Solve equations with variables on each side
3w+6=4w
a+18=7a
8c=5c+21

Answers

Answer 1

Answer:

a) w=6

b) a=3

c) c=7

Step-by-step explanation:

[tex]3w+6=4w[/tex]

[tex]\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}[/tex]

[tex]3w+6-6=4w-6[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]3w=4w-6[/tex]

[tex]\mathrm{Subtract\:}4w\mathrm{\:from\:both\:sides}[/tex]

[tex]3w-4w=4w-6-4w[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-w=-6[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-1[/tex]

[tex]\frac{-w}{-1}=\frac{-6}{-1}[/tex]

[tex]w=6[/tex]

___________________________________________

[tex]a+18=7a[/tex]

[tex]\mathrm{Subtract\:}18\mathrm{\:from\:both\:sides}[/tex]

[tex]a+18-18=7a-18[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]a=7a-18[/tex]

[tex]\mathrm{Subtract\:}7a\mathrm{\:from\:both\:sides}[/tex]

[tex]a-7a=7a-18-7a[/tex]

[tex]\mathrm{Simplify}[/tex]

[tex]-6a=-18[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-6[/tex]

[tex]\frac{-6a}{-6}=\frac{-18}{-6}[/tex]

[tex]a=3[/tex]


Related Questions

Scott has 18 3/4 gallons of gas in his tank. If he uses 3/50 gallons of gas per mile he drives how many miles can he drive before his tank is empty.? Pls help!

Answers

Answer:

Step-by-step explanation:

I’m sorry that i can’t fully help and that i answered it wrong twice i also got stuck. I hope someone else helps you and that you get an a

18 3/4 as an improper fraction is 75/4.

75/4 can be re-written as 1875/100 (multiply both sides by 25)

3/50 can be re-written as 6/100 (multiply both sides by 2)

At midnight, the temperature was 31.2°F. In the morning, the temperature was −6.7°F. Which statement describes the temperatures?

At midnight, the temperature was 31.2 degrees above 0, and in the morning, it was 6.7 degrees lower.
At midnight, the temperature was 31.2 degrees below 0, and in the morning, it was 6.7 degrees higher.
At midnight, the temperature was 31.2 degrees above 0, and in the morning, it was 6.7 degrees below 0.
At midnight, the temperature was 31.2 degrees below 0, and in the morning, it was 6.7 degrees above 0.

Answers

Answer:

The third statemnet

Step-by-step explanation:

I say the third statement is correct because it says its 31.2 degrees above 0 which is positive. Also it says in the morning it was 6.7 below 0 which is negative which equlas-6.7. So that is why statement 3 is the correct answer.

Fran runs 5.4 miles a day. How far will he run in 6 days?

Answers

32.4 miles in 6 days.

Step-by-step explanation-

Given:-

Fran runs 5.4 miles a day.

To find:-

How far will he run in 6 days.

Solution:-

Multiply using the formula

[tex]d = s \times t[/tex]

So, multiply:-

[tex]5.4 \times 6[/tex]

[tex] => \: 32.4 \: miles[/tex]

Therefore, he ran 32.4 miles in 6 days.

✍️ By Benjemin ☺️

Which of the following are valid names for the given triangle? Check all that apply

Answers

Step-by-step explanation:

i think the answer is c MAX

What is 441 divided by 7 with a remainder

Answers

Answer:

63

Step-by-step explanation:

Answer:  

The answer to 441 divided by 7 calculated using Long Division is:

63

0 Remainder

Step-by-step explanation:

pls help me pls pls pls

Answers

Answer: I helped you. Troll!

Given j∥k and m∠1=40°. What is m∠6 ? Enter your answer in the box.

Answers

Answer:

140

Step-by-step explanation:

-3(x+3)+5<-3
How do you solve this inequality

Answers

Answer:

x<1/-3

Step-by-step explanation:

Distribute -3 to (x+3)

-3x-9+5<-3

add like terms (-9+5=-4)

-3x-4<-3

add 4 to both sides

-3x<1

divide both sides by -3

x<1/-3

At a department store, a woman's total was $284.00 for 7 items.

