Sitting in your sailboat looking at the horizon, you see a lighthouse 500 feet away. Looking up at a 20*, you see the light at the top of the lighthouse. How far off the ground is the light in the lighthouse? Round your answer to the nearest tenth.

Answer:

Step-by-step explanation:

The volume of the trapezoidal prism having side lengths x, (x+2), (x+4) and height of 2x is 2x³+6x² option first is correct.

It is defined as a three-dimensional space enclosed by an object or thing.

We know the volume of the trapezoidal prism can be given:

[tex]\rm V=\frac{1}{2} (a+b)\times h \times L[/tex]

Where V = The volume of the trapezoidal prism:

Length of the trapezoid L = x

Top width  a = (x+2)

Base width  b = (x+4)

Height of the trapezoidal prism  h = 2x

[tex]\rm V=\frac{1}{2} (x+2+x+4)\times 2x \times x[/tex]

[tex]\rm V=\frac{1}{2} (2x+6)2x^2\\\\\rm V= (2x+6)x^2\\\\\rm V= (2x^3+6x^2)[/tex]

Thus, the volume of the trapezoidal prism is  [tex]\rm (2x^3+6x^2)[/tex]

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Answer:

A.

Step-by-step explanation:

right on edge

Answer:

D) -22 < 25

Step-by-step explanation:

If the number is 47 units to the right, then the number will be larger than -22, because negative values get larger the closer they are to zero.

47 units right from -22 is the same as: -22 + 47, which equals 25.

So, we can conclude that -22 < 25 is the inequality.

hope this helps!

Answer:

the answer is 12

Step-by-step explanation:

it is what it is

Answer:

The answer is 20p – 10 or 10(2p – 1)

Step-by-step explanation:

4(2p + 2) + 6(2p − 3)

8p + 8 + 12p – 18

20p – 10 or 10(2p – 1)

Answer:

Math-Graphing Inequalities on a Number Line (the basics)

Step-by-step explanation:

Answer:

Part A

Let d = number of dogs

Let c = number of cats

Given:

⇒ d + c = 165

Given:

⇒ c = 2d - 24

Part B

Substitute  c = 2d - 24  into  d + c = 165  and solve for d:

⇒ d + 2d - 24 = 165

⇒ 3d - 24 = 165

⇒ 3d = 189

⇒ d = 63

Substitute found value of d into  d + c = 165  and solve for c:

⇒ 63 + c = 165

⇒ c = 102

Therefore, 63 dogs and 102 cats are adopted in the shelter.

Answer:

y=12

Step-by-step explanation:

y=k*x

3=5*k

k=3/5

y= (3/5)*x

y=(3/5)*20

y=12

Answer:

The answer is 24 cm.

Step-by-step explanation:

Since we know two sides, we can find the third side. Using the pythagorean theorm, a^2 + b^2 = c^2, this gives us:

6^2 + 8^2 = c^2

36 + 64 = c^2

100 = c^2

Square root of 100 = c

10 = c.

Hope this helps!

Step-by-step explanation:

30: 225 = 25: X

30/225= 25/X

30×X = 225×25

30X = 5625

X = 187.5

Answer:

Mean: 54
Median: 61.5
Mode: 0
Range: 54

Step-by-step explanation:

Mean: Add everything up and divide by the amount of numbers
(47 + 31 + 84 + 50 + 68 + 85 + 67 + 56 = 488/8 = 54)

Median: Put all numbers in order from smallest to largest, the middle number is the median. Since we have 2 middle numbers, we add both 67 and 67 together, then divide them by 2.
31, 47, 50, 56, 67, 68, 84, 85
(56 + 67 = 123/2 = 61.5

Mode: The mode is the number that appears most often in the set of given numbers.
(There are no numbers that appear more than once so the mode is 0)

Range: The range is the largest number subtracted by the smallest number.
(85 - 31 = 54)

Answer:

7.5

Step-by-step explanation:

Yes they are proportional

Answer:

A- yes

Step-by-step explanation:

If you never buy the popcorn because you think that it is too expensive then the only thing you are paying for is the tickets therefore the price you pay is proportional to the number of tickets you buy.

Answer:

heyy do you still need help

Step-by-step explanation:

Answer:

c; 63 square cm

Step-by-step explanation:

the area of a trapezoid can be described by the equation a = (1/2)(h)(b1 + b2)

this means the height times base 1 and base 2 added together divided by 2

(1/2)(6)(8 + 13) is the equation

this can become 3(21)

which is ultimitaly 63

Answer:

it's gonna be 63cm^2

Step-by-step explanation:

First, were gonna find the area of the rectangular portion, which is 8x6, which is 48cm^2

Next, well do the triangle part. So, we have to subtract 13-8 to get the width of the triangle.

Next, we have to find the area for the triangle. The formula is length x width / 2.

So, we have to multiply 6x5 to get 30.

Then, well divide it by 2, which will give us 15cm^2

Finally, we add the areas of rectangle and the triangle together. 15 + 48 is 63.

Bada-bing, bada-boom, we got 63cm^2 as our answer :)

Answer:

$724.11

Step-by-step explanation:

This requires the use of the growth formula.

