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Ad libitum [116K]

3 years ago

9

Kylie is looking for a job cutting hair. One option is self-employment at the Greenpoint Salon, where she would pay $600 per mon

th to rent a station and keep all of her earnings. Another option is to work at a franchise, where she would just have to pay the salon $10 for every haircut. If she performed a certain number of haircuts every month, the amount paid to either salon would be the same. How much would Kylie pay?

1 answer:

Tanzania [10]3 years ago

7 0

Answer: how much does a haircut cost

Step-by-step explanation:

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An expression is given : 9x — 7y — 6x

Dmitry_Shevchenko [17]

Answer: 3x-7y

Step-by-step explanation:

9x-6x=3x you can't do anything with the y

4 0

3 years ago

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What is the volume of a rectangular prism with length 6 mm, height 5 mm, and width 11 mm? V = lwh A. 330 mm B. 330 mm2 C. 330 mm

shepuryov [24]

The answer is 330mm3

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4 years ago

the model shows -3x + 5= -2x -1. What value of x makes the equation true? look at the picture please..

Stels [109]

Answer:

D. x=6

Step-by-step explanation:

-3x + 5= -2x -1

more variables to left hand side and change its sign

-3x+2x+5=-1

move constant to right hand side and change its sign

-3x+2x=-1-5

collect like terms

-x=-1-5

calculate the difference

-x=-6

change the signs on both sides of the equation

x=6

5 0

3 years ago

Match the parabolas represented by the equations with their foci.

Elenna [48]

Function 1 $f(x)=- x^{2} +4x+8$

First step: Finding when $f(x)$ is minimum/maximum
The function has a negative value $x^{2}$ hence the $f(x)$ has a maximum value which happens when $x=- \frac{b}{2a}=- \frac{4}{(2)(1)}=2$ . The foci of this parabola lies on $x=2$ .

Second step: Find the value of y-coordinate by substituting $x=2$ into $f(x)$ which give $y=- (2)^{2} +4(2)+8=12$

Third step: Find the distance of the foci from the y-coordinate
$y=- x^{2} +4x+8$ - Multiply all term by -1 to get a positive $x^{2}$
$-y= x^{2} -4x-8$ - then manipulate the constant of y to get a multiply of 4
$4(- \frac{1}{4})y= x^{2} -4x-8$
So the distance of focus is 0.25 to the south of y-coordinates of the maximum, which is $12- \frac{1}{4}=11.75$

Hence the coordinate of the foci is (2, 11.75)

Function 2: $f(x)= 2x^{2}+16x+18$

The function has a positive $x^{2}$ so it has a minimum

First step - $x=- \frac{b}{2a}=- \frac{16}{(2)(2)}=-4$
Second step - $y=2(-4)^{2}+16(-4)+18=-14$
Third step - Manipulating $f(x)$ to leave $x^{2}$ with constant of 1
$y=2 x^{2} +16x+18$ - Divide all terms by 2
$\frac{1}{2}y= x^{2} +8x+9$ - Manipulate the constant of y to get a multiply of 4
$4( \frac{1}{8}y= x^{2} +8x+9$

So the distance of focus from y-coordinate is $\frac{1}{8}$ to the north of $y=-14$
Hence the coordinate of foci is (-4, -14+0.125) = (-4, -13.875)

Function 3: $f(x)=-2 x^{2} +5x+14$

First step: the function's maximum value happens when $x=- \frac{b}{2a}=- \frac{5}{(-2)(2)}= \frac{5}{4}=1.25$
Second step: $y=-2(1.25)^{2}+5(1.25)+14=17.125$
Third step: Manipulating $f(x)$
$y=-2 x^{2} +5x+14$ - Divide all terms by -2
$-2y= x^{2} -2.5x-7$ - Manipulate coefficient of y to get a multiply of 4
$4(- \frac{1}{8})y= x^{2} -2.5x-7$
So the distance of the foci from the y-coordinate is - $\frac{1}{8}$ south to y-coordinate

Hence the coordinate of foci is (1.25, 17)

Function 4: following the steps above, the maximum value is when $x=8.5$ and $y=79.25$ . The distance from y-coordinate is 0.25 to the south of y-coordinate, hence the coordinate of foci is (8.5, 79.25-0.25)=(8.5,79)

Function 5: the minimum value of the function is when $x=-2.75$ and $y=-10.125$ . Manipulating coefficient of y, the distance of foci from y-coordinate is $\frac{1}{8}$ to the north. Hence the coordinate of the foci is (-2.75, -10.125+0.125)=(-2.75, -10)

Function 6: The maximum value happens when $x=1.5$ and $y=9.5$ . The distance of the foci from the y-coordinate is $\frac{1}{8}$ to the south. Hence the coordinate of foci is (1.5, 9.5-0.125)=(1.5, 9.375)

8 0

3 years ago

Subtract the quantity 12a <br><br> 2<br><br> −8a+4 from the quantity 12−7a <br><br> 2

SIZIF [17.4K]

Answer:

11a-8

Step-by-step explanation:

Please Note that i assume 12a and 2 are positive.

(12a+2−8a+4)-(12−7a+2)

=12a+2-8a+4-12+7a-2

=12a-8a+7a+2+4-12-2

=11a-8

6 0

3 years ago