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2 years ago

K12 help??? 3.12 Congruence and Rigid Motions

Mathematics

2 answers:

Kryger [21]2 years ago

7 0

Congruent because you can map the triangles using a reflection across the y-axis which is a rigid motion

VikaD [51]2 years ago

6 0

Answer: ΔPQR is congruent to ΔP'Q'R' because We can map ΔPQR to ΔP'Q'R' using reflection across y-axis. which is a rigid motion.

Step-by-step explanation:

Given : The coordinates of ΔPQR are P(1,4) , Q(2,2) and R(-2, 1).

The coordinates of ΔP'Q'R' are P(-1,4) , Q(-2,2) and R(2, 1).

Note that the sign of x-coordinate is changed but the magnitude of x and y coordinates remains unchanged.

It means we can ΔP'Q'R' is a mirror image of ΔPQR across y-axis (∵ y-values are exactly same.)

i.e. We can map ΔPQR to ΔP'Q'R' using reflection across y-axis.

Since reflection is a rigid motion and all rigid motions produces congruent images.

⇒ ΔPQR is congruent to ΔP'Q'R'

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A soft drink machine outputs a mean of 27 ounces per cup. The machine's output is normally distributed with a standard deviation

postnew [5]

Answer: P(22 ≤ x ≤ 29) = 0.703

Step-by-step explanation:

Since the machine's output is normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = output of the machine in ounces per cup.

µ = mean output

σ = standard deviation

From the information given,

µ = 27

σ = 3

The probability of filling a cup between 22 and 29 ounces is expressed as

P(22 ≤ x ≤ 29)

For x = 22,

z = (22 - 27)/3 = - 1.67

Looking at the normal distribution table, the probability corresponding to the z score is 0.047

For x = 29,

z = (29 - 27)/3 = 0.67

Looking at the normal distribution table, the probability corresponding to the z score is 0.75

Therefore,

P(22 ≤ x ≤ 29) = 0.75 - 0.047 = 0.703

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2 years ago

5d-2/3c if d =4 and c =3 evaluate fast fast

Mademuasel [1]

Answer:

Step-by-step explanation:

Plug 4 in for d and 3 in for c

5d-2/3c

5(4)-2/3(3)

Multiply in the numerator and the denominator

20-2/9

Subtract in the numerator

18/9

Hope this helps! :)

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2 years ago

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Liula [17]

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Andreas93 [3]

Reverse engineer

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so its 1

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2 years ago

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Gnoma [55]

Answer:

Step-by-step explanation: hope this helps :)

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