Growth Formula:

[tex]y = a*(1+r)^x[/tex]

y = total/answer

a = starting value

r = rate (1.25 = 25%)

x = the amount of time (years/months)

Equation:

[tex]y = 6200 * (1+0.028)^4[/tex]

Solving:

y = $6924.11

$6924.11 - $6200 =  total interest

$724.11

[tex]~~~~~~ \textit{Simple Interest Earned} \\\\ I = Prt\qquad \begin{cases} I=\textit{interest earned}\\ P=\textit{original amount deposited}\dotfill & \$6200\\ r=rate\to 2.8\%\to \frac{2.8}{100}\dotfill &0.028\\ t=years\dotfill &4 \end{cases} \\\\\\ I = (6200)(0.028)(4)\implies I=694.4[/tex]

Answer:

[tex] \frac{1}{2} of \: the \: invitations = \frac{1}{2} \times 54 \\ = 27invitations[/tex]

you made 27 of the invitations

The simplified form of the expression is [tex]\frac{14+5\sqrt{3}}{11}[/tex]

Given the surd function expressed as:

[tex]\frac{\sqrt{3} +5}{\sqrt{3} - 5 }[/tex]

Multiply by the conjugate of the denominator to have:
[tex]= \frac{\sqrt{3} +5}{\sqrt{3} - 5 } \times \frac{\sqrt{3} +5}{\sqrt{3} + 5 } \\=\frac{\sqrt{9}+5\sqrt{3}+5\sqrt{3}+25 }{3-25}[/tex]

Simplify the resulting expression
[tex]\\=\frac{3+10\sqrt{3}+25 }{-22}\\=\frac{28+10\sqrt{3}}{-22} \\= \frac{14+5\sqrt{3}}{11}[/tex]

Hence the simplified form of the expression is [tex]\frac{14+5\sqrt{3}}{11}[/tex]

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Answer:

It's C because we are adding a number on the x but here we skip 5 so it's 6, and on y we add 4 up but since we skipped 5 we add 8 and we get 24. 6, 24. You may say "but SpiritBear, 17 plus eight is 25" and that is true, but if you notice the lowest dot actually starts on 5, not 4 making C right.

Hope this helped and wasn't too confusing

Answer:

15

Step-by-step explanation:

To solve you have to get x by itself on one side.

x/3+7=12

First, you move the seven over.

x/3+7-7=12-7

Simplify.

x/3=5

Now to get x by itself you can multiply both sides by 3.

x/3*3=5*3

Simplify.

x=15

Answer:

x = 15

Step-by-step explanation:

x/3 + 3⋅7/3 = 12

x+3⋅7/3=12

x+21/3

X=15

Answer:

b. [tex]6\sqrt{3}[/tex]

Step-by-step explanation:

[tex]\frac{6}{x} =\frac{x}{18}[/tex]

[tex]x^{2} =[/tex][tex](6)(18)=108[/tex]

[tex]x=\sqrt{108} =\sqrt{(36)(3)} =6\sqrt{3}[/tex]

Hope this helps

The length of x, the altitude of triangle ABC  is [tex]6\sqrt3[/tex]

From the given figure, we have the following equivalent ratio:

6 : x =x: 18

Express as fraction

6/x = x/18

Cross multiply

[tex]x^2 = 6 * 18[/tex]

Evaluate the product

[tex]x^2 = 108[/tex]

Take the square root of both sides

[tex]x = 6\sqrt3[/tex]

Hence, the length of x, the altitude of ABC  is [tex]6\sqrt3[/tex]

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Answer:

Either 74° and 32°

or 53° and 53°

Step-by-step explanation:

An isosceles triangle has at least two congruent angles.

There are two possibilities in this problem.

1)

The 74° angle is one of the two congruent angles.

Then, one other angle measures also 74°.

The third angle measures 180° - 74° - 74° = 32°

2)

The 74° is not one of the two congruent angles.

Then the other two angles are congruent.

180° - 74° = 106°

The sum of the measures of the two congruent angles is 106°, so each of the two congruent angles measures 53°.

Answer:

Either 74° and 32°

or 53° and 53°

10 green cubes and 6 yellow cubes

hope it helps...!!!

The ratio of the area of triangle AEC and area of triangle BCD is 21:14 if the A, B and C are points on the line 2x+y=8

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have line;

2x+y=8

x/4 + y/8 = 1

Coordinate for A(4, 0) and B(0, 8)

To find the coordinate C we will use external section formula:

Let (a, c) be a coordinate for C

AB : BC = 2:1

AC:BC = 3:1  

[tex]\rm C(a, b) =( \dfrac{-4}{3-1}, \ \dfrac{24}{3-1})[/tex]

C(a, b) = (-2, 12)

Let coordinate for E(0, e) and for D(f, 0)

EC:DC=1:2 and C(-2, 12)

So after applying section formula, we will get:

E(0, -3) and D(0, 36)

Area of triangle AEC = (1/2)(7)(12) = 42 square units

Area of triangle BCD = (1/2)(28)(2) = 28 square units

ratio of area of triangle AEC : area of triangle BCD = 42:28

= 21:14

Thus, the ratio of the area of triangle AEC and area of triangle BCD is 21:14 if the A, B and C are points on the line 2x+y=8

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[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

As we know :

Length of arc = Radius × Angle made by Arc at center [ in radians ]

[tex]\qquad \tt \dashrightarrow \: arc = radius \times angle \: \: ( in \: \: rad)[/tex]

[tex]\qquad \tt \dashrightarrow \: arc = 9 \times { \pi}{} [/tex]

[tex]\qquad \tt \dashrightarrow \: arc = 9\pi \dfrac{ }{} \: \: units[/tex]

or

[tex]\qquad \tt \dashrightarrow \: arc = 9 \times 3.14 = 28.26 \: \: units\dfrac{ }{} \: \: [/tex]

Arc length

Answer:

i think four but im prolly wrong

Step-by-step explanation:

Answer:

Draw your y and x axis , the y axis is going to be a vertical line while the x axis is going to be a horizontal line

Answer:

3

Step-by-step explanation: