A 32-foot ladder is leaning against a building and forms a 29.37° angle with the ground. How far away from the building is the base of the ladder? Round your answer to the nearest hundredth.

15.69 feet
18.01 feet
27.89 feet
36.72 feet

Answer:

Option A. y = 4x

Step-by-step explanation:

From the question given above, the following data were obtained:

X >> Y

3 >> 12

4 >> 16

5 >> 20

6 >> 24

7 >> 28

Next, we shall use each of the options to obtain the first two value of y to which will correspond to the table above. This is illustrated below:

For Option A:

1. y = 4x

x = 3

y = 4 × 3

y = 12

2. y = 4x

x = 4

y = 4 × 4

y = 16

For Option B:

1. y = 4x + 12

x = 3

y = 4(3) + 12

y = 12 + 12

y = 24

2. y = 4x + 12

x = 4

y = 4(4) + 12

y = 16 + 12

y = 28

For Option C:

1. y = ¼ x

x = 3

y = ¼ × 3

y = ¾

2. y = ¼ x

x = 4

y = ¼ × 4

y = 1

For Option D:

1. y = ¼x + 12

x = 3

y = ¼(3) + 12

y = ¾ + 12

y = 51/4

2. y = ¼x + 12

x = 4

y = ¼(4) + 12

y = 1 + 12

y = 13

From the calculations made above, only option A ie. y = 4x correspond to the data given in the table above.

Answer:

6 units

Step-by-step explanation:

The total area that the surface of a 3-dimensional object would cover if its sides were laid flat is called it's surface area. Surface area is measured in square units. The surface area of a unit cube is 6 square units.

Answer:

its c

Step-by-step explanation:

Answer:. 151/99

Step-by-step explanation:

Take the repeating digits from the decimal equivalent, 52 and place them as the numerator of a fraction with 99 as the denominator. That is 52/99

We can verify this value by doing the long division, or enter the values as 52÷99 on a calculator.

For the improper fraction:

Convert the whole number, 1, to its equivalent, 99/99. ( If the whole number is other than 1, multiply it by the denominator and use the product as the numerator. )

Add the numerators: 52 + 99 = 151

Our improper fraction equivalent of 1.525252 is 151/99

Answer:

[tex]\displaystyle V=\frac{4}{81}\cdot \pi\ cm^3[/tex]

Step-by-step explanation:

The Volume of a Sphere

The volume of a sphere of radius r is given by:

[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot r^3[/tex]

A. )

If the diameter of the sphere is d, the radius is r=d/2. Substituting:

[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot \left (\frac{d}{2} \right )^3[/tex]

Operating

[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot \frac{d^3}{8}[/tex]

Simplifying

[tex]\displaystyle V=\frac{1}{6}\cdot \pi\cdot d^3[/tex]

B.)

The diameter of the sphere is 2/3 cm, thus the volume is:

[tex]\displaystyle V=\frac{1}{6}\cdot \pi\cdot \left (\frac{2}{3} \right )^3[/tex]

Operating:

[tex]\displaystyle V=\frac{1}{6}\cdot \pi\cdot \frac{8}{27}[/tex]

[tex]\displaystyle V=\frac{8}{27}\frac{1}{6}\cdot \pi[/tex]

[tex]\boxed{\displaystyle V=\frac{4}{81}\cdot \pi\ cm^3}[/tex]

Answer: d

Step-by-step explanation:

Answer:

They each got 1/10th of the bag

Step-by-step explanation:

you just divide 1/5th by 2 which is 1/10

Step-by-step explanation:

[tex]y = {2}^{x} [/tex]

This is a basic exponential function.

[tex]y = {2}^{ - x} same \: as \: y = 0.5 {}^{x} [/tex]

The (-x) exponent makes a reflection in the y-axis.

Answer:

y = x + 9/4     or     y = x + 2 1/4

Step-by-step explanation:

y - 4x = 9

y - x = 9/4 (divide both sides by 4)

y = x + 9/4 (Add x to both sides)

Answer: 7

i took the test

Answers:

Up to down (The y-coordinate is the vertical line in the coordinate plane)

Zero (A slope is made from how much the line rises divided by the distance it takes to do so, a flat, horizontal line will not rise, and therefore will have a slope of 0)

Answer:

1. is B: Up to Down

2. is C: zero

Step-by-step explanation:

The y-coordinate is the vertical line of the graph, so it is up to down.

When you have a horizontal line, that means you have a zero function meaning there is no coordinate on the x-axis.

Answer:

The circumference is 37.7 mm.

Answer:

answer is c:36. 240x.15=36

Answer:

[tex]r=11[/tex]

Step-by-step explanation:

The equation of a circle is commonly denoted as:

[tex](x-h)^2+(y-k)^2=r^2[/tex], where [tex](h, k)[/tex] is the center of the circle.

