the 2 equations given are vertical angles which mean they would equal the same.
Set the two equations to equal each other to solve for x:
6(x-2) = 3x+30
Simplify the left side:
6x-12 = 3x+30
Add 12 to eac side:
6x = 3x+42
Subtract 3x from each side"
3x = 42
Divide both sides by 3:
X = 42/3
X = 14
Now you know X, replace x with 14 in the equation for DHG:
DHG = 6(x-2)
6(14-2)
Simplify:
6(12)
Multiply:
72
Angle DHG is 72 degrees.
The answer would be letter B
(a) First find the intersections of

and

:

So the area of

is given by

If you're not familiar with the error function

, then you will not be able to find an exact answer. Fortunately, I see this is a question on a calculator based exam, so you can use whatever built-in function you have on your calculator to evaluate the integral. You should get something around 0.5141.
(b) Find the intersections of the line

with

.

So the area of

is given by


which is approximately 1.546.
(c) The easiest method for finding the volume of the solid of revolution is via the disk method. Each cross-section of the solid is a circle with radius perpendicular to the x-axis, determined by the vertical distance from the curve

and the line

, or

. The area of any such circle is

times the square of its radius. Since the curve intersects the axis of revolution at

and

, the volume would be given by
Down payment is 20% of the price of the home. Since the couple saved $35,000, and assuming they will pay the whole money as down payment, the highest priced home they can get is a price whose 20% is $35,000.
We can setup an equation in x (being the price of home) to get the price of the most expensive home they can buy.
<em>Which number (x) , multiplied by 20%, is equal to $35,000?</em>
<em>
</em>
So, the most expensive house they can buy is worth $175,000.
ANSWER: $175,000
Answer:
-10 > (-4x - 6) > -22
Step-by-step explanation:
Given inequality is 5 < 2x + 3 < 11
Now we will multiply this inequality by (-2) resulting,
5(-2) > (2x + 3)(-2) > 11(-2)
-10 > (-4x - 6) > -22 (Sign of inequality gets reversed when the inequality is multiplied or divided by a negative number)
Therefore, the possible range of (-4x - 6) is between -22 and -10.