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3 years ago

Please help due today and ignore the answer i put i misclicked.20 points

Mathematics

1 answer:

Anna [14]3 years ago

6 0

Answer:

$3\sqrt{2}$ /2

Step-by-step explanation:

first we take the square root of the top and bottom:

$\frac{\sqrt{72} }{\sqrt{16} }$

The denominator is 4. The numerator is harder to solve. To solve, we need to look at the factors of 72.

72= 8 * 9. This means that $\sqrt{72} =\sqrt{8} *\sqrt{9} \\$

We know that the square root of 9 is 3, so now we have

$\frac{3\sqrt{8} }{4}$

We're almost done!

Since 8= 2*4, and the square root of 4 is 2,

$\frac{3*2*\sqrt{2}}{4}$

last, we simplify and get

$\frac{3\sqrt{2}}{2}$

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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,

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

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

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$x=4,-3$

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 $x=\frac{1}{2}$ .

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4 years ago

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Answer:

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Step-by-step explanation:

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