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maksim [4K]
2 years ago
15

What is the range of the function f(x) = 3x2 + 6x – 8?

Mathematics
1 answer:
Fudgin [204]2 years ago
3 0

Answer:

Range → {y| y ≥ -11}

Step-by-step explanation:

Range of a function is the set of of y-values.

Given function is,

f(x) = 2x² + 6x - 8

By converting this equation into vertex form,

f(x) = 3(x^2+2x-\frac{8}{3})

     = 3(x^2+2x+1-1-\frac{8}{3})

     = 3[(x+1)^2-\frac{11}{3}]

     = 3(x+1)^2-11

Vertex of the parabola → (-1, -11)

Therefore, range of the function will be → y ≥ -11

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If a standard vodka martini recipe at La-ti-da Lounge calls for 2.5 oz of premium vodka that sells for $35/liter, .5 oz of dry v
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Answer: (A) 19.3%

<u>Step-by-step explanation:</u>

\text{Vodka: }2.5\text{ oz }\times\dfrac{\$35}{1\text{ liter }}\times\dfrac{1\text{ liter }}{33.814\text{ oz }}=\$2.59\\\\\text{Vermouth: }0.5\text{ oz }\times\dfrac{\$7.99}{1\text{ liter }}\times\dfrac{1\text{ liter }}{33.814\text{ oz }}=\$0.12\\\\\text{Olive: }\$0.15

Vodka + Vermouth + Olive = Total Cost

$2.59  +   $0.12      + $0.15 = $2.86

\dfrac{\text{cost to make}}{\text{selling price}} = \dfrac{\$2.86}{\$15} = 0.19 = 19\%

4 0
3 years ago
A square has an area of 576 square inches. How long is each side in feet?
Maru [420]
The area of this square is said to be 576 square inches.
The formula for the area of a square is the length of one side squared.
Let's use l to represent the side length.
This means l^2 = 576.
To find l, find the square root of both sides.
<span>√576 = 24
</span>
The length of each side of the square is 24 inches.
But the question is asking for it in feet.
12 inches = 1 foot so 24 inches = 2 feet
This means each side of the square is 2 feet long.

Answer:
2 feet
5 0
2 years ago
A group of workers is harvesting berries at a constant rate. An equation that represents the number of baskets of berries the wo
wolverine [178]
What do you want to know?
7 0
3 years ago
-18=-10-1.5m<br> can someone help
Brums [2.3K]

Answer:

<h2><u><em>m= 16/3</em></u></h2>

Step-by-step explanation:

-18=-10-1.5m

-18+10=-1.5m

-8=-1.5m

m=-8:(-1.5)

m=80:15

m= 16/3

4 0
1 year ago
Which graph represents the function of f(x) = the quantity of 9 x squared plus 9 x minus 18, all over 3 x plus 6
lora16 [44]

Answer:

The answer is the option C

graph of 3x minus 3, with discontinuity at negative 2, negative 9

Step-by-step explanation:

we have

f(x)=\frac{9x^{2}+9x-18}{3x+6}

Simplify

f(x)=9\frac{(x^{2}+x-2)}{3(x+2)}

f(x)=3\frac{(x^{2}+x-2)}{(x+2)}

Step 1

Convert to a factored form the numerator

x^{2}+x-2=0    

Group terms that contain the same variable, and move the constant to the opposite side of the equation

x^{2}+x=2

Complete the square. Remember to balance the equation by adding the same constants to each side.

x^{2}+x+0.25=2+0.25

x^{2}+x+0.25=2.25

Rewrite as perfect squares

(x+0.5)^{2}=2.25

Square root both sides

x+0.5=(+/-)1.5

x=-0.5(+/-)1.5

x=-0.5+1.5=1

x=-0.5-1.5=-2

so

x^{2}+x-2=(x-1)(x+2)  

Step 2

Simplify the function f(x)

f(x)=3\frac{(x^{2}+x-2)}{(x+2)}=3\frac{(x-1)(x+2)}{(x+2)}

The domain of the function f(x) is all real numbers except the number x=-2

Because the denominator can not be zero

f(x)=3\frac{(x-1)(x+2)}{(x+2)}=3(x-1)=3x-3  

f(x)=3x-3  ------> with a discontinuity at x=-2

f(-2)=3(-2)-3=-9

The discontinuity is at point (-2,-9)

the answer in the attached figure

8 0
3 years ago
Read 2 more answers
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