A pole 11 feet tall is used to support a guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Jayden measures the distance from the pole to the stake and from the pole to the tower, as shown in the diagram below. Find the length of the guy wire, to the nearest foot. 11 ft 20 ft-8 ft​

Given:

The given equation is:

[tex]y=-4x+3[/tex]

A line is perpendicular to the given line and passes through the point (4,-1).

To find:

The equation of required line.

Solution:

The slope intercept form of a line is:

[tex]y=mx+b[/tex]

Where, m is slope and b is y-intercept.

We have,

[tex]y=-4x+3[/tex]

Here, the slope of the line is -4 and the y-intercept is 3.

Let the slope of required line be m.

We know that the product of slopes of two perpendicular lines is -1. So,

[tex]m\times (-4)=-1[/tex]

[tex]m=\dfrac{-1}{-4}[/tex]

[tex]m=\dfrac{1}{4}[/tex]

The slope of required line is [tex]m=\dfrac{1}{4}[/tex] and it passes through the point (4,-1). So, the equation of the line is:

[tex]y-(-1)=\dfrac{1}{4}(x-4)[/tex]

[tex]y+1=\dfrac{1}{4}(x)-\dfrac{4}{4}[/tex]

[tex]y=\dfrac{1}{4}x-1-1[/tex]

[tex]y=\dfrac{1}{4}x-2[/tex]

Therefore, the equation of the required line is [tex]y=\dfrac{1}{4}x-2[/tex].

Answer:

D)

Step-by-step explanation:

All sides are congruent because all sides are the same.

Hope this helps!

-kiniwih426

Answer:

x = 4

Step-by-step explanation:

[tex]\frac{14}{2x-1} = \frac{10}{5} \\10(2x-1) = 5*14\\20x - 10 = 70\\20x = 70+10\\20x = 80\\x = 80:20\\x = 4[/tex]

Answer:

[tex]\text{C) } y=1[/tex]

Step-by-step explanation:

A asymptote represents a control for a function where the function will never touch. We see that as the [tex]y[/tex] approaches 1, [tex]x[/tex] approaches infinity, from either direction. However, the function never touches nor crosses the line [tex]y=1[/tex], and never will. Thus, the horizontal asymptote is located at [tex]y=1[/tex].

y=0 is correct answer but is not in the selection.

Step-by-step explanation:

SOLUTION

For these solutions, we will use \displaystyle f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}, q\left(x\right)\ne 0f(x)=

q(x)

p(x)

,q(x)≠0.

\displaystyle g\left(x\right)=\frac{6{x}^{3}-10x}{2{x}^{3}+5{x}^{2}}g(x)=

2x

3

+5x

2

6x

3

−10x

: The degree of \displaystyle p=\text{degree of } q=3p=degree of q=3, so we can find the horizontal asymptote by taking the ratio of the leading terms. There is a horizontal asymptote at \displaystyle y=\frac{6}{2}y=

2

6

or \displaystyle y=3y=3.

\displaystyle h\left(x\right)=\frac{{x}^{2}-4x+1}{x+2}h(x)=

x+2

x

2

−4x+1

: The degree of \displaystyle p=2p=2 and degree of \displaystyle q=1q=1. Since \displaystyle p>qp>q by 1, there is a slant asymptote found at \displaystyle \frac{{x}^{2}-4x+1}{x+2}

x+2

x

2

−4x+1

.

Synthetic division of the polynomial x^2-4x+1 by x+2 in which it only contains the coefficients of each polynomial.

The quotient is \displaystyle x - 6x−6 and the remainder is 13. There is a slant asymptote at \displaystyle y=x - 6y=x−6.

\displaystyle k\left(x\right)=\frac{{x}^{2}+4x}{{x}^{3}-8}k(x)=

x

3

−8

x

2

+4x

: The degree of \displaystyle p=2\text{ }<p=2 < degree of \displaystyle q=3q=3, so there is a horizontal asymptote y = 0.

Median is the middle value.

Writing the values from smallest to largest you have :

1/8, 1/8, 2/8, 2/8, 2/8, 3,8, 3/8, 4/8, 5/8

There are 9 values. The middle value ( median) would be the 5th number ( this would give you 4 numbers below it and 4 numbers above it.

The Median is 2/8

Answer:

2/8 is the median. In decimal, it is 0.25.

Happy learning!

--Applepi101

Answer:

13 points

Step-by-step explanation:

Equation for "There are 50 athletes signed up for a neighborhood basketball competition. Players can select to play in the 6-player games ("3 on 3") or the 2-player games ("1 on 1").

