MATHEMATICS HIGH SCHOOL

Select all of the terms that are "like."a. xy 2
b. 2xy
c. x 2
d. -xy
e. 2x 2y
f. xy

Answers

Answer 1
Answer:

Final answer:

The terms that are 'like' are: 2xy, -xy, and xy.

Explanation:

In mathematics, like terms are expressions that have the same variables raised to the same powers. When adding or subtracting like terms, you can combine them by adding or subtracting their coefficients while keeping the variables and exponents unchanged. This simplifies algebraic expressions and equations, making them easier to work with. For example, in the expression "3x + 2y - 5x + 7y," "3x" and "-5x" are like terms because they both have the variable "x" raised to the first power, so they can be combined to simplify the expression as "(-2x) + 2y + 7y."

The terms that are 'like' are: b. 2xy, d. -xy, and f. xy. To be 'like' terms, they must have the same variables raised to the same powers. In this case, all three terms have the variables x and y raised to the power of 1. The coefficients (the numbers multiplied by the variables) can be different. For example, 2xy, -xy, and xy are all 'like' terms because they have the same variables raised to the power of 1.

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Answer 2
Answer:

Final answer:

In mathematics, like terms are terms that have the same variables and powers. In this case, the like terms are '2xy', '-xy', and 'xy' as they have the same variable part 'xy'.

Explanation:

In mathematics, like terms are terms whose variables have the same powers. The coefficients of these terms do not matter. Coefficients are the number part of the terms, while the variable part are the letters.

Looking at the options:

  • a. xy^2
  • b. 2xy
  • c. x^2
  • d. -xy
  • e. 2x^2y
  • f. xy

In these options, b. 2xy, d. -xy, and f. xy are like terms; they all have the same variable part 'xy'. The coefficients are different, but this does not affect their classification as like terms.

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At a constant rate of flow, it takes 20 minutes to fill a swimming pool if a large hose is used and 30 minutes if a small hose is used. At these constant rates, how many minutes will it take to fill the pool when both hoses are used simultaneously?
The cost, in dollars, of parking a car in a busy downtown area for h hours is $10 + $3h.Which statement is correct?A. For every hour the car is parked, the cost increases by $10.B. For every hour the car is parked, the cost increases by $7.C. For every hour the car is parked, the cost increases by $13.D. For every hour the car is parked, the cost increases by $3.
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A function f (x)=-8x^2. What is f (-3)?

Answers

f(x) = -8x²

To find the value of f(-3), put -3 in place of 'x' in the definition of the function.

f(-3) = -8(-3)²

f(-3) = -8(9) = -72
f(x)= -8x²

f(-3)= -8* (-3)²

f(-3)= -8 * 9

f(-3)= -72

Julia is saving money for the down payment on a car. She plans to save for one year. Her parents have offered to contribute $50 a month to her savings. How much does Julia need to save each month in addition to her parents' contribution if she wants to have a $2700 down payment on a car at the end of the year? Define a variable and write an equation to represent this situation.

Answers

Answer:

12x+600=2700

$175

Step-by-step explanation:

Let x represent money saved by her in one month.

So money saved by her in one year (12 months) would be 12x.

We can represent our given information as:

12x+600=2700\n12x=2700-600\n12x=2100\nx=(2100)/(12)\nx=175

Therefore, she needs to save $175 per month.

Simplify a × 3a3b.

A. 6a4b2
B. 2a4b7
C. 4a2b2
D. 3a4b

Answers

Answer:

D. 3a^4b

Step-by-step explanation:

We have: a.3a^3b in order to simplify this expression, we have to apply the rule of the exponents.

This rule says that:

a^b.a^c=a^(^b^+^c^)

If you have the same base, the exponents can be added.

We can rewrite the expression a.3a^3b as 3(a.a^3)b

Then we have:

a.a^3=a^1.a^3=a^(^1^+^3^)=a^4

Finally:

a.3a^3b=3(a^4)b=3a^4b

The correct option is D.
Use:a^n\cdot a^m=a^(n+m)\n\na\cdot3a^3b=3a^(1+3)b=3a^4b\n\nAnswer:\boxed{D.\ 3a^4b}

What is the circumference of a circle that has a radius of 10 centimeters? Round your answer to one decimal place. C = a0 cm

Answers

Answer:  62.8 centimeters

Step-by-step explanation:

We know that the circumference of a circle is given by :_

\text{Circumference}=2\pi r, where r is the radius of the circle.

Given : The radius of the circle : r= 10 centimeters.

Then , the circumference of the circle is given by :-

\text{Circumference }=2(3.14)(10)\n\n\Rightarrow\ \text{Circumference }=62.8\ cm

Hence, the circumference of the circle = 62.8 centimeters
C=2*3.14*10=20*3.14=62.8cm

A textbook company will ship a box of textbooks to college students. The weight of the box in pounds can be determined by the function w(x) = 7.5x + 2, where x is the number of textbooks in the box. The company requires a student to order at least 2 books but not more than 6 books. What is the range of the function for this situation? *A. 2 ≤ x ≤ 6
B. 17 ≤ y ≤ 47
C. {17, 24.5, 32, 39.5, 47}
D. {2, 3, 4, 5, 6}

Answers

The range of the function for this situation is 17 ≤ w ≤ 47

An equation is an expression used to show the relationship between two or more variables.

Let x represent the number of textbooks in the box

The company requires a student to order at least 2 books, hence:

x ≥ 2.

w(2) = 7.5(2) + 2 = 17

Also they do not require more than 6 books, hence:

x ≤ 6

w(6) = 7.5(6) + 2 = 47

The range of a function is the set of possible dependent variables.

Hence, the range of the function for this situation is 17 ≤ w ≤ 47

Find out more on range at: brainly.com/question/14145389

Answer:

I think its D

Step-by-step explanation:

It's obviously not A, because A has an x instead of y. B makes no sense because the range is 2-6. C makes no sense. D is the only logical answer.

Point O is between points G and D on line m. Which of the following statements is not necessarily true?a. O, G and D are collinear.
b. O, G and D are coplanar.
c. GO + OD = GD
d. GO = OD

Answers

Answer: d. GO = OD

Step-by-step explanation:

Given: Point O is between points G and D on line m.

It means that they are on same line m.

We know that collinear points are the points lie in the same line.

Hence O, G and D are collinear.

Also, coplanar points are the points lie in the same plane.

Since if three points are collinear, then they are coplanar.

Therefore, O, G and D are coplanar.

The statement which is not necessarily true is d. GO = OD because it is not given that o lies exactly middle to points G and D.
c. GO + OD = GD

hope this helps
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