Directions: Determine the axiom that justifies each of the following statements.

1. 2( -a + 5) = (2)(-a) + (2)(5)

2. 2/5 ⋅ 1 = 2/5

3. (x + 5) + 2 = x + (5 + 2)


Answers

Answer 1

Answer:

distributive propertymultiplicative identity elementassociative property of addition

Step-by-step explanation:

1.

The distributive property of multiplication over addition tells you a factor outside parentheses will multiply each term inside parentheses. That fact is used to expand the given expression. In general, ...

  a(b +c) = ab +ac

  2(-a +5) = 2(-a) +2(5)

__

2.

The multiplicative identity element is the value that can multiply any expression and leave it unchanged. It is 1. That is, multiplying anything by 1 leaves it unchanged.

This fact is generally used to cancel factors common to a numerator and denominator: (2x)/2 = x(2/2) = x(1) = x, for example. It is also used extensively in units conversion.

__

3.

The associative property of addition lets you group the terms of a sum any way you like. It lets you move parentheses at will. (Beware subtraction.)

Here, the parentheses are moved from grouping the first two terms to instead grouping the last two terms.

_____

Additional comment

These are part of the vocabulary of math. Even if you don't remember the specific definitions, it is essential to remember what these properties allow. Making use of them is the way that expressions are simplified and equations are solved.

Answer 2

Answer:

Distributive Property of MultiplicationIdentity Property of MultiplicationAssociative Property of Addition

Step-by-step explanation:

Distributive Property of Multiplication

The distributive property of multiplication is to distribute or multiply one term by all terms.

2(-a + 5)     Distrbute 2 to -a and 52(-a) + 2(5)-2a + 10

Identity Property of Multiplication

Identity property is to multiply by 1. This doesn't change the value, so it keeps the value, identity, the same.

2/5 * 1 = 2/5

Associative Property of Addition

The associative property is to group terms differently, preferably like terms. 2 and 5 are like terms, because they are integers.

(x + 5) + 2x + (5 + 2)x + 10

-Chetan K


Related Questions

will deposited $1550 in an account that pays 8% annually. How much would be in the account at the end of 24 months? ​

Answers

Will will have $1798 I’m the account after 24 months.

Answer:

$1798

Step-by-step explanation:

You take the money of 1550 and multiply the 16% for the 2 years, which is just 1.16 and you get 1798

What is the equation of the line?

Answers

Answer: 5x + 4y - 6 = 0

Step-by-step explanation:

Find the slope of the line by finding 2 points that are on the line

(-2,4) and (2,-1)

(4--1)/(-2-2) = 5/-4

y = -5x/4 + c

Substitute (2,-1)

-1 = -10/4 + c

6/4 = c

So the equation is y = (6-5x)/4

4y = 6-5x

5x + 4y - 6 = 0

(Side note: So many people are asking about line equations)

Daniel and Saquon are each saving money.
Daniel starts with $50 in his savings account and adds $8 per week.
Saquon starts with $65 in his savings account and adds $5 each week.
QUESTION: After how many weeks will Daniel and Saquon have the same amount of money in their savings account?

Answers

It would take 5 weeks for their savings accounts to be equal.

Daniel starts with $50 and each week he adds $8. To find out the amount he has in any given week, the following formula would work:
= 50 + 8x
The x is the number of weeks and is multiplied by 8 because the amount of money he has increase by 8 every week.
After 4 weeks he would have:
= 50 + (8 * 4)
= 50 + 32
= $82
Saquon
Applying the same formula:
= 65 + 5x
After 4 weeks:
= 65 + (5 * 4)
= 65 + 20
= $85
Saquon has more money after 4 weeks.
Number of weeks it would take for both of them to have the same amount.
To find this out, equate both formulas and solve for x.
50 + 8x = 65 + 5x
8x - 5x = 65 - 50
3x = 15
x = 15/3
x = 5 weeks
At 5 weeks they will both have:
50 + 8 * 5 = $90
65 + 5 * 5 = $90

How much paneling needs to be removed?

Answers

I'll draw it for you cause im nice. (Blue bit is the part we dont have paneling on).

So the the total surface area of panelling needed to remove will be (8 x 6 1/2) x 2 = 104. And also 3 x 8 x 2 = 48. So total surface area = 152. So its 152ft^2

=A

⭐ Answered by Foxzy0⭐

⭐ Brainliest would be appreciated, I'm trying to reach genius!

⭐ If you have questions, leave a comment, I'm happy to help! ⭐

Members of a lacrosse team raised $1793.50 to go to a tournament. They rented a bus for $757.50 and budgeted $64.75 per player for meals. Write and solve an equation which can be used to determine
x
x, the number of players the team can bring to the tournament.

Answers

Answer:

They can bring 16 students to the tournament

Step-by-step explanation:

$1793.50 - $757.50 = 1063

$1063 / $64.75 = 16

Answer:

16 students

Step-by-step explanation:

Hello :)

This question gave us a flat charge of 757.50 dollars for the bus, which means it does not depend how many members of the lacrosse team ride the bus.

