G(n) = |n|; Find g(-8)

The first equation that you can make can be a + b = 25 because the number of 2-seated cars plus the number of 4-seated cars is going to equal a total of 25 cars.

The next equation you can make is 2a + 4b = 70 because the number of seats provided by the 2-seated cars plus the number of seats provided by the 4-seated cars will equal 70 total seats.

Next, line up the equations and solve:

Step one: Line up the equations

a + b = 25

2a + 4b = 70

Step two: Multiply the top equation by -2 so that you can add both of the equations together

-2(a) + -2(b) = 25(-2) ⇒ -2a - 2b = -50

2a + 4b = 70 ⇒ 2a + 4b = 70

Step three: Add the equations

-2a - 2b = -50

+ 2a + 4b = 70

______________

2b = 20

Step four: Divide both sides by 2 in order to solve for b

2b = 20 ⇒ b = 10

Because b represents the number of 4-seated cars, you now know that there are 10 4-seated cars on the ride.

3 0

3 years ago

Mr.Williams, a parking lot owner, sold 20% of his lot to his neighbor. Later that year he sold 20% of the remainder of his lot t

riadik2000 [5.3K]

Answer: He still owns 64% of the Mr.Williams' original parking.

Step-by-step explanation:

Let x = Area of the original parking plot.

First he sold 20% of his lot to neighbor .

Sold plot = 20% of x = 0.20x [Replace 'of' by '×' and divide number by 100 to remove %]

Reminder= x-0.20x= (1-0.20)x=0.80x

Again he sold 20% of the remainder .

Sold plot = 20% of (0.80x) = 0.20 (0.80x)

= 0.16x

Remainder plot = 0.80x-0.16x= 0.64x

Percent of Mr.Williams' original parking lot does he still own = $\dfrac{0.64x}{x}\times100=64\%$

Hence, he still owns 64% of the Mr.Williams' original parking.

4 0

3 years ago

Find the standard form of the equation for the circle with the following properties.

nataly862011 [7]

Answer:

$(x+6)^2+(y+\frac{7}{6})^2=\frac{49}{36}$

Step-by-step explanation:

So, we know that the center of the circle is at (-6, -7/6).

To find the equation of our circle that is tangent to the x-axis, we just need to find the vertical distance from our center to the x-axis.

Our center is at (-6, -7/6). The vertical distance from this to the x-axis directly above will be (-6, 0).

So, find our distance by subtracting our x-values:

$d=r=0-(-7/6)$

Subtract:

$d=r=7/6$

So, our distance, which is also our radius, will be 7/6.

Now, we can use the standard form for a circle, which is:

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

Where (h, k) is the center and r is the radius.

Substitute -6 for h, -7/6 for k, and 7/6 for r. This yields:

$(x+6)^2+(y+\frac{7}{6})^2=\frac{49}{36}$

We can confirm by graphing (using a calculator):

7 0

3 years ago