Lydia wants to find the height of a flagpole. She measures the height of a tree and the length of the shadow it casts. The tree is 14 feet tall, and its shadow is 21 feet long. Next, Lydia measures the shadow cast by the flagpole, and finds it is 30 feet long. What is the height of the flagpole?

Answer:

We know that the figure has a symmetry

angle 1 = angle 2

angle 1 =180°-(18°+90°) = 180° - 108°=72°

Therefore, angle 2 =72°.

Answer:

x = 2, y = 13

(2, 13)

Step-by-step explanation:

hope this helps!

0.75 pizza

Step-by-step explanation: 0.75 x 12 equals 8, that's basically it.

Answer:

0.666667

Step-by-step explanation:

8 pizzas ÷ 12 people = 0.66667 pizzas for each.

(a) For some given x, A(x) gives the signed area under f(t) on the interval [a, x]. Since f(t) is simple to integrate, and with a = 2, you can compute it exactly:

A(x) = ∫₂ˣ f(t) dt

A(x) = ∫₂ˣ (3t + 2) dt

A(x) = (3/2 t ² + 2t ) |₂ˣ

A(x) = 3/2 x ² + 2x - 10

which is parabolic and easy to graph.

(b) Differentiating A(x) is also easy if you use the "closed" form above:

A'(x) = (3/2 x ² + 2x - 10)'

A'(x) = 3x + 2

and this function tells you how the area under f(t) changes as you adjust the size of the integration interval.

You can get the same result using the fundamental theorem of calculus:

A'(x) = d/dx ∫₂ˣ f(t) dt = f(x) = 3x + 2

Answer: 11/24

Step-by-step explanation:

whenever u see this — (

it means the opposite of. so the opposite of -5/8 is +5/8.

-1/6 + 5/8 = 11/24

Answer: 2 rays that meet an endpoint

Answer:

The amount to be paid for insurance will be $ 937,500. In this context, it is reasonable that insurance costs increase proportionally, as the ride will have a greater use and, therefore, a greater exposure to risk.

Step-by-step explanation:

Given that the amusement park Diablo's Domain ride generated $ 250,000,000 in revenue, and the company paid $ 750,000 in insurance for that game ($ 3 for every $ 1,000 in profit), to determine the amount of insurance that should be paid if the winnings increase by 25% and the same proportion of 3/1000 to be paid is maintained, the following calculation must be made:

(250,000,000 x 1.25) x (3/1000) = X

312,500,000 x 0.003 = X

937,500 = X

Therefore, the amount to be paid for insurance will be $ 937,500.

Answer:

The first step is to slove the numbers in the brackets

Step-by-step explanation:

[(x+7) x -2] / 4 = 7

-2(x+7) / 4 = 7

-2x-14 / 4 = 7

-2x-14 = 28

-2x = 42

x = -21

PEMDAS

Answer:

D :)

Step-by-step explanation:

Answer:

the probability of a client owning stocks OR bonds is 0.825

Step-by-step explanation:

The computation of the probability of a client owning stocks OR bonds is given below:

= P(stocks) + P(bonds) - P(stocks and bonds)

= 0.60 + 0.50 - (0.55 × 0.50)

= 0.60 + 0.50 - 0.275

= 0.825

Hence, the probability of a client owning stocks OR bonds is 0.825

Answer:

please refer to the above attachment

Answer:

z = 25

Step-by-step explanation:

adjacent angles in a rhombus are supplementary

3z - 15 + 7z - 55 = 180

10z - 70 = 180

10z = 250

z = 25

Answer:

Scale factor = 1.5

Step-by-step explanation:

Formula for the scale factor,

Scale factor = [tex]\frac{\text{Measure of one side of the Image}}{\text{Measure of one side of the preimage}}[/tex]

In this question, image is triangle Y and preimage is triangle X.

Scale factor of X to Y = [tex]\frac{15}{10}[/tex]

                                    = 1.5

Therefore, scale factor = 1.5 is the answer.

Answer:

The angles of the triangle are approximately 87.395º, 57.271º and 35.334º.

