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3 years ago

15

Kini and Duke are each working during the summer to earn money in addition to their weekly allowance, and they are saving all of

their money. Kini earns $9 an hour at her job, and her allowance is $8 per week. Duke earns $7.50 an hour, and his allowance is $17 per week. How many hours do Kini and Duke need to work in order to save the same amount of money in one week?

1 answer:

Tatiana [17]3 years ago

7 0

Answer:

Step-by-step explanation:

9x + 8 = 7.5x + 17

1.5x = 9

x = 6 hours

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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

Which size would you see on the box for a new television whose screen measures 32 inches wide by 18 inches high?

zzz [600]

Answer:

37

Step-by-step explanation:

The calculation of size for a new television is shown below:-

With the help of Pythagoras theorem

$h^2 = b^2 + p^2$

where

h indicates hypotenuse which is the diagonal length

b indicates the base which is the length of the horizontal side

p indicates perpendicular which is the TV length of the vertical side.

$h^2 = \sqrt{b^2 + p^2}$

now, we will put the values into the above formula

$= \sqrt{32^2 + 18^2} \\\\ = \sqrt{1024 + 324} \\\\ = \sqrt{1348}$

Which gives result

= 36.7

or

= 37

5 0

3 years ago

185 for 4 tickets whats the price per ticket

Olin [163]

46.25 according to my calculator

3 0

3 years ago

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MrRissso [65]

D is the correct answer

7 0

3 years ago

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Ahmed received a box of gifts. The box is a rectangular prism with the same height and width, and the length

liubo4ka [24]

Answer:

12 inches

Step-by-step explanation:

Ahmed received a box of gifts. The box is a rectangular prism with the same height and width, and the length

is twice the width. The volume of the box is 3,456 in? What is the height of the box?

Volume of a Rectangular pyramid = Length × Width × Height

From the above question

Height = Width = x

Length = 2 × Width

Length = 2x

Volume = 3,456 cubic inches

Hence,

3,456 = 2x × x × x

3456 = 2x³

x³ = 3456/2

x³ = 1728

Cube root both sides

Cube root(x³) = cube root (1728 cubic Inches)

x = 12 inches

Therefore, the height is 12 inches

3 0

3 years ago