This equation is already written in that format, therefore:

[tex]r^2=121,\\r=\fbox{$11$}[/tex],

Answer:

Because the first has () and the second doesn't so if u multiply the first one you will have to start with the () but if u answer the second u can start with anything

Step-by-step explanation:

540 = 4x-10+5x-11+128+4x+2+132

23= x

RST=104

QRS=82

TPQ=94

The value of x from the figure is 23

The sum of the interior angle of the pentagon is 540 degrees

Taking the sum of all the angles:

4x+2+132+4x-10+128+5x-11 = 540

4x+4x+5x+241 = 540

13x = 540 - 241

13x = 299

x = 299/13

x = 23

Hence the value of x from the figure is 23

Learn more on polygons here: https://brainly.com/question/24966296

Answer:

math waaayys can help you

Step-by-step explanation:

Answer:

s=8

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

Answer:

19

Step-by-step explanation:

Sub the x with 6

30 - 11 = 19

Answer:

Mike's average monthly salary is $ 1,814.

Step-by-step explanation:

To determine Mike's average monthly salary, taking into account that he earns $ 284, $ 292, $ 418, $ 350, and $ 470 weekly, these amounts must be added for the 5-week duration of the month through the following calculation:

284 + 292 + 418 + 350 + 470 = X

1814 = X

Thus, given that this sum totals $ 1,814, Mike's average monthly salary is $ 1,814.

Answer:

22-18-25,

19-24-30,

7-24-25

Step-by-step explanation:

In a triangle with side lengths [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex], any two sides must have a sum larger than the third.

Using this rule, the possible side lengths out of these choices that could form a triangle are:

22-18-25,

19-24-30,

7-24-25

Answer:

line plots do you mean number line, cos no pic is attached

Answer:

300 times

Step-by-step explanation:

Answer:

The answer is out of every 5, the desired out come will be approximately 2 times.  

Step-by-step explanation:

The solutions to the functions are

a) x → –∞, y → +∞ and as x → +∞, y → –∞

b) The real solutions to the equation 4x³ - x² - 4x + 1 = 0 is x = -1 , 1 , 1/4

c) The zeros of the function f ( x ) = x³ + 6x² + 8x is x = 0, -2, -4

d) The function is odd

e) The three factors of the function are (x - 3)(x + 2)(x + 5)

f) The translation f (x - 2) + 3 means the function will shift right 2 and upward 3

g) The factor of the function is a = x - 3

Brackets should be expanded in the following ways to factorize an expression

For an expression of the form A = a ( b + c ) , the expanded version is given by A = ab + ac, i.e., multiply the term outside the bracket by everything inside the bracket

For an expression of the form A = ( a + b ) ( c + d ) , the expanded version is given by A = ac + ad + bc + bd, in other words everything in the first bracket should be multiplied by everything in the second.

Given data ,

a)

Let the function be represented as f ( x )

Now , the value of f ( x ) = -5x³ + 3x² + x - 9

The end behavior of the function is given as

As x → –∞, y → +∞ and as x → +∞, y → –∞

b)

Let the function be represented as f ( x )

Now , the value of f ( x ) = 4x³ - x² - 4x + 1

On factorizing the equation , we get

f ( x ) = x² ( 4x - 1 ) - 1 ( 4x - 1 )

f ( x ) = ( x² - 1 ) ( 4x - 1 )

Taking the common factors of the expression , we get

f ( x ) = ( x + 1 ) ( x - 1 ) ( 4x - 1 )

f ( x ) = ( x - 1 ) ( x + 1 ) ( x - 1/4 )

Therefore , the solutions of the equation are x = -1 , 1 , 1/4

c)

Let the function be represented as f ( x )

Now , the value of f ( x ) = x³ + 6x² + 8x

On factorizing the equation , we get

f ( x ) = x ( x² + 6x + 8 )

Taking the common factors of the expression , we get

f ( x ) = x ( x + 4 ) ( x + 2 )

So , the solution of the function are x = 0, -2, -4

d)

The given function f ( x ) = 3x⁵ - 9 is neither odd nor even function

e)

The fourth degree polynomial function is A = ( x + 3 ) ( x - 2 ) ( x - 5 )

f)

Let the function be f ( x )

Now , the translated function is g ( x ) = f ( x - 2 ) + 3

The translation of f (x - 2) + 3 means the function will shift right 2 and upward 3

g)

The factors of the function f ( x ) = x³ - 3x² is f ( x ) = x² ( x - 3 )

Hence , the functions are solved and factorized

To learn more about factorizing click :

https://brainly.com/question/804076

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Answer: C) 1/7

Step-by-step explanation:

Find the Slope

(−7, 0) , (0, 1)

Slope is equal to the change in y over the change in x, or rise over run.

           change in y

    m =  _________

           change in x

The change in x is equal to the difference in x-coordinates (also called run), and the change in y

is equal to the difference in y-coordinates (also called rise).

            [tex]y_2 -y_1[/tex]

    m = ______

           [tex]x_2 - x_1[/tex]

Substitute in the values of x and y into the equation to find the slope.

            1 − (0)

    m =  ______

            0 − (−7)

Simplify the numerator.

                1

    m =  ______

            0 − (−7)

Simplify the denominator.

Multiply −1 by −7.

                1

    m =  _____

             0 + 7

Add 0 and 7.

             1        

    m = ___

             7

Answer:

164

Step-by-step explanation:

add everything together 10+9+13+122 = 164.