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77julia77 [94]
3 years ago
8

SHOW ALL WORK BUT KEE IT SIMPLE AND EASY TO UNDERSTAND:)

Mathematics
1 answer:
7nadin3 [17]3 years ago
5 0
To do this problem, you need to use a process called completing the square. Let me explain:  

To complete the square on the function f(x) = x² + 8x +13, first group the first two terms in (  )  and leave some space at the end as follows:
f(x) = (x² + 8x          ) + 13  Now our next step is to fill in the space and adjust our expression on the right hand side of the function.  To do this, we take half of the middle number 8 and then square it:  so 4² = 16 and we fill in our space inside the ( ) with this value 16;   
f(x) = (x² + 8x + 16) + 13  now what we have done is to increase the overall value of our expression on the right by 16, but we want the overall value to remain the same.  To fix this we simply need to subtract 16 at the end like this:  f(x) = (x² + 8x + 16) + 13 -16   we can simplify and get the following.
f(x) = (x² + 8x + 16) - 3   At this point we're almost done.. All we need to do now is to rewrite the what is in the parentheses in a slightly different form.  Here is what it will look like:  f(x) = (x + 4)² - 3  notice all I did was take the sum of the square root of x² and the square root of 16 originally in the (  ) to get then new expression inside the ( ) and then square that  ( )²

Now this is a nice form to have because you can get the vertex straight from this form.. IN FACT this is called vertex form or (h,k) form for short.  In general the form is f(x) = a(x - h)² + k  don't worry about the 'a'  for now.. you might see that in our case it is just 1 and will not effect our equation.  You only have to consider this if the original leading coefficient of the quadratic is not 1 to begin with...

So you can see that our vertex is (-4,-3)  
Hope this is helpful, but if you have questions let me know.
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What is the following product
dangina [55]

Option B is correct.

Step-by-step explanation:

We need to solve: \sqrt[3]{x^2}\sqrt[4]{x^3}

We know that: \sqrt[n]{x}\sqrt[b]{x} =\sqrt[n*b]{x.x}= \sqrt[n*b]{x^2}

Applying the above rule:

\sqrt[3]{x^2}\sqrt[4]{x^3}\\=\sqrt[3*4]{x^2.x^3}\\=\sqrt[12]{x^5}

So, Option B is correct.

Keywords: Solving with Exponents

Learn more about Solving with Exponents at:

  • brainly.com/question/4934417
  • brainly.com/question/13174254
  • brainly.com/question/13174255

#learnwithBrainly

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If point A (-5, -3) is reflected across the X-axis, What quadrant will the reflection be located in?​
AnnyKZ [126]
It will be (-5, 3) so quadrant 2
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The equation y = mx + b is in ___-____ form. (2 words)
poizon [28]
<span>The equation y = mx + b is in Slope - intercept form.</span>
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3 years ago
Read 2 more answers
Please help. Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact valu
o-na [289]

Answer:

Area = (18 + 4.5π) cm²

Perimeter = (6√2 + 12 + 3π) cm

Step-by-step explanation:

The shaded region given is made up of triangle ABC and a semicircle

AB = BC = 6 cm (note that the triangle is a portion of a square)

Diameter of semi-circle (d) = BC = 6cm

Radius (r) = ½*6 = 3 cm

==>Area of the shaded region in terms of π

Area of shaded region = area of triangle + area of semicircle

Area = ½*a*b + ½*πr²

Area = ½*6*6 + ½*π3²

Area = 18 + ½*π9

Area = 18 + 4.5π

<em>Area of the shaded portion = (18 + 4.5π) cm²</em>

==>Perimeter of shaded region in terms of π

Perimeter of shaded region = perimeter of triangle + perimeter of semicircle

= Sum of all sides of the triangle + ½πd

Sides of triangles are AB = 6 cm, BC = 6 cm

Use Pythagorean theorem to find side AC:

AC² = AB² + BC²

AC² = 6² + 6² = 36 + 36 = 72

AC = √72 cm

Perimeter of shaded triangle = √72 + 6 + 6 = √72 + 12 = (6√2 + 12) cm

Perimeter of semicircle = ½*πd = ½π6

= 3π

<em>Perimeter of the whole shaded region in terms of π = (6√2 + 12 + 3π) cm</em>

<em></em>

3 0
3 years ago
I JUST NEED HELP PLZZ<br> AND THANK YOU
Kamila [148]

Answer:

43

Step-by-step explanation:

Based on the pattern of the scatter plot, 43 seems to be the better option.

6 0
3 years ago
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