Pattern rule for 1, 5,25,125

Answers

Answer 1

Answer: All the numbers are being multiplied by 5!
1*5=5
5*5=25
25*5=125

Answer 2

Answer: Rule is: 5^n starting from n=0 , to n=3

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A cheese pizza costs $5. Additional toppings cost $1.50 each. Write and graph an equation in two variables that represents the total cost of a pizza. Let tt represent the number of toppings and c represent the total cost of the pizza. An equation in two variables that represents the total cost of a pizza is c=____

Answers

$6.50 I guess, because I added $5 and $1.50 and got $6.50

Find the equation of the axis of symmetry and the coordinates of the vertex of the graph of the function Y=2x^2+12x+13
axis of symmetry:
vertex:

Answers

Answer:

Axis of symmetry: –3

Vertex: (–3, –5)

Step-by-step explanation:

For a quadratic function in standard form, the axis of symmetry is a vertical line $x=-(b)/(2a)$ . Therefore:

$x=-(b)/(2a)=-(12)/(2(2))=-(12)/(4)=-3$

For the vertex, –3 is the x-coordinate and we solve for y to find the y-coordinate:

y = 2x² + 12x + 13

y = 2(–3)² + 12(–3) + 13

y = 2(9) + 12(–3) + 13

y = 18 – 36 + 13

y = –5

Therefore, the vertex is (–3, –5).

Which of the following functions best represents the graph?f(x) = x3 + x2 − 4x − 4
f(x) = x3 + 4x2 − x − 4
f(x) = x3 + 3x2 − 4x − 12
f(x) = x3 + 2x2 − 4x − 8

Answers

Answer:

$f(x)=x^3+x^2-4x-4$

Step-by-step explanation:

From the graph, the x-intercepts are;

$x=-2$

$x=-1$

$x=2$

These are root of the polynomial function represented by the given graph.

By the remainder theorem;

$f(-2)=0,f(-1)=0,f(2)=0$

According to the factor theorem, if $(x-a)$ is a factor of $f(x)$ , then $f(a)=0$

This implies that;

$(x+2),(x+1),(x-2)$ are factors of the required function.

Hence; $f(x)=(x+1)(x-2)(x+2)$

We expand using difference of two squares to obtain;

$f(x)=(x+1)(x^2-4)$

We expand using the distributive property to get;

$f(x)=x^3-4x+x^2-4$

Rewrite in standard form to obtain;

$f(x)=x^3+x^2-4x-4$

Answer:

Choice A: f(x) = x^3 + x^2 − 4x − 4

Step-by-step explanation:

Here's a great and simple answer.

Ok first we need to take the x intercepts to solve.

If we look at the graph we see the x ints are -2,+1 and +2.

To solve we need to put them into factor form

= (x-2) (x+2) and (x+1)

Simplify: (x-2) (x+2) = (x^2-4) and (x+1)

Now we take (x^2-4) and (x+1) and multiply them to find our answer

(x^2-4) (x+1)

= x^2(x) and x^2(1) = x^3 and x^2.

now the other: -4(x) and -4(+1) = -4x and -4

We have nothing common here so we just join them

= x^3 + x^2 - 4x - 4, and that is the same as choice A.

12
x
−
8
y
=
24
6
x
−
y
=
21

Answers

Answer: x=4

y=3

Step-by-step explanation:

12x-8y=24

6x-y=21

---------------------

y=6x-21

12x-8(6x-21)=24

12x-48x+168=24

-36x=-144

x=144/36

x=4

y=24-21

y=3

Martin ordered a pizza with a 16-inch diameter. Ricky ordered a pizza with a 20-inch diameter. What is the approximate difference in area of the two pizzas?ANSWER FAST