MATHEMATICS COLLEGE

Look at the set of ordered pairs.{(4, 6), (−7,−15), (13, 15), (−21, 8), (?, ?)}

Which of the following could replace the missing ordered pair to make the set not a function?

(−2, 4)
(21, 9)
(−7, 15)
(6, 8)
(13,−15)

Answers

Answer 1
Answer:

The ordered pair that could replace the missing ordered pair to make the set not a function is given as follows:

(−7, 15).

When does a set of ordered pairs represent a function?

A set of ordered pairs represents a function if every input (first component of the ordered pair) is associated with exactly one output (second component of the ordered pair). In other words, if no two ordered pairs in the set have the same first component but different second components.

Hence the ordered pair (-7,15) would make the relation not a function, as the set already has the ordered pair (-7,-15), in which the input 7 is already mapped to an output of -15, hence it cannot be mapped to an output of 15.

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A hole is punched in a piece of metal to make a part for a machine. What is the area of the metal part, or the shaded region shown?

Answers

The area of the metal part, or the shaded region shown is 10x + 45.

calculation:

= (x+ 7)^2 - (x-2)^2\n\n= (x^2 + 14x + 49) - (x^2 - 4x + 4)\n\n= (14 - 4)x + (49 - 4)

= 10x + 45

Learn more about the area here; brainly.com/question/17064026

Answer:

The area of the metal part or shaded area is S=10x+45.

Step-by-step explanation:

The shaded area can be calculated substracting the little square area (the hole) from the big square area (the original metal part).

This is:

S=S_(original)-S_(hole)=(x+7)^2-(x-2)^2\n\nS=(x^2+14x+49)-(x^2-4x+4)\n\nS=(14-4)x+(49-4)\n\nS=10x+45

The area of the metal part or shaded area is S=10x+45.

Express M=cos3A + cos A and N = sin3A + sin A as a product form​

Answers

Answer:

2cosAcos2A, 4sinAcos^2A

Step-by-step explanation:

cos3A+cosA

2cos((3A+A)/2)cos((3A-A)/2)

2cos(4A/2)cos(2A/2)

2cosAcos2A

sin3A+sinA

2sin((3A+A)/2)cos((3A-A)/2)

2sin(4A/2)cos(2A/2)

2sin2AcosA

4sinAcos^2A

Combine the like terms to create an equivalent expression. 7z + 15 + 2

Answers

Answer: 7z + 17

Step-by-step explanation: add 15 and 2

8 Line in the xy-plane contains points from each of Quadrants II, III, and IV, but no points from Quadrant I. Which of the following must be true? A) The slope of line is undefined. B) The slope of line is zero. C) The slope of line is positive. D) The slope of line is negative. CONTINUE

Answers

Answer:

The correct option is D.

Step-by-step explanation:

The slope of a line is the change in y with respect to x.

m=(y_2-y_1)/(x_2-x_1)

If the slope of a line is undefined it means it is a vertical line and a vertical line  can not passes through three quadrants. So, option A is incorrect.

If the slope of a line is 0 it means it is a horizontal line and a horizontal line  can not passes through three quadrants. So, option B is incorrect.

If the slope of a line is positive it means the value of y increases as x increases.

Since it is an increasing line, therefore after a certain period both x and y will positive. It means the line will passes through first quadrant. So, option C is incorrect.

If the slope of a line is negative it means the value of y decreases as x increases. It can passes through each of Quadrants II, III, and IV.

Therefore the correct option is D.

Please hurry

Solve for t: 5t - 4 = 11

Answers

Answer:

t=3

Step-by-step explanation:

5t-4=|11

+4 |+4

5t= | 15

÷5 | ÷5

t = 3

Instead of having a cake, Ruben wants to make ice cream sundaes at his next birthday party.He thinks each person will eat 2 cups of ice cream, and there will be 24 people at his party.
How many 1-gallon tubs of ice cream should he buy?
tubs

Answers

Final answer:

Ruben should buy 3 tubs of ice cream for his party.

Explanation:

To find the number of 1-gallon tubs of ice cream Ruben should buy, we need to determine the total amount of ice cream needed and then divide by the capacity of each tub. Since each person will eat 2 cups of ice cream and there will be 24 people at the party, the total amount of ice cream needed is 2 cups/person x 24 people = 48 cups. To convert cups to gallons, we divide by the number of cups in a gallon, which is 16. So, 48 cups ÷ 16 cups/gallon = 3 gallons. Therefore, Ruben should buy 3 tubs of ice cream for his party.

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Answer:

he should buy 3 gallons

Step-by-step explanation:

There are 16 cups in a gallon, and if each person will eat 2 cups, and there are 24 ppl, multiply 24 by 2 to get the number of cups.

24 x 2 = 48.

Then, divide that by 16 (the number of cups in a gallon) to t how many gallons.

48 ÷ 16 = 3

so, he needs 3 gallons

hope this helped!  
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