However, the meals cost 64.75 per member.

So to make an equation, the bus charge would be the y-intercept (If no member went, they still paid for the bus fee) and the meals would be the slope (since it is dependent on how many members ride the bus.)

The total would add up to be 1783.50, so the equation would be:

1793.50=64.75x+757.50 where x=the number of players the team can bring to the tournament without going outside of their budget

Let's solve now.

1793.50=64.75x+757.50

-757.50              -757.50

1036=64.75x

x=16

Find m CF
44
D
5
-52

Answers

Answer:

Step-by-step explanation:

Answer:

  148°

Step-by-step explanation:

The external angle at E is half the difference of the measures of arcs FD and FC.

  (CF -44°)/2 = 52°

  CF -44° = 104° . . . . multiply by 2

  CF = 148° . . . . . . . . add 44°

The measure of arc CF is 148°.

Which is the one of the correct formula of T.S.A of cylinder with himsphere *

πr(3r+h)
3πr^3+2h
πr(3r+2h)

Answers

Answer:

[tex]\pi \: r(3r + 2h) \: is \: the \: answer[/tex]

Pls answer this I need it

Answers

Answer:

f = 42 , q = 127

Step-by-step explanation:

3f + 1 and 127 are alternate angles and are congruent , so

3f + 1 = 127 ( subtract 1 from both sides )

3f = 126 ( divide both sides by 3 )

f = 42

q and 127 are corresponding angles and are congruent , so

q = 127

q = 127°=========================3f + 1 = 127Subtract both sides minus 1 3f + 1 - 1 = 127 - 13f = 126 Divide both sides by 3 3f ÷ 3 = 126 ÷ 3f = 42

BTW I like ur name hahahah

Have great day.

What is the first step in solving 31 + 2 - 8(3)

Answers

Answer:

[tex]31 + 2 - 8(3) \\ \\ = 31 + 2 - 24 \\ \\ 33 - 24 \\ \\ = 9[/tex]

# be careful#

Answer:

Multiply 8x3

Step-by-step explanation:

Orders of operations state that parenthesis should be the first step in solving an equation

P-parenthesis

E-exponents

M- multiplication

D-division

A- addition

S- subtraction

approximate the square root of 110 ​

Answers

Answer:

10.4880885 or 10.5

Step-by-step explanation:

The square root of 110 is a decimal ... 10.4880885

If we round up it will be 10.5

Answer:

10.488 to nearest thousandths

Step-by-step explanation:

If you mean using a calculator, sqrt(110) is approximately 10.488.

If you mean by hand (unlikely), there are methods such as Newton-Raphson method that converge quite quickly (after around 10 iterations it's basically no different than your calculator)

Trina runs 4 laps around a park. each lap is 1/3 of a mile. trina wants to know how many total miles she runs

Answers

Answer:

1 1/3 miles

Step-by-step explanation:

4 laps times 1/3 mile per lap equals 1 1/3 miles

Answer:

1 1/3 mile(s)

Step-by-step explanation:

Multiply laps by miles: 4 times 1/3

= 4/3 or 1 1/3

questions in the photos. 40 points if you answer correctly. ​

Answers

Answer:

V

Step-by-step explanation:

The point in the question is U

When reflected in the x-axis, it becomes W

When W is reflected in the y-axis, it becomes V

Answer:

U

Step-by-step explanation:

the answer is U because -6.5 is negative and 1 is positive

Which expression Is equivalent to x^2+10x+24

Answers

Answer:

(x+4)(x+6)

Step-by-step explanation:

First we factorise:

x²+4x+6x+24

x(x+4)+6(x+4)

(x+4)(x+6)

So the last one is equivalent

Answer:

(x+4)(x+6)

Step-by-step explanation:

A phone line runs east along a field of 1 miles and then north along the edge of the same field for 3 miles. If the phone line cost 3500 per mile to install, how much could have been saved if the phone line had been installed diagonally across the field?

Answers

Answer:

nsnenenenwnneennenewnw

per description, this is a right triangle, a triangle with a vertical angle.
let L to be the length of diagonal line, so L^2 = 1.8^2 + 2.75^2 =>3.29
so the saving is (1.8+2.75-3.29)*3500=4410

first responder gets

Answers

Step-by-step explanation:

Storage facility => 12x²y³ • 4x⁴y²

Storage facility => 48x⁶y⁵

[tex]\implies \: \frac{12 {x}^{6} {y}^{ - 4} z {}^{2} }{3x {}^{2} {y}^{ - 6} z {}^{3} } \\ \implies \: 4( {x}^{6 - 2} ) \times ({y}^{ -4 + 6} ) \times( {z}^{2 - 3} ) \\ \implies \: 4 {x}^{4} \times {y}^{2} \times {z}^{-1} \\ \implies \: \frac{4 {x}^{4} {y}^{2}}{z} [/tex]

Factor: 10m^3 + 12m^2-35m -42
we are doing factoring trinomials and factor by grouping

Answers

Answer:

( 5m + 6 ) ( 2m² - 7 )

Step-by-step explanation:

please refer the image

Marshall scored 80 on his first quiz and 70 on his second quiz. What was the percent of decrease in his scores?