Equation for "If the neighborhood holds 13 total games and all 50 athletes participate"

How many 6 player games?

How many 2 player games?

The answer to this question is:

7 two-player games are played

6  six-player games are played

What are system of equations?

A collection of two or more equations with the same set of unknowns is referred to as a system of equations.

Systems of linear equations in two variables can be solved in one of three ways:

Solution:

Given:

Total games = 13

Total number of athletes participated = 50

Find:

6-player games played = ?

2-player games played = ?

Step-1:

let x denote the total 2-player games played &

    y denote the total 6-player games played.

Hence the equation for the total number of games played is:

                     x + y = 13 ..............eq(1)

Now, the equation for the total number of games played by the athletes is:

                    2x + 6y = 50............eq(2)

Further eq(2) can be reduced as-

                   2(x + 3y) = 50

                    x + 3y = 50/2

                     x + 3y = 25.........eq(2)

Step-2:

Solving eq(1) and eq(2) by using elimination method as follows:

                      x + y = 13

                      x + 3y = 25

Step-3:      

In the elimination method positive signs changes to negative and x gets eliminated so we get the y value as:    

-2y = -12

y = 6

Substituting y value in eq(1): x+ y = 13

                                               x + 6 = 13

                                               x = 13 - 6

                                              x = 7

Hence we found out that total 7 two-player games and 6 six-player games were played.  

Learn more about "System of equations" here:

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Answer:

C

Step-by-step explanation:

f(-2) = 4(-2) + 5

f(-2) = -8 + 5

f(-2) = -3

Answer:

-3

Step-by-step explanation:

f(x) = 4x + 5

Let x = -2

f(-2) = 4(-2) + 5

        =-8+5

           -3

[tex]\longrightarrow{\green{C.\:30 \sqrt{11} }}[/tex] ✔

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]3 \sqrt{50} \times \sqrt{22} \\ \\ = 3 \sqrt{50 \times 22} \\ \\ = 3 \sqrt{1100} \\ \\ = 3 \sqrt{2 \times 2 \times 5 \times 5 \times 11} \\ \\ = 3 \sqrt{ {2}^{2} \times {5}^{2} \times 11} \\ \\ = 3 \times 2 \times 5 \sqrt{11} \\\\ = 30 \sqrt{11} [/tex]

[tex]\bold{ \green{ \star{ \orange{Mystique35}}}}⋆[/tex]

Answer:

[tex]5x^2-9x-1[/tex]

Step-by-step explanation:

f - g

[tex]=5x^2-4x -(5x+1)\\\\=5x^2-4x-5x-1\\\\=5x^2-9x-1[/tex]

Answer:

y=41

Step-by-step explanation:

Let us start by writing an equation. 4 plus y divided by 5 equals to 9 :

[tex]\frac{4+y}{5}=9[/tex]

Great! Now let us solve for the variable, y, by isolating the terms:

[tex]4+y=45\\y=41[/tex]

I hope this helps! Let me know if you have any questions :)

Answer:

I think 2 points

Step-by-step explanation:

I may be wrong bc I suck at algebra. literally who is gonna use algebra ever?

Answer: two points hope it helps

Answer:

Translate 4 units to the left and reflect over the x-axis

Step-by-step explanation: hope this helps :)

The composition of the transformations given in the figure is translate 4 units to the left and then reflect over the X axis.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

After translation, the original figure is shifted from a place to another place without affecting it's size.

After Reflection, figure is flipped. In other words, a figure becomes it's mirror image.

Consider the point P.

Before undergoing reflection, the figure must be above the X axis.

And the point P will be translated 4 units to the left.

After reflection, since the figure moved towards the other side of the X axis, the figure is reflected across the X axis.

Hence the missing parts are filled.

Learn more about Translation and Reflections here :

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Answer:

The angle is 60°

Step-by-step explanation:

A supplement angle is the angle whose sum is equal to 180°.

The supplement angle = 180° - x

A complement angle is the angle whose sum is equal to 90°.

The complement angle = 90° - x

Given,

supplement angle = 4 × complement angle

(180° - x) = 4 × (90° - x)

180° - x = 360° - 4x

4x - x = 360° - 180°

3x = 180°

x = 60°

The supplement angle = 180° - x

⇒ 180° - 60°

⇒ 120°

The complement angle = 90° - x

⇒ 90° - 60°

⇒ 30°

Answer:

The angle is 60 degrees.

