Khan Academy: Right triangles and trigonometry 2

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Answer:

32

Step-by-step explanation:

Since it is to the fifth power, you multiply the number 2 five times:

2 x 2 x 2 x 2 x 2 = 32

Answer:

11,990

9% of 5500 is 495

(495+5500) [one year] x 2 [two years] = $11,990

At the end of 2 years, Aldo will owe $11,990.

Hope it helps

Answer:

Width = 7 inches, Length = 11 inches

Explanation:

Call the width of the rectangle x.

Length = x + 4

Perimeter = x + x + (x + 4) + (x + 4) = 4x + 8

Area is equal to 5 inches more than 2 times the perimeter:

Area = 5 + 2(4x + 8) = 8x + 21

The area of a rectangle also equals length times width = x(x + 4) = x² + 4x

Therefore: x² + 4x = 8x + 21

Rearrange: x² - 4x - 21 = 0

Factorize: (x - 7 )(x + 3) = 0

Therefore: x = 7, -3

Since you can't have a negative length, width is 7 inches.

(Using the first equation:)

Length is therefore = 7 + 4 = 11 inches

Answer:

306 square meters.

Step-by-step explanation:

Divide the shape into 2 rectangles.

Lets do the one that is sticking to the top first.

The area is 6 * 15, which is 90.

Lets do the second rectangle. The area is:

27 * 8, which is 216.

Add them all up (90 + 216), which is 306.

Answer:

306m²

Step-by-step explanation:

Split the shape into two rectangles with the accureate lengths

The top-most of the two rectangles with length 6m and width 15m:

6 x 15 = 90 m² (area of rectangle A)

The bottom rectangle:

27(full length) x 8m(full width) = 216m²

Add the two areas together for the full shape

216 + 90 = 306m²

Given that a line is parallel to another line (y = -4x + 5), and it passes through the point (-2, 8), the equation of the parallel line is derived as;

Note that when two lines are parallel, their slopes are equal. Therefore, having calculated the value of b as 0, and given the slope as -4 (coefficient of x), the equation of the parallel line is;

The line that is parallel to y = -4x + 5 and passes through the point (-2, 8) is;

y = -4x

The solution to the inequality 1 + 3r > 10 is r > 3.

This means that any value of r greater than 3 will satisfy the inequality.

To solve the inequality 1 + 3r > 10, we need to isolate the variable r on one side of the inequality sign.

Let's begin by subtracting 1 from both sides of the inequality:

1 + 3r - 1 > 10 - 1

This simplifies to:

3r > 9

Next, we can divide both sides of the inequality by 3 to solve for r:

(3r)/3 > 9/3

This simplifies to:

r > 3

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8/9 - 1/3

To subtract these two fractions, first find a common denominator.

The common denominator will be the

least common multiple for the two denominators.

In this case, the least common multiple of 9 and 3 is 9.

So to subtract, a denominator of 9 is needed in each fraction.

8/9 already has 9 in the denominator so it stays the same.

To get a 9 in the denominator of 1/3, multiply top and bottom by 3.

This gives us 3/9.

So we have 8/9 - 3/9 which is 5/9.

Answer:

Five-ninths

Step-by-step explanation:

Since the denominators are different (9 and 3) we need to change one of them.

9 is divisible by 3 therefor we do not need to change Eight-ninths.

3 times 3 = 9, nine becomes the new denominator, but remember, whatever we do to the bottom (denominator), we must also do to the top (numerator).

1 times 3 = 3

Now the equation is 8/9 - 3/9, we must only subtract the numerators. The answer is 5/9.

Answer:

the answer is 39 and 14.

The solution is, the numbers are 20 and 29.

Subtraction is the process of taking away a number from another. It is a primary arithmetic operation that is denoted by a subtraction symbol (-) and is the method of calculating the difference between two numbers.

Here, we have,

given that,

The sum of two numbers is 49

and the difference between these two numbers is 9.

let, the numbers are x & y

so, we get,

according to question:

x+y = 49 ...1

x-y = 9 ....2

so, simplifying we get,

2x = 58

or, x = 29

so, we get,

y = 20

Hence, The solution is, the numbers are 20 and 29.

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Answer:

(5, 4)

Step-by-step explanation:

(x + 2, y + 3)

(3  + 2, 1 + 3)

(5, 4)

Answer:

B' (5, 4 )

Step-by-step explanation:

the translation rule (x, y ) → (x + 2, y + 3 )

means add 2 to the original x- coordinate and add 3 to the original y- coordinate , then

B (3, 1 ) → B' (3 + 2, 1 + 3 ) → B' (5, 4 )

On solving the provided question we can say that - from the graphs n f (x) and g( x) are 1 and 5 .

Graphs are visual representations or charts used in mathematics to methodically express data or values. A relationship between two or more objects is frequently represented by a point on a graph. A non-linear data structure called a graph is made up of nodes, or vertices, and edges. Connect the nodes, also known as vertices. This graph comprises a set of vertices V= 1, 2, 3, 5, and a set of edges E= 1, 2, 1, 3, 2, 4, and (2.5), (3.5), (4.5). Statistics graphs (bar charts, pie charts, line charts, etc.) Exponential diagrams. triangle graph, a logarithmic graph

by graphs of the function f (x) and g( x).

\(lim f ( x) + lim g ( x )\\= -1 + 2 = 1\\ f ( -1 ) + lim g ( x)\\= 3 + 2\\= 5\)

from the graphs n f (x) and g( x) are 1 and 5 .

