4.5(8 - x) + 36 = 102 - 2.5(3x + 24)

Answers

Answer 1

Answer:

x = -10

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Step-by-step explanation:

Step 1: Define equation

4.5(8 - x) + 36 = 102 - 2.5(3x + 24)

Step 2: Solve for x

Distribute:                                   36 - 4.5x + 36 = 102 - 7.5x - 60Combine like terms:                   -4.5x + 72 = -7.5x + 42Add 7.5x on both sides:             3x + 72 = 42Subtract 72 on both sides:        3x = -30Divide 3 on both sides:              x = -10

Step 3: Check

Plug in x into the original equation to verify it's a solution.

Substitute in x:                    4.5(8 - -10) + 36 = 102 - 2.5(3(-10) + 24)Simplify:                               4.5(8 + 10) + 36 = 102 - 2.5(3(-10) + 24)Multiply:                               4.5(8 + 10) + 36 = 102 - 2.5(-30 + 24)Add:                                     4.5(18) + 36 = 102 - 2.5(-6)Multiply:                               81 + 36 = 102 + 15Add:                                     117 = 117

Here we see that 117 does indeed equal to 117.

∴ x = -10 is a solution of the equation.


Related Questions

Question 2 plz help I’ll try my best to mark brainliest

Answers

Answer:

F. [tex]\sqrt{x}[/tex]

Step-by-step explanation:

if you replace x with 2 and plug these into your calculator, you can see that [tex]\sqrt{x}[/tex] has the least value

Coach South and Mr. Dr. Coach Rhodes are having a problem solving competition. Mr. Dr. Coach Rhodes can solve four more problems than twice the number of Coach South. If Mr. Dr. COach Rhodes has solved twenty problems, how many problems has Coach South solved?

Answers

Answer: 8

Step-by-step explanation: if Coach Rhodes solves 4 more than twice Coach South then that would mean Coach South solves 8.

Twice 8 equals 16, plus 4 equals 20.

I need help and the time is running please help

Answers

Answer:

I think its B

Step-by-step explanation:

I'm sorry if I'm wrong. I'm busy

Answer:

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HELP HERE PLESSS. :)
***

Answers

Answer:

is reflected across the line x=4

4x+5y=9
4x−2y=2
x= y=

Answers

Answer:

For example, the solution to the equations 2x + 3y = 15 and x - y = -10 is x = -3 ... Equation 2: 4x + 2y = 20

Answer:

x=0, y=0 this is so easy

%84, percent of Astrid's books are fiction. What fraction of Astrid's books are fiction?

Answers

Answer:

the fraction would be

84/100

Answer:

84/100

Step-by-step explanation:

84% is out of a hundred.

In the following activity, write an equation to represent each verbal statement, and use it to find the value of each unknown number. Then, put the solution values in order from smallest to largest. [Note: The smallest solution is "first", and the largest solution is "fifth".]


1. fourth


Half of a number is added to four. This sum is equivalent to negative one.


2. first


The sum of a number and three is divided by five. The result is negative two.


3. third


The difference between four times a number and five has a result of negative eight.


4. second


The difference between a number and five is multiplied by negative two. The

resulting product equals fourteen.


5. fifth


The sum of a number and two is equal to the quotient of six and negative four.




I WILL GIVE BRAINLEST

Answers

Answer:

First x=-13 (The sum of a number and three is divided by five. The result is negative two.)

Second x=-10 (Half of a number is added to four. This sum is equivalent to negative one.)

Third x=-3.5 (The sum of a number and two is equal to the quotient of six and negative four.)

Fourth x=3.25 (The difference between four times a number and five has a result of negative eight.)

