degrees. If realistic limits are imposed on your choices, what would be a reasonable distance from the cliff? What would be a reasonable angle if elevation? Explain.

Answers

If realistic limits are imposed on the choices I would go with 1000 ft. For the angle of elevation I would chose 34°. This because as we know an angle of elevation is the angle between the observer's’ line of sight and a horizontal line when the observer looks upward.

If you wanted to find the height of the cliff you would use the following:

Tan34 = x/1000

x = tan(34)*1000

x = 674.51 ft.

I hope this helps, Regards.

There were 20 apples in the bag. Rachel used 2/5 of the apples for a pie. Hermother used 1/2 of the apples for apple crisp. How many apples are left in
the bag?

Answers

Answer : 2 apples

Step by step explanation:

Which of the following represents the probability of 3 successes in 5 trials?a. 3C5P(S)*P(775
c. 3C5P(S)?P(A15
b. 5C3P(S)3P(F2
d. 5C3P(S)3P(F)5

Answers

Final answer:

The probability of 3 successes in 5 trials is represented by '5C3P(S)³P(F)²'. This equation reflects the combination of possible successful events, multiplied by the probability of success raised to the number of successes, and the probability of failure raised to the number of failures.

Explanation:

The correct answer is d. 5C3P(S)³P(F)².

Probability of success in binomial problems is given by the equation P(S) = nCr * (p)ⁿ * (q)ⁿ-r where n is the number of trials, r is the number of successful trials, p is the probability of success, and q is the probability of failure (1-p). In this case, there are 5 trials and 3 successes, so your p to the power of 3 (P(S)³) represents the probability of success and the your q to the power 2 (P(F)²) represents the probability of failure. The 5C3 in front is a combination which shows how many ways 3 successes can occur in 5 trials.