Expand the following 3(x+9) 4(x-1) 5(5x+2) 8(3x-y)

Question 1) When multiplying powers with the same base, keep the base and _______________ the exponents.

nika2105 [10]

The rules are

$x^a\cdot x^b = x^{a+b}$

$\dfrac{x^a}{x^b} = x^{a-b}$

Let me show you why with a couple of examples: suppose we want to multiply

$4^3\cdot 4^2$

Since powers are just repeated multiplications, we have

$4^3\cdot 4^2 = \underbrace{4\cdot 4\cdot 4}_{4^3}\cdot\underbrace{4\cdot 4}_{4^2}=4^5 = 4^{3+2}$

Similarly, we have

$\dfrac{4^3}{4^2} = \dfrac{4\cdot 4 \cdot 4}{4\cdot 4} = 4 = 4^1 = 4^{3-2}$

8 0

2 years ago

The chorus at an elementary school is made up on fifth and sixth graders. This year, the chorus had 12 fifth-grade girls, 9 fift

klemol [59]

Answer:

A: 19:26 B:7:8 C:26:45

Step-by-step explanation:

Question A

First to find the ratio between the boys and girls you would add all of the different groups with boys and girls. This would be done by,

Boys

9+10=19

Girls

12+14=26

Now that you have the total number of boys and girls you make this ratio,

19:26

That is the final answer

Question B

For this it is very similar to the boys to girls ratio. You still add the total on each side and then form a ratio. From before you would start by adding both of the different sides which would be done by,

Fifth Graders

12+9=21

Sixth Graders

14+10=24

Now that you have the total number of both of the different grades you make this ratio,

21:24

You can simplify this by finding the lowest common factor which would be

7:8

Question C

To answer this it is very similar to the first two but instead you will find one group and all of the groups to form the ratio. Now you need to add all of the people in each of the groups.

Girls

12+14=26

All

12+9+14+10=45

Now with the total number of both you will form a ratio

26:45

This is your final answer because you cant simplify this any further

8 0

2 years ago

A venue plans to host trucking events regularly throughout the year. The expected revenue from each event is $100,000. The cost

NikAS [45]

Answer:

47 meetings

Step-by-step explanation:

1. You know the company generates 100,000 dollars in profits, and pays 50,000 dollars to host the event, therefore, subtract both numbers to determine how much profit they make.

100,000 - 50,000 = 50,000 dollars

2. You now know that company generates 50,000 dollars in profits for each meeting

3. You also know that the company is aiming for a profit of 2.35 million, so you would divide the the goal by the total profits per meeting

2,350,000/50,000 = 47

It takes 47 meetings for the company to reach their goal.

4 0

2 years ago

Factor 3/4 out of 3/4z + 6

Alenkasestr [34]

ANSWER

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 8 )$

EXPLANATION

We want to factor
$\frac{3}{4}$
out of

$\frac{3}{4} z + 6$

The first term is already having a factor of
$\frac{3}{4}$
The constant term which is the second term is not having a factor of
$\frac{3}{4}$
so we need to use a trick of multiplying and dividing by the same factor to obtain,

$\frac{3}{4} z + 6 = \frac{3}{4} z + \frac{3}{4} \times \frac{6}{ \frac{3}{4} }$

We can now factor
$\frac{3}{4}$
out of the right hand side to obtain,

$\frac{3}{4} z + 6 = \frac{3}{4} (z + \frac{6}{ \frac{3}{4} } )$
Let us rewrite the right most fraction using the normal division symbol.

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 6 \div \frac{3}{4} )$

We simplify to obtain,

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 6 \times \frac{4}{3} )$

This further gives us,

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 2 \times 4 )$

$\frac{3}{4} z + 6 = \frac{3}{4} (z + 8 )$

5 0

3 years ago

Read 2 more answers

Chantal is building a fence around her swimming pool. The pool is 25 ft long and12 ft wide, and she wants a 6-ft wide rectangula

Alex_Xolod [135]

25 /12*6 =12.5 or thats what i got

4 0

2 years ago