A tent pole that is 9 feet tall is secured to the ground with a piece of rope that is 15 feet long from the top of the tent pole to the ground. Determine the number of feet from the tent pole to the rope along the ground.

Answer:

                         8

3x² + 2x - 2 - ----------

                      3x + 8

Step-by-step explanation:

                 3x² + 2x - 2

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

3x + 8     |  9x³ + 30x² + 10x - 24

                 -9x³ - 24x²     ↓

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

                             6x² + 10x

                             -6x² - 16x    ↓

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

                                       -6x - 24

                                       +6x + 16

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

                                               -8

I hope this helps!

If two lines are parallel, then they have the same slope.

If two lines are perpendicular, then the slope of one line is the negative reciprocal of the other line.

The equation of a given line is expressed as

y = mx + b

Where

m represents slope

c represents y intercept

Considering the first equa

The given expression is

Factor out the greatest common factor between 15x and 20y.

Then, use the product property to expand the logarithm.

At last, simplify the first logarithm because its base is equal to its argument.

Therefore, the simplest form of the logarithm is

Answer:

ASA

Step-by-step explanation:

there are two congruent angles with an included side in between

Answer: Triangle RHS and NKW are congruent through the Congruence Theorem Angle-Side-Angle.

Step-by-step explanation:

The side HS is congruent to the side KW.

The angle H is congruent to angle K.

The angle S is congruent to angle S.

The current is defined as rate of flow of charge I = dq/dt.

The approximate range of the current is 299.5.

The current is defined as rate of flow of charge I = dq/dt

Let the equation be [tex]$q=\int i d t$[/tex]

Given: I(t) = 10 cos(120πt - 12π) + 5

We will substitute it in the above equation

q = [tex]$$\int[/tex] 10 cos(120πt - 12π) + 5 dt

now here limits of time is from t = 0.1 to t = 60 s

so here it will be given as

[tex]$\int 10 cos(120\pi t - 12\pi ) + 5 dt[/tex]

Rewrite using trig identities

[tex]$=\int_{0.1}^{60} 10 \cos (120 \pi t)+5 d t$$[/tex]

Apply the Sum Rule:

[tex]$\int f(x) \pm g(x) d x=\int f(x) d x \pm \int g(x) d x$[/tex]

substitute the values in the above equation, we get

[tex]$=\int_{0.1}^{60} 10 \cos (120 \pi t) d t+\int_{0.1}^{60} 5 d t$[/tex]

simplifying the equation,

[tex]$\int_{0.1}^{60} 10 \cos (120 \pi t) d t=0[/tex]

[tex]$\int_{0.1}^{60} 5 d t=299.5$[/tex]

= 0 + 299.5

= 299.5

Therefore, the approximate range of the current is 299.5.

To learn more about integrals refer to:

https://brainly.com/question/11477170

#SPJ13

Answer:

[tex](f \circ g)(24)=-36[/tex]

Step-by-step explanation:

Given functions:

[tex]\begin{cases}f(x)=-9x+9\\g(x)=\sqrt{x+1}\end{cases}[/tex]

Function Composition is applying one function to the results of another.

The composite function (f o g)(x) means to substitute the function g(x) in place of the x in function f(x).  

Therefore (f o g)(24) means to substitute the result of g(24) in place of the x in the function f(x).

Calculate g(24) by substituting x = 24 into function g(x):

[tex]\begin{aligned}\implies g(24)&=\sqrt{24+1}\\&=\sqrt{25}\\&=5 \end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\implies (f \circ g)(24) & = f[g(24)]\\& = f(5)\\& = -9(5)+9\\&=-45+9\\&=-36\end{aligned}[/tex]

Answer:

(f∘g)(24) = -36

Step-by-step explanation:

We are given f(x) = -9x + 9 and  [tex]g(x)= \sqrt{x+1}[/tex].

We want to find (f∘g)(24).

This means that we first want to find g(24), then substitute the value of that into f(x).  

Start by substituting 24 for x in g(x).

