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4 years ago

Which line segments are diameters of circle E?

Mathematics

1 answer:

sertanlavr [38]4 years ago

8 0

A diameter of a circle has to pass through the centre of the circle
The lines that pass through the centre are BD and AC

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Consider the quadratic function f(x) = -x^2 + 1x + 12. Determine the following: (enter all numerical answers as integers, fracti

vovikov84 [41]

Answer and Explanation:

Given : The quadratic function $f(x)=-x^2+x+12$

To find : Determine the following ?

Solution :

The x -intercept are where f(x)=0,

So, $-x^2+x+12=0$

Applying middle term split,

$-x^2+4x-3x+12=0$

$-x(x-4)-3(x-4)=0$

$(x-4)(-x-3)=0$

$x=4,-3$

The x-intercepts are (4,0) and (-3,0).

The smallest x-intercept is x=-3

The largest x-intercept is x=4

The y -intercept are where x=0,

So, $f(0)=-(0)^2+0+12$

$f(0)=12$

The y-intercept is y=12.

The quadratic function is in the form, $y=ax^2+bx+c$

On comparing, a=-1 , b=1 and c=1 2

The vertex of the graph is denote by (h,k) and the formula to find the vertex is

For h, The x-coordinate of the vertex is given by,

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

$h=-\frac{1}{2(-1)}$

$h=\frac{1}{2}$

For k, The y-coordinate of the vertex is given by,

$k=f(h)$

$k=-h^2+h+12$

$k=-(\frac{1}{2})^2+\frac{1}{2}+12$

$k=-\frac{1}{4}+\frac{1}{2}+12$

$k=\frac{-1+2+48}{4}$

$k=\frac{49}{4}$

The vertex of the function is $(h,k)=(\frac{1}{2},\frac{49}{4})$

The x-coordinate of the vertex i.e. $x=-\frac{b}{2a}$ is the axis of symmetry,

So, $x=-\frac{b}{2a}=\frac{1}{2}$ (solved above)

The axis of symmetry is $x=\frac{1}{2}$ .

4 0

4 years ago

Someone please check this if this is right by giving me an explanation.

fomenos

Answer:

Its correct

Step-by-step explanation:

Its correct since its correct

4 0

3 years ago

Read 2 more answers

Which expressions simplify to 0? Check all that apply. 8g – 8g, (–2g) – 2g, 5g + (–5g), One-half g + one-half, g Negative two-th

victus00 [196]

We have been given 4 expressions. We are asked to choose the expressions, which simplifies to 0.

Let us check our given choices one by one.

1. $8g-8g$

$8(g-g)$

$8(0)=0$

When we will subtract 8g from 8g, we will get 0. Therefore, expression $8g-8g$ simplifies to 0.

2. $(-2g)-2g$

Let us remove parenthesis.

$-2g-2g$

Upon combining like terms, we will get:

$-4g$

Since $(-2g)-2g$ simplifies to $-4g$ , therefore, expression $-2g-2g$ is not a correct choice.

3. $5g+(-5g)$

Let us remove parenthesis.

$5g-5g$

Upon combining terms, we will get:

$5g-5g=0$

Since $5g+(-5g)$ simplifies to 0, therefore, expression $5g+(-5g)$ is a correct choice.

4. $\frac{1}{2}g+\frac{1}{2}g-\frac{2}{3}g+\frac{2}{3}g$

Let us combine the terms as:

$\frac{1+1}{2}g-\frac{2}{3}g+\frac{2}{3}g$

$\frac{2}{2}g-\frac{2}{3}g+\frac{2}{3}g$

$g-g(-\frac{2}{3}+\frac{2}{3})$

$g-g(0)$

$g-(0)=g$

Since $\frac{1}{2}g+\frac{1}{2}g-\frac{2}{3}g+\frac{2}{3}g$ simplifies to $g$ , therefore, expression $\frac{1}{2}g+\frac{1}{2}g-\frac{2}{3}g+\frac{2}{3}g$ is not a correct choice.

6 0

4 years ago

Read 2 more answers

the area of a circle is 81 pi m^2. what is the circumference, in meters? express your answer in terms of pi.

mestny [16]

<h3>Answer: 18pi</h3>

============================================================

Explanation:

The area 81pi square meters leads to the radius 9 meters

Use the formula A = pi*r^2 to see why this is the case. You plug in A = 81pi and solve for r to get r = 9.

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

Once you know the radius, you can determine the circumference C

C = 2*pi*r

C = 2*pi*9

C = 2*9*pi

C = 18pi

The circumference is the perimeter, or distance, around the circle.

8 0

3 years ago

Find the value of x. Please help

inna [77]

I guess this is the answer
$67 \times 2 = 134$
then:
$16 x - 10 = 134 \\ 16x = 10 + 134 = 144 \\ x = \frac{144}{16} = 9$
x=9

8 0

3 years ago