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2 years ago

ΔABC is dilated using a scale factor of 12 to produce ΔA'B'C'. Select all of the statements that apply to the transformation.

Mathematics

1 answer:

GalinKa [24]2 years ago

3 0

Answer:

Options (3) and (6)

Step-by-step explanation:

ΔABC is a dilated using a scale factor of $\frac{1}{2}$ to produce image triangle ΔA'B'C'.

Since, dilation is a rigid transformation,

Angles of both the triangles will be unchanged or congruent.

m∠A = m∠A' and m∠B = m∠B'

Since, sides of ΔA'B'C' = $\frac{1}{2}$ of the sides of ΔABC

Area of ΔA'B'C' = $\frac{1}{2}(\text{Area of triangle ABC})$

Area of ΔABC > Area of ΔA'B'C'

Since, angles of ΔABC and ΔA'B'C' are congruent, both the triangles will be similar.

ΔABC ~ ΔA'B'C'

Therefore, Option (3) and Option (6) are the correct options.

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Triangle G E F is shown. Angle G E F is a right angle. The length of hypotenuse F G is 14.5 and the length of F E is 11.9. Angle

jekas [21]

Answer:

B. cos−1(StartFraction 11.9 Over 14.5 EndFraction) = θ

Step-by-step explanation:

From definition:

cos(θ) = adjacent/hypotenuse

The adjacent side respect angle GFE (or θ) is side FE, and side FG is the hypotenuse. Replacing with data and isolating θ:

cos(θ) = 11.9/14.5

θ = cos^-1(11.9/14.5)

3 0

2 years ago

Read 2 more answers

The data set below represents the ages of 36 executives. find the percentile that corresponds to an age of 4141 years old. 2828

solong [7]

Answer:

37th percentile.

Step-by-step explanation:

We have been given a data set that represents the ages of 36 executives. We are asked to find the percentile that corresponds to an age of 41 years.

28, 29, 29, 32, 32, 33, 34, 34, 34, 34, 37, 37, 38, 41, 41, 42, 45, 45, 47, 47, 47, 48, 50, 51, 53, 56, 56, 56, 61, 61, 62, 63, 64, 64, 65, 66.

Let us count the number of data points below and at 41.

We can see that the number of data points at and below 41 is 13.

We will use percentile formula to solve our given problem.

$\text{Percentile rank of x}=\frac{\text{Number of values below x}}{\text{Total number of data points}}\times 100$

$\text{Percentile rank of 41}=\frac{13}{36}\times 100$

$\text{Percentile rank of 41}=0.361111\times 100$

$\text{Percentile rank of 41}=36.11\approx 37$

Therefore, the percentile rank that corresponds to age of 41 years old is 37th percentile.

8 0

2 years ago

It takes one machine 25 minutes to pick a bale of cotton and another machine 30 minutes to compete the same job. If both machine

gladu [14]

The first machine works at the rate x = 1 bale/ 25 min.
The second machine works at the rate y = 1 bale/30 min.

The combined rate is
x + y = 1/25 + 1/30 bales/min
= (30 + 25)/(25*30) = 55/750
= 11/150 bales/min

The time for both machines to pick 1 bale of cotton is
(1 bale)/(11/150 bales/min) = 150/11 min = 13.64 min

Answer: 13.6 minutes

6 0

2 years ago

Initially, there were only 86 weeds in the garden. The weeds grew at a rate of 29% each week. The following function represents

Orlov [11]

Step-by-step answer:

The base of the exponential function is 1.29 for 7 days, as in

f(x) = 86*(1.29)^x

The new rate for days can be calculated by dividing x by 7 (where x remains the number of weeks), namely

f(x) = 86*1.29^(x/7)

Using the law of exponents, b^(x/a) = b^(x*(1/a)) = (b^(1/a))^x

we simplify by putting b=1.29, a=7 to get

f(x) = 86*(1.29^(1/7))^x

f(x) = 86*(1.037)^x since 1.29^(1/7) evaluates to 1.037

Rounding 1.037 to 1.04 we get a (VERY) approximate function

f(x) = 86 * (1.04^x)

1.04 is very approximate because 1.04^7 is supposed to get back 1.29, but it is actually 1.316, while 1.037^7 gives 1.2896, much closer to 1.29.

7 0

2 years ago

Read 2 more answers

Order 93% nine tenths 0.099 0.915% and 0.092 from least to greatest

andrew11 [14]

1. 0.915% (0.00915)
2. 0.092 (9.2%)
3. 0.099 (9.9%)
4. 9/10 (.9 or 90%)
5. 93% (.93)

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2 years ago