Alberto uses the steps below to solve the equation One-half x minus 3 equals 7. Step 1: One-half x minus 3 plus 3 equals 7 plus 3 Step 2: One-half x plus 0 equals 10 Step 3: One-half x equals 0 Step 4: 2 (one-half) x equals 2 (10) Step 5: 1 x equals 20 Step 6: x equals 20 Which justifies Step 6 of his work?

Answers

Answer 1

Answer:

Identity property of multiplication

Step-by-step explanation:

From step 5:

[tex] 1x = 20 [/tex]

Here, to solve for x so that the variable x stands alone, Alberto uses the identity property of multiplication, which justifies what he has in step 6.

Step 6:

[tex] x = 20 [/tex]

According to the identity property of multiplication, any value you multiply by 1 gives you that same value.

Therefore, 1x = 1 × x = x.

The variable x multiplied by 1 will give you x.


Related Questions

The table below shows Britney's distance, in miles, from her destination after different time intervals in hours: Time (hours) (x) 2 4 1 3 6 5 7 Distance from destination (miles) (y) 1,000 880 1,060 940 760 820 690 What is the correlation coefficient for the data, and what does it represent? (5 points) 0; it represents no correlation between x and y 0.999; it represents a linear positive correlation between x and y −0.999; it represents a linear negative correlation between x and y 0.999; it represents a linear negative correlation between x and y

Answers

Answer:

-0.999

Step-by-step explanation:

Answer:

-0.999

Step-by-step explanation:

took test

Aldo the trainer has two solo workout plans that he offers his clients: plan a and plan b. Each client does either one or the other (not both). On friday there 8 were clients who did plan a and 3 who did plan b. On saturday there were 3 clients who did plan a and 5 who did plan b. Aldo trained his friday clients for a total of 7 hours and his saturday clients for a total of 6 hours. How long does each of the workout plans last?

Answers

Answer:

x = number of hours to train plan a clients

x = 0.55 hour

y = number of hours to train plan b clients

y = 0.87 hours

Step-by-step explanation:

Friday

Plan a = 8 clients

Plan b = 3 clients

Total hours = 7

Saturday

Plan a = 3 clients

Plan b = 5 clients

Total hours = 6

Let

x = number of hours to train plan a clients

y = number of hours to train plan b clients

8x + 3y = 7 (1)

3x + 5y = 6 (2)

Multiply (1) by 5 and (2) by (3)

40x + 15y = 35 (3)

9x + 15y = 18 (4)

Subtract (4) from (3)

40x - 9x = 35 - 18

31x = 17

Divide both sides by 31

x = 17 / 31

= 0.548 hour

Approximately

x = 0.55 hour

Substitute x = 0.55 hour into (1)

8x + 3y = 7

8(.55) + 3y = 7

4.4 + 3y = 7

3y = 7 - 4.4

3y = 2.6

Divide both sides by 3

y = 2.6 / 3

= 0.867 hours

Approximately

y = 0.87 hours

x = number of hours to train plan a clients

x = 0.55 hour

y = number of hours to train plan b clients

y = 0.87 hours

PLS HELP 15 POINTSSSSSSSSS

Answers

Answer:

Rational  it's a  fraction of two integers  Irrational  can't be written as a fraction Irrational  can't be written as a fraction Rational  it can be multiplied by two numbers Irrational can't be put in even a fraction:) Hope you enjoy this :)

f(x) = 4x^2 - 7x + 7 find f(7)

Answers

Answer:

ummmm what grade do you are

Answer:

f(7)=140

Step-by-step explanations:


11. A car is travelling at the average speed of 50 km/hr. How much distance would it travel in
1 hour 12 minutes?

Answers

Answer: Twelve minutes is 12/60 = 1/5 = 0.2 hours. So the car travelled for 1.2 hours. The car travelled at an average of 50 km/hr for 1.2 hours, so it travelled 50 km/hr * 1.2 hours = 60 km.

Lisa and John are working at a summer camp. The amount of money John earned is represented by the equation m=8.5h, where h represents the number of hours John works and m represents the amount of money he earns, in dollar. The table below shows the amount of money Lisa earns while working at summer camp.

Answers

Answer:

0.4625

Step-by-step explanation:

Multiply two top numbers and get 0.4625

Answer:

0.4837

Step-by-step explanation:

Add the top number to the bottom and write “tape diagram on paper “

Which ordered pair is a solution and f the equation? y-3=5(x-2)

Answers

Answer:

135=

3=5−10

Step-by-step explanation:

im not good at this but my mom said to try so i its not right

Helpppp, what is a solution set for |a|=6

A
B
C
D

Answers

the answer should be a hope this helps :]

Complete the table to show the number of times per year that account 3 compounds interest. Then, use that value to write the exponential expression that models the amount of money Brianna would have for account 3 after t years. The math process used to write the exponential expression for account 4 has been modeled for you:

Account 4: r = 0.03425, and n = 365 because the interest is compounded daily.

