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tresset_1 [31]
3 years ago
14

Complete the square to find the minimum value of the expression 4x^2+8x+23

Mathematics
1 answer:
Kay [80]3 years ago
5 0
Alright! so how do we complete the square? you're first step is to take the coefficient in front of your middle value, or 8x. 8 would we the coefficent. now, you divide that value by 2.

so we have :

8/ 2 = 4

so what do we do with 4? we square it.

4^2 = 16

okay. so I've made you do some stuff. what do we do now? we add AND SUBTRACT this value from our equation. since I both add and subtract, I haven't changed the value of my equation.

4x^2 + 8x + 23 +16 -16

now, we isolate the positive version of the number we solved for--or 16, and all the terms that have a varaible. by this I mean:

(4x^2 + 8x + 16) + 23 - 16

all I've done is move stuff around. no values have been changed. so what now? well, you factor that portion in the parenthesis.

if you don't know how to factor, I can go over r that seperately, but I'm gonna assume you can factor. when I factor this, I get:

4x^2 + 8x + 16 = (x+ 4)(x + 4) = (x + 4)^2

so now I have

(x+4)^2 + 23 - 16

I can now combine like terms, which include 23-16, which equals 7.

finally, I have:

(x+4)^2 + 7

so I have officially completed the square. ^^^that's your process of doing that. so how do I find the minimum value? well, run with me for a sec. if I just look at (x+4)^2, what type of values will I always get? well, anything squared is POSITIVE, so I will Never get a negative number. in fact, I only get numbers from 0 to infinity. so, if the lowest number I can get there is 0, the lowest value this polynomial can have overall is 0+ 7, which is 7. hope that helps!
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In a sequence of numbers, a3=0, a4=4, a5=8, a6=12, and a7=16. Based on this information, which equation can be used to find the
LekaFEV [45]

Answer:

an=−4n+12

A sub n is equal to negative 4 n plus 12,

Step-by-step explanation:

5 0
3 years ago
CAN SOMEONE PLS ANSWER-If W(- 10, 4), X(- 3, - 1) , and Y(- 5, 11) classify AEXY by its sides . Show all work to justify your an
AnnZ [28]

Answer:

  • WX = \sqrt{74} \approx 8.6023253\\\\
  • XY = 2\sqrt{37} \approx 12.1655251\\\\
  • WY = \sqrt{74} \approx 8.6023253\\\\
  • Classify:  Isosceles

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

Explanation:

Apply the distance formula to find the length of segment WX

W = (x1,y1) = (-10,4)

X = (x2,y2) = (-3, -1)

d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-10-(-3))^2 + (4-(-1))^2}\\\\d = \sqrt{(-10+3)^2 + (4+1)^2}\\\\d = \sqrt{(-7)^2 + (5)^2}\\\\d = \sqrt{49 + 25}\\\\d = \sqrt{74}\\\\d \approx 8.6023253\\\\

Segment WX is exactly \sqrt{74} units long which approximates to roughly 8.6023253

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

Now let's find the length of segment XY

X = (x1,y1) = (-3, -1)

Y = (x2,y2) = (-5, 11)

d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-3-(-5))^2 + (-1-11)^2}\\\\d = \sqrt{(-3+5)^2 + (-1-11)^2}\\\\d = \sqrt{(2)^2 + (-12)^2}\\\\d = \sqrt{4 + 144}\\\\d = \sqrt{148}\\\\d = \sqrt{4*37}\\\\d = \sqrt{4}*\sqrt{37}\\\\d = 2\sqrt{37}\\\\d \approx 12.1655251\\\\

Segment XY is exactly 2\sqrt{37} units long which approximates to 12.1655251

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

Lastly, let's find the length of segment WY

W = (x1,y1) = (-10,4)

Y = (x2,y2) = (-5, 11)

d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-10-(-5))^2 + (4-11)^2}\\\\d = \sqrt{(-10+5)^2 + (4-11)^2}\\\\d = \sqrt{(-5)^2 + (-7)^2}\\\\d = \sqrt{25 + 49}\\\\d = \sqrt{74}\\\\d \approx 8.6023253\\\\

We see that segment WY is the same length as WX.

Because we have exactly two sides of the same length, this means triangle WXY is isosceles.

8 0
3 years ago
HELP ME PLEASE thank you so much to who helps me :)
igor_vitrenko [27]

Answer:

π(12.1)²

Step-by-step explanation:

12.1 is the radius

Formula for base = πr²

= π(12.1)²

3 0
2 years ago
The distance a car drives, in miles, is proportional to the number of gallons of gas it uses. The graph shows this relationship.
Minchanka [31]

Answer:

21 miles per gallon

Step-by-step explanation:

The formula for slope is

m=\frac{y_2-y_1}{x_2-x_1}

Using the points (0, 0) and (1, 21), we have

m = (21-0)/(1-0) = 21/1 = 21

This means they get 21 miles per gallon of gas.

6 0
4 years ago
Rob has a dog that weighs 3 times as much as ricks dog the total weight of both dogs is 76 pounds how much does robs dog weigh d
rewona [7]

76 / 4 = 19

19 * 3 = 57

Rob's dog is 57 pounds.

Rick's dog is 19 pounds.

6 0
3 years ago
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