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Radda [10]
3 years ago
9

What is the solution of 4x = 32 - x2?

Mathematics
1 answer:
nydimaria [60]3 years ago
7 0
4x = 32 - 2x
Add -2x (or subtract 2x) from each side
2x = 32
Divide both sides by 2
x = 16
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On a coordinate plane, a parabola opens up. It goes through (negative 2, 4), has a vertex at (0.25, negative 6), and goes throug
serg [7]

The statements true about the the function f(x) = 2x2 – x – 6 are-

  • The vertex of the function is (one-quarter, negative 6 and one-eighth).
  • The function has two x-intercepts.

<h3>What is vertex of parabola?</h3>

The vertex of parabola is the point at the intersection of parabola and its line of symmetry.

Now the given function is,

f(x) = 2x^2 – x – 6

Also, it is given that the vertex is located at (0.25, -6)  and the parabola opens up, the function has two x-intercepts.

Comparing the given function with standard form,

f(x) = a x^2 bx + c

By comprison we get,

a = 2

b = -1

c = -6

Now, x-coordinate of vertex is given as,

x = -b/2a

put the values we get,

x = -(-1)/2*2

or, x = 1/4

Put the value of x in given function, so y-coordinate of the vertex is given as,

f(1/4) = 2(1/4)² - 1/4 - 6

        = -49/6

       = -6 1/8

Hence, The statements true about the the function f(x) = 2x2 – x – 6 are-

  • The vertex of the function is (one-quarter, negative 6 and one-eighth).
  • The function has two x-intercepts.

More about vertex :

brainly.com/question/86393

#SPJ1

3 0
1 year ago
in addition to dog walking on Tuesday Eric made $45 dog sitting at one of his customers homes if he made $168 on Tuesday right i
Rus_ich [418]

Since we don't know how much Eric makes per dog, let's let <em>x </em>represent that value. Let's also let <em>y</em> represent our answer.

First, let's consider the two numbers we KNOW will be in the equation. The 56 that Eric made dog sitting and the 168 he made in total on Tuesday. Now, we're going to need to use subtraction and division in this equation.

(168 - 45) ÷ <em>x</em> = <em>y</em>


Hope this answer helped you out. :)

8 0
3 years ago
Solve equation <br> √ 13x+27=√ 4x
natima [27]
What you have to do is rearrange the equation by subtracting what is on the right of the equal sign from both sides of the equation 

so it would be 4*x-13*x-(27)=0
5 0
3 years ago
(cos 2theta)/(1 + sin 2theta) = (1 - tan theta)/(1 + tan theta)
andre [41]

Step-by-step explanation:

Here is the solution...hope it helps:)

3 0
2 years ago
What is the distance between the points?! round to the nearest tenth i need to show work
Maru [420]

Answer:

c=\sqrt{52}

Step-by-step explanation:

a=height=6

b=length=4

using pythagorean theorem

a^2+b^2=c^2

36+16=c^2

c=\sqrt{36+16}

c=\sqrt{52}

6 0
3 years ago
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