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3 years ago

400.04 in expanded form

Mathematics

1 answer:

vampirchik [111]3 years ago

3 0

The answer is 400 + .04. Or if you want a big answer, then it would be. 400 + 00 + 0 + .0 + .04.

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the axis of symmetry for the graph of the function is f(x) = 1/4x2 bx 10 is x = 6. what is the value of b?

Lady bird [3.3K]

we have

$f(x)=\frac{1}{4} x^{2} +bx+10$

This is a vertical parabola open upward

The axis of symmetry is equal to the x-coordinate of the vertex

The vertex is the point (h,k)

the equation of the axis of symmetry is $x=h$

In this problem

$x=6$

so the x-coordinate of the vertex is $h=6$

Convert the quadratic equation in vertex form

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$f(x)-10=\frac{1}{4} x^{2} +bx$

Factor the leading coefficient

$f(x)-10=\frac{1}{4}(x^{2} +4bx)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$f(x)-10+b^{2}=\frac{1}{4}(x^{2} +4bx+4b^{2})$

Rewrite as perfect squares

$f(x)+(b^{2}-10)=\frac{1}{4}(x+2b)^{2}$

$f(x)=\frac{1}{4}(x+2b)^{2}-(b^{2}-10)$

remember that

$h=6$

$(x+2b)=(x-6)$

$2b=-6$

$b=-3$

substitute in the equation

$f(x)=\frac{1}{4}(x-6)^{2}-((-3)^{2}-10)$

$f(x)=\frac{1}{4}(x-6)^{2}+1$

therefore

the answer is

$b=-3$

8 0

4 years ago

Read 2 more answers

5x+15+10x+7 5(x+3)+2x+7

Marta_Voda [28]

Step-by-step explanation:

1. Combine Like Terms (Add):

$5x+15+10x+7$

$15x+22$

2. Use Distributive Property:

$5(x+3)+2x+7$

$5x+15+2x+7$

Combine Like Terms:

$7x+22$

5 0

2 years ago

The table shows values of f(x) .

scoray [572]

9514 1404 393

Answer:

f(3) = 9

Step-by-step explanation:

The table entry ...

x ... f(x)

3 ... 9

means f(3) = 9.

5 0

3 years ago

What is the value of x?

shusha [124]

Answer:

135????

Step-by-step explanation:

6 0

4 years ago

Read 2 more answers

How many positive integers between 100 and 999 inclusive are divisible by three or four?

Gnoma [55]

999 - 100 + 1 = 900
There are 900 numbers between 100 and 999 (inclusive)

We group the numbers into groups of 3s. So we find one number divisible by 3 in every group.
Number of numbers that can be divided by 3 = 900 ÷ 3 = 300
Number of numbers that can be divided by 3 = 300

We group the numbers into groups of 4s. So we find one number divisible by 4 in every group.
Number of numbers that can divided by 4 = 900 ÷ 4 = 225
Number of numbers that can divided by 4 = 225
Among the group of 4s, there is 1/3 that are already inclusive in divisible by 3.
225 ÷ 3 = 75
Number of numbers that can divided by 4 = 225 - 75 = 150

Total numbers of positive integers divisible by three and fours = 300 + 150 = 450

8 0

3 years ago