Fifth  x=12 ( The difference between a number and five is multiplied by negative two. The  resulting product equals fourteen. )

Step-by-step explanation:

We will consider number = x

1. Half of a number is added to four. This sum is equivalent to negative one.

[tex]\frac{1}{2}x+4=-1[/tex]

Now solving to find value of x

[tex]\frac{1}{2}x+4=-1\\\frac{1}{2}x=-1-4\\\frac{1}{2}x=-5\\x=-5*2\\x=-10[/tex]

So, value of x=-10

2. The sum of a number and three is divided by five. The result is negative two.

[tex]\frac{x+3}{5}=-2[/tex]

Solving:

[tex]\frac{x+3}{5}=-2\\x+3=-2*5\\x+3=-10\\x=-10-3\\x=-13[/tex]

So, value of x=-13

3. The difference between four times a number and five has a result of negative eight.

[tex]4x-5=-8[/tex]

Solving:

[tex]4x-5=8\\4x=8+5\\4x=13\\x=13/4\\x=3.25[/tex]

So, value of x=3.25

4. The difference between a number and five is multiplied by negative two. The  resulting product equals fourteen.

[tex](x-5)*-2=-14[/tex]

Solving

[tex](x-5)*-2=-14\\-2x+10=-14\\-2x=-14-10\\-2x=-24\\x=-24/-2\\x=12[/tex]

So, value of x=12

5. The sum of a number and two is equal to the quotient of six and negative four.

[tex]x+2=\frac{6}{-4}[/tex]

Solving:

[tex]x+2=\frac{6}{-4}\\x+2=-\frac{3}{2}\\x= -\frac{3}{2}-2\\x=\frac{-3-2*2}{2} \\x=\frac{-3-4}{2} \\x=\frac{-7}{2} \\x=-3.5[/tex]

So, value of x=-3.5

Now arranging based on values of x

x=-10, x=-13, x=3.25, x=12, x=-3.5

First x=-13 (The sum of a number and three is divided by five. The result is negative two.)

Second x=-10 (Half of a number is added to four. This sum is equivalent to negative one.)

Third x=-3.5 (The sum of a number and two is equal to the quotient of six and negative four.)

Fourth x=3.25 (The difference between four times a number and five has a result of negative eight.)

Fifth  x=12 ( The difference between a number and five is multiplied by negative two. The  resulting product equals fourteen. )

Every week, Hector’s 20 hours earns $210.00. He earns a constant amount of money per hour.

Part B
Write an equation that can be used to determine Hector's earnings, in dollars, m, for h hours of work.

Answers

Answer: 20 weeks in 1 week

in 2 weeks 40

Step-by-step explanation:

This proves that the equation is true

Please ANSWER Correctly The Question will be Placed first then the graphs will be placed in order for answer choices from A - D

Answers

Answer:

C

Step-by-step explanation:

Answer:

Option C

Step-by-step explanation:

By looking at the points for (x,y) in the tables, we notice that the only graph that has the points at (-1,-3), (1,2) and you can assume the other points will be on the graph from the table.

Question 6 (5 points)
(03.02 MC)
What is the length of the third side of the window frame below? (5 points)
(Figure is not drawn to scale.)


30 inches
36 inches
50 inches
75 inches

Answers

Answer:

30 inches

Step-by-step explanation:

using a^2+b^2=c^2

72^2=5184

30^2=900

5184+900=6084

√6084=78

Answer:

30

Step-by-step explanation:

⬚︎ - 5 = 6. what is the value of the square

Answers

11 is the value of the square

Determine how (if possible) the triangles can be proved similar.

Answers

Answer:

It's not similar :)

hope this helps<3

The triangles are not similar because the sides are not proportional.

What are Similar Triangles?

Similar triangles are those triangles which has the same shape but different size.

The length of sides and angles are proportional in similar triangles.

So we know that length of sides are proportional.

If we find the ratio of corresponding sides of the two triangles, then they must be equal to a common value.

We have only the length of two sides of each triangle.

If those sides are proportional, we must have an angle of each triangle to be equal.

Here, the angles formed by the intersecting lines are vertical angles and are thus equal.

Let's look if the sides are proportional.

20 / 36 = 5/9

24 / 42 = 4/7

Sides are not proportional.

Hence the given triangles are not similar.