Because $250 is the initial deposit, P = 250.
I need know for 3rd year

Answers

Answer:

1 1 250(1.035)t

2 12 250(1.002896)12t

3 52 250(1.0006635)52t

4 365 250(1.0000938)365t

Step-by-step explanation:

From Plato

The complete details is shown below:

What is interest?

Interest, in its most simple form, is calculated as a percent of the principal.

Given:

r = 0.03425, and n = 365

P = 250.

                                          Table

Expression for the Amount of Money             Number of Times Interest

after t Years                                                       is Compounded per Year

                                                                                  Account

250(1.035)                                                                    1

250(1.002896)12                                                        12

250(1.0000938)365+                                               365

So,

1 *[250(1.035)t] 12* [250(1.002896)12t] 52* [250(1.0006635)52t] 365* [250(1.0000938)365t]

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This table represents a proportional relationship. Find the constant of proportionality.

Type the answer in the box below.

Table 1

s P
2 8
3 12
5 20
10 40
1. What is the constant of proportionality?

2. Complete the equation that represents the relationship.

Complete the equation in the box below.

Answers

Answer:

1. 4

2. y = 4x

Step-by-step explanation:

1.

Divide any y value by its corresponding x value to find the constant of proportionality.

8/2 = 4

Constant of proportionality: 4

2.

Equation of proportional relation:

y = kx, where k is the constant of proportionality.

y = 4x

the position of a deep sea probe is -2 3/4 fathoms relative to the sea level. after finishing taking data, it moves to -2 5/8 fathoms relative to sea level. which was deeper, the first mission, or the second. (i’m in modern high school which means i get collage questions, i only have 1 hour left to get this done, someone help!)

Answers

Answer:

The first mission

Step-by-step explanation:

The depth readings are

The first mission:  - 2 3/4 fathomsThe second mission: - 2 5/8 fathoms

Comparing the readings

- 2 3/4 = - 2 6/8  and  - 2 5/8

Absolute values compared

2 6/8 > 2 5/8

Indicating the greater value on the first mission

As per above, the first mission was deeper

Hana rents a car for a day. Her car rental company charges $50 per day and $0.40 per mile. Peter rents a car from a different company that charges $70 per day and $0.30 per mile. How many miles do they have to drive before Hana and Peter pay the same price for the rental for the same number of miles?

Answers

50 + .4x = 70 + .3x

.4x = .3x + 20

.1x = 20

x = 200

Let x be the number of miles.

They have to drive 200 miles.

They will drive 200 miles before paying same amount.

Let the number of miles that they will drive together and pay the same amount be represented by x.

Since Hana's car rental company charges $50 per day and then $0.40 per mile, this can be represented as:

= 50 + (0.40 × x)

= 50 + 0.40x

Since Peter rents a car from a different company that charges $70 per day and then $0.30 per mile, this will be:

= 70 + (0.30 × x)

= 70 + 0.30x

Then we will equate both Hana's and Peter's equation together and this will be:

50 + 0.40x = 70 + 0.30x

Collect like terms

0.40x - 0.30x = 70 - 50

0.1x = 20

x = 20/0.1

x = 200

In conclusion, they will drive 200 miles before paying thesame amount

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1.5x + 4.5y = 18. Where does the graph intersect the y-axis?

Answers

Answer:

4

Step-by-step explanation:

Substitute x for 0 and solve.

1.5(0)+4.5y=18

4.5y=18

y=4

For the equation, 1.5x + 4.5y = 18 at x = 0 the graph will intersect at 4 of y -the axis.

What is coordinate geometry?

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

Given that the equation is 1.5x + 4.5y = 18. For the value of y substitute x for 0 and solve.

1.5x + 4.5y = 18

1.5(0)+4.5y=18

4.5y=18

y=4

The value of y is equal to 4 means that the graph will intersect the y-axis at 4.

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which of the following expressions are equivalent to 16/5?
choose all answers that apply:

Answers

Answer:

None of the above.

Step-by-step explanation:

16/5 is equal to 3.2

If you calculate a.) The answer comes out to negative so no

b.) Answer comes out to negative again so no

C.) None of the above YES

Because none of them have a positive outcome like the original

Anne has $5000 in her savings account and decides to leave there for three years. After one year the account increases by 10%, the following year it decreases by 5% and in the third year it increases by 15%. How much is in the account after three years?

Answers

791.25 because if it increases by 10 percent which is 5500 and then it decrease by 5%
10%=550
5%=275
Which is 275 and later it increases by 15% so that’s basically it

Choose all the number sentences that have a sum greater than 495,000
A) 125,678 + 98,567
B) 250,000 + 250,001
C) 382,761 + 108,912
D) 76,850 + 422,074
E) 345,632 + 149,456

Answers

Answer:

B, D and E are the correct answers.