[tex]g(24)= \sqrt{24+1}[/tex]

Add 24 and 1 together.

[tex]g(24)= \sqrt{25}[/tex]

Take the square root of 25.

g(24) = 5

Now, substitute 5 as x in f(x) = -9x + 9.

f(5) = -9(5) + 9

Multiply.

f(5) = -45 + 9

Add the numbers together.

f(5) = -36

f(5) in this case has the same value as (f∘g)(24)

This means that (f∘g)(24) = -36

About 50% of Americans households have a tv except  who live in low-income, single-parent, or disadvantaged homes

Proportion: Proportion is a central principle of architectural theory and an important connection between mathematics and art. It is the visual effect of the relationships of the various objects and spaces that make up a structure to one another and to the whole

Virtually all American households have at least one tv except for adolescents who live in low-income, single-parent, or disadvantaged homes, the majority of American households have at least one tv. More than 50% of American households have at least one tv.

however, about 50% of Americans households have a tv

to learn more about Proportion visit:

brainly.com/question/24232216

#SPJ4

Answer: [tex]x=5\sqrt{3}, y=15[/tex]

Step-by-step explanation:

[tex]\sin 60^{\circ}=\frac{x}{10}\\\\x=10 \sin 60^{\circ}\\\\x=5\sqrt{3}\\\\\\\tan 30^{\circ}=\frac{5\sqrt{3}}{y}\\\\\sqrt{3}=\frac{y}{5\sqrt{3}}\\\\y=15[/tex]

Answer:

1st option

Step-by-step explanation:

Answer:

9.  [tex]256u^8 v^{16}[/tex]

10.  [tex]-32x^{10} y^{35}[/tex]

11.  [tex]-x^{12}y^{20}[/tex]

12.  1

13.  [tex]\frac{2}{3xy^3}[/tex]

14.  [tex]\frac{h^8}{3j^6k^6}[/tex]

15.  [tex]\frac{1}{4z}[/tex]

Answer:

9.  256u^8 v^16

10.  -32x^10 y^35

11.  x^12 y^21

12.  1

Step-by-step explanation:

If you can, please give me a Brainliest; thank you! I put a lot fo times to solve it !

Answer:

Explanation:

The angular coefficient is also referred to as the slope of the line.

Given that the slope of the lining joining these pair of points are the same:

• (-2, 1) and (1, 4)

• (1, -2) and (3, p)

Then:

We solve the equation for p:

The vertical line test is a visual test to determine if a graph represents a function; since a function can only have one output for every input if a vertical line intersects a curve in more that one point the it is not the graph of a function.

In this case we any vertical line will only intersect one point then we conclude that:

The graph represents a function. Using the vertical line test, the graph intersects any vertical line at only one point.

Answer:

A=40, formula for area of a rectangle is a=L×W

Step-by-step explanation:

A=L×W = 10×4

SOLUTION

The equation of the parabola is defined using

Since the vertex is at the origin the equation becomes

Since the directrix is y=5

The distance from the focus to the vertex is equal to the distance from the vertex to the directrix

It follows

Thus the equation becomes

Therefore the equation of the required parabola is

Answer: Y=-1/20x^2

Step-by-step explanation:

Answer:217.625

Step-by-step explanation:

ANSWER

-4.5

EXPLANATION

We want to find the opposite of the number 4.5

The opposite of a number is the number that is the same distance from 0 on the number line but on the other side.

So, if the number is on the right hand side, its opposite is on the left hand side.

In simpler terms, the opposite of a number is the negative of a number.

So, the opposite of 4.5 is -4.5.

The given function is

The expression f(-16) means we have to evaluate the function when x = -16.

Answer:

C

Step-by-step explanation:

1 we need you to provide the function for people to better understand how to answer.

2 Option c was the only one that made sense.

pls mark brainliest

The salesperson needs to make weekly sales of $9,500 to earn the same amount with each option.

