A teacher spends $354 on costumes and microphones for six cast members in a play. Each cast member receives a costume that costs $38 and a microphone that costs $c What did the teacher spend on each microphone? The teacher spent $ ___on each microphone. Question 2 Justify your answer.

Answers

Answer 1

The teacher spend some amount on buying costumes and microphones for 6 cast members.

GiveN:

Cost of each costume = $38Cost of each microphone = $cTotal money spent = $354

Let's frame the equation. Total money is the total amount spent for 6 cast members.

Money spent on costumes = $38 × 6

Money spent on microphone = $c × 6

Equation:

[tex]6 \times 38 + 6 \times c = 354[/tex]

Taking 6 as common,

[tex]6(38 + c) = 354[/tex]

Dividing 6 from both sides,

[tex] \dfrac{6(38 + c)}{6} = \dfrac{354}{6} [/tex]

[tex]38 + c = 59[/tex]

Solving further,

[tex]38 + c - 38 = 59 - 38[/tex]

[tex]c = 21[/tex]

So, the cost of each microphone = $21

The teacher spent this much on each microphone.

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Answer 2

The teacher spent  $21 on each microphone.

How to form an equation?

Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.

In other words, an equation is a set of variables that are constrained through a situation or case.

The total amount of teachers have = $354

Cost of costume for all 6 members ;

6 × 38 = $228

Cost of microphone for all 6 members ;

6 × c = 6c

Now,

Cost of microphone  + Cost of costume =  total amount

6c + 228 = 354

6c = 126

c = 21

Hence "The teacher spent  $21 on each microphone".

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Related Questions

what is 987 rounded to the nearest tenth? plzzzzz help

Answers

Answer:

990 that's the answer .

Answer:

990

Step-by-step explanation:

What is the product of 5/8 x 3/4 ?

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Answer:

15/32 or 0.46875

Step-by-step explanation:

Answer:

Step-by-step explanation:

B

Can someone please please pleaseee helppp

Answers

Step-by-step explanation:

Hey there!!!

Here,

The point is, (-3,1).

Using one point formula.

(y-1)= m(x+3)....1st equation.

It has said that it is also perpendicular to the line y = 1/3x + 2 .......2nd equation.

Now, the equation with y = mx + c.

We get slope (m2) = 1/3.

Now,

As per the condition of perpendicular lines,

[tex]m1 \: \times m2 = - 1[/tex]

[tex]m1 \times \frac{1}{3} = - 1[/tex]

Simplifying them we get,

m1 = -3.

Therefore the slope is -3.

Hope it helps...

helppp first to answer get brainlist​

Answers

Answer: c

Step-by-step explanation:

Solve using the order of Operations:
- 5- (- 4 + 2)2
O -1
0-9
O 9
O 1
Math

Answers

Hey there! I'm happy to help!

Order of operations is PEMDAS. Parentheses comes first.

(-4+2)=-2

So, now we have -5-(-2)2

The next available option is multiplication.

-5-(-4)

Now we do addition and subtraction.

-5+4

-1.

Have a wonderful day! :D

f(x) = 2x – 5
g(x) = 4x – 1
Find f (g(x)).
help please !!

Answers

Answer:

Hey there!

g(x) is 4x-1

f(g(x) is f(4x-1)

f(4x-1)=2(4x-1)-5

f(4x-1)=8x-2-5

f(4x-1)=8x-7

The answer is 8x-7

Let me know if this helps :)

how to solve the value for x

Answers

Answer:

x>6;x>2 or just x>2 if u combine intervals

Step-by-step explanation:

x^2-8x+12>0

factor: (x-6)(x-2)>0

split: x-6>0; x-2>0

add 6 and 2: x>6;x>2

combine intervals: x>2

can someone help solve this math problem with steps and detail pls :) I really confused

Answers

Division first:

-2/5 / 8/15

When dividing two fractions flip

The second one over and multiply:

-2/5 x 15/8 = (-2x15)/(5x8) = -30/40 = -3/4

Now you have:

2-3/4-3/4

2-3/4 = 1 1/4

1 1/4 - 3/4 = 1/2

The answer is 1/2

what is this answer and please show me how you got it so I can know how you got it.y= 3 [tex]\sqrt{x + 4} -6[/tex] please hurry also :0 giving 35 points to those who answer first

Answers

X=2


To find -intercept/zero, substitute y=0


Divide both sides of the equation by 3

The only way a root could be 0 is when the radicand equals 0

Calculate the difference
And you should get x=2


can a rational number + a rational number = irrational number

Answers

Answer:

no

Step-by-step explanation:

its just like a positive number + a positive number cannot equil a negitive number.

i need help please and thanks a lot ​

Answers

Step-by-step explanation:

[tex] \huge \: K = \frac{1}{2} m {v}^{2} \\ \\ \huge \: 2 K =m {v}^{2} \\ \\ \huge \purple{ \boxed{m = \frac{2 K}{ {v}^{2} } }}[/tex]

NEED HELP ASAP SHOW WORK PLSSSS

Answers

Answer:

Hey there!

