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3 years ago

15

Which equation represents the yearly cost for a nonmeber at the same video game arcade based on the total number of game tokens

purchased in a year

1 answer:

olganol [36]3 years ago

3 0

Answer: c) y=1/5x

Step-by-step explanation: took da test

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A circle has the equation 2x²+12x+2y²−16y−150=0.

KonstantinChe [14]

Answer: B. The coordinates of the center are (-3,4), and the length of the radius is 10 units.

Step-by-step explanation:

The equation of a circle in the center-radius form is:

$(x-h)^{2} +(y-k)^{2}=r^{2}$ (1)

Where $(h,k)$ are the coordinates of the center and $r$ is the radius.

Now, we are given the equation of this circle as follows:

$2x^{2}+12x+2y^{2}-16y-150=0$ (2)

And we have to write it in the format of equation (1). So, let's begin by applying common factor 2 in the left side of the equation:

$2(x^{2}+6x+y^{2}-8y-75)=0$ (3)

Rearranging the equation:

$x^{2}+6x+y^{2}-8y=75$ (4)

$(x^{2}+6x)+(y^{2}-8y)=75$ (5)

Now we have to complete the square in both parenthesis, in order to have a perfect square trinomial in the form of $(a\pm b)^{2}=a^{2}\pm+2ab+b^{2}$ :

<u>For the first parenthesis:</u>

$x^{2}+6x+b^{2}$

We can rewrite this as:

$x^{2}+2(3)x+b^{2}$

Hence in this case $b=3$ and $b^{2}=9$ :

$x^{2}+2(3)x+3^{2}=x^{2}+6x+9=(x+3)^{2}$

<u>For the second parenthesis:</u>

$y^{2}-8y+b^{2}$

We can rewrite this as:

$y^{2}-2(4)y+b^{2}$

Hence in this case $b=-3$ and $b^{2}=9$ :

$y^{2}-2(4)y+4^{2}=y^{2}-8y+16=(y-4)^{2}$

Then, equation (5) is rewritten as follows:

$(x^{2}+6x+9)+(y^{2}-8y+16)=75+9+16$ (6)

<u>Note we are adding 9 and 16 in both sides of the equation in order to keep the equality.</u>

Rearranging:

$(x-3)^{2}+(y-4)^{2}=100$ (7)

At this point we have the circle equation in the center radius form $(x-h)^{2} +(y-k)^{2}=r^{2}$

Hence:

$h=-3$

$k=4$

$r=\sqrt{100}=10$

8 0

3 years ago

Alina has 3/2 hours to complete her homework. She plans to split apart rhentime equally between 3 assignments. Which expression

e-lub [12.9K]

C. 3/2 divided by 3

Alina has 3/2 hours to complete her homework. She should divide her 3/2 hours by the 3 assignments to determine how much time she will spend on each assignment. This turns out to be 1/2 hours, or 30 minutes, on each assignment. 3/2 hours is the same thing as 90 minutes, so this answer makes sense. We want the time to be divided by the number of assignments, not vice versa.

5 0

3 years ago

Please help me and explain it please questions 28

klasskru [66]

Answer:

$1.35

Step-by-step explanation:

x: quarter=$0.25

y: dime=$0.10

z: nickel=$0.05

so total amount of changes

= (0.25*x)+(0.10*y)+(0.05*z)

x=3, y=5, z=2

substituting into the eqn

total = (0.25*3)+(0.10*5)+(0.05*2)

= 0.75 + 0.5 + 0.1

= $1.35

5 0

2 years ago

Read 2 more answers

Fiona is choosing flower bouquets for her wedding. The probability that a bouquet has roses is 0.98, has orchids is 0.87, or has

Digiron [165]

You would find the average of the probability for roses and daisies, which would be .98 + .94 = 1.92. Divide this by 2 to get .96. The probability of the bouquet having roses or daisies is .96.

3 0

2 years ago

I really need help with this one...

tiny-mole [99]

C because it makes complete common sense but idk though just in case I'm wrong and u can't blame me lol

5 0

3 years ago