The amount he earns by option A can be calculated as follows;

As he works 40 hours per week and the hourly wage is $19; therefore the amount he will earn can be determined by multiplication as follows;

Option A earning: 40 × 19 = $760

Thus, the salesperson earns $760 through option A.

Consider x to be the amount of weekly sales;

As the commission rate is 8% of sales therefore 8% of x should be equal to $760 for the salesman to earn the same amount with both options.

(8/100)x = 760

0.08x = 760

x = 760 / 0.08

x = 9,500

Hence the salesman needs to make weekly sales of $9,500 to earn the same amount with both options.

Although there is a mistake in your question, you might be referring to this question;

A salesperson works 40 hours per week at a job where he has two options for being paid option a is an hourly wage of $19 option B is a commission rate of 8% sales how much does he need to sell in a given week to earn the same amount with each option

To learn more about the commission rate; click here:

https://brainly.com/question/11614671

#SPJ4

The predicted distance of the ball would be 27.1.93 yards when the ball travels for a duration of 5 seconds.

Velocity is defined as the displacement of the object in a given amount of time and is referred to as velocity.

The distance, y, is measured in yards and the speed, s, is measured in miles per hour.

The regression line is defined as ŷ = 3.98 + 53.59s  ... (i)

The slope and y-intercept of the regression line must be determined.

The general equation for a linear regression line is y = a + bx...(ii), where x is a variable. The variable is indicated by s in the above equation.

When I and (ii) are compared, we obtain a = 3.98 and b = 53.59.

It indicates that the slope is 53.59 and the y-intercept is 3.98.

The slope, b = 53.59, implies that for every mile per hour of speed, the distance rises by 53.59 yards.

The ball travels for a duration of 5 seconds

Substitute the value of s = 5 in equation (i) to get

ŷ = 3.98 + 53.59(5)

ŷ = 271.93

Thus, the predicted distance of the ball would be 27.1.93 yards.

Learn more about Velocity here:

https://brainly.com/question/12904979

#SPJ1

Answer:

271.93

Step-by-step explanation:

Answer:

1. 1600

2. 3,000

3. 6,000

4. 7,000

5. 10,000

6. 9,000

Step-by-step explanation:

A) We round the number up to the nearest hundred if the last two digits in the number are 50 or above.

B) We round the number down to the nearest hundred if the last two digits in the number are 49 or below.

C) If the last two digits are 00, then we do not have to do any rounding, because it is already to the hundred.

In this case, Rule A applies and 1565 rounded to the nearest hundred is:

1600

In the sample space, the annotation for the event where both E and G but not F occurs is given as:( E ∩ G ) ∩ Fc (Option B).

An event is a specified set of results of a random experiment in probability theory. Because the sample space is the collection of all potential outcomes of a random experiment, another definition of an event is any subset of a sample space.

Colloquially, the sample space for a given set of events is the collection of all potential values for the events. Technically, a sigma-algebra is formed by the set of probable occurrences for a given random variate, and sample space is defined as the biggest set in the sigma algebra.

Learn more about events:
https://brainly.com/question/25821071
#SPJ1

Full Question:

Let S be any sample space, and E, F, and G be any three events. Describe the event that E and G occur, but not event F.

a) ( Ec ∪ G ) ∩ Fc

b) ( E ∩ G ) ∩ Fc

c) ( E ∪ G ) ∪ Fc

d) ( Ec ∪ Gc ) ∩ F

e) ( E ∩ G ) ∩ F

f) None of the above.

The annotation for the event in the sample space when E and G both occur but F does not is given as:( E ∩ G ) ∩ Fc which is the correct answer would be an option (B).

In probability theory, an event is a predetermined group of outcomes from a random experiment. Another definition of an event is any subset of a sample space, which is the collection of all possible results of a random experiment.

We are allowed to use here for the necessary notation, though one way to indicate this is the complement of E U F U G. This would be the area in the sample space S that lies outside E, F, and G in a Venn diagram.

