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Liula [17]
3 years ago
6

You lean a 30 foot ladder against your house and it reaches exactly to the top. The ladder makes a 24 degree angle with the grou

nd. How tall is your house?
Mathematics
1 answer:
zhenek [66]3 years ago
4 0
A right triangle is formed with the ladder as the hypotenuse. Since the angle made by the ladder with with ground is given, we can use trigonometric functions to solve for the height of the house.

If we let x be the height of the house and using sine function:
sin 24 = x/30
x = 30 sin 24
x = 12.20 ft

Therefore, the house is 12.20 ft tall
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Quadrilateral ABCD is inscribed in a circle. Find the measure of each of the angles of the quadrilateral. Show your work.
LuckyWell [14K]

Step-by-step explanation:

Quadrilateral ABCD is inscribed in a circle.

Opposite angles of a Quadrilateral are Supplementary.

\therefore \: \angle A + \angle C = 180° \\  \therefore \:(2x + 3) \degree+ (2x + 1) \degree = 180° \\  \therefore \: (4x + 4) \degree = 180° \\ \therefore \: (4x + 4) = 180 \\ \therefore \: 4x = 180 - 4 \\ \therefore \: 4x = 176 \\ \therefore \: x =  \frac{176}{4}  \\ \therefore \: x =  44 \\  \\  m\angle A  = (2x + 3) \degree \\  = (2 \times 44 + 3) \degree \\ = (88 + 3) \degree \\  \huge \red{ \boxed{ \therefore \: m\angle A  =91 \degree}} \\  \\ m\angle  C = (2x + 1) \degree \\  = (2 \times 44 + 1) \degree \\ = (88 + 1) \degree \\  \huge \red{ \boxed{ \therefore \: m\angle   C=89\degree}}  \\  \\ m\angle  D= (x - 10) \degree \\  = (44 - 10) \degree \\  \huge \red{ \boxed{ \therefore \: m\angle  D =34\degree}}  \\  \\ similarly \\  \\  \huge \red{ \boxed{ \therefore \: m\angle  B  = 146\degree}}   \\  \\

6 0
3 years ago
Of the following equations below, which equation represents a direct variation between x and y?
spin [16.1K]

Answer:

C. y +3 = x +3

Step-by-step explanation:

We need to find in below option x has direct variation with y.

We solve for each;

A. 2y = 3x-7

From above equation we can state that 2 times y is equal to 7 less than 3 times of x.

Hence it doesn't represent direct variation.  

B. y-4 = x+6

Solving above expression we get;

y-4 = x+6\\y = x+6+4\\y=x+10

From above equation we can state that y is equal to 10 more than x.

Hence it doesn't represent direct variation.

C. y+3 = x+3

Solving above expression we get;

y+3 = x+3\\y = x+3-3\\y=x

From above equation we can state that y is equal to x.

Hence it represent direct variation.

D. 4y+1 = 4x-1

Solving above expression we get;

4y+1 = 4x-1\\4y = 4x-1-1\\4y=4x-2

From above equation we can state that 4 times y is equal to 2 less than 4 times of x.

Hence it doesn't represent direct variation.

Hence the Answer which represent direct variation of x and y is,

C. y+3 = x+3

7 0
3 years ago
Rewrite the quadratic function in vertex form.<br> Y=5x^2-10x+2
Natalka [10]

Answer:

y = 5x2 + 10x - 15

We want this in format y = a(x-h)2 + k

where the vertex will be at (h,k)

y = 5(x2+2x) - 15

Complete the square on x2+2x

y = 5(x2+2x+1) - 15 - 5

We subtract 5 at the end because we are actually adding 5(1) = 5

so we need to remove it also to keep the total equal

y = 5(x+1)2 - 20

The vertex is at (-1,-20)

3 0
3 years ago
What is the interior angles cut by transversal t.​
gregori [183]

Answer:

When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles . If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent

5 0
3 years ago
The area of a rectangle is represented by the function A = n^3 - 6n^2 - 8n + 48.
aliya0001 [1]

Answer:

P = 2(n - 6) + 2(n^2 - 8)

Step-by-step explanation:

Remembering that Area = Length times Width, we factor the given function

A = n^3 - 6n^2 - 8n + 48 in the expectation that the resulting factors represent the length and width respectively:

A = n^3 - 6n^2 - 8n + 48 factors as follows:

A = n^2(n - 6) - 8(n - 6), or A = (n - 6)(n^2 - 8)

We can label '(n - 6)' "width" and '(n^2 - 8'

length.

Then the perimeter, P, of the rectangle is P = 2(length) + 2(width). which works out here to:

P = 2(n - 6) + 2(n^2 - 8)

5 0
3 years ago
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