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Simplify Each Expression By Combining Like Terms.
1) 11x+9x
2) 8y-7y
3) 5t-7t
4) -n+4n
5) 5w^2 + 12w^2
6) 2x^2 - 9x^2
7) -4y^2 + 9y^2
8) 6c-4 + 2c-7
9) 5-3x+y+6

Answers

Answer:

1) 11x + 9x

= 20x

2) 8y - 7y

= 1y

= y

3) 5t - 7t

= -2t

4) -n + 4n

= 3n

5) 5w² + 12w²

= 17w²

6) 2x² - 9x²

= -7x²

7) -4y² + 9y²

= 5y²

8) 6c - 4 + 2c - 7

= 8c - 11

9) 5 - 3x + y + 6

= 11 - 3x + y

After school, Maya and Naomi headed to the beach, 6 miles away. Maya decided to bike while Naomi took a bus. The graph below shows their journeys, indicating the time and distance traveled. What was the difference, in miles per hour, between Naomi's and Maya's average speeds?

Answers

Answer:

24

Step-by-step explanation:

You take the end points for the graphs and ignore the bumpy areas since it is taking the average and that is irrelevant to the question. naomi is 6 m/10 min which is 36 mph and maya is 12 mph. 36-12=24.

Answer:

Step-by-step explanation:

Need answers for this please.

Answers

Answer:

Step-by-step explanation:

Which equation has x = -i and x = = 21v3 as two of its solutions?

Answers

Answer:

The equation in option A is correct.

Step-by-step explanation:

Given the equation

[tex]\:y=x^4+13x^2+12[/tex]

Let us find the solution by setting y=0

[tex]x^4+13x^2+12=0\:\:\:\:\:[/tex]

[tex]\mathrm{Rewrite\:the\:equation\:with\:}u=x^2\mathrm{\:and\:}u^2=x^4[/tex]

[tex]u^2+13u+12=0[/tex]

if [tex]ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]

[tex]u+1=0\quad \mathrm{or}\quad \:u+12=0[/tex]

[tex]u=-1,\:u=-12[/tex]

[tex]\mathrm{Substitute\:back}\:u=x^2,\:\mathrm{solve\:for}\:x[/tex]

[tex]x^2=-1,\:x^2=-12[/tex]

solving

[tex]x^2=-1[/tex]

[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=\sqrt{-1},\:x=-\sqrt{-1}[/tex]

[tex]x=i,\:x=-i[/tex]            ∵ [tex]\:\sqrt{-1}=i[/tex]

solving

[tex]x^2=-12[/tex]

[tex]\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=\sqrt{f\left(a\right)},\:\:-\sqrt{f\left(a\right)}[/tex]

[tex]x=\sqrt{-12},\:x=-\sqrt{-12}[/tex]

[tex]x=2\sqrt{3}i,\:x=-2\sqrt{3}i[/tex]

Hence, the solutions are:

[tex]x=i,\:x=-i,\:x=2\sqrt{3}i,\:x=-2\sqrt{3}i[/tex]

Therefore, the equation in option A is correct.

We are planning a reception for our daughter. The hall that we are renting charges a $90 cleanup fee. In addition to the cleanup fee, they charge $29 per guest for food and drinks.
If we have $3,100.00 available, what is the maximum number of guest we can invite without going over our budget?

Answers

Answer:

The equation is y = 29x + 90. So, if you plug in 3,100.00 for y.

3,100.00 = 29x + 90

3,100.00 - 90 = 29x

3,010.00 = 29x

3,010.00/29 = 29x/29

x = 103 guests

isolate the variable on the following problem. show your work.

11z= 4​

Answers

Divide by 11 to make z by itself
z = 4/11
(1/11)(11z)= 4(1/11)
Z= 4/11 is the answer in fraction form

( 2 + 2i )^20=
(a) 2^20
(b) 2^30
(c) 2^20i
(d) -2^30​

Answers

24

34

22i

-34

yup your welcome

Figure PQRS is shown below.
(Figure P Q R S has 4 congruent sides. 2 angles are right angles.)
Which names accurately describe figure PQRS? Select three options.
- parallelogram
- pentagon
- rectangle
- rhombus
- trapezoid
Thanks! Will be awarding brainliest to the person who answers the quickest.

