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1 year ago

Given: FPST is a trapezoid, FP=ST, m∠F=45°, PF=8, PS=10 Find: The midsegment MN.

Mathematics

1 answer:

kodGreya [7K]1 year ago

8 0

Answer:

$4\sqrt{2}+10$

Step-by-step explanation:

In trapezoid FPST, FP=ST, then this trapezoid is isosceles, so

$m\angle F=m\angle T=45^{\circ}.$

Draw the height PH. Triangle FPH is right triangle with two angles of measure 45°. This means that FH=HP. By the Pythagorean theorem,

$FH^2+PH^2=PF^2,\\ \\2FH^2=8^2,\\ \\FH^2=32,\\ \\FH=4\sqrt{2}.$

Since trapezoid FPST is isosceles, the base FT hasthe length

$FT=2FH+PS=8\sqrt{2}+10.$

Then the length of the midline is

$MN=\dfrac{FT+PS}{2}=\dfrac{8\sqrt{2}+10+10}{2}=4\sqrt{2}+10.$

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2 years ago

The statement tan theta -12/5, csc theta -13/5, and the terminal point determined by theta is in quadrant 2."

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Answer:

Answer C:

Cannot be true because $csc(\theta)$ is greater than zero in quadrant 2.

Step-by-step explanation:

When the csc of an angle is negative, since the cosecant function is defined as:

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Therefore, the correct answer is:

Cannot be true because $csc(\theta)$ is greater than zero in quadrant 2.

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2 years ago

Say a certain service industry has 78.9 thousand jobs in 2003, but expects to increase at an average annual rate of 2.65 thousan

Alex_Xolod [135]

Answer:

33%

Step-by-step explanation:

In 2003, there were 78.9 thousand jobs in the industry and it increases annually by 2.65 thousand jobs from 2003 to 2013.

Hence, from 2003 to 2013, i.e. 10 years the jobs have increased by (2.65×10) = 26.5 thousand.

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1 year ago

Choose the table that represents g(x) = −2⋅f(x) when f(x) = x + 4.

grigory [225]

Answer: THIRD OPTION.

Step-by-step explanation:

Since $g(x) = -2f(x)$ , then $g(x)$ is:

$g(x)=-2( x + 4)\\\\g(x)=-2x-8$

In order to find which table represents $g(x) = -2f(x)$ when $f(x) = x + 4$ , you can follow these steps:

1. Substitute $x=1$ into the function $g(x)=-2x-8$ :

$g(1)=-2(1)-8\\\\g(1)=-10$

2. Substitute $x=2$ into the function $g(x)=-2x-8$ :

$g(2)=-2(2)-8\\\\g(2)=-12$

3. Substitute $x=3$ into the function $g(x)=-2x-8$ :

$g(3)=-2(3)-8\\\\g(3)=-14$

Notice that those ouput values (for $x=1,\ x=2$ and $x=3$ ) matches with the table provided in the third option. That table represents $g(x) = -2f(x)$ when $f(x) = x + 4$ :

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1 year ago

Read 2 more answers

When you select a random person, the probability that this person will go to Ches

insens350 [35]

Answer: a= 0.0231

Step-by-step explanation:

n=8

p=0.75

q=1 - 0.75 = 0.25

(p=x)

p(5) = 8C5 (0.25)^5 (0.75)^8-5

p(5)= 0.0231

Or 2.31%

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1 year ago