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2 years ago

The sum of two prime numbers is 85. What is the product of these two prime numbers?

1 answer:

6 0

Observe that 85 is an odd number. That means, one of the prime numbers must be even to have an odd sum with another odd number. As we know, the only even prime number is 2. Hence, the other number is 83. So, the product of these two prime numbers is 83 x 2 = 166. Thus, the answer is 166<span>. </span>

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What is a radius in geometry, and what are some examples of it?

mixer [17]

A radius is a straight line from the centre to the edge of a circle. i’m not sure about any examples sorry :/

6 0

2 years ago

Question Number 22 You work for a company that manufactures large tarps used for groundcover. An order was placed for a rectangu

Colt1911 [192]

Answer: the area of the finished tarp is 131872 square inches

Step-by-step explanation:

Search strip of tarp is rectangular. The formula for determining the area of a rectangle is expressed as

Area = length × width

An order was placed for a rectangular tarp that will be made up of 8 strips of fabric. Each strip is 26 inches wide and 634 feet long. The area of each strip of tarp is

Area = 26 × 634 = 16484 square inches

Therefore, the area of the finished tarp would be

8 × 16484 = 131872 square inches

4 0

3 years ago

Which of these sets of ordered pairs would define a line with a positive slope?

Serhud [2]

The correct answer is D

8 0

2 years ago

Pls help me divide this radical and pls show work

Alenkinab [10]

Let's start by rationalizing the radical:

4√6/√50 * √50/√50

This gets rid of the radical in the denominator, giving us:

4√300/50

√300 can be simplified to √3 * √100 or 10√3. Now we can insert this back into the numerator:

4 * 10√3/50

This is equivalent to:

40√3/50

40/50 can be simplified to 4/5.

Therefore, the answer is 4√3/5.

5 0

3 years ago

Need help, please kfvleknfv

omeli [17]

Problem 18

Answers:

~P -> Q: "if it is not fall, then the leaves change colors"

~P -> ~Q: "if it is not fall, then the leaves don't change colors"

P -> ~Q: "If it is fall, then the leaves don't change colors"

Q -> ~P: "If the leaves change colors, then it is not fall"

----------

Explanation:

Simply replace each letter with the corresponding definition. We replace each P with "it is fall" and each ~P with "it is not fall". The squiggly line means "not". The same idea applies with Q and ~Q.

==========================================

Problem 19

Answer: Choice A) 134

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Explanation:

AB = CD

8x = 4x+24

8x-4x = 24

4x = 24

x = 6

BC = 18x+26

BC = 18*6+26

BC = 134

==========================================

Problem 20

Answer: Choice C) x = 5 and y = 11

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Explanation:

(anglePQR)+(angleRQS) = 90

(12x-2)+(6x+2) = 90

18x = 90

x = 5

angle TQU = 90

10y-20 = 90

10y = 110

y = 11

==========================================

Problem 21

Answer: 99

----------

Explanation:

The remote interior angles add to the exterior angle (remote interior angle theorem)

(angle RPQ) + (angle PQR) = angle PRS

(3x-29) + (7x-42) = 6x-3

10x-71 = 6x-3

10x-6x = -3+71

4x = 68

x = 68/4

x = 17

angle PRS = 6x-3

angle PRS = 6*17-3

angle PRS = 99

==========================================

Problem 22

Answer: 116

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Explanation:

Refer to the diagram below.

Solve 105+x = 180 to get x = 75

Solve 135+y = 180 to get y = 45

Solve x+y+z = 180 to get z = 60

Solve z+82+p = 180 to get p = 38

Solve p+78+q = 180 to get q = 64

Solve q+r = 180 to get r = 116

==========================================

Problem 23

Answer: B) between 4 and 44 inches

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Explanation:

We use a variation of the triangle inequality theorem here.

If p is the missing side length, then

24-20 < p < 24+20

4 < p < 44

So,

4 < XY < 44

The side XY cannot be 4 inches and it cannot be 44 inches either.

==========================================

Problem 24

4 Answers: A, B, C, D

----------

Explanation:

Same idea as problem 23

24-10 < x < 24+10

14 < x < 34

So we'll select values between 14 and 34, excluding each endpoint. Those values are x = 16, 18, 24, 26

In other words, only 12 and 34 are non-answers.

==========================================

Problem 25

Answer: C) 84 degrees

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Explanation:

The given exterior angle is 152 degrees

Subtract that from 180 to get the adjacent interior angle 180-152 = 28

Now let's find the missing angle of triangle DEB

D+E+B = 180

28+68+B = 180

96+B = 180

B = 180-96

B = 84

This is the measure of angle DBE

This is also the measure of angle ABC because the two angles are vertical angles.

Vertical angles are always congruent.

4 0

3 years ago