Answers

Answer:

40.5714

Step-by-step explanation:

Based on the given conditions, formulate: 284 ÷ 7

Evaluate the equation/expression: 40.5714

get the result: 40.5714

Answer: 40.5714

What is 0.000000037 written in scientific notation?

Answers

The scientific notation is 3.7 × 10^-8

:)


Simplify the algebraic expressions: 9(7x - 7)+(5x - 9)

Answers

the answer would be 68x-72

Answer:

7x-7=0

5x-9=4x

4x(9)=36

x=36

OA.
Simplify the expression -3: (-3)
.
-7
-1
Oc. 1
OD. 71 격
CIH NIH
O B.
O .

Answers

Answer:

I hope I help you with your Q

THANKS GIVE MY LIKE

represent the following situations using quadratic equation in standard form
1. If the square of a number is added to 8 times the number, the result is 100
2. Mr. Apoloan wants to lay out a rectangular playground with an area of 30 square feet. The desired length will be 7 times the width​

Answers

1. If the square of a number is added to 8 times the number, the result is 100.

Let x be the number.

Equation: x² + 8x - 100 = 0

2. Mr. Apoloan wants to lay out a rectangular playground which will contain 30 square feet. The desired length will be 7 times the width.

Area: 30ft²

Length: 7w

Width: w

Area of a rectangle: LW

(7w)w = 30ft²

Equation: 7w² - 30 = 0

How many real solutions does the equation have? √3x-1 =2x-5

Answers

Answer: 2 soulutions

Step-by-step explanation: Just factor them and solve the answer would be x = 4 √3 + 8 in its exact form and x = 14.92820323... in its decimal form

Describe how to round set to the best
HELP PLEASE QUICKLY

Answers

Round the number to the nearest ten or hundredth or thousands ex: 177 you would round it to 200

Please help me due soon

Answers

he bought 20 pounds of pet food

The circumference of the inner circle is 44 ft.
The distance between the inner circle and the outer circle is 4 ft.

Answers

Answer:176 is the answer if your asking for the outer circles circumfer

Step-by-step explanation:

Which of the following equations is the translation 2 units down of the graph of y = |x|?
y= lx - 2|
y= |x + 2|
y=|x| - 2
y=|x| + 2

Answers

Answer is: y = | x | - 2

I am cooking a recipe. It requires 7/2 of sugar. I only have a 1⁄4 cup to measure the sugar with. How many quarter cups would I need to measure the correct amount of

Answers

Answer:

14

Step-by-step explanation:

Convert [tex]\frac{7}{2}[/tex] to a fraction with a common denominator

[tex]\frac{7}{2} (\frac{2}{2} )=\frac{14}{4}[/tex]

You now divide the fractions to find the amount of correct measurements needed.

[tex]\frac{\frac{14}{4} }{\frac{1}{4} }[/tex] For dividing by a fraction it is the same a multiplying by its reciprocal.

This becomes [tex]\frac{14}{4} (\frac{4}{1} )=\frac{14}{4} (4)=14[/tex]

You will need 14 correct measurements.

HELPPPP

Which expression is a perfect square?
A. x² - 4x + 4
B. x2 - 4x - 4
C. 12 - 9x + 9
D. 12 - 9x – 9

Answers

Answer: Choice A

========================================================

Explanation:

A perfect square trinomial is of the form

(m+n)^2 = m^2 + 2mn + n^2

We can see why this works through use of the FOIL rule.

So the first and last terms must be perfect squares, and they must be positive. This rules out choices B and D since we have -4 and -9 as those last terms being negative.

Choice C is ruled out because the middle coefficient -9 isn't correct. The middle coefficient must be some even number since 2 is a factor of 2mn.

This leaves choice A. We can do a bit of trial and error to find that

(x-2)^2 = x^2 - 4x + 4

showing that choice A is a perfect square trinomial.