Step-by-step explanation:

Let the angle be x.

Then its supplement = 180-x.

Its complement = 90-x, so we have the equation:

180 - x = 4(90 - x)

180 - x = 360 - 4x

-x + 4x = 360 - 180

3x = 180

x= 60 degrees.

Answer:

1550m^3

Step-by-step explanation:

Volume of the prism= 7750m^3

Factor of dilated prism= 1/5

7750×1/5= 1550m^3

Answer:

x = 0

Step-by-step explanation:

3(x + 6) = 18

distribute

3x + 18 = 18

Subtract 18 from both sides

3x = 0

Divide both sides by 3

x = 0

Answer:

x = 5, y = 7

Step-by-step explanation:

x – y = -2 ——— 1

5x – 4y = -3 —– 2

x = -2 + y ——— 3

3 in 2 ≈ 5(-2 + y) – 4y = -3

-10 + 5y – 4y = -3

y = -3 + 10

y = 7

Putting y = 7 in 3, we have;

x = -2 + (7)

x = 5

Hence (x, y) = (5, 7)

Answer:

not touching x-axis

Step-by-step explanation:

the graph is not touching the x-axis, that is all i can say

Answer:

([tex]x^{2}[/tex] + [tex]x[/tex] + [tex]\frac{1}{2\\}[/tex] )

https://www.symbolab.com/solver/step-by-step/%5Cleft(1%5Cright)%2F%5Cleft(x%5E%7B%5Cleft(-2%5Cright)%7D%5Cright)%2B%5Cleft(1%5Cright)%2F%5Cleft(x%5E%7B%5Cleft(-1%5Cright)%7D%5Cright)%2B%5Cleft(1%5Cright)%2F%5Cleft(2%5Cright)

You can  use the  link above :))

Answer:

geometric

common ratio 2/3

Step-by-step explanation:

We know that the sequence is not arithmetic

3-2 =1

2-4/3 = 6/3 -4/3 = 2/3

The common difference is not the same

Now check geometric

The common ratio:

Take the second term over the first term

2/3

Now take the third term over the second term

4/3 ÷ 2

4/3 * 1/2 = 2/3

The common ratio is the same so the sequence is geometric with a common ratio of 2/3

Step-by-step explanation:

So for this question just substitute the value and work out. I thought it it to the power of 2 as I can't tell from the question.

Answer:

x/7 - 2 = y

Step-by-step explanation:

To find the inverse of a function, we switch f(x) and x and then solve for f(x). We thus have

x = 7f(x) + 14

subtract 14 from both sides to isolate the f(x) and its coefficient

x - 14 = 7 f(x)

divide both sides by 7 to isolate the f(x)

(x-14)/7 = f(x)

f(x) is synonymous with y here. so we havt

(x-14)/7 = y

This can also be written as

x/7 - 14/7 = y

x/7 - 2 = y

Answer:

    x            y

    -1           2

    0           3

    1            1

     2          -1

Step-by-step explanation:

Answer:

she is correct

Step-by-step explanation:

because according to the Pythagorean theorem the interior of a triangle has to be 180 degrees total.

and a straight line has an angle of 180

so the inside of the C angle is 50

60+50+70=180

Answer:

AB = A'B', AD = A'D', CD = C'D', CB = C'B'

Step-by-step explanation:

There is more then one way to give this problem a solution. The point of the question is to explain or provide an argument that will prove that the square ABCD is the same as A'B'C'D.

The way to prove it is by saying that the sides are equal, meaning the answer I provided above, by claiming that side AB is also equal to A'B', and so forth with all four sides.

Answer:

The Coordinates are (3, 1)

Step-by-step explanation:

Use the substitution method to solve the system of equations.

Let y = x - 2 be Equation 1

Let y = -2x + 7 be Equation 2

We know that the coordinates are (3, 1) because we graphed the slope intercept equations in part one. Its asking to use the substitution method to prove that the coordinates (3, 1) are viable or satisfies both Equation 1 and 2.

The substitution method is nothing but substituting x and y back into the equation to prove that the coordinates are viable.

For this I'll use equation 1 first,

y = x - 2

1 = 3 - 2

So yes, the coordinates (3, 1) satisfy Equation 1

Lets check equation 2 now,

y = -2x + 7

1 = -2*3 + 7

1 = -6 + 7

This is also another equation where the coordinates (3, 1) satisfy equation 2

So this means that the coordinates (3, 1) are viable for both equations

Hope this helps!