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3 years ago

15

You play video games online. When you sign up with the game site, you get 200 points. You earn 20 more points for each hour that

you play. How many hours do you have to play to get to 500 points?

1 answer:

uranmaximum [27]3 years ago

3 0

Hey there! The answer is 30 hours!

Work: 500 - 200 = 300

15 x 20 = 300

200 + 300 = 500

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Two angles are supplementary if their sum is 180°. the larger angle measures five degrees more than four times the measure of a

wlad13 [49]

Let x represent the smaller angle.
Let y represent the larger angle.

The problem states that the larger angle measures five degrees more than four times the measure of the smaller angle.
With this given information, we can create the following equation.

$y=4x+5$

Also, they a supplementary, meaning that they add up to 180. We can create another equation.

$x+y=180$

Since we have two linear equations and we want to find the solution, we have a system of linear equations. Let's solve this system by using the substitution method.

Substitute $y=4x+5$ into $x+y=180$

$x+y=180$

After substituting, you get

$x+4x+5=180$

Now, combine the x's

$5x+5=180$

Subtract both sides by 5

$5x=175$

Divide both sides by 5.

$x=35$

Now, we can solve for y using the equation $x+y=180$ since we know the value of x.

$35+y=180$

Subtract both sides by 35.

$y=145$

The smaller angle has a measure of 35 degrees and the larger one has a measure of 145 degrees. Have an awesome day! :)

5 0

3 years ago

Armand deposited 389.42 in a savings account that earns 3.2% simple interest what is Amands account balance after seven years

Vinvika [58]

Account balance = $389.42 + $389.42 (0.032) (7)

$389.42 + $87.23 = $ $476.65 (answer)

5 0

3 years ago

Use the given transformation x=4u, y=3v to evaluate the integral. ∬r4x2 da, where r is the region bounded by the ellipse x216 y2

exis [7]

The Jacobian for this transformation is

$J = \begin{bmatrix} x_u & x_v \\ y_u & y_v \end{bmatrix} = \begin{bmatrix} 4 & 0 \\ 0 & 3 \end{bmatrix}$

with determinant $|J| = 12$ , hence the area element becomes

$dA = dx\,dy = 12 \, du\,dv$

Then the integral becomes

$\displaystyle \iint_{R'} 4x^2 \, dA = 768 \iint_R u^2 \, du \, dv$

where $R'$ is the unit circle,

$\dfrac{x^2}{16} + \dfrac{y^2}9 = \dfrac{(4u^2)}{16} + \dfrac{(3v)^2}9 = u^2 + v^2 = 1$

so that

$\displaystyle 768 \iint_R u^2 \, du \, dv = 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2 \, du \, dv$

Now you could evaluate the integral as-is, but it's really much easier to do if we convert to polar coordinates.

$\begin{cases} u = r\cos(\theta) \\ v = r\sin(\theta) \\ u^2+v^2 = r^2\\ du\,dv = r\,dr\,d\theta\end{cases}$

Then

$\displaystyle 768 \int_{-1}^1 \int_{-\sqrt{1-v^2}}^{\sqrt{1-v^2}} u^2\,du\,dv = 768 \int_0^{2\pi} \int_0^1 (r\cos(\theta))^2 r\,dr\,d\theta \\\\ ~~~~~~~~~~~~ = 768 \left(\int_0^{2\pi} \cos^2(\theta)\,d\theta\right) \left(\int_0^1 r^3\,dr\right) = \boxed{192\pi}$

3 0

2 years ago

After 3000 impressions, ad A has a CTR of 2% and a conversion rate of 25%, and ad B has a CTR of 4% and a conversion rate of 10%

leva [86]

Answer: A

Step-by-step explanation:

3000 impressions

A CTR 2% conversion 25%

2% of 3000 = 2/100 . 3000 = 60 clicks

25% of 60 = 25/100 . 60 = 15

B CTR 4% conversion 10%

4% of 3000 = 4/100 . 3000 = 120 clicks

10% of 60 = 10/100 . 120 = 12

This way, A converted more than B

8 0

3 years ago

Set up an equation and solve for this problem.

viktelen [127]

Your equation might look like this,
Since the ticket is $8, and her budget is 50, your gonna have to divide.
Then the remaining answer would be, 6.25.
So, your equation= $50/$8=6.25
Your answer is 6, 6 tickets can be bought with the remainder of 0.25 cents.

7 0

3 years ago