Thus, the annotation for the event in the sample space when E and G both occur but F does not is given as:( E ∩ G ) ∩ Fc

Learn more about the Events here:

https://brainly.in/question/4042290

#SPJ1

The question seems to be incomplete the correct question would be

Let S be any sample space, and E, F, and G be any three events. Describe the event that E and G occur, but not event F.

a) ( Ec ∪ G ) ∩ Fc

b) ( E ∩ G ) ∩ Fc

c) ( E ∪ G ) ∪ Fc

d) ( Ec ∪ Gc ) ∩ F

e) ( E ∩ G ) ∩ F

f) None of the above.

Answer:

a: 120 = 2x + 40

80 = 2x

x = 40

b: (3x + 10) + (x-30) = 180

4x - 20 = 180

4x = 200

x = 50

c: 105 = 2x - 11

116 = 2x

58 = x

d: 8y + 36 = 14y - 24

-6y = -60

y = 10

64 = 48 + x

16 = x

y = 10, x = 16

e: 75 + (2x - 5) = 180

70 + 2x = 180

2x = 110

x = 55

2(55) - 5 =y

y = 105

f: (2x + 8) + (3x + 17) = 180

5x + 25 = 180

x = 31

3(31) + 17 = 5y + 15

110 = 5y + 15

95 = 5y

y = 19, x = 31

The expression is equal to 0.00333333333.

A = 0.00333333333

B = 0.00426666666

C = 0.03125

D = 33.3333333333

Therefore, the answer is A. Hope this helps! :)

The proof of △AED is congruent to △BEC

What is congruency?

Two figures or objects are congruent in geometry if they have the same shape and size, or if one has the same shape and size as its mirror counterpart. In more technical terms, two sets of points are said to be congruent if and only if one of them can be changed into the other by an isometry, which is a combination of rigid movements such as translation, rotation, and reflection. This implies that one item may be relocated and reflected (but not scaled) to perfectly align with the other. So two separate plane figures on a piece of paper are congruent if they can be cut out and then entirely matched up. It is OK to flip the paper over.

Given, △ABC is congruent to △BAD.

and △AEB is common in both, so

△AED is congruent to △BEC (proved)

To know more about congruency, click on the link

https://brainly.com/question/17239461

#SPJ13

Answer: 0-10

1-9

2-8

Step-by-step explanation:

With the width and length being held constant, the height of the box decreases at rate  5 cm/s

Let:

l = length

w = wide

h = height

Then, the volume of the box is given by:

V = l . w. h

The length and the width are assumed to be constant. Hence, the derivative with respect to time is:

dV/dt = l . w dh/dt

Parameters given:

dV/dt = - 541 cm³/dt

l = 9 cm

w = 12 cm

Plug these parameters into the formula:

-541 = 12 . 9 . dh/dt

dh/dt = 5 cm/s

Learn more about derivative here:

https://brainly.com/question/22716418

#SPJ4

Answer:

The number is 40.

Step-by-step explanation:

Step 1: Assume your variables

Consider the 'number' to be [tex]x[/tex].

Step 2: Create an equation(s)

The information in the question states that the difference between [tex]\frac{2}{5}[/tex] of [tex]x[/tex] and [tex]9[/tex], is [tex]7[/tex].

Representing this mathematically gives us:

[tex](\frac{2}{5}\times x) -9=7[/tex]

Step 3: Solve the equation

The equation we have is:

[tex](\frac{2}{5}\times x) -9=7[/tex]

So, let's solve it:

[tex](\frac{2}{5}\times x) -9=7\\\\\text{Add 9 to both sides:}\\(\frac{2}{5}\times x) -9+9=7+9\\\\\text{Simplify:}\\(\frac{2}{5}\times x)=16\\\\\text{Multiply by}~\frac{5}{2}~\text{on both sides:}\\\frac{5}{2}\times\frac{2}{5}\times x=16\times \frac{5}{2}\\\\\text{Simplify:}\\1\times x=\frac{80}{2}\\\\\text{Calculate:}\\x=40[/tex]