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3 years ago

Rewrite the function by completing the square f(x) =4x2+12x+9

Mathematics

1 answer:

Ilya [14]3 years ago

7 0

Answer:

see explanation

Step-by-step explanation:

Given

f(x) = 4x² + 12x + 9

The coefficient of the x² term must be 1 so factor out 4 from the first 2 terms

f(x) = 4(x² + 3x) + 9

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 3x

f(x) = 4(x² + 2( $\frac{3}{2}$ )x + $\frac{9}{4}$ - $\frac{9}{4}$ ) + 9

= 4(x + $\frac{3}{2}$ )² - 9 + 9

= 4(x + $\frac{3}{2}$ )²

Thus

f(x) = 4x² + 12x + 9 = 4(x + $\frac{3}{2}$ )²

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Riverside Elementary School is holding a school-wide election to choose a school color. 5/8 of the voters were for blue 5/9 of t

padilas [110]

Answer:

There were 180 voters for blue color.

Step-by-step explanation:

Let the total number of voters be 'x'.

Given:

Number of Voters for blue color = $\frac{5}{8}x$

Number of Voters for green color = $\frac{5}{9}(x-\frac58x)=\frac59x(1-\frac58)$

Now we will use LCM to make the denominator common we get;

Number of Voters for green color = $\frac59x(\frac88-\frac58)=\frac59x(\frac{8-5}{9})=\frac59x(\frac38)=\frac{15x}{72}$

Number of Voters for red color = 48

We need to find the number of voters for blue color.

Solution:

Now we can say that;

total number of voters is equal to sum of Number of Voters for blue color, Number of Voters for green color and Number of Voters for red color.

framing in equation form we get;

$x=\frac58x+\frac{15x}{72}+48$

Combining like terms we get;

$x-\frac58x-\frac{15x}{72} = 48$

Now we will make denominators common using LCM we get;

$\frac{72x}{72}-\frac{5x\times9}{8\times9}-\frac{15x\times1}{72\times 1} = 48\\\\\frac{72x}{72}-\frac{45x}{72}-\frac{15x}{72} = 48$

Now denominators are common so we will solve the numerators we get;

$\frac{72x-45x-15x}{72}=48\\\\\frac{12x}{72}=48\\\\\frac{x}{6}=48$

Now multiplying both side by 6 we get;

$\frac{1}{6}x\times6=48\times6\\\\x = 288$

Number of voters for blue color = $\frac{5}{8}x=\frac{5}{8}\times 288= 180$

Hence There were 180 voters for blue color.

4 0

3 years ago

Mr. Champion invests 34,000 into a money-market fund that pays 4.8% simple interest. How long will it take for him to earn $8,16

Tanzania [10]

Answer:

5 years

Step-by-step explanation:

Step one:

Given Information

Principal= $34,000

rate = 4.8%

SImple interest = $8,160

Required

The time T of the investment

Step two:

the expression for simple interest is

$SI= PRT/100$

substitute

$8160 = 34000*4.8*T/100$

cross multiply we have

$8160*100= 34000*4.8*T\\\\816000= 163200T\\\\$

divide both sides by 163200

$816000/163200= T\\\\T= 5 years$

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3 years ago

Your gross income is $56k and the standard deduction is $12,200, how much do you owe in taxes?

Neko [114]

8 percent is the answer

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Mr. Bob has 45 1/2 pounds of dog food. He is going to equally separate the dog food into 4 containers. How much dog food will be

Fynjy0 [20]

It's simple, just divide 45 1/2 by four. A, 11 3/7

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2 years ago

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nora draws a figure on a piece of paper as shown what is the area of her figure round to the nearest hundredth?

9966 [12]

Answer:

maybe 100000

Step-by-step explanation:

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3 years ago