Answer:

A) x² - 4x + 4

Step-by-step explanation:

Given the following special factoring formulas on perfect square trinomials:

u² + 2uv + v² = (u + v)²

u² - 2uv + v² = (u - v)²

Apply these concepts on the given set of equations to see which special factoring formulas apply on the given options. I will only work on one of the given options, and you could apply these same techniques on the other ones to compare the results with your calculations.

To find the binomial factors of quadratic equations, you must find factors with product uv, and sum v.

In Option A: x² - 4x + 4

Right off the bat, it seems like the difference of squares may apply to this equation.  You must find the factors that will product of 4 and a sum of -4.

The possible factors are:

product uv: -2 × -2  = 4,

sum v :  -2 + -2 = -4

Hence, the binomial factor of x² - 4x + 4 =  (x - 2)²

If you expand this binomial through FOIL method:

(x - 2)(x - 2) = x² - 2x - 2x + 4 = x² - 4x + 4

This means that the trinomial x² - 4x + 4 produces a perfect square binomial factors of (x - 2)².

Therefore, the correct answer is Option A) x² - 4x + 4.

Please mark my answers as the Brainliest, if you find this helpful :)

Can someone maybe help me on number 6 and 7?

Answers

Answer:

39 and 22

Step-by-step explanation:

your adding by 5 so if you continue that you'll get 39

as for the bottom one it's adding by by 3 so if we continue that we'll get 22

4/12 x 2/3 =___________=quien me diga le doy corona

Answers

Answer:

8/36= 2/9

Step-by-step explanation:

Answer:2/9

Step-by-step explanation:

1.) Keisha's kitchen is shaped like a square. The room has an area of 256 feet squared. Which is the length of one side of Keisha's kitchen?

Also the attachment, and is it rational or irrational?

Answers

Answer:

1.  16 ft

[tex]\sf 2.\quad \dfrac{29}{99}[/tex]

Step-by-step explanation:

Question 1

Formula

Area of a square = s²  (where s is the side length)

Given:

Area = 256 ft²

Substitute the given area into the formula and solve for s:

[tex]\sf \implies 256=s^2[/tex]

[tex]\sf \implies \sqrt{256}=\sqrt{s^2}[/tex]

[tex]\sf \implies s=\pm 16[/tex]

As distance is positive, the length of one side of Keisha's kitchen is 16 ft.

Question 2

Converting a recurring decimal to a fraction

Let x equal the recurring decimal:

[tex]\implies \sf x=0.292929...[/tex]

Create another number with recurring 29s by multiplying the above by 100:

[tex]\implies \sf 100x=29.292929...[/tex]

To solve these two equations and write x as a fraction, subtract the first equation from the second to remove all the recurring digits after the decimal point:

[tex]\begin{array}{r r c l}& \sf 100x &= &\sf 29.292929...\\- & \sf x&=& \sf \phantom{..}0.292929...\\\cline{1-4} & \sf 99x&=& \sf29\\\cline{1-4}\end{array}[/tex]

Therefore:

[tex]\implies \sf 99x=29[/tex]

[tex]\implies \sf x=\dfrac{29}{99}[/tex]

Therefore:

[tex]\sf \implies 0.\overline{29}=\dfrac{29}{99}[/tex]

Learn more about converting recurring decimals to fractions here:

https://brainly.com/question/27788661

https://brainly.com/question/27643441

HELPP HURRY PLEASEE!!

Answers

its (a

Answer:

because h is being multipling by πr² and if we swich v for h

h going to be at front and v dividing all the acuation

Sam had $25 more than Mary, and together they had enough money to buy a video game for $57 and to pay $16 for two movie tickets. How much money did Mary have?

Answers

Answer:

Mary had $24

Step-by-step explanation:

So to solve this question, we first have to create an equation.

Mary's money=x

Since Sam had $25 more than Mary, $Sam+$Mary is (25+x)+x.

With this money, they can buy something worth $57 and something worth $16, so that means (25+x)+x=57+16

Now we solve the equation-->

(25+x)+x=57+16

Combine x and x to get 2x.