Step-by-step explanation:

From statement we know all sides of the triangle ([tex]a[/tex], [tex]b[/tex], [tex]c[/tex]), but all angles are unknown ([tex]A[/tex], [tex]B[/tex], [tex]C[/tex]). (Please notice that angles with upper case letters represent the angle opposite to the side with the same letter but in lower case) From Geometry it is given that sum of internal angles of triangles equal 180º, we can obtain the missing information by using Law of Cosine twice and this property mentioned above.

If we know that [tex]a = 19[/tex], [tex]b = 16[/tex] and [tex]c = 11[/tex], then the missing angles are, respectively:

Angle A

[tex]a^{2} = b^{2}+c^{2}-2\cdot b\cdot c \cdot \cos A[/tex] (1)

[tex]A = \cos^{-1}\left(\frac{b^{2}+c^{2}-a^{2}}{2\cdot b\cdot c} \right)[/tex]

[tex]A = \cos^{-1}\left[\frac{16^{2}+11^{2}-19^{2}}{2\cdot (16)\cdot (11)} \right][/tex]

[tex]A \approx 87.395^{\circ}[/tex]

Angle B

[tex]b^{2} = a^{2}+c^{2}-2\cdot a\cdot c \cdot \cos B[/tex] (2)

[tex]B = \cos^{-1}\left(\frac{a^{2}+c^{2}-b^{2}}{2\cdot a\cdot c} \right)[/tex]

[tex]B = \cos^{-1}\left[\frac{19^{2}+11^{2}-16^{2}}{2\cdot (19)\cdot (11)} \right][/tex]

[tex]B\approx 57.271^{\circ}[/tex]

Angle C

[tex]C = 180^{\circ}-A-B[/tex]

[tex]C = 180^{\circ}-87.395^{\circ}-57.271^{\circ}[/tex]

[tex]C = 35.334^{\circ}[/tex]

The angles of the triangle are approximately 87.395º, 57.271º and 35.334º.

Answer:

1/8

Step-by-step explanation:

That's the same assignment I have and you just have to think it through mate.

Answer:

Explained below

Step-by-step explanation:

A rational number is one that can be expressed in form a of a fraction whereby both the numerator and the denominator are integers.

Also, if it results in a recurring decimal it is still a rational number but if the decimal is not recurring, then it is not a rational number.

Now, for example let's consider the number 5.

It is a rational number because it can be expressed as; 5/1; 10/2; 20/4; -5/-1 e.t.c

Now, the opposite of these fractions like we are told to check in the question results in;

1/5; 2/10; 4/20; -1/-5;

The opposite will give us still a rational number because both numerator and denominator are still integers and also the value of the division is 0.2 which is a definite decimal and also can be expressed as an integer.

Answer: 5

Step-by-step explanation:

x = common side length

2x + (2x - 6) = 14

4x - 6 = 14

4x = 20

x = 5

Answer:

46.2

Step-by-step explanation:

46.188= 46.2

This equation has infinite solutions, any real number makes it true.

Answer:

The answer is C

Step-by-step explanation:

The graph has a normal distribution, mean at 3.6, and a standard deviation of 0.6

Answer:

the Correct Answer Is c

Step-by-step explanation:

PLZ PLZ PLZ MARK AS BRAINLIEST LOL PLZ

Answer:

A 4040 bag sample 25.0425.0 grams. A level of significance of 0.020.02

the decision rule. Assume the standard deviation is known to be 11.011.0.

Step-by-step explanation:

The answer is 6

Explanation:

Your monthly allowance and your friend's monthly allowance is $50 and $40 respectively.

From the given tape diagram, the ratio of your monthly allowance to your friend's monthly allowance is 5:4.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

Here, 5+4=9

Now, your monthly allowance = 5/9 × 90

= 50

So, your friend's monthly allowance = 90-50 = 40

Therefore, your monthly allowance and your friend's monthly allowance is $50 and $40 respectively.

To learn more about the ratio visit:

brainly.com/question/13419413.

#SPJ2

Answer:

8

Step-by-step explanation:

180=90+40+6x+2

180=132+6x

48=6x

x=8

Answer:

x=4 i think havent done this in a long time

Step-by-step explanation: