A hot air balloon is 1,200 feet above the ground. The angle of depression from the basket of
the hot air balloon to the base of a monument is 54°.

Which equation can be used to determine the distance, d, in feet, from the basket of the hot
air balloon to the base of the monument?

Answer:

240

Step-by-step explanation:

V = L x W x H

L= 3

W= 10

H= 8

V = 3 x 10 x 8

= 240 cubic meters

Answer:

240

Step-by-step explanation:

All you have to do is multiply all of these numbers to get the answer.

The rational expression for the ratio between the perimeter and the area is:

R = 4/3x

We want to find the ratio, as a rational expression, between the perimeter and the area.

Remember that for a square of sidelength S, the perimeter is:

P = 4*S

And the area is:

A = S^2

Then the ratio between these two is:

R = P/A = (4*S)/(S^2) = 4/S

In this case, the sidelength is 3x, then S = 3x, replacing that we get:

R = 4/3x

If you want to learn more about rational expressions, you can read:

https://brainly.com/question/1851758

Answer:

$4500 in interest.

Step-by-step explanation:

9% of 10,000 is 900, 900 x 5 is 4500

Answer:

14x^2y^2 - 21x^2y + 56xy^2 + 63xy

Step-by-step explanation:

Remark

This is a disguised form of the distributive property. Nothing can be simplified inside the brackets. So the plan is to remove them.

7xy*2xy - 3x*7xy + 8y*7xy + 9*7xy      Combine the terms

14x^2y^2 - 21x^2y + 56xy^2 + 63xy

You cannot symplify anything further. If nothing could be combined before, it cannot be simplified now.

Answer:

2.5

Step-by-step explanation:

3 hours after 7 is 10 so add 1.9 to 0.6

Answer:
To convert 27 kg to mg, you would move the decimal point 6 places to the right.

hope that's helpful to you!

Answer:

Step-by-step explanation:

First Container.

Total = 7 + 2 + 6 = 15

Probility blue = 7 / 15 = 0.467

Second Container

Total = 4 + 2 +2 =  8

Probability Blue = 4/8 = 1/2 = 0.5

Answer: You are much better off drawing from the Second Container.

Answer:

3:6

Step-by-step explanation:

27=3*3*3

216=6*6*6

Therefore the answer is 3:6

then to the lowest term = 1:2

1200 cards

All measurements should be taken in centimeters

Calculate the area of large rectangular card:

Calculate the area of each small cards:

Divide the area of large card by area of small card

Number of small cards: 1200 cards

For bigger rectangle:-

Area:-

For smaller rectangle

Area:-

Total cards:-

Answer:

Hope the picture will help you.......

Answer:

1 (one)

Step-by-step explanation:

Answer:

1

----------------------------------------------------------------------------------------------------------

First things first, evaluate all square roots in order, starting with the square root of 12

The next step is to divide, despite multiplication always coming before division, you cannot multiply without first knowing the values of the division.

[tex]3.5 / 3.2 = 1.09\\\\2.2 / 2.4 = 1.09[/tex]

Now, you can multiply.

[tex]1.09 * 1.09 = 1.1881[/tex]

That said, 1.1881 is closest to 1 because it has a 1 in the tenths place, the greatest place in a decimal number.

$4.76 per card

hope it helps...!!!

Answer:

there is no picture attached here I really wish I could help

Answer:

I will not give in answer but will give an example

Step-by-step explanation:

The area of irregular shapes can be determined by dividing the given shape into smaller regular shapes. The area of irregular shapes can be determined by dividing the given shape into smaller regular shapes.

In real life figures are often irregular shapes - a little bit messy. Think of your messy bedroom once more ‐ is it a perfect rectangle?

The trick is to break these figures into shapes that you know well and whose area you know how to find.

1. Find the area of this room:

3- 2 -4 -6 irregular shape

This can be done in two different ways but ill only give one example on how to find an area.

Method #1

Divide the figure into two rectangles and find all missing lengths.

The larger rectangle has an area of

4cm x 7cm = 28cm2

The smaller rectangle has an area of

4cm x 2cm = 8cm2

If we combine these we will find the total area:

28cm2 x 8cm2 = 36cm2

hope this helps :)

Reason:

Subtract any pair of adjacent terms

Each time we get the same value to confirm that we have an arithmetic sequence of common difference 18.

An expression has numbers, variables, and mathematical operations. The factors of the expression 4x³+x²-8x-2 by grouping are x²(4x+1)-2(4x+1).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The factors of the expression by grouping can be done as,

[tex]4x^3+x^2-8x-2[/tex]

Take x² as the common factor from the first two terms while -2 from the last two terms,

[tex]4x^3+x^2-8x-2\\\\=x^2(4x+1)-2(4x+1)[/tex]

Thus, the factors of the expression 4x³+x²-8x-2 by grouping are x²(4x+1)-2(4x+1).

Learn more about Expression:

https://brainly.com/question/13947055

Using proportions, it is found that the unit rate is of 1.33 cups of brown sugar for a batch of cookies.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

2/3 cups of brown sugar are used for half a batch of cookies. The unit rate is the amount used for one batch. Hence, the rule of three is given by:

2/3 cups - 1/2 batch

x cups - 1 batch.

Applying cross multiplication:

[tex]\frac{1}{2}x = \frac{2}{3}[/tex]

[tex]x = \frac{4}{3}[/tex]

The unit rate is of 1.33 cups of brown sugar for a batch of cookies.

More can be learned about proportions at https://brainly.com/question/24372153

it's 46/99

whenever you get a question like this, you need to think: what would those fractions even be?

well it sure is not a bc 3/6 is already 0.5 and you need a lower number

it's not b either bc 4/16= 1/4 and that is 0.25

and well it can't be d either bc 13/16 is that not far away from 1

====================================================

Explanation:

Let x = 0.464646...

Multiplying both sides by 100 gets to 100x = 46.464646... which moves the decimal point over two spots to the right.

Then subtract the two equations

100x - x = 46.464646... - 0.464646...

99x = 46

x = 46/99

Notice how the decimal portions cancel out when we subtract. This is because they line up perfectly.

To confirm the answer, your calculator should show that

46/99 = 0.46464646

The "46"s going on forever.

At some point, your calculator may round the last '4' to a 5 to have it read something like 0.464646465 but this is of course rounding error.

On some calculators I tried, I noticed it displayed 0.46464646464647 which is even more strange considering the next digit (4) isn't five or larger. So that 6 shouldn't have bumped up to the 7.

Answer:

Side = 3 cm

Step-by-step explanation:

Given:

[tex]\text{Volume of cube} = 27 \ \text{cm}^{3}[/tex]

The formula to calculate the volume is (Side)³.

Thus, we obtained the following equation:

[tex](\text{Side})^{3} = 27 \text{cm}^{3} \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\text{Side}^{3} = \text{Volume of cube}][/tex]

Cube root both sides to obtain the side length of the cube:

[tex]\implies \sqrt[3]{\text{(Side)}^{3}} = \sqrt[3]{27 \ \text{cm}^{3} }[/tex]

Evaluate the side of the cube:

[tex]\implies \sqrt[3]{\text{(Side)}^{3}} = \sqrt[3]{27 \ \text{cm}^{3} }[/tex]

[tex]\implies \sqrt[3]{\text{(Side)}\text{(Side)(Side})} = \sqrt[3]{3 \times 3 \times 3 \times \text{(cm)(cm)(cm)}}[/tex]

[tex]\implies \text{Side = 3 cm}[/tex]

Answer:

3 cm

Step-by-step explanation:

Formula

Volume of a cube = [tex]a^3[/tex]  (where a is the side length)

Given that the volume of the cube is 27 cm³, to find the side length, substitute the given volume into the equation and solve for [tex]a[/tex]:

[tex]\implies 27\: \sf cm^3=a^3[/tex]

Cube root both sides:

[tex]\implies \sqrt[3]{27\: \sf cm^3} =\sqrt[3]{a^3}[/tex]

[tex]\implies \sqrt[3]{27}\sqrt[3]{\sf cm^3} =\sqrt[3]{a^3}[/tex]

[tex]\implies 3\: \sf cm=a[/tex]

[tex]\implies a=3\: \sf cm[/tex]

Therefore, the length of each side of the cube is 3 cm.

Answer:

what how

Step-by-step explanation:

Answer:

you have to solve the first equation for y

Step-by-step explanation:

Step-by-step explanation:

At first put the value of y that is 3x in equation 2x=y-1.

Then put the value of x in equation y=3x that comes from the first solving part.

it's a mixed fraction

hope it helps..,!!!

↪Given 15 cot A = 8. Find sin A and sec A

Hope this helps...☆

Answer:

139 ft³

Step-by-step explanation:

Diameter of the cylinder is 3 ft. Therefore, the radius is 1.5 ft

Volume of the cylinder = πr²h

= 3 × 1.5 × 1.5 × 4

= 27 ft³

Volume of the cuboid (rectangular prism) = lbh

= 7×4×4

= 112 ft³

Volume of the figure = 112 + 27 = 139 ft³

Answers:

Final velocity = 29 m/s

Distance traveled = 73.5 meters

========================================================

Work Shown:

The given data is

[tex]v_i = 20 \text{ m}/\text{s} = \text{initial velocity}\\\\a = 3 \text{ m}/\text{s}^2 = \text{acceleration}\\\\t = 3 \text{ s} = \text{time duration}\\\\[/tex]

This leads to

[tex]v_f = v_i + a*t\\\\v_f = 20 + 3*3\\\\v_f = 20 + 9\\\\v_f = 29\\\\[/tex]

The final velocity is 29 m/s.

----------

We can use that final velocity to find the distance traveled.

[tex]x = 0.5*(v_i+v_f)*t\\\\x = 0.5*(20+29)*3\\\\x = 0.5*(49)*3\\\\x = 24.5*3\\\\x = 73.5\\\\[/tex]

The distance traveled is 73.5 meters.

----------

An alternative way to calculate the distance is to do this

[tex]x = \frac{(v_f)^2 - (v_i)^2}{2a}\\\\x = \frac{(29)^2 - (20)^2}{2*3}\\\\x = \frac{841 - 400}{6}\\\\x = \frac{441}{6}\\\\x = 73.5\\\\[/tex]

Or you could do this

[tex]x = v_i*t + 0.5*a*t^2\\\\x = 20*3 + 0.5*3*3^2\\\\x = 20*3 + 0.5*3*9\\\\x = 60 + 13.5\\\\x = 73.5\\\\[/tex]

For more information, check out the Kinematics equations.

Answer:

(-2,1)

Step-by-step explanation:

1 unit up will change the y-value as it is moving vertically. Will make it (-2,-1)

Then, reflecting over x-axis means x-value stays the same and the sign of y-value switches.

so,

(-2,1)