25+2x=57+16

Add 57 and 16 to get 73.

25+2x=73

Subtract 25 from both sides.

2x=73−25

Subtract 25 from 73 to get 48.

2x=48

Divide both sides by 2.

x= 2/48

Divide 48 by 2 to get 24.

x=24

reflection rule over x-axis , (x,y) =(x,-y). reflect over x-axis C(2,3) what is C

Answers

Answer:

(2, -3)

Step-by-step explanation:

Your answer was in the question, just apply the rule that was given (x, -y).

The coordinates of C(2, -3).

What is reflection?

A reflection is a type of transformation that involves flipping a shape, known as the preimage, across a line, known as the line of reflection, to produce a new shape (called the image). You can picture what would happen if you turned the form across the line to graph a reflection.

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point.

Given:

The Rule for reflection is  (x,y) =(x,-y).

As, the coordinates C(2, 3).

Now, after applying the reflection the coordinate of C become

c(2, 3) ----> C(2, -3).

Hence, the coordinates of C(2, -3).

Learn more about reflection here:

https://brainly.com/question/15487308

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1 + -(2/3) - (-m) m = 9/2

Answers

answer

[tex]m = + 5 \div \sqrt{6 \: } \: \: \: or \: - 5 \div \sqrt{6} [/tex]

Sarah has a credit card balance of $9,450 with an APR of 17%. With her current budgeted payment, Sarah will be able to pay off this debt in 36 months. But Sarah’s best friend just invited her to spend two months in Europe with her in 9 months. Wanting to have her credit card balance paid off before she goes to Europe, Sarah decides to take on a second job. What additional monthly income will Sarah need in order to pay off her credit card in 9 months?
a.
$336.92
b.
$467.23
c.
$788.85
d.
$1125.77

Answers

Sarah needs an additional monthly income of $1125.77 to pay off her credit card in 9 months.

What is an expression?

An expression contains one or more terms with addition, subtraction, multiplication, and division.

We always combine the like terms in an expression when we simplify.

We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.

Example:

1 + 3x + 4y = 7 is an expression.

3 + 4 is an expression.

2 x 4 + 6 x 7 – 9 is an expression.

33 + 77 – 88 is an expression.

We have,

Using the information given,

We can find the current monthly payment Sarah is making using the formula for the present value of an annuity:

[tex]PMT = PV \times r \times (1 + r)^n / [(1 + r)^{n - 1}][/tex]

where PV is the present value (balance), r is the monthly interest rate (APR/12), and n is the number of months (36).

PMT.

[tex]= 9450 \times 0.17/12 \times (1 + 0.17/12)^{36} / [(1 + 0.17/12)^{36} - 1][/tex]

= $338.48

To pay off the balance in 9 months, Sarah needs to increase her monthly payment.

Let's call this additional payment x.

Then, we have:

[tex]9450 \times 1.17^{9/12} = (338.48 + x) \times ((1 + 0.17/12)^{9 - 1}) / (0.17/12)\\[/tex]

Solving for x, we get:

x = $1125.77

Therefore,

Sarah needs an additional monthly income of $1125.77 to pay off her credit card in 9 months.

Learn more about expressions here:

https://brainly.com/question/3118662

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plssss answer the question

Answers

40 apps in one minute
There are 5 sections of 12 seconds in a minute.
If he can download 8 apps every 12 seconds, then in a minute he can download 5 times as that. So 8*5 is 40.
8 apps- 12 seconds
16 apps-24 seconds
24 apps- 36 seconds
32 apps- 48 seconds
40 apps- 60 seconds/ 1 minute
you have to set up a proportion that would be 8/12 and x/60 then you cross multiply 8*60 then divide that by 12 to get x. the answer is 40.

Simplify to create an equivalent expression.
(3n+6)⋅3+(2n+2)⋅4

Please help as soon as possible. Thanks! =D

Answers

Answer:

i don"t know ask your mom

Answer:

[tex](9n + 18) + (8n + 8) \\ = (9n + 8n) + (18 + 8) \\ = 17n + 26[/tex]

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