1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Olin [163]
3 years ago
13

The total number of seats in a movie theater is calculated by adding the area of the upper section given by 8x2 and the area of

the lower section given by 6x2. The theater plans to add an addition of front row seats given by 4x for a total of 138 seats. Which equation could be used to solve for the number of seats in the front row addition?
Mathematics
1 answer:
e-lub [12.9K]3 years ago
3 0
8x^2+6x^2+4x=138  combine like terms on left side

14x^2+4x=138 since the number of seats in the from row is just 4x, subtract 14x^2 from both sides

4x=138-14x^2  that would be the general solution, if you wanted the actual number you would have to solve for x and then multiply that value by 4 to know what "4x" is...

14x^2+4x-138=0

14x^2-42x+46x-138=0

14x(x-3)+46(x-3)=0

(14x+46)(x-3)=0

2(7x+23)(x-3)=0, since x>0

x=3 and thus

4x=12 seats

So there are 12 seats in the front row addition.


You might be interested in
F(x) = 3x^3 - 2x^2 - 11x + 10; (x + 2)<br><br> I need to factor and find the zeros.
Ratling [72]

Answer:

\textsf{Factored function}: \quad f(x)=(x+2)(3x-5)(x-1)

\textsf{Zeros}: \quad x=-2, \quad x=\dfrac{5}{3},\quad x=1

Step-by-step explanation:

<u>Given function</u>:

f(x)=3x^3-2x^2-11x+10

If (x + 2) is a factor then:

\implies f(x)=(x+2)(ax^2+bx+c)

Expand:

\implies f(x)=ax^3+bx^2+cx+2ax^2+2bx+2c

\implies f(x)=ax^3+2ax^2+bx^2+2bx+cx+2c

\implies f(x)=ax^3+(2a+b)x^2+(2b+c)x+2c

To find <em>a</em>, compare the coefficients of x³:

\implies a=3

To find <em>b</em>, substitute the found value of <em>a</em> into the coefficient for x² and compare:

\implies 2a+b=-2

\implies 2(3)+b=-2

\implies b=-8

To find <em>c</em>, compare the constants:

\implies 2c=10

\implies c=5

Therefore:

\implies f(x)=(x+2)(3x^2-8x+5)

Now factor (3x²-8x+5):

\implies 3x^2-3x-5x+5

\implies 3x(x-1)-5(x-1)

\implies (3x-5)(x-1)

Therefore the factored function is:

\implies f(x)=(x+2)(3x-5)(x-1)

<u>Zero Product Property</u>

\boxed{\text{If \; $a \cdot b = 0$ \; then either \; $a = 0$ \;or \;$b = 0$ (or both)}.}

To find the zeros, set each factor equal to zero and solve for x:

\implies x+2=0 \implies x=-2

\implies 3x-5=0 \implies x=\dfrac{5}{3}

\implies x-1=0 \implies x=1

Therefore, the zeros of the function are:

x=-2, \quad x=\dfrac{5}{3},\quad x=1

3 0
1 year ago
A house is being purchased at the price of $138,000.00. The 30-year mortgage has a 10% down payment at an interest rate of 4.875
Mama L [17]

Answer:

  $238,600

Step-by-step explanation:

The amount being borrowed is 100% -10% = 90% of the purchase price, or ...

  0.90 × $138,000 = $124,200.

Then the monthly payment can be computed using the amortization formula:

  A = P(r/12)/(1 -(1 +r/12)^(-12t))

  A = 124200(.04875/12)/(1 -(1 +.04875/12)^(-12·30)) ≈ 657.28

and the total repaid is ...

  (360 months) × ($657.28/month) = $236,619.58*

The cost of mortgage insurance is considered part of the cost of the loan. That amount is ...

  (77 months) × ($25.88/month) = $1992.76

so the total amount paid for the loan is ...

  $236,619.58 +1992.76 = $238,612.34

The cost of the loan is about $238,600.

_____

* In figuring the total repayment cost, we used the full-precision value for the loan payment. The actual repayment amount will depend on the rounded value of the loan payment and the way the final payment is made. When rounded to the nearest $100, these details become unimportant.

3 0
3 years ago
F=5/4(n-90)<br> Find n <br> Helppp
padilas [110]

Answer:

n= 4f/5+90

Step-by-step explanation:

f=  ​5(n−90) /4 (simplify)

f * 4=5(n−90)  (multiply 4 on both sides)

4f=5(n−90)  (regroup)

4f/5 ​​ =n−90 (divide 5 on both sides)

4f/5 ​​ +90=n  (add 90 to both sides)

​​  

4 0
3 years ago
The four corners of a square are located at (-7, -2), (-7,5), (0,5), and (0, -2). What is the perimeter of the square?
12345 [234]

Answer:

A)14 Units is the answer for this question

but check it

8 0
3 years ago
What’s the correct answer for this question?
crimeas [40]

ANSWER

l

Or

Or

EXPLANATION

The given line has slope,

and

We can find the equation in the point slope form, which is given by,

We substitute the point and slope to get,

We can also simplify further to get,

We make y the subject to get,

This is called the slope intercept form.

We could also write in standard form to get

Or

5 0
3 years ago
Other questions:
  • Which expressions are polynomials? Select each correct answer.
    6·2 answers
  • What's the value of 3.872
    7·1 answer
  • There are 4 red and 6 green marbles in a jar. What is the probability of drawing two green marbles, with replacement?
    7·1 answer
  • 32ft/sec to meters/him
    11·1 answer
  • PLEASE HELP!!! Trapezoid ABCD was dilated to create trapezoid A'B'C'D'. Which statements are true about the trapezoids? Check al
    9·1 answer
  • In the year 2005, the average cost of a car could be modeled by the equation C= -15x^2 + 20x - 3 where x is the number of years
    12·1 answer
  • A candidate scored 32 marks out of 80, find his percentage score
    6·1 answer
  • WHO EVER AWNSERS FIRST AND CORRECT GETS BRAINLYIST AND 50 POINTS
    8·2 answers
  • Please help! image is shown below
    10·2 answers
  • What was her score on this exam, rounded to the nearest integer
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!