# Plz help me simply this

Step-by-step explanation:

## Related Questions

A theater has a seating capacity of 750 and charges $3 for children, s5 for students, and$7 for adults. At a certain screening with fll ttendance, there were combined. The receipts totaled $3450. How many children attended the show? ### Answers Answer: Between 150 and 450 Step-by-step explanation: We are going to find the number by resolving a system of linear equations. First we write the system equations : Where C : children, S : students and A : adults The equation represents the ''full attendance'' The second equation : This equation represents the totaled receipts. The system : has the following associated matrix : By performing elementary matrix operations we find that the matrix is equivalent to The new system : Working with the equations : Our solution vector is : For example : If 0 adults attended ⇒ A = 0 This verify the totaled receipts equation : 150($3)+600($5) =$ 3450

A ≥ 0 ⇒ If A = 0 ⇒ C = 150

C = 150 is the minimum children attendance

From the equation :

S ≥0

600 - 2A ≥ 0

600 ≥ 2A

300≥ A

A is restricted to the interval [ 0, 300]

When A = 0 ⇒ C = 150

When A = 300 ⇒C = 150 + A = 150 + 300 = 450

Children ∈ [ 150,450]

With C being an integer number (including 0)

Also S and A are integer numbers (including 0)

Simplify 8X +7 - 2X -4

6x + 3

Step-by-step explanation:

8x - 2x + 7 -4

Lookattheattachedpicture

Haveagreatday..

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The quadratic function f(x) has a vertex at (9, 8) and opens upward. If g(x) = 4(x − 8)2 + 9, which statement is true?A.
The maximum value of f(x) is greater than the maximum value of g(x).
B.
The maximum value of g(x) is greater than the maximum value of f(x).
C.
The minimum value of f(x) is greater than the minimum value of g(x).
D.
The minimum value of g(x) is greater than the minimum value of f(x).

D.
The minimum value of g(x) is greater than the minimum value of f(x).

EXPLANATION

It was given that;

has a vertex at

and opens upwards.

This means that f(x) is a minimum graph and hence have a minimum value of 8.

Also ,

When we compare this function to

We can see that,a=4, h=8 and y=9.

The vertex is

Since a>0, the graph opens upwards.

The graph has a minimum point which is (8,9) and hence the minimum value is 9.

We can see that, the minimum value of g(x) is greater than the minimum value of f(x).

Therefore the correct answer is D.

Find an equation of the sphere with center (-3, 2 , 5) and radius 4. What is the intersection of this sphere with the yz-plane.

The equation of the sphere with center (-3, 2 , 5) and radius 4 is

The intersection of the sphere with the yz- plane gave the equation which is a 2D- circle with center (0,2,5) and radius .

Step-by-step explanation:

The equation of a sphere of radius r, with center (a,b,c) is given by

where, and are the coordinates of the points on the surface of the sphere.

Hence, the equation of the sphere with center,  (-3, 2 , 5) and radius 4 becomes

Then,

This is the equation of the sphere with center (-3, 2 , 5) and radius 4,

Now, for the intersection of this sphere with the yz- plane,

The plane is where , then we set

Them the equation becomes

This equation is the equation of a 2D- circle with center (0,2,5) and radius

This is the part of the sphere that intersects with the yz-plane.

A

Step-by-step explanation:

this is only what I know correct me if I'm wrong thank you

(c) Simplify fully
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