6x+1+3=8x+1

6x+4=8x+1

6x+3=8x

3=2x

x=1.5

6(1.5)+1

10

SR is 10 units long.

Let me know if this helps :)

Juan purchased 16 lemons and used 5 on the first day of making lemonade. On the second day, he purchased 12 lemons and used 11. Juan wrote this expression to find how many lemons he should have left.

(16 – 5) + (12 – 11)

Answers

You do what is in the parentheses first and then add them together.
So:
11+1=12

Answer:

Juan purchased 16 lemons and used 5 on the first day of making lemonade. On the second day, he purchased 12 lemons and used 11. Juan wrote this expression to find how many lemons he should have left.

Step-by-step explanation:

11+1=12

the correct simplified form of 2y5+4y5−3y3−5y3

Answers

Hey there! I'm happy to help!

Numbers with the same variable and exponent are like terms and can be simplified.

[tex]2y^5+4y^5=6y^5[/tex]   (variable is y, exponent is 5)

[tex]-3y^3-5y^3=-8y^3[/tex] (variable is y, exponent is 3)

So, our final simplified form is [tex]6y^5-8y^3[/tex].

Have a wonderful day! :D

answerers about Caca Andika from Indonesia

show all steps for 4.7x+90=5.6x+2.1x

Answers

Answer:

x=30

Step-by-step explanation:

4.7x+90=5.6x+2.1x4.7x+90=7.7xSubtract 4.7 on both sides 3x=90x=30

An investment company pays 7​% compounded semiannually. You want to have $24000 in the future. ​ How much should you deposit now to have that amount 5 years from​ now?

Answers

Answer: You should deposit about $17014 or little more

Step-by-step explanation:

use the compound interest formula.

A= p( 1 + r/n)^nt

Where A is the amount you will save over some  years .

p is the principal or start up  amount mostly known as the initial fee.

r is the interest rate represent by a decimal so 7% will be 0.07.

n is the number of times the interest is being applied annually. Semiannually means  twice.  So n will be 2.

T is the time the money will elapsed. So in 5 years the money will elapse. Now input the values into the formula and solve for p the principal.

24,000 = p( 1 + 0.07/2)^2*5

24,000= p( 1 + 0.035)^10

24000 = p( 1.035)^10

24000 = p( 1.41059876062)  Divide both sides by 1.41059876062

p = 17104  

Which means you should deposit about $17014 or little more

Find the distance between (5,3)and(9,7)

Answers

Answer:

wouldnt it be 4,4?

Step-by-step explanation:

Answer:

Step-by-step explanation:

Calculate the distance between two points by filling in the x and y values of both coordinates. How do you find the distance between two points? Distance Formula : Example: For two points, (3,2) and (15, 10) the distance is calculated as: Distance = 14.42 (rounded to the nearest 100th)

2.9 x 10^5 + 8.7 x 10^5

Answers

Answer:

So this is scientific notation what you do is

2.9x10^5 so you put however many zeros the is powered to 10. See there is a 5 It has to be behind or in front of the decimal you might be saying how do you know if its behind or in front well negative is in front and positive is behind .

290,000 there was a number already behind the decimal so there you go 5 number behind the decimal.  

Same for the second one

290,000  870,000 is your answers so now you add hem together

1,160,000 is your final answer

Step-by-step explanation:

solve for T

10t = -50​

Answers

Answer: t=-5

Step-by-step explanation:

if 10t=-50, you have to solve for the equation. to solve, you have to get the variable by itself. to get the variable by itself, you have to divide both sides by 10. 10t/10=-50/10. t=-5

absolute value of 100​

Answers

Answer:

100

Step-by-step explanation:

Think of the absolute of a number as the distance from that number to zero on the number line. The distance from 100 to 0 on the number line is 100, so absolute value of 100 is 100. Notice that -100 is also at a distance of 100 from zero, so |-100| = 100.

|100| = 100

Find the midpoint between each pair of points.
(7,-2) and (-4,2)

Answers

Answer:

Midpoint: [tex](\frac{3}{2} ,0 )[/tex]

Step-by-step explanation:

Midpoint Formula: [tex](\frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} )[/tex]

Step 1: Define variables

x₁ = 7

x₂ = -4

y₁ = -2

y₂ = 2

Step 2: Plug into midpoint formula

[tex](\frac{7-4}{2} ,\frac{-2+2}{2} )[/tex]

