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3 years ago

Two consecutive positive integers have a product of 132. what are the integers?

1 answer:

3 0

$x(x+1)=132\implies x^2+x-132=(x-11)(x+12)=0$

If $x>0$ , that leaves you with $x=11$ , and so the two integers are 11 and 12.

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The sum of two numbers is 64. One number is 8 more than the other. What are the two numbers?

lisabon 2012 [21]

Answer:

28 and 36.

Step-by-step explanation:

Alright, so we are given that the sum of two numbers is 64. Based on this, we know that we are going to be adding because the question said "the sum of two numbers is 64." Sum is the answer to an addition problem. Lets write an equation.

We need a variable, let x be the variable which is the value of the smaller number.

the equation is x+x+8=64

x= to the smaller number

x+8= to the number that is eight more than x or the smaller number.

Before we isolate for x, we need to simplify the expression by combining the like terms.

x plus x equals 2x.

Therefore, we have 2x+8=64.

Our goal is to isolate x, so we need to subtract 8 from both sides. 8 mius 8 is 0, and 64 mius 8 is 56.

Now, we have 2x=56.

We still need to isolate x by dividing both sides by 2. 2 divided by 2 is 1, so we are left with 1x or x. 56 divided by 2 is 28.

x=28.

Great, we found what x or the smaller value is.

Now, we need to find the larger number.

Substitute x as 28 into x+8 to find the number that is 8 more than the smaller number or x. You'll then get 36. If you add 36 and 28, you get 64. Also, 36 is 8 more than 28, so this answer is correct.

Hope this helps!

4 0

3 years ago

Find the sum of 7a³ + 14a + 12 and -6a³ + 12a² -7

maw [93]

Answer: $a^3+12a^2+14a+5$

Step-by-step explanation:

$7a^3+14a+12+(-6a^3+12a^2-7)$

$7a^3+14a+12-6a^3+12a^2-7\\a^3+12a^2+14a+5$

7 0

3 years ago

Eric has 4 pieces of clay he cut out each piece of clay into thirds how many 1/3 size pieces of clay does Eric have

Ivahew [28]

Answer:

ERIC HAD 12 PIECES OF CLAY LEFT

Step-by-step explanation:

1/3 + 4 = 12

4 0

3 years ago

Three of these expressions are equal to the volume of the barn shown. Which expression is not?

timurjin [86]

The statement that does not match the others is the one at lower right.

_____

The barn's volume can be decomposed into a rectangular prism and a triangular one. Thus the upper right expression is a true represenation of the barn's volume:

... Volume of triangular prism + Volume of rectangular prism

The volume of a rectangular prism is the product of its dimensions. The dimensions of the rectangular prism portion of the barn's volume are a, b, c, so the volume of that portion is ...

... Volume of rectangular prism = a·b·c

The volume of a triangular prism is the area of the triangular base multiplied by the length of the prism. Here, the triangular base has base dimension b and height (d-c), so its area is ...

... Area of triangular barn end = (1/2)b(d-c)

Since the length of the barn is "a", the volume of the triangular prism is ...

... Volume of triangular prism = (1/2)b(d-c)a = (1/2)·a·b·(d-c)

The total volume is the sum of the volumes of the parts ...

... a·b·c + (1/2)·a·b·(d-c) . . . . . . matches the upper right selection

This can be factored by removing a·b to outside parentheses:

... a·b·((1/2)·(d-c) + c) . . . . . . . . . matches the lower left selection

___

Since the two left selections match the one at upper right, the odd one is the one at lower left.

7 0

3 years ago

Read 2 more answers

If xt = 3y -1 and us = 28, find the value of y

olga55 [171]

3y - 1 = 28
+ 1 + 1
----------------
3y = 29
---- ----
3 3
y= 9.66

8 0

3 years ago