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raketka [301]
3 years ago
9

Complete the square to determine the maximum or minimum value of the function defined by the expression. x2 + 30x + 21 A) maximu

m value at 15 B) maximum value at 30 C) maximum value at −15 D) minimum value at −204
Mathematics
2 answers:
AveGali [126]3 years ago
8 0
X^2 + 30x + 21
=   ( x + 15)^2 - 225 + 21
= (x + 15)^2 - 204

Its D  minimum at -204
kramer3 years ago
6 0

Answer:

x^2 + 30x + 21=(x+15)^2-204

Option D - minimum value at −204

Step-by-step explanation:

Given : Expression x^2 + 30x + 21

To find : Complete the square to determine the maximum or minimum value of the function defined by the expression?

Solution :  

The general form of quadratic equation is   ax^2+bx+c=0

To convert into complete square the form is a(x+d)^2+e=0

Where, d=\frac{b}{2a} and e=c-\frac{b^2}{4a}

Now, comparing the given equation x^2 + 30x + 21

a=1 , b=30, c=21        

d=\frac{b}{2a}=\frac{30}{2(1)}=15

e=21-\frac{30^2}{4(1)}=21-225=-204

Substitute in a(x+d)^2+e=0

1(x+15)^2+(-204)=0

(x+15)^2-204=0

[tex]x^2 + 30x + 21[/tex]

By Completing the square we get,            

x^2 + 30x + 21=(x+15)^2-204

The minimum value of this is when x+15 = 0 ⇒ x=-15

i.e, (-15+15)^2-204=-204

Therefore, Option D is correct.

Minimum value of the function is at -204.

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MArishka [77]

Answer:

The answer is option 1.

Step-by-step explanation:

In order to simplify the expressions, you have to collect like terms :

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7 0
2 years ago
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8 0
3 years ago
Three of the four vertices of a rectangle are located at (4, 2), (7, 2) and (4, 8). a. What are the coordinates of the missing v
34kurt

Answer:

a) The coordinates of the missing vertex = (7, 8)

b) Area = 18 square units

   Perimeter = 18 units

Step-by-step explanation:

a) We know three of the four vertices:

A: (4, 2)           C ______ D(?)

B: (7, 2)               |             |

C: (4, 8)           A |______| B  

To find the coordinates of the missing vertex we need to calculate the distance in the x-direction from point A to point B:

B_{x} - A_{x} = 7 - 4 = 3                    

Hence, the distance of point D from point C in the x-direction is:

D_{x} = C_{x} + 3 = 4 + 3 = 7

Now, to find the coordinate in "y" we need to calculate the distance in the y-direction between point C and point A:

C_{y} - A_{y} = 8 - 2 = 6  

Then, the distance of point D from point B in the y-direction is:

D_{y} = B_{y} + 6 = 2 + 6 = 8

Therefore, the coordinates of the missing vertex (point D) are:

D = (D_{x}, D_{y}) = (7, 8)    

b) The area of the rectangle is:

a = (B_{x} - A_{x})*(C_{y} - A_{y}) = 3*6 = 18 units^{2}

The perimeter is given by:

p = 2*(3 + 6) = 18 units

I hope it helps you!          

8 0
2 years ago
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Liono4ka [1.6K]
Together both shane and isabella have 42$

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Find the value of x in the figure below if MP is parallel to RA.
lawyer [7]

Answer: 4.5 units

Step-by-step explanation:

6 0
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