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3 years ago

A circular picture is 8 inches in diameter.

Mathematics

1 answer:

velikii [3]3 years ago

7 0

The formula of an area of a circle with radius r:

$A=\pi r^2$

Part A.

We have diameter of the circle d = 8 in. The diameter of a circle is equal two times length of a radius.

Therefore:

$r=\dfrac{d}{2}\to r=\dfrac{8}{2}=4\ in$

Calculate the area:

$A=\pi\cdot4^2=16\pi\ in^2$

Answer: C. 16π square inches.

Part 2.

Look at the picture.

Total area:

$A=\pi\cdot6^2=36\pi\ in^2$

Answer: C. 36π square inches

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Y=x^2-6x+3 help write the vertex form of the equation

Artist 52 [7]

Answer:

$y=(x-3)^2-6$

Step-by-step explanation:

$y=x^2-6x+3$

This is written in the standard form of a quadratic function:

$y=ax^2+bx+c$

where:

ax² → quadratic term
bx → linear term
c → constant

You need to convert this to vertex form:

$y=a(x-h)^2+k$

where:

(h,k) → vertex

To find the vertex form, you need to find the vertex. For this, use the equation for axis of symmetry, since this line passes through the vertex:

$x=-\frac{b}{2a}$

Using your original equation, identify the a, b, and c terms:

$a=1\\\\b=-6\\\\c=3$

Insert the known values into the equation:

$x=-\frac{(-6)}{2(1)}$

Simplify. Two negatives make a positive:

$x=\frac{6}{2} =3$

X is equal to 3 (3,y). Insert the value of x into the standard form equation and solve for y:

$y=3^2-6(3)+3$

Simplify using PEMDAS:

$y=9-18+3\\\\y=-9+3\\\\y=-6$

The value of y is -6 (3,-6). Insert these values into the vertex form:

$(3_{h},-6_{k})\\\\y=a(x-3)^2+(-6)$

Insert the value of a and simplify:

$y=(x-3)^2-6$

:Done

6 0

2 years ago

11. Which is an equation of the circle whose center is

VladimirAG [237]

I think that it is b sorry if I’m wrong

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2 years ago

The summer sports training camp has a maximum capacity of 250 students. If 85 have preregistered, then how many students can sti

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2 years ago

How do the graphs of y =1/x and y = 3/x – 4 compare?

Pie

The graphs of y =1/x and y = 3/x – 4 can be compared by saying that c<span>ompared to the graph of y =1/x , the graph of y =3/x – 4 is a vertical stretch by a factor of 3 and a translation of 4 units down. This can be seen clearly when you graph the functions on a x-y coordinate plane.</span>

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3 years ago

The SAT is standardized to be normally distributed with a mean µ = 500 and a standard deviation σ = 100. What percentage of SAT

Aliun [14]

Answer:

34.134%

68.268%

Step-by-step explanation:

Given that:

Mean (m) = 500

Standard deviation (s) = 100

Percentage between 500 and 600

P(500 < x < 600)

P(x < 600) - P(x < 500)

Z = (x - m) / s

P(x < 600)

Z = (600 - 500) /100 = 1

P(x < 500)

Z = (500 - 500) / 500 = 0

P(Z< 1) - P(Z < 0)

0.84134 - 0.5

= 0.34134

= 0.34134 * 100%

= 34.134%

B.) Between 400 and 600

P(x < 400)

Z = (400 - 500) /100 = - 1

P(x < 600)

Z = (600 - 500) / 500 = 1

P(Z< 1 ) - P(Z < - 1)

0.84134 - 0.15866

= 0.68268

= 0.68268 * 100%

= 68.268%

8 0

2 years ago