Step 3: Simplify/Evaluate

[tex](\frac{3}{2} ,\frac{0}{2} )[/tex]

[tex](\frac{3}{2} ,0 )[/tex]

What is the missing statement and the missing reason in step 5? A 2-column table with 7 rows. Column 1 is labeled statements with the entries measure of angle A D E = 60 degrees and measure of angle C D F = (3 x + 15) degrees, angle A D E and angle C D F are vertical angles, angle A D E is-congruent-to angle C D F, measure of angle A D E = measure of angle C D F, question mark, 45 = 3 x, and, 15 = x. Column 2 is labeled reasons with the entries given, definition of vertical angles, vertical angles congruent, definition of congruency, question mark, subtractive property, division property. Statement: 60 = 3x + 15; Reason: substitution Statement: x = 15; Reason: subtraction property of equality Statement: 60 = 3x + 15; Reason: transitive property Statement: x = 15; Reason: subtraction and division properties of equality

Answers

Answer:

Statement: 60 = 3x + 15; Reason: substitution

(aka A)

Step-by-step explanation:

The missing statement and the missing reason in step 5 is;

Statement: 60 = 3x + 15;   Reason: substitution

Here,

We have to find the missing statement and missing reason.

What is Substitution method?

Substitution method is algebraic method to solve the linear equations .

Now,

Column 1 and column 2 are labeled here as;

Angle A D E = 60 degrees                ( entries given)

Angle C D F = (3 x + 15) degrees

Angle A D E and Angle C D F are vertical angles.  (definition of vertical angles)

Angle A D E is-congruent-to Angle C D F.  ( definition of congruency)

Measure of angle A D E = Measure of angle C D F.

 60 = 3x + 15      ( substitution )

⇒  45 = 3 x            ( subtractive property )

⇒  15 = x             ( division property )

Hence, The missing statement and the missing reason in step 5 is;

Statement: 60 = 3x + 15;   Reason: substitution

Learn more about the substitution method visit:

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Mr. Bins sold 1/2 of his farm to Mr. Frost and 100 acres to Mr. Slate. He now has 1/5 of his original farm land. How big was his farm originally? How much land does he have now?

Answers

Answer:

Step-by-step explanation:

1/2

PLEASE HELP!!! Write a quadratic equation if its roots are: [tex]\sqrt{3} -1/2[/tex] and [tex]\sqrt{3} +1/2[/tex]

Answers

Answer:

x²- √3 x +1/2

Step-by-step explanation:

To write a quadratic equation with roots only:

x² -(sum of the roots)x+(product of roots)

x²-((√3-1/2)+(√3+1/2)x + ((√3-1/2)(√3+1/2)

x² -(2√3)/2 + ( 9-1)/4

x²- √3 x +1/2

(7x7x7x7x7x7x7)-3x-3x-3

Answers

Answer:

823516

Step-by-step explanation:

hope this helps

Answer:

7^7 times -3^3, or -22235661

Step-by-step explanation:

Solve the polynomial by graphing. Round to the nearest tenth.
3x^5-8x^4+2x^3+5x^2-2x+1=0

Answers

d trust me edge 2020

Graph the system below and write its solution. Y=1/2x-1
-2x+y=4
You can answer no solution or infinitely many

Answers

Answer:

x = -3.3333333

y = -2.666666

Step-by-step explanation:

y = 1/2 x - 1

y = 2x + 4 The second equation has the 2x moved to the right side. The y's must be equal so equation the two equations.

1/2x -1 = 2x + 4             Subtract 1/2x from both sides.

-1 = 2x - 1/2 x + 4          Combine

-1 = 1.5x + 4                   Subtract 4 from both sides

-1 - 4 = 1.5x

- 5 = 1.5x                       Divide both sides by 1.5

-5/1.5 = x

x = - 3.333333

Now put x = - 3.333333 into either one of the two given equations. The first one will require one less step, but it does not matter.

y = 1/2 (- 3.3333333) - 1

y = - 1.6666666 - 1

y = -2.6666666

what is the answer to -5x-x

Answers

Answer:

- 6x

Step-by-step explanation:

Step 1:

- 5x - x

Answer:

- 6x

Hope This Helps :)

- 6x

Step 1:   - 5x - x

Answer:  - 6x

Sarah sold 12 boxes of girl scouts cookies. If Sarah sold three times as many boxes as Amiyah, how many boxes did Amiyah sell?

Answers

Answer:4

Step-by-step explanation:

Amiyah sold 4 boxes.

you would set this up as 3x = 12.
to solve, just divide the 12 by 3, leaving you with X = 4.

The perimeter of a rectangle is 50 inches.if the width of the rectangle is 5 inches smaller then twice the length,find the AREA of the rectangle in square inches

Answers

Twice it size it’s 10 set 5 x10 to 50
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