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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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If the acute angles in a right triangle are in the ratio of 5:4 find the measure of the smallest angle
deff fn [24]
Let's create this right triangle.  We will call it triangle ABC with angle B as the right angle, angle A being the larger of the angles A and C.  If the ratio is 5:4, then it is A:C.  5+4 = 9.  The measure of the right angle, angle ABC = 90, and 90 divided by 9 is 10.  So angle A is 5 * 10 which is 50 degrees, and angle C is 4 * 10 which is 40 degrees.  The smallest angle, angle C, is 40 degrees.
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3 years ago
Please help me with this homework
4vir4ik [10]
The answer is 1.25.

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6 0
2 years ago
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A theater has 49 seats in the first row 52 seats in the second row 55 seats in the third row how many seats are in the 16th row
devlian [24]

Answer:

94 seats

Step-by-step explanation:

We solve using Arithmetic sequence formula

an = a + (n + 1)d

Where

a = First term = 49

d = Common difference = 52 - 49 or 55 - 52 = 3

n = 16th row

Hence,

a16 = 49 + (16 - 1)3

a16 = 49 + (15 × 3)

a16 = 49 + 45

a16 = 94

Therefore, the number of seats on the 16th row is 94 seats

3 0
3 years ago
.8x-.3y=5<br> 1.4x-.9y=11
PolarNik [594]

Answer:

(x,y)=(-22/49,-5566/147)

Step-by-step explanation:

6 0
3 years ago
The​ z-score with a​ two-tail probability of 0.55 is
katrin2010 [14]

Answer:

-0.61

Step-by-step explanation:

0.55/2=0.275

Read 0.275 from normal distribution tables

Gives -0.61

7 0
2 years ago
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