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Answer:

12.6

Step-by-step explanation:

Use long multiplication to evaluate.

Answer:

12.6

Step-by-step explanation:

0.12*105=12.6

Answer:

\(\frac{7}{10}\)

Step-by-step explanation:

100\(m^{2}\) -5 = 44  Add 5 to both sides

100\(m^{2}\) = 49  Divide both sides by 100

\(m^{2}\) = \(\frac{49}{100}\)

\(\sqrt{m^{2} }\) = \(\frac{\sqrt{49} }{\sqrt{100} }\)

m = \(\frac{7}{10}\)

Answer:

5,670,279

Step-by-step explanation:

3,840,159 reversed is, 9,510,483 so, 9,510,483 - 3,840,159 = 5,670,279

Answer: 3 + a + 10b

Step-by-step explanation: combine like terms

Answer:

i think the anwser is a+4b+3

Step-by-step explanation:

Answer:

9 = 3 x 3

Explanation:

Given the equation of a quadratic function:

First, we will find the x-intercepts to find the largest x-intercept

So, substitute f = 0, then solve for x as follows:

So, The largest x-intercept = 7

Second, we will find the y-coordinate of the y-intercept

So, substitute x = 0

So, The y-coordinate of the y-intercept = -28

Answer:

A dynamic environment is a business environment that is rapidly changing. In a dynamic market, businesses have to adapt quickly to changes and develop new ideas, products and services to keep up with technology and new trends.

Step-by-step explanation:

Answer:

214 cubic feet (rounded to the nearest cubic foot)

Step-by-step explanation:

Step 1  Determine the volume of 1 box

Volume of a box or rectangular prism = dimensions multiplied by each other

Here, the given dimensions are 11 in by 8 in by 12 in

So the volume of one box would be 11 x 8 x 12 = 1056 cubic inches

Step 2 Determine volume of all 350 boxes

Volume of 1 box = 1056

So volume of all 350 boxes = 1056 x 350 = 369600 cubic in

Step 3 Convert cubic in to cubic ft

To convert to cubic feet we divide the amount of cubic inches by 1728 (this is because there are 1728 cubic inches in 1 cubic foot)

369600 / 1728 = 214 cubic feet (to the nearest cubic foot)

214 cubic feet of warehouse space is required for 350 boxes with the dimensions of 11in by 8in by 12in

Answer:

0.274714403

Step by step explanation:

Answer:

A

Step-by-step explanation:

Apply the rule x^m/n=n√x^m  to rewrite the exponentiation as a radical.

6√x^5

-hope it helps

Answer: 3,348 cubic inches

Step-by-step explanation:

1. Since we know that volume= length x width x height, then we can plug our values into this equation.

2. So, we would do volume= 9 x 12 x 21.

3. 9 x 12 = 108, and 108 x 21 =2,268.

4. Now that we have both of the volumes, we have to add them together.

5. 1,080 + 2,268 = 3,348

6. The combined volume is 3,348 cubic inches.

Answer:

1/x-2/3=3/2x

-2/3=3/2x-1/x

-2/3=(3-2)/2x

-2/3=1/2x

by cross multiplication

-2(2x)=1(3)

-4x=3

x= -3/4

Step-by-step explanation:

I hope this will help

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Answer:

15.1 yd

Step-by-step explanation:

Since the circumference formula is C = πd, d = C/π

and in this case d = (47.5 yd) / 3.14 = 15.1 yd

The approximate diameter of the pad is 15.1 yd.

The approximate diameter of the helicopter pad is,

⇒ d = 15.12 yards

The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.

Given that;

A helicopter pad has a circumference of 47.5 yards.

Now,

We know that;

Circumference of circle = 2πr

Hence, We get;

⇒ 47.5 = 2 × 3.14 × r

⇒ 47.5 = 6.28r

⇒ r = 47.5 / 6.28

⇒ r = 7.56

Thus, the approximate diameter of the helicopter pad is,

⇒ d = 2r

⇒ d = 2 × 17.56

⇒ d = 15.12 yards

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Answer:

n=1/3

Step-by-step explanation:

Answer:

There’s no error

Step-by-step explanation:

Answer:A "Pythagorean Triple" is a set of positive integers, a, b and c that fits the rule: a2 + b2 = c2. Example: The smallest Pythagorean Triple is 3, 4 and 5

Step-by-step explanation:

Answer:25.13

Step-by-step explanation:

use the formulas

C=2πr

d=2r

Answer:

lo i just gto 100 %

Step-by-step explanation:

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The mean of the distribution is 3

Arithmetic mean is defined as the ratio of the sum of observations to the total number of observations. It can be referred to as the average of a specific set of data or the arithmetic mean. One of the basic methods used to acquire a result, the term "Mean" is commonly used in the field of statistics.

The formula for the mean of a given set of data is as follows:

Mean = Sum of Observations/Total number of observations

According to the first graph,

Given the bar of observations as :

0, 5, 6, 3, 1, 1, 3, 6, 4, 1

Here the Sum of Observations = 30

And the total number of observations = 10

The mean of the distribution = 30/10

The mean of the distribution = 3

According to the second graph,

Given the bar of observations as :

0, 1, 3, 3, 9, 0, 9, 4, 4, 1

Here the Sum of Observations = 34

And the total number of observations = 10

The mean of the distribution = 34/10

The mean of the distribution = 3.4

The mean of the distribution = 4 (closest)

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