Try this you will get 10 point i think please try to do correct

A Broadway theater has 800 seats, divided into orchestra, main, and balcony seating. Orchestra seats sell for $ 40 comma main

KatRina [158]

Answer:

<em>orchestra seats: main seats: balcony seats: 160: 400: 240</em>

Step-by-step explanation:

Let number of orchestra seats = x

Let number of main seats = y

Let number of balcony seats = z

As per given statement, total seats are 800

$x +y+z=800 ..... (1)$

Sales price of each orchestra seat = $40

Sales price of each main seat = $30

Sales price of each balcony seat = $20

If all the seats are sold, total revenue is $23200.

$\Rightarrow 40x + 30y+20z=23200 ...... (2)$

If all the main and balcony seats are sold, but only half the orchestra seats are sold, the gross revenue is $ 20 comma 000.

$\Rightarrow 40\times \dfrac{x}{2} + 30y+20z=20000\\\Rightarrow 20x + 30y+20z=20000 ...... (3)$

Here, we have 3 variables and 3 equations. Let us solve them.

Subtracting Equation (3) from equation (2):

$\Rightarrow 20x = 3200\\\Rightarrow x = 160$

Putting value of x in equations (1) and (2):

Equation (1)

$\Rightarrow 160 +y+z=800\\\Rightarrow y+z=640 ...... (4)$

Equation (2)

$\Rightarrow 40\times 160 +30y+20z=23200\\\Rightarrow 30y+20z=16800\\\Rightarrow 3y +2z=1680 ...... (5)$

Equation (5) - 2 $\times$ Equation(4):

$\Rightarrow y =400$

Putting value of y in equation (4):

$400 +z = 640\\\Rightarrow z =240$

Hence, answer is:

<em>orchestra seats: main seats: balcony seats: 160: 400: 240</em>

4 0

3 years ago

Is f(x)=5x^2+6x^3 a polynomial function

anastassius [24]

Polynomials are expressions whose exponents are non-negative integers and the coefficients are real numbers. The leading term is the term with the highest power. The coefficient of the leading term is the leading coefficient. The power of x in the leading term is called the degree of the polynomial! Here are some examples of polynomials:
Degree Name Example
0 constant 11
1 linear 4x + 7
2 quadratic 3x2 + 4x + 5
3 cubic 4x3 + 3x + 7
4 quartic 3x4 + 2x2 + 4
5 quintic x5 + 3x + 1
Any value of x such that P(x) = 0 is a root of the equation and a zero of the function.
Review of synthetic substitution
To use synthetic substitution, do the following:
1) Write the polynomial in descending order.
2) Make sure any missing terms are replaced with zero!
3) Bring down the leading coefficient.
4) Multiply by the divisor and add to the next term.
5) Repeat the process until the last coefficient is reached.

Example
Use synthetic division to find P(2) for P(x) = 2x3 - 9x2 + 27
2| 2 -9 0 27
4 -10 -20
2 -5 -10 7 The value of P(2) = 7, the last number!!
Sample Problems
1) State whether each is a polynomial function. If yes, find the degree and the zeros.
Problem Polynomial? Degree zeros
a) f(x) = 5 - 4x yes 1 5/4
b) f(x) = 3x2 - 6x yes 2 0, 2
c) f(x) = x - 3/x no
d) f(x) = 18 yes 0 none
e) f(x) = (x-3)/(x+2) no
2) Use synthetic substitution to find P(3) for each function:
a) P(x) = 4x3 - 5x2 + 3
3| 4 -5 0 3
12 21 63
4 7 21 66
Therefore, P(3) = 66

b) P(x) = 3x4 + 2x3 - 5x - 2

3| 3 2 0 -5 -2
9 33 99 282
3 11 33 94 280
Therefore, P(3) = 280

3) If 4 is a zero of f(x) = 3x3 + kx - 2, find the value of k.
Since 4 is a zero, the value of f(4) = 0. Use synthetic substitution.
4| 3 0 k -2
12 48 192 + 4k
3 12 48 + k 190 + 4k
Now 190 + 4k = 0, solve for k
4k = -190
k = -190/4 = -47.5

3 0

4 years ago

How many one-fourth cup servings are in 9 cups of peanuts?

musickatia [10]

So the question is "How many 1/4ths are inside 9 cups?"

We can divide 9 by 1/4:

9/1 ÷ 1/4.

Reciprocal and multiplication symbol:

9/1 * 4/1

36.

There are 36 one-fourth cups servings in 9 cups of peanuts.

6 0