Solve each equation and show all your work.

6x - 5 = 2x + 7

3z - 2 = 5z + 19

5x - 15 + 2x = 4x + 12

35x + 2 = 7

Answers

Answer 1

Answer:

x = 3

z = (-21)/2

x = 9

x = 1/7

Step-by-step explanation:

Solve for x:

6 x - 5 = 2 x + 7

Subtract 2 x from both sides:

(6 x - 2 x) - 5 = (2 x - 2 x) + 7

6 x - 2 x = 4 x:

4 x - 5 = (2 x - 2 x) + 7

2 x - 2 x = 0:

4 x - 5 = 7

Add 5 to both sides:

4 x + (5 - 5) = 5 + 7

5 - 5 = 0:

4 x = 7 + 5

7 + 5 = 12:

4 x = 12

Divide both sides of 4 x = 12 by 4:

(4 x)/4 = 12/4

4/4 = 1:

x = 12/4

The gcd of 12 and 4 is 4, so 12/4 = (4×3)/(4×1) = 4/4×3 = 3:

Answer: x = 3

____________________________________

Solve for z:

3 z - 2 = 5 z + 19

Subtract 5 z from both sides:

(3 z - 5 z) - 2 = (5 z - 5 z) + 19

3 z - 5 z = -2 z:

-2 z - 2 = (5 z - 5 z) + 19

5 z - 5 z = 0:

-2 z - 2 = 19

Add 2 to both sides:

(2 - 2) - 2 z = 2 + 19

2 - 2 = 0:

-2 z = 19 + 2

19 + 2 = 21:

-2 z = 21

Divide both sides of -2 z = 21 by -2:

(-2 z)/(-2) = 21/(-2)

(-2)/(-2) = 1:

z = 21/(-2)

Multiply numerator and denominator of 21/(-2) by -1:

Answer: z = (-21)/2

________________________________________

Solve for x:

5 x + 2 x - 15 = 4 x + 12

Grouping like terms, 5 x + 2 x - 15 = (5 x + 2 x) - 15:

(5 x + 2 x) - 15 = 4 x + 12

5 x + 2 x = 7 x:

7 x - 15 = 4 x + 12

Subtract 4 x from both sides:

(7 x - 4 x) - 15 = (4 x - 4 x) + 12

7 x - 4 x = 3 x:

3 x - 15 = (4 x - 4 x) + 12

4 x - 4 x = 0:

3 x - 15 = 12

Add 15 to both sides:

3 x + (15 - 15) = 15 + 12

15 - 15 = 0:

3 x = 12 + 15

12 + 15 = 27:

3 x = 27

Divide both sides of 3 x = 27 by 3:

(3 x)/3 = 27/3

3/3 = 1:

x = 27/3

The gcd of 27 and 3 is 3, so 27/3 = (3×9)/(3×1) = 3/3×9 = 9:

Answer: x = 9

__________________________________________

Solve for x:

35 x + 2 = 7

Subtract 2 from both sides:

35 x + (2 - 2) = 7 - 2

2 - 2 = 0:

35 x = 7 - 2

7 - 2 = 5:

35 x = 5

Divide both sides of 35 x = 5 by 35:

(35 x)/35 = 5/35

35/35 = 1:

x = 5/35

The gcd of 5 and 35 is 5, so 5/35 = (5×1)/(5×7) = 5/5×1/7 = 1/7:

Answer: x = 1/7


Related Questions

BRAINIEST IF RIGHT George and his dad are planning to attend the state fair. An adult ticket is $19.00. The price of an adult ticket is one third the price of a student ticket plus $15.00. Write an equation to determine how much George will pay for a student ticket.


A one thirdx + 19 = 15

B one thirdx + 15 = 19

C one thirdx − 19 = 15

D one thirdx − 15 = 19

Answers

Answer:

1/3x+15=19

Step-by-step explanation:

so B

Answer:

its b

Step-by-step explanation:

you dont know the price if the student tick so it represents x... one third of a student ticket would be one thirdx. after you do that you will have to add the extra 15 dollars to it in order to get the price if 19 dollars per adult ticket.

An equation is shown below:

4(x − 3) − 5(x + 1) = 3

Which statement shows a correct next step in solving the equation?

The equation can become 4x − 3 − 5x + 1 = 3 by applying the associative property of multiplication.
The equation can become 4x − 3 − 5x + 1 = 3 by applying the distributive property.
The equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.

Answers

Answer:

The equation can become 4x − 12 − 5x − 5 = 3 by applying the distributive property.

Step-by-step explanation:

By applying the distributive law to this equation, we can produce the equation :

     4x − 12 − 5x − 5 = 3;

The distributive property is a mathematical function in which each element in the parentheses is multiplied by the one outside of it;

   4(x − 3) − 5(x + 1) = 3

In the equation;

  4 distribute over the first parentheses and -5 over the second one;

   So we expand;

      4x - 13 - 5x -5  = 3

In distributive property, expansion simply takes place.

Question 4
2 pts
If a = -3, b = 2 and c = -4 find the value of the expression.
a2 +b²

Answers

Answer:

-2

Step-by-step explanation:

Order of Operations: BPEMDAS

Step 1: Define

a2 + b²

a = -3

b = 2

c = -4

Step 2: Substitute and Evaluate

2(-3) + 2²

-6 + 4

-2

Answer:

1

Step-by-step explanation:

answer plss. Money here.

Answers

Answer:

Both angles are equal because they are corresponding so:

2x + 5 = 3x - 7

2x + 12 = 3x

x = 12

A 2-column table the first column is labeled Minutes per Week of Moderate/Vigorous Physical Activity with entries 30, 90, 180, 330, 420. The second column is labeled Relative Risk of Premature Death with entries 1, .8, .73, .64, .615.

According to the data, how does a persons relative risk of premature death change in coloration to changes in physical activity?


The risk of dying prematurely increases as people become more physically active.

The risk of dying prematurely does not change in correlation to changes in physical activity.

The risk of dying prematurely declines as people become more physically active.

The risk of dying prematurely declines as people become less physically active

Answers

Answer:

its c on edge

Step-by-step explanation:

Answer:

C. The risk of dying prematurely declines as people become more physically active.

Explanation: This is the correct answer on Edge 2021, just did the assignment. Hope this helps ^-^.

Is the following relation a function?

Answers

Answer:

Step-by-step explanation:

It’s a function

Answer:

yes it is a function

Step-by-step explanation:

since the x values dont repeat itself like there are no two of any of the x values then it is a function

Arrange the four numbers shown in order from least to greatest

6.7%
0.67
6/9
6.7×10-3

Answers

Answer:

Step-by-step explanation:

6.7 x 10 - 3

6.7%

6/9

0.67

In my opinion this should be the answer

I need help on these questions who ever answers this question will be the brainliest!!

Answers

B=102°
A=78
C=78°

The Opposite angles are equal which means B is equal to 102° and lines on a straight line equals 180 so 180-102=78

Help math question 1 ,2 ,3 grade 12

Answers

Answers:

1.

a. 20%

60/300 × 100/100

= ( 60 × 100 / 300 ) × 1/100 = 20/100

Calculator: 60 ÷ 300 × 100

b. 90%

270/300 × 100/100

270/300 × 100/100= ( 270 × 100 / 300 ) × 1/100 = 90/100

Calculator: 270 ÷ 300 × 100

c. 58.33%

175/300 × 100/100

100/100= ( 175 × 100 / 300 ) × 1/100 = 58.33/100

Calculator: 175 ÷ 300 × 100

2.

a. 35 Students

Calculator: 10 × 350 / 100

b. 93

Calculator: 10 × 930 / 100

c. 118

Calculator: 10 × 1180 / 100

d. 1036

Calculator: 10 × 10,360 / 100

3.

a. 11.1 (Repeated)

Calculator: 50 / 450 × 100%

b. 6.67 (6 Repeated)

Calculator: 50 / 750 × 100%

c. 4.167 (6 Repeated)

Calculator: 50 / 1200 × 100%

Hopefully this helps:)

I need help!!!
-10 = -5 (v-4)
a) 12
b) 6
c) 3
d) -8
What's the answer I need to know?!

Answers

Answer:

i think it is B

Step-by-step explanation:

i am not 100% sure

Answer:

B.

Step-by-step explanation:

-10 = -5 (v-4)

-10=-5v+20

-30=-5v

6=v

Please help! Will give brainliest!

Answers

Answer:

D.5

Step-by-step explanation:

4*5=20

8*5=40

12*5=60

..etc

brainliest?


What is the percent of change in the cost of a DVD set that originally sold for $49.99 and is now
on sale for $24.99? Round to the nearest percent.

Answers

Answer:

50% decrease

Step-by-step explanation:

49.99 - 29.99 = 25

25

---- = 0.5(100) = 50%

49.99

Answer: I dont know witch one you want me to round so I will do both. $49.99 = $50.00 and $24.99 = $25.00 and if you want to add them it would be $75.00

Given m|n, find the value of x.

Answers

Answer:

33 degrees

Step-by-step explanation:

Corresponding Angles Postulate

Answer:

33°

Step-by-step explanation:

if m||n then the angle represented with x° and 33° must be equal because these angles are corresponding.

What is the slope of the line that passes through the points M (-3,5) and N (1,8)

Answers

Answer:

m=3/4

Step-by-step explanation:

See the attached above.

Hope it helps :)

The slope of line passing through M (-3,5) & N (1,8) will be 3/4.

We have been given a line passing through points M (-3,5) & N (1,8) .

We have to find out what will be the slope of the line ?

What is the formula for slope of a line ?

Slope of line is given by , m = (y2-y1) / (x2-x1).

Given that line is passing through points M (x1 , y1) and N (x2,y2) or M (-3,5) & N (1,8).

here , x1 = -3 , y1 = 5 , x2= 1 . y2 = 8

The slope (m) of line will be ;

∵ m = ( y2-y1) / (x2-x1)

m = ( 8-5) / (1- (-3))

m = 3 / 4

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Name a segment that is perpendicular to segment AB.
G
E
A
D
H
F
B
С

Answers

Answer:

BC

Step-by-step explanation:

Which expression uses the associative property to make it
easier to evaluate 6(1/3•7/5)
O A. (6.1/3)7/5
O B. (6•5/7)1/3
O C. 6(7/5•1/3)
OD 3(1/6•7/5)

Answers

Answer:

A

Step-by-step explanation:

Here, we want to select which of the expressions correctly use the associative property

The associative property deals with rearrangement

So for (a + b) + c

we can have (a + c) + b

In the case of this question, the associate property is the one that makes the evaluation easier

Thus;

we need to bring 1/3 and 6 together since 3 is a factor of 6

We have;

(6•1/3)7/5

Name 1 and 2 another name

Answers

Answer:

triangle, square, circle, pentagon, and horcux.

jk whats the question

Step-by-step explanation:

Hey there!

Answer:

One, two, three, delta, pi, hexagon, octagon, pentagram....

Step-by-step explanation:

Name another name of what??

Your question doesn't make a lot of sense but I thought that maybe I could share a few really cool shape and number names that maybe you didn't know!

Hope you enjoy!

:D

1. To participate in a school trip, Kim had to earn $85 in one week. Kim could earn $8 per
hour babysitting and $15 per hour for yard work, but Kim's parents limit work time to 8
hours per week. How many hours should she spend doing each type of work?
a
First define your variables.
b. Write two equations, one that represents the condition on the total number of hours to be
worked and the other which relates the number of hours worked at each job towards her
goal.

Answers

It has given you that to earn $85 in one week. Kim could earn $8 per hour babysitting and $15 per hour for yard work with work time limited to 8 hours per week. Now we have to represent the variable X is the numbers of hours spent doing babysitting in the week. And Y represents the number of hours spent doing yard work in the week. The equation representing the condition on the total number of hours to be worked is: x+y= 8. The equation relating the number of hours working at each job toward the fund- raising goal is: 8x+ 15y= 85 and your final answer should be x= 5

A basketball hoop has a
diameter of approximately
18 inches. What is the
circumference of the
basketball hoop?

Answers

The perimeter of the basketball hoop is 18π inches.

The circumference of a circle can be found using the formula:

C = πd

where C is the circumference and d is the diameter of the circle.

In this case, the diameter of the basketball hoop is approximately 18 inches. So we can plug this value into the formula to get:

C = π(18)

Using a calculator or approximating π to 3.14, we can evaluate this expression to get:

C ≈ 56.52 inches

Therefore, the circumference of the basketball hoop is approximately 56.52 inches.

Learn more about perimeter here:

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3^3 / 3^-4 = ?
Will mark brainliest plz hurry

Answers

2187 pls mark me brainliest

Answer:

[tex]2187[/tex]

Step-by-step explanation:

[tex]\frac{3^3}{3^-^4}[/tex]

When attempting to solve this, we have to consider the exponent rule of fractional exponents:

[tex]\frac{x^a}{x^b} =x^a^-^b[/tex]

Therefore, our initial problem would become:

[tex]3^3^-^(^-^4^)\\[/tex]

Two negatives become positive:

[tex]3^3^+^4[/tex]

Add:

[tex]3^7[/tex]

[tex]3[/tex] × [tex]3[/tex] × [tex]3[/tex] × [tex]3[/tex] × [tex]3[/tex] × [tex]3[/tex] × [tex]3[/tex]

[tex]= 2187[/tex]

Emily plans to put her graduation money into an account and leave it there for 4 years while she goes to college. She receives $750 in graduation money that she puts into an account that earned $127.50 in interest. What was the interest rate that the bank provided

Answers

Answer:

887.40

Step-by-step explanation:

amount = principal(1i)^n

i = .0425/2 = .02125 , n = 8 , principal = 750

amount = 750(1.02125)^8 = 887.40

In what form is an equation that relates two proportional quantities x and y? Explain your thinking.

Answers

Answer:

A proportional relationship exists between two values x and y when they can be expressed in the general form.       Hope this helps

Step-by-step explanation:

12a^3b^2c
A: The degree is 6
B: The degree is 3
C: The degree is 4
D: The degree is 5

Answers

Answer:

b. the degree is 3

Step-by-step explanation:

degree is the highest exponent

I NEED A ANSWER ASAPP!!!!!



A linear regression has a correlation coefficient of r=0.82


. Would this be a good correlation coefficient? What is the best value you could have for a correlation coefficient? Explain your reasoning completely.

Answers

Answer:

not very good

Step-by-step explanation:

the correlation should be almost 1  to be a good representation of the data. 0.82 isn't very close.  This would be a pretty "rough" approximation at best.  Maybe that's all that's needed but usually something close to 1.. like 0.99 is needed.

Find the range for the measure of the third side of a triangle given the measures of the other two sides are 4 and 8

Answers

Answer:

4 < x < 12

Step-by-step explanation:

Given 2 sides, then let x be the third side and

difference of 2 sides < x < sum of 2 sides , that is

8 - 4 < x < 8 + 4

4 < x < 12

Solve each of these equations.

3(n+2)=9(6-n)

Answers

Answer:

n= 4

Step-by-step explanation:

3n+6= 54- 9n

12n= 48

n=4

Answer:

4

Step-by-step explanation:

3n+6=54-9n

-3n

6=54-12n

-54

-48=-12n

N=4

You move up 4 units and right 2 units. You end at (-1, 3). Where did you start?

Answers

Answer:

You started at (-3,-1)

Solve the equation for z.
-8z + 1 = z-8

Answers

Answer:

z= 1

Step-by-step explanation:

move the like terms, collect then calculate, divide on both sides :)

Answer:

z equals -1

Step-by-step explanation:

-8z + 1 = z-8

-9z + 1 = -8

-9z + 9

-9z ÷ 9

z = -1

382.993 to the nearest hundredth​

Answers

Answer:

That number rounds to the nearest hundredth to this number: 382.99

Find the measure of 1 in the​ figure, shown to the right.

Answers

Answer:

∠1 = 81°

Step-by-step explanation:

∠1 and 81° are corresponding angles and corresponding angles are equal to each other.

The measure of ∠1 in the figure is 81°.

What are Angles?

Angles are the figure formed by the intersection of two lines or rays by sharing a common point. This point is called the vertex of the angle.

Angles are usually measured in degrees or radians.

Given is a figure of two parallel lines which is cut by a transversal line.

There are many properties for the angles formed by the transversal lines.

One of the property is that corresponding angles are equal.

Corresponding angles are the pair of angles which are on the same side of each parallel lines and at the same side of the transversal but at different intersections.

In the given figure,

∠1 and 81°, ∠3 and ∠7, ∠2 and ∠6, ∠4 and ∠8 are corresponding angles.

Since ∠1 and 81° are corresponding angles ∠1 = 81°.

Hence, measure of angle 1 is 81 degrees.

To learn more about Angles, click on the link :

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