Prove that (cos X)2 + (sin x)2 = 1

In the diagram below, GH is parallel to DE . If GH is 3 more than EH FH=10, and DE=12 find the length of EH. Figures are not nec

steposvetlana [31]

Answer: 5

Step-by-step explanation:

Since $\overline{GH} \parallel \overline{DE}$ , by the corresponding angles theorem, $\angle FGH \cong \angle FDE, \angle FHG \cong \angle FED$ . This means $\triangle FGH \sim \triangle FDE$ by AA.

As corresponding sides of similar triangles are proportional,

$\frac{10}{x+3}=\frac{10+x}{12}\\(10)(12)=(10+x)(x+3)\\120=x^{2}+13x+30\\x^{2}+13x-90=0\\(x+18)(x-5)=0\\x=-18, 5$
However, as distance must be positive, we consider the positive solution, x=5.

Therefore, the answer is 5

6 0

2 years ago

Write an expression that represents the area of a circle with radius 3x^3. (For any circle with radius r, a=π r^2 = π .r .r ^.)

aalyn [17]

9514 1404 393

Answer:

B. 9πx^6

Step-by-step explanation:

Putting the given radius into the area formula gives ...

A = πr^2

A = π(3x^3)^2 = π(3^2)(x^(3·2))

A = 9πx^6

6 0

3 years ago

Simplify <img src="https://tex.z-dn.net/?f=4%20%2B%20%20%5Cfrac%7B3%7D%7B7%7Dx%20-%202%20-%20%20%5Cfrac%7B2%7D%7B7%7Dx%20%20

Sloan [31]

$4 + \frac{3}{7}x - 2 - \frac{2}{7}x\\\\\text{combine like terms}\\\\\left(\dfrac{3}{7}x-\dfrac{2}{7}x\right)+(4-2)=\dfrac{3-2}{7}x+2=\boxed{\dfrac{1}{7}x+2}$

6 0

3 years ago

Read 2 more answers

Select a value: addition property of equality

Whitepunk [10]

Answer:

Addition prop of equality, multiplication prop of equality, multiplication prop. of equality

Step-by-step explanation:

For the first one, we know that in order to solve the equation, we need to add 3 to both sides of the equation. When you add a value to both sides of the equation, you're using the addition property of equality.

For the second one, we know that in order to solve the equation, we need to multiply both side by 1/6 (to cancel the 6 out on the left side). When you multiply something to both sides of the equation, you're using the multiplication property of equality.

For the third one, we know that in order to solve the equation, we must multiply both sides of the equation by 5. Like the second problem, this would be the multiplication property of equality (since you're multiplying both sides of the equation by the same thing).

3 0

3 years ago

Dwayne drove 18 miles to the airport to pick up his father and then returned home. On the return trip he was able to drive an av

Nesterboy [21]

Answer:

30 mph

Step-by-step explanation:

Let d = distance (in miles)

Let t = time (in hours)

Let v = average speed driving to the airport (in mph)

⇒ v + 15 = average speed driving from the airport (in mph)

Using: distance = speed x time