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qaws [65]
2 years ago
11

On a coordinate plane, 2 quadrilaterals are shown. Quadrilateral Q R S T has points (negative 1, 0), (5, 0), (3.5, negative 6) a

nd (negative 2.5, negative 6). Quadrilateral Q prime R prime S prime T prime has points (negative 1, 2), (1, 2), (0.5, 0), and (negative 1.5, 0). Quadrilateral QRST is dilated and translated to form similar figure Q'R'S'T'. What is the scale factor for the dilation?
Mathematics
2 answers:
dimulka [17.4K]2 years ago
5 0

Answer:

\dfrac{1}{3}.

Step-by-step explanation:

In quadrilateral QRST, Q(-1,0), R(5,0), S(3.5,-6), T(-2.5,-6).

In quadrilateral Q'R'S'T', Q'(-1,2), R'(1,2), S'(0.5,0), T'(-1.5,0).

Distance formula:

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Using distance formula , we get

QR=\sqrt{(5-(-1))^2+(0-0)^2}=\sqrt{6^2}=6

Q'R'=\sqrt{(1-(-1))^2+(2-2)^2}=\sqrt{2^2}=2

Now,  

\text{Scale factor}=\dfrac{Q'R'}{QR}

\text{Scale factor}=\dfrac{2}{6}

\text{Scale factor}=\dfrac{1}{3}

Therefore the scale factor is \dfrac{1}{3}.

Kazeer [188]2 years ago
5 0

Answer:

1/3

Step-by-step explanation:

Correct on edge!

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The probability that an appliance is in repair is 0.8. if an apartment complex has 100 such appliances, what is the probability
AleksandrR [38]

Answer:

P(X\geq90) =0.00878

Step-by-step explanation:

This situation can be modeled by a binomial distribution of parameters:

p = 0.8\\\\q = 0.2\\\\n = 100

We want to find the probability that at least 90 are in repair.

<u><em>We can approximate this problem to a normal distribution, where:</em></u>

\mu = np

\mu = 80

\sigma = \sqrt{npq}\\\\\sigma = 4

Then we look for

P(X\geq90) = P(X>90 -0.5)\\\\P(X\geq90) = P(X>89.5)

Then we must find the normal standard statistic Z-score

Z = \frac{X-\mu}{\sigma}

Therefore:

P(X>89.5) = P(\frac{X-\mu}{\sigma}>\frac{89.5-80}{4})\\\\P(X>89.5) =P(Z>2.375)

Looking in the standard normal table we obtain:

P(Z>2.375) = 0.00878

8 0
2 years ago
What is the approximate length of arc s on the circle below? Use 3.14 for Pi. Round your answer to the nearest tenth.
slega [8]

Answer:

The approximate length of arc s is 14.1 inches

Step-by-step explanation:

<u><em>The picture of the question in the attached figure</em></u>

step 1

Find the circumference of the circle

The formula to calculate the circumference is equal to

C=2\pi r

we have

r=6\ in\\\pi=3.14

substitute

C=2(3.14)(6)\\C=37.68\ in

step 2

Find the approximate length of arc s

we know that

The circumference of a circle subtends a central angle of 360 degrees

so

using proportion

Find the arc length s for a central angle of 135 degrees

\frac{37.68}{360}=\frac{x}{135}\\\\x=37.68(135)/360\\\\x= 14.1\ in

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2 years ago
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Answer:


Step-by-step explanation:

The area of solutions of the first inequality lies above an orange straight line.

The area of solutions of the second inequality lies below a blue straight line.

These areas are crossed in the yellow field.

The green field does not meet a condition of the second inequality and therefore does not enter the area of the solution of a system of inequalities

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2 years ago
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Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24. Jeana shops at a different store and buys sev
Brilliant_brown [7]

Answer:

If both Kelsey and Jeana purchase 6 pairs of uniform pants then they would pay the same amount for their purchases.

Step-by-step explanation:

The information provided is as follows:

  • Kelsey buys several pairs of uniform pants for $17.95 each, and a sweater for $24.
  • Jeana shops at a different store and buys several pairs of uniform pants for $18.95 each, plus a sweater for $18.

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Thus, if both Kelsey and Jeana purchase 6 pairs of uniform pants then they would pay the same amount for their purchases.

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Answer:

Different timings for drinking before the run can decrease the accuracy of the outcome.

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