Answers

Answer:

parallelogram, rectangle, rhombus

Step-by-step explanation:

have a wonderful day

Parallelogram, rectangle, rhombus  names accurately describe figure PQRS.

What is Quadrilateral?

A quadrilateral is a four-sided polygon, having four edges and four corners.

The given figure PQRS is a quadrilateral.

A parallelogram is a two-dimensional geometrical shape whose sides are parallel to each other.

A rectangle is a special case of a parallelogram in which each pair of adjacent sides is perpendicular.

A rhombus is a quadrilateral whose four sides all have the same length.

The figure satisfies the properties of parallelogram, rectangle and rhombus.

Hence, parallelogram, rectangle, rhombus  names accurately describe figure PQRS.

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FIRST CORRECT ANSWER WILL GET BRAINLIEST
What is the y-intercept of the line on the given graph?

A)4

B)-2

C)2

D)-4

Answers

Answer:

2

The y intercept is the point at which a line crosses the y axis. In the graph the y axis is crossed at 0, 2 or just 2

Step-by-step explanation:

plsss help i especially need 4 & 5 pls ill give brainliest to right answer

Answers

Answer:

4. y = 15x

5. y = 0.375x ([tex]y=\frac{3}{8}x[/tex])

Step-by-step explanation:

15 * 1 = 15

6/16 = 0.375

3. Ms. Turner's garden has side lengths of V17 yards and V24 yards.

Mr. Webster's garden has side lengths of V5 yards and 138 yards.

Compare the areas of the gardens. Decide whose garden is larger and by how much. Be sure to

explain your thinking. (A = lw)

+

10:04 PS

Answers

Answer:

Mr. Webster's garden is greater than Ms. Turner's garden by 282 sq. yards.

Step-by-step explanation:

Representing the length of the garden by l and width of the garden by w.

For turner's garden, given that l= 24 yards and w= 17 yards.

As the area, A, of the rectangular garden having  length l and width w is

So, the area of Ms. Turner's garden, = 24x17=408 sq. yards

For turner's garden, given that l= 5 yards and w= 138 yards.

So, by using equation (i),

the area of Mr. Webster's garden, = 5x138=690 sq. yards

Here, [tex]A_2 > A_1[/tex], and  

= 690-408= 282 sq. yards.

Hence, Mr. Webster's garden is greater than Ms. Turner's garden by 282 sq. yards.

Solve for x and then find the measure of angle, A.

Answers

X= 25 because you set both equations equal to each other so 6x - 2 = 4x + 48 then to find the measure of the angle you plug in the value of X. So angle A = 6(25) -2 = 148

Answer:

x = 25 ; m∠A = 148°

Step-by-step explanation:

∠A ≅ ∠B (alternate exterior angles)

(6x - 2)° = (4x + 48)°

2x = 50

x = 25

m∠A = 6(25) - 2 = 148°

Divide. Write your answer as a fraction or a mixed number in simplest form

8 2/3 • 1 7/9

Answers

The addition of the fraction 8 2/3 + 1 7/9 is 10 4/9.

What is a fraction?

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, the addition of the fraction will be:

= 8 2/3 + 1 7/9

= 8 6/9 + 1 7/9

= 9 13/9

= 9 + 1 4/9

= 10 4/9

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What is the y-intercept of the function f()=4-5x? ​

Answers

Answer:

Step-by-step explanation:

4

How much higher is 500 than -400m

Answers

Answer:

Obvious 500 is higher than -400m

YOU GET CORRECT YOU GET BRAINLIEST!!!!!!!

Answers

The answer is 6 you just divide

Answer: 6

Step-by-step explanation:

PLEASE HELP ME I WILL GIVE YOU BRAINIEST ANSWER

Answers

Answer: What is the question?

Step-by-step explanation: The slope is 1x and the equation is y=x+3

f(x) = x2. What is g(x)?

Answers

Answer:

its C. yw

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

i did the test

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