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2 years ago

Consider the line segment below that is five feet long. Is Q the midpoint of PR? Justify your answer.

Mathematics

1 answer:

givi [52]2 years ago

4 0

Answer:

Q is not the midpoint of PR

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If Q is the midpoint of PR

then

PQ=QR

substitute the given values and solve for x

$15x-2=5x+3\\15x-5x=3+2\\10x=5\\x=0.5$

Remember that

$PR=5\ ft$ ----> given problem

$PR=PQ+QR\\PR=(15x-2)+(5x+3)$

substitute the value of x

$PR=(15(0.5)-2)+(5(0.5)+3)$

$PR=(5.5)+(5.5)$

$PR=11\ ft$

Compare with the given value of PR

$5\ ft\neq 11\ ft$

therefore

Q is not the midpoint of PR

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man drove his car a distance of 315 miles in 5 hours. If continuing at this rate is possible, he will travel ____ miles in 9 hou

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Answer:

567

Step-by-step explanation:

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2 years ago

The figure below shows the dimensions of a city park in feet. Shannon thinks the area of city park is 73,084 square feet. Do you

Andreyy89

Answer:

We need to solve for the 4th side

4th side base = 75.5 -60.5 = 10 feet

4th side height = 16

4th side LENGTH^2 = 10^2 + 16^2

4th side = sq root (356) = 18.8679622641

Trapezoid Area = [(sum of the bases) / 2 ] * height

Trapezoid Area = [(136)/2] * 16

Trapezoid Area = 1,088 square feet, which is MUCH smaller

than 73,084

Step-by-step explanation:

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1 year ago

If the heights of 300 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many studen

Lunna [17]

Given:
μ = 68 in, population mean
σ = 3 in, population standard deviation

Calculate z-scores for the following random variable and determine their probabilities from standard tables.

x = 72 in:
z = (x-μ)/σ = (72-68)/3 = 1.333
P(x) = 0.9088

x = 64 in:
z = (64 -38)/3 = -1.333
P(x) = 0.0912

x = 65 in
z = (65 - 68)/3 = -1
P(x) = 0.1587

x = 71:
z = (71-68)/3 = 1
P(x) = 0.8413

Part (a)
For x > 72 in, obtain
300 - 300*0.9088 = 27.36

Answer: 27

Part (b)
For x ≤ 64 in, obtain
300*0.0912 = 27.36

Answer: 27

Part (c)
For 65 ≤ x ≤ 71, obtain
300*(0.8413 - 0.1587) = 204.78

Answer: 204

Part (d)
For x = 68 in, obtain
z = 0
P(x) = 0.5
The number of students is
300*0.5 = 150

Answer: 150

3 0

2 years ago

Lin knows that there are 4 quarts in a gallon. She wants to convert 6 quarts to a gallon, but cannot decide if she should multip

defon

Given:

There are 4 quarts in a gallon.

She wants to convert 6 quarts to a gallon.

To find:

Whether she should multiply 6 by 4 or divide 6 by 4 to find her answer.

Solution:

We have,

$4\text{ quarts}=1\text{ gallon}$

$1\text{ quarts}=\dfrac{1}{4}\text{ gallon}$

$6\text{ quarts}=\dfrac{6}{4}\text{ gallon}$

Here, 6 quarts is equal to $\dfrac{6}{4}$ gallon. It means we need to multiply 6 by 4 in $4\text{ quarts}=1\text{ gallon}$ to find the answer.

5 0

2 years ago

A 12-centimeter rod is held between a flashlight and a wall as shown. Find the length of the shadow on

choli [55]

Answer:

48 cm

Step-by-step explanation:

Given:

Distance of rod from the wall = 45 cm

Distance of rod from the light = 15 cm

Length of rod = 12 cm

We can see that <DAM and <BAF are equal

Also, <DMA and <BFM are equal because they are corresponding angles

To find the length of the shadow, let's take the equation

$\frac{DM}{BF} = \frac{AM}{A.F}$

Where.:

DM = ½ of length of the rod = ½*12 = 6

A.F = 15 + 45 = 60 cm

AM = 15 cm

Therefore,

$\frac{DM}{BF} = \frac{AM}{A.F}$

$= \frac{6}{BF} = \frac{15}{60}$

Cross multiplying, we have:

15 * B.F = 60 * 6

15 * B.F = 360

$BF = \frac{360}{15}$

BF = 24 cm

The shadow on the wall =

2 * BF

= 2 * 24

= 48 cm

The shadow on the wall is 48 cm

7 0

1 year ago