Read the problem and answer question 4 and 5 i’ll give brainliest.

What is the axis of symmetry of the function f(x)=-(x+9)(x-21)

Firlakuza [10]

Carry out the mult.: f(x) = -[x^2 - 21x + 9x - 189]

Combine like terms: f(x) = -[x^2 - 12x - 189]
Eliminate the brackets [ ]: f(x) = -x^2 + 12x + 189
Identify coefficients a, b and c: a= -1, b=12, c=189

The equation of the axis of symmetry is x = -b/(2a), which here equals

x = -(12)/[2(-1)], or x = 6

This is also the x-coordinate of the vertex. Plug x=6 into the original equation to calculate the y-coordinate.

3 0

3 years ago

Does 6n-18=4(n+2) equal 1n?

Mariulka [41]

Answer:

No.

Step-by-step explanation:

If we were to fill in the slots, the equation would be...

6x3-18=4

6 times three is 18, and 18 - 18 equals 0. So the answer would not be 1.

4 0

3 years ago

(50 points and brainliest.Need help ASAP)

Aleksandr-060686 [28]

Answer: " 2x (2x - 1) (x + 1) " .

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Step-by-step explanation:

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Given:

f(x) = 9x³ + 2x² − 5x + 4 ;

g(x) = 5x³ − 7x + 4 ;

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What is: f(x) − g(x) ?

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Plug in: " 9x³ + 2x² − 5x + 4 " for: " f(x) " ;

and: " (5x³ − 7x + 4) " ; for: "g(x)" ;

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→ " f(x) − g(x) =

" 9x³ + 2x² − 5x + 4 − (5x³ − 7x + 4) " .

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Rewrite this expression as:

→ " 9x³ + 2x² − 5x + 4 − 1(5x³ − 7x + 4) " .

→ {since: " 1 " ; multiplied by "any value" ; is equal to that same value.}.

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Now, let us example the following portion of the expression:

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" − 1(5x³ − 7x + 4) "

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Note the "distributive property" of multiplication:

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→ a(b + c) = ab + ac ;

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Likewise:

→ a(b + c + d) = ab + ac + ad .

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As such:

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→ " − 1(5x³ − 7x + 4) " ;

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= (-1 * 5x³) + (-1 * 7x) + (-1 * 4) ;

= - 5x³ + (-7x) + (-4) ;

= - 5x³ − 7x − 4 ;

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Now, add the "beginning portion of the expression" ; that is:

" f(x) " ; to the expression ; which is:

→ 9x³ + 2x² − 5x + 4 ;

→ as follows:

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→ 9x³ + 2x² − 5x + 4 − 5x³ − 7x − 4 ;

→ {Note that the: " - " sign; that is;

the "negative sign", in the term: " -5x³ " ;

becomes a: " − " sign; that is; a "minus sign" .}.

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Now, combine the "like terms" of this expression; as follows:

+ 9x³ − 5x³ = + 4x³ ;

− 5x − 7x = − 2x ;

+ 4 − 4 = 0 ;

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and we have:

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→ " 4x³ + 2x² − 2x ".

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Now, to write this answer in "factored form" :

Note that among all 3 (three) terms in this expression, each term has a factor of "2" . The lowest coefficient among these 3 (three) terms is "2" ; so we can "factor out" a "2".

Also, each of the 3 (three) terms in this fraction is a coefficient to a variable. That variable takes the form of "x". The term in this expression with the variable, "x"; with the lowest degree has the variable: "x" (i.e. "x¹ = x" ) ; so we can "factor out a "2x" (rather than just the number, "2".).

So, by factoring out a "2x" ; take the first term [among the 3 (three) terms in the expression] —which is: "4x³ " .

2x * (?) = 4x³ ? ;'

↔ $\frac{4x^3}{2x} =$ ? ;

→ 4/2 = 2 ;

$\frac{x^{3}}{x} = \frac{x^3}{x^1} = x^{(3-1)} = x^{2}$ ;

As such: 2x * (2x²) = 4x³ ;

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Now, by factoring out a "2x" ; take the second term [among the 3 (three) terms in the expression] — which is: "2x² " .

2x * (?) = 2x² ? ;

↔ $\frac{2x^{2}}{2x} =$ ?

→ 2/2 = 1 ;

→ $\frac{x^{2}}{x} = \frac{x^2}{x^1}= x^{(2-1)} } = x^1 = x$ ;

As such: 2x * (x) = 2x²

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Now, by factoring out a "2x" ; take the third term [among the 3 (three) terms in the expression] — which is: " − 2x " .

2x * (?) = - 2x ;

↔ $\frac{-2x}{2x} =$ -1 ;

As such: 2x * (-1) = − 2x .

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So:

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Given the simplified expression:

→ " 4x³ + 2x² − 2x " ;

We can "factor out' a: " 2x " ; and write the this answer is: "factored form" ; as:

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"2x (2x² + x − 1 ) . "

Now, we can further factor the:

" (2x² + x − 1) " ; portion;

Note: "(2x² + x - 1)" =

2x² + 2x - 1x -1 = (2x -1) + x (2x - 1 ) =

(2x - 1) ( x + 1)

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Now, bring down the "2x" ; and write the Full "factored form" ; as follows:

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→ " 2x (2x - 1) (x + 1) " .

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Hope this helps!

Wishing you the best!

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7 0

3 years ago

A gym teacher has $250 to spend on volleyball equipment. She buys 4 volleyball nets for $28 each. Volleyball cost $7 each. How m

Sonbull [250]

First find out how much the 4 volleyball nets are by using 4*28 which would equal to 112. Now subtract 112 from 250 and that leaves you with 138. Then you divide 138 by 7 which will give you about 19.7 which you need to take all decimals out since it isn’t an whole number. The gym teacher can only buy 19 volleyballs.

6 0

3 years ago

A Gardner is planting two types of trees

Nina [5.8K]

It will take 6 years for the trees to have same height.

Step-by-step explanation:

Type A tree;

Initial height = 9 feet

We will convert feet into inches because growth is in inches.

1 feet = 12 inches

9 feet = 12*9 = 108 inches

Growth rate = 6 inches per year

Let,

x be the number of years.

A(x) = 108 + 6x

Type B;

Initial height = 4 feet = 4*12 = 48 inches

Growth rate = 16 inches per year

B(x) = 48 + 16x

The height will be same, when functions are equal

A(x) = B(x)

$108+6x=48+16x\\108-48=16x-6x\\60=10x\\10x=60$

Dividing both sides by 6

$\frac{10x}{10}=\frac{60}{10}\\x=6$

It will take 6 years for the trees to have same height.

Keywords: function, division

Learn more about division at:

#LearnwithBrainly

4 0

3 years ago