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3 years ago

Given the median QR and trapezoid MOPN, what is the value of x?

Mathematics

1 answer:

EleoNora [17]3 years ago

8 0

Answer:

D. 5

Step-by-step explanation:

Based on the midsegment theorem of a trapezoid, thus:

QR = ½(OP + MN)

Substitute

27 = ½((5x - 7) + (6x + 6))

27 = ½(5x - 7 + 6x + 6)

Add like terms

27 = ½(11x - 1)

Multiply both sides by 2

2*27 = 11x - 1

54 = 11x - 1

54 + 1 = 11x

55 = 11x

55/11 = x

5 = x

x = 5

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a student either knows the answer or guesses. Let 3434 be the probability that he knows the answer and 1414 be the probability t

Arlecino [84]

Answer: $\dfrac{12}{13}$

Step-by-step explanation:

Let A = he known the answer then A' = he guess the answer.

B = he answered it correctly

As per given , we have

$P(A)=\dfrac{3}{4}\ \ ,\ \ P(A')=\dfrac{1}{4}$

$P(B|A)=1$

$P(B|A')=\dfrac{1}{4}$

By Bayes theorem , we have

$P(A|B)=\dfrac{P(B|A)P(A)}{P(B|A)P(A)+P(B|A')P(A')}\\\\ P(A|B)=\dfrac{1\times\dfrac{3}{4}}{1\times\dfrac{3}{4}+\dfrac{1}{4}\times\dfrac{1}{4}}\\\\= \dfrac{12}{13}$

The probability that the student knows the answer given that he answered it correctly is $\dfrac{12}{13}$ .

6 0

3 years ago

Trigonometric identities assignment 4

kykrilka [37]

Answer:

Answer: choice D.

Step-by-step explanation:

Trigonometric Functions

We need to recall some properties and definitions of the trigonometric functions.

$\displaystyle \tan \theta=\frac{\sin\theta}{\cos\theta}$

$\displaystyle \sec \theta=\frac{1}{\cos\theta}$

We need to simplify the following expression:

$5\sin\theta\sec\theta$

Substituting the identity for the secant:

$\displaystyle 5\sin\theta\sec\theta=5\sin\theta.\frac{1}{\cos\theta}$

Operating:

$\displaystyle 5\sin\theta\sec\theta=5\frac{\sin\theta}{\cos\theta}$

Substituting the definition of the tangent:

$\displaystyle 5\sin\theta\sec\theta=5\tan\theta$

Correct choice D.

6 0

3 years ago

PLEASE HELP ME ! IMAGE IS BELOW IF YOU GET IT RIGHT I'LL MARK BRAINLIEST

jarptica [38.1K]

Answer:

x = 17

y = 8

QPR = 35º

QRP = 60º

Step-by-step explanation:

2x + 1 = x + 18

Subtract x from both sides

x + 1 = 18

Subtract 1 from both sides

x = 17

QPR = 2x + 1

QPR = 2(17) + 1

QPR = 35º

-------------------------------

8y - 4 = 4y + 28

Subtract 4y from both sides

4y - 4 = 28

Add 4 to both sides

4y = 32

Divide both sides by 4

y = 8

QPR = 8y - 4

QRP = 8(8) - 4

QRP = 60º

7 0

3 years ago

Find the solution of the system of equations. 3x – 3y = 18 3x – 8y = -2

Oksi-84 [34.3K]

Answer:

x=10, y=4

Step-by-step explanation:

3x-3y=18

(-)3x-(-)8y=-(-)2 -3x+8y=2 add to first equation to eliminate x

5y=20

y=4

substitute y with 4

3x-3(4)=18

3x=30

x=10

x=10,y=4

5 0

3 years ago

A company that manufactures small canoes has a fixed cost of $24,000. It costs $100 to prod canoes produced and sold.) a. Write

sweet-ann [11.9K]

Answer:

a. C(x) = 24,000 + 100x

b. R(x) = 200x

c. Break-even point is 240 canoes

Step-by-step explanation:

a. Cost function is C(x) = FC + pcost * x

C(x) = 24,000 + 100x

Where

FC=Fixed cost = 24,000

pcost=costs to prod canoes = $100

x=produce quantity

b.Revenue function

R(x) = Px * x

R(x) = 200x

Where

Px=Price

x=produce quantity

c. Break-even point is the amount of canoes where revenue are the same as cost. We cover the total cost with the sales.

So, FC + pcost * x=Px * x

24,000 + 100x=200x

Isolating x

24,000 =200x- 100x

100x=24000

x=24,000/100

x=240

3 0

3 years ago