Answers

Answer:

12.5% Decrease

Step-by-step explanation:

(10/80)*100

Rosenfeld enjoys a delicious meal at BJs, and the bill comes back at $24.50. The service was amazing, so she wants to leave a 25% tip. How much do you pay total (bill and tip together)?

Answers

Answer:

30.62

Step-by-step explanation:

24.50 x .25 = 6.12

24.50 + 6.12 = 30.62

Brainliest to whoever can answer this question the best + 50 pts.
Solve the system of linear equations BY ELIMINATION. Show a step-by-step process.
3x - 2y = -2
5x - 3y = -4

Answers

3x-2y=-2--(1)5x-3y=-4--(2)

(1)×5 and (2)×3

[tex]\\ \tt\hookrightarrow 15x-10y=-10--(3)[/tex]

[tex]\\ \tt\hookrightarrow 15x-9y=-12--(4)[/tex]

Subtracting

[tex]\\ \tt\hookrightarrow -y=+2[/tex]

[tex]\\ \tt\hookrightarrow y=-2[/tex]

Put in eq(1)

[tex]\\ \tt\hookrightarrow 3x+4=-2[/tex]

[tex]\\ \tt\hookrightarrow x=-2[/tex]

Answer:

x = -2 and y = -2

Explanation:

Given equations:

3x - 2y = -2

5x - 3y = -4

---------------------

Make the value before y equal:

( 3x - 2y = -2 ) * 3

9x - 6y = -6 .........equation 1

( 5x - 3y = -4 ) * 2

10x - 6y = -8 ...........equation 2

solve them by elimination:

10x - 6y = -8

-9x + 6y = +6

----------------------

x = -2

If x is -2

Then y:

10x - 6y = -8 .................from equation 2

-6y = -8-10x

y = [-8 - 10(-2)]/-6

y = -2

For problems 12-17, write each number as a percent.

Answers

Answer: There's not picture????? or Queston

Step-by-step explanation:

Calculate the following problem
what is 24 plus 12 minus 53 plus 100 and the divide it by 2

Answers

Answer:

33

Step-by-step explanation:

Answer:

(4.5)

Step-by-step explanation:

i hope its help
brainliest me

#CARRYONLEARNING

Pls pls pls pls pls pls help me I’ll help you

Answers

Answer:

minimum of -3

Step-by-step explanation:

Because that is the lowest point on the graph

NEED HELP ASAP DUE SOON!!!!

Answers

Answer:

Step-by-step explanation:

We can easily get 'a' in the equation by setting x to zero which will get rid of the b variable leaving us with:

a = 2

Now for b, we know the second point is (1,6), so let's plug it into the function

6 = 2 * b^1

b = 3

Thus the function is [tex]y = 2*3^{x}[/tex]

Hope that helps!

HELP 20 POINTS!!!!!!Using the equation y = 3x – 5, what would the output be for an input of 4?
3
7
-3
-5

Answers

Answer:

7

Step-by-step explanation:

3(4)=12

12-5=7

which is greater 4/9 or 12/18​

Answers

Answer:

12/18

Step-by-step explanation:

4/9 = 0.4444....

12/18 = 2/3 = 0.66666....

12/18 is greater than 4/9

use solve for θ and round to the nearest tenth
1) sinθ=0.99
2) tanθ=0.27
3) cosθ=0.39
4) tanθ=0.87
5) sinθ=0.08​​

Answers

Answer:

2 tan0 have fun hope it helps you

Step-by-step explanation:

chvfghcc


When a figure rotates around a point, this point is called the

Answer:

A image
B. origin
C. graph
D. center of rotation

Answers

Answer:

Your answer is D. center of rotation!

Step-by-step explanation:

A rotation is a transformation in a plane that turns every point of a figure through a specified angle and direction about a fixed point. The fixed point is called the center of rotation . The amount of rotation is called the angle of rotation and it is measured in degrees.

The answer is: D - center of rotation

HELP FAST PLS YOU GUYS

Answers

Answer:

Function increase (-4,inf)

Step-by-step explanation:

cause it increases as the it rises from left to right

I’m so sorry i Don’t know the answer I would help if I could

please help, quick, this is my last question

Answers

Answer:

5/2 I think bec a was moved to 1/1 before it was 6/3

At the local bakery Ariel bought 2 oatmeal cookies for $1.50. Mei bought 1/2 dozen oatmeal cookies for $4.50. Becky bought 8 oatmeal cookies for $6.00 what does the point (1,0.75) represent in...

Answers

Answer:

Its proportional because when you divide each oatmeal bought and the amount you will end up with .75

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