Step-by-step explanation:

250,000 + 250,001 = 500,001

76,850 + 422,074 = 498,924

345,632 + 149,456 = 495,088

-19, -26, -33, -40,.
Find a

Answers

Answer:

The next one after -40 would be -47

Step-by-step explanation:

Add negative -7 to every answer

Answer:

Idek I'm.new

Step-by-step explanation:

hom4krid7dndiei3

At noon, the minute and the hour hands of a clock overlap. In how long will they again overlap?

Answers

Answer:

In an hour and 5 minutes

(or 60 seconds but it will only overlap for a second)

Explanation:

After 60 minutes it will be an hour and the clock will show 1o'clock, after 5 minutes, the minute hand will be at the "1" so they will over lap at 1:05

Answer: 5.45

(the way I solved it is in the picture)

what is the surface area?

Answers

I cant see the image it won’t load

(6-4p)(4p+6)
EXPAND IT AND PLEASE EXPLAIN HOW

Answers

[tex]36-16p^{2}[/tex]

Apply Difference of Two Squares Formula

(6-4p)(4p+6)=[tex]6^{2}[/tex]-([tex]4p^{2}[/tex])

BUT

(6-4p)(4p+6)

is already in the expanded form you probably want to simplify it.

:)Hope you enjoy this:)

The classrooms in the Oakhurst School District are painted every summer. Seven gallons of paint are needed to paint 3 classrooms. How many more gallons are need to paint the 129 classrooms at North High School than the 48 classrooms at Edgewater Elementary?

Answers

Answer:

189 gallons

Step-by-step explanation:

7 gallons for 3 classrooms, so 7/3 for 1 classroom

multiply 7/3 * 129 to get 301 gallons at North High School

multiply 7/3 * 48 to get 112 gallons at Edgewater Elementary

301 - 112 = 189 gallons more at North High School than at Edgewater Elementary

The more gallons should be 189 gallons

The calculation is as follows:

7 gallons for 3 classrooms, so 7 by 3 for 1 classroom

Now  

we have to multiply 7 by 3 with 129 so that 301 gallons at North High School could come

Now  

multiply 7 by 3 with 48 to get 112 gallons at Edgewater Elementary

Now

=  301 - 112

= 189 gallons more

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Solve for p 7(p - 9) = -34.3
p=__?

Answers

the answer should be p=4.1

Answer: p = 4.1

Step-by-step explanation:

13-17 (my report comes tomorrow so i need help)

Answers

Answer:

44444444444444444

Step-by-step explanation:

PLEASE GIVE ME ANSWER PLEASE ​

Answers

sqrt((x2-x1)^2+(y2-y1)^2)

Answer:

a)sol...A/Q

x+130=180(Sum of angles on a straight line is 180 degree)

=>x=180-130

=>x=50

Hrnce,the value of x is 50 degree.

b)sol...A/Q

[tex]circumference\ of\ circle=2\pi y\\

2\pi r=2\pi y\\

r= \frac{2\pi y }{2\pi} \\

Hence,r=radius=y[/tex]

i can’t solve this, which choice is it?

Answers

As OP bisects ∠AOR, ∠AOP = ∠POR = 55°

So, ∠AOR = ∠AOP + ∠POR = 55° + 55° = 110°

As OS bisects ∠ROB, ∠ROS = ∠SOB = x

As total angle on a line is 180°,

110° + x + x = 180°

=> 2x = 70

=> x = 35°

∠POS = ∠POR + ∠ROS = 55° + x = 55° + 35°

=> ∠POS = 90°

It is E because you should multiply 55 by 2

18-53) + 6 + (18 - 2)
Susie
578

Answers

Answer:

565

Step-by-step explanation:

18-53=-35

-35+6=-29

18-2=16

16+-29=-13

-13+578=565

Could I please have BRAINLIEST?

what’s the answer to this equation?

Answers

the answer to that equation is. v= -1/7

The segments shown below could form a triangle.

A. True

B. False

Answers

Answer:

the answer is true :A

The ratio y/x is called the all of these EXCEPT which one?
1. Unit Rate
2. Constant of proportionality
3. multiplicative inverse
4.constant multiplier

Answers

Unit rate and constant of porportionaluty is the same thing just a tip

30 POINTS PLZ HELP I WILL MARK BRAINLIEST
An archer shoots an arrow into the sky where the motion of the arrow can be modeled by the equation
() = −162 + 80 where t is time in seconds and f(t) is height in feet. Find how long it will take the
arrow to hit the ground using an algebraic method. Show all of your reasoning/steps used with this algebraic
method.

what is being asked in the problem?
show work when you solve
explain your answer

Answers

Answer:

Since 162 is negative you subtract 162-80 which is 82

Step-by-step explanation:

So it will take 82 seconds for the arrow to hit the ground I believe I’m checking my answer real quick. Ya it’s right can I maybe brainliest?

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