Can the numeric value for the area of a circle ever equal the numeric value for the circumference of the same circle? Explain

Given: ST ║ RP , SD ⊥ PR , SP = TR, SD = 5, ST = 15, PR = 24 Find: m∠P, m∠PST, m∠T, m∠R, PS, TR

makkiz [27]

Answer:

Part 1) $m\angle P=48.01^o$

Part 2) $m\angle PST=131.99^o$

Part 3) $m\angle T=131.99^o$

Part 4) $m\angle R=48.01^o$

Part 5) $PS=\sqrt{45.25}\ units$ , or $PS=6.7\ units$

Part 6) $TR=\sqrt{45.25}\ units$ , or $TR=6.7\ units$

Step-by-step explanation:

see the attached figure to better understand the problem

In this problem we have an isosceles trapezoid

Part 1) Find the measure of angle P

Find the value of side PD

we have that

$PR=PD+ER+ST$ ---> by addition segment postulate

$PD=ER$ ----> by isosceles trapezoid

so

$PR=2PD+ST\\PD=(PR-ST)/2$

substitute the given values

$PD=(24-15)/2$

$PD=4.5\ units$

In the right triangle PSD

$tan(P)=\frac{SD}{PD}$

$P=tan^{-1}(\frac{SD}{PD})$

substitute the given values

$m\angle P=tan^{-1}(\frac{5}{4.5})$

$m\angle P=48.01^o$

Part 2) Find the measure of angle PST

we know that

In a trapezoid ST ║ RP

so

$m\angle P+m\angle PST=180^o$ ---> by consecutive interior angles

we have

$m\angle P=48.01^o$

substitute

$48.01^o+m\angle PST=180^o$

$m\angle PST=180^o-48.01^o$

$m\angle PST=131.99^o$

Part 3) Find the measure of angle T

we know that

In this problem we have an isosceles trapezoid

so

$m\angle T=m\angle S$

we have

$m\angle PST=m\angle S=131.99^o$

therefore

$m\angle T=131.99^o$

Part 4) Find the measure of angle R

we know that

In this problem we have an isosceles trapezoid

so

$m\angle R=m\angle P$

we have

$m\angle P=48.01^o$

therefore

$m\angle R=48.01^o$

Part 5) Find the measure of segment PS

we know that

In the right triangle PSD

Applying the Pythagorean Theorem

$PS^2=SD^2+PD^2$

substitute the given values

$PS^2=5^2+4.5^2$

$PS^2=45.25$

$PS=\sqrt{45.25}\ units$

$PS=6.7\ units$

Part 6) Find the measure of segment TR

we know that

TR=PS ---> by isosceles trapezoid

we have

$PS=\sqrt{45.25}\ units$

therefore

$TR=\sqrt{45.25}\ units$

$TR=6.7\ units$

3 0

4 years ago

Which algebraic expression is equivalent to the expression below?

natka813 [3]

Simple....

you have 7(5x+3)+3(12-x)....

just take them apart....

7(5x+3)

distribute the 7...

7*5x=35x
and
7*3=21

Now, the other part...

3(12-x)

Distribute the 3...

3*12=36
and
3*-x=-3x

Now, add what you have found....

35x+21+36-3x

32x+57

Thus, your answer, A.

8 0

4 years ago

Tôi cần mọi người giúp :tìm m để delta > 00

Papessa [141]

Answer:

Salamat po thank you for your success as a result

5 0

3 years ago

A line has a slope of 8 and includes the points (1, z) and (2,8). What is the value of z?

NISA [10]

The value of z is zero

Step-by-step explanation:

The slope is the steepness of the line.

The formula for slope is given by:

$m=\frac{y_2-y_1}{x_2-x_1}\\Here\\(x_1,y_1)\ are\ the\ coordinates\ of\ first\ point\ on\ line\\(x_2,y_2)\ are\ the\ coordinates\ of\ second\ point\ on\ line$

Here

(x1,y1) = (1,z)

(x2,y2) = (2,8)

So,

$m=\frac{y_2-y_1}{x_2-x_1}\\8 = \frac{8-z}{2-1}\\8=\frac{8-z}{1}\\8-8 = -z\\z = 0$

The value of z is zero

Keywords: slope, Line

Learn more about slope at:

#LearnwithBrainly

6 0

3 years ago

(4z³ – 5z + 2)6z product

Colt1911 [192]

Answer:

24z^4-30z^2+12z

Step-by-step explanation:

hope this helps :)

6 0

4 years ago