MATHEMATICS HIGH SCHOOL

The vertex form of a function is g(x) = (x – 3)2 + 9. How does the graph of g(x) compare to the graph of the function f(x) = x2?

Answers

Answer 1

Answer:

we have

$g(x)=(x-3)^(2)+9$

This is the equation of a vertical parabola with vertex at point $(3,9)$

The parabola open upward------> the vertex is a minimum

$f(x)=x^(2)$

This is the equation of a vertical parabola with vertex at point $(0,0)$

The parabola open upward------> the vertex is a minimum

the rule of the translation is

$f(x)------> g(x)$

$(x,y)-----> (x+3,y+9)$

that means

the translation is $3$ units to the right and $9$ units up

the graph of the function g(x) is the translated graphic of the function f(x) $3$ units to the right and $9$ units up

therefore

the answer is

g(x) is shifted $3$ units right and $9$ units up

Answer 2

Answer: in y=a(x-h)^2+k
vertex=(h,k)

f(x)=x^2,
the vertex is (0,0)
it opens up

g(x)=(x-3)^2+9
vertex is (3,9)
opens up

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What is the value of x if 2x+5=10

A square and a rectangle have the same area. The length of the rectangle is twelve more than twice times the side of the square. The width of the rectangle is eight less than the side of the square. Let x be the length of the side of the square. Using the information above, what is the value of x?

Answers

Answer:

$x = 12$

Step-by-step explanation:

Given

Shapes: Square and Rectangle

Square:

$Length = x$

Rectangle:

$Length = 12 + 2x$

$Width = x- 8$

Required

Find x

First, we calculate the area of the square.

$Area = x * x$

$Area = x^2$

Next, we calculate the area of the rectangle

$Area = (12 + 2x) * (x - 8)$

$Area = 12x -96 + 2x^2 - 16x$

$Area = 2x^2 - 16x + 12x -96$

$Area = 2x^2 -4x -96$

Since both areas are equal, we have:

$x^2 = 2x^2 -4x -96$

Equate to 0

$2x^2 -x^2 -4x -96= 0$

$x^2 -4x -96= 0$

Expand:

$x^2 - 12x + 8x -96 = 0$

$x(x - 12) + 8(x - 12) = 0$

$(x + 8)(x - 12) = 0$

$x + 8 = 0$ or $x - 12 = 0$

$x = -8$ or $x = 12$

But x can't be negative.

Hence:

$x = 12$

Choose all the numbers that 116 is divisible by.2
3
4
5
6
9
10

Answers

2,4, only two of these.

Only 2 and 4 are divisible by 116 i think

Mai bought a television for $325. The tax rate is 8%. Which proportion can be used to find the amount of tax Mai will pay?

A.8/325=x/100

B.8/325=100/x

C.8/100=325/3

D.8/100=x/325

Answers

the answer is
A. 8/225 = x/100

If Tina had 4.6 gallons of water in one bucket and 2.3 gallons in another bucket, how many gallons did she have all together?

Answers

Hey!

Since it says "all together", that means you have to add both amounts.

In one bucket, she had 4.6 gallons, and in another, she had 2.3 gallons. Add 4.6 and 2.3

$4.6 + 2.3 = 6.9$

$\framebox{She had 6.9 gallons of water altogether}$

What is the perimeter of a rhombus-shaped street sign with a 35-cm side? A. 280 cm
B. 140 cm
C. 1,225 cm
D. 70 cm

Answers

A rhombus has a total of 4 sides. All sides are equal. The formula of getting the perimeter of a rhombus is:
Perimeter = 4 * S
Perimeter = 4 * 35 cm
Perimeter = 140 cm.

So the perimeter of a rhombus-shaped street sign that has a 35-cm side is equal to (B) 140 cm.

I don't know how i would even go about this question without more information

Answers

Because the trapezoid is isosceles, the desired angle is equal to 180-31=149.

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