A pole 5 feet tall is used to support guy wire for a tower, which runs from the tower to a metal stake in the ground. After placing the pole, Zoe 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

The measure of ∠ A is 44 degrees.

Given that:-

∠ A and ∠ B are complementary angles.

∠ A = (6x +2) degrees

∠ B = (4x + 18) degrees

We have to find the measure of ∠ A.

We know that the sum of two complementary angles is 90 degrees.

Hence, we can write,

(6x + 2) + (4x + 18) = 90

(6x + 4x) + (2 + 18) = 90

10x + 20 = 90

10x = 90 - 20

10x = 70

x = 70/10

x = 7 degrees

Hence,

∠ A = 6*7 + 2 = 42 +2 = 44 degrees.

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Plotted Answers:

12.) See attached for my work

13.) See attached for my work

14.) See attached for my work

Simplified Answers:

12.) y > –24

13.) x ≥ –12

14.) x > –7

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Step-by-step explanation:

This should be the right solution.

Answer:

Step-by-step explanation:

Factorize the polynomial using the given details.

Since one of the factors known, try to factor it out and futher:

Find its zero's:

Answer:

[tex]x=1, \quad x=\dfrac{3}{2}, \quad x=2[/tex]

Step-by-step explanation:

Factor Theorem

If f(x) is a polynomial, and f(a) = 0, then (x – a) is a factor of f(x).

If the coefficients in a polynomial add up to 0, then (x - 1) is a factor.

Given polynomial function:

[tex]f(x)=2x^3-9x^2+13x-6[/tex]

Sum the coefficients:

[tex]\implies 2-9+13-6=0[/tex]

As the sum of the coefficients is zero, (x - 1) is a factor.

Therefore:

[tex]\implies f(x)=(x-1)(ax^2+bx+c)[/tex]

Expand the brackets:

[tex]\implies f(x)=ax^3+bx^2+cx-ax^2-bx-c[/tex]

[tex]\implies f(x)=ax^3+(b-a)x^2+(c-b)x-c[/tex]

Compare the coefficients with the given polynomial.

As the coefficient of the leading term of the polynomial is 2:

[tex]\implies a=2[/tex]

As the coefficient of the term in x² is -9:

[tex]\implies b-a=-9[/tex]

[tex]\implies b-2=-9[/tex]

[tex]\implies b=-7[/tex]

As the constant of the given polynomial is -6:

[tex]\implies c=6[/tex]

Substitute the found values of a, b and c into the factored form of the polynomial:

[tex]\implies f(x)=(x-1)(2x^2-7x+6)[/tex]

Factor the quadratic:

[tex]\implies 2x^2-7x+6[/tex]

[tex]\implies 2x^2-4x-3x+6[/tex]

[tex]\implies 2x(x-2)-3(x-2)[/tex]

[tex]\implies (2x-3)(x-2)[/tex]

Therefore, the fully factored polynomial is:

[tex]\implies f(x)=(x-1)(2x-3)(x-2)[/tex]

To find the zeros, set the function to zero:

[tex]\implies f(x)=0[/tex]

[tex]\implies (x-1)(2x-3)(x-2)=0[/tex]

Apply the zero-product property:

[tex]\implies x-1=0 \implies x=1[/tex]

[tex]\implies 2x-3=0 \implies x=\dfrac{3}{2}[/tex]

[tex]\implies x-2=0 \implies x=2[/tex]

Therefore, the real zeros of the given polynomial are 1, ³/₂ and 2.

The given elevation of New Orleans of 2 feet below sea level gives the possible elevation of Salton City by using a number line, as 3 feet below sea level.

A number line pictorially presents the set of real numbers, showing their position in order of their magnitude, such that the numbers increases positively as we move from left to right with negative numbers increasing from the zero mark as we move further left.

The given elevation of New Orleans with reference to the sea level = 2 feet below (lower than) sea level

The elevation of Salton City = Lower than the elevation of New Orleans

Required; The possible elevation of Salton City

The elevation of Salton City can be found by presenting the given information on a number line as follows;

Let SL represent the sea level, let N represent New Orleans and let S represent Salton City, we have;

<___|-3______|-2____|0______>

' S. N. SL

A level higher than the elevation of New Orleans is given by a point to the right of the -2 mark on the above number line, while an elevation lower than that of New Orleans is given by a point to the left of -2 on the number line. The location of Salton City should therefore be to the left of -2, which is a point, x < -2 feet

The elevation of Salton City is less than 2 feet below sea level, which is given by the set x < -2 feet

-3 feet is less than -2 feet, therefore, a possible elevation in feet of Salton City is x = 3 feet below sea level, which is less than (<) 2 feet below sea level

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Answer:

[tex] 7^2[/tex]

Step-by-step explanation:

Answer:

7²

Step-by-step explanation:

the product of a number and its multiplicative inverse is equal to 1 , that is

a ×[tex]\frac{1}{a}[/tex] = 1

given

[tex]7^{-2}[/tex] , then multiplicative inverse is [tex]\frac{1}{7^{-2} }[/tex] = 7² and

[tex]7^{-2}[/tex] × 7² = [tex]7^{0}[/tex] = 1

First, we can start input small whole numbers in the function to see if we get a whole number. Let's try with 0, 1 and 2:

None of those values worked. Let's try negative integers, such as -1 and -2:

We get integer coordinates if we use negative integers. Then, we need at least 5 points. Let's use x = -1, -2, -3, -4, -5

We have the points:

(-1, -8), (-2, -7), (-3, -5), (-4, -1) and (-5, 7)

If we locate them in the cartesian plane:

And now, we can estimate the graph. An exponential function where the base is smaller than 1, describes an exponential decay, and the term "-9" is applying a shift 9 units down, and also y = -9 is a horizontal asymptote. With all this and the points we just found:

The value of (f- g)(x) is  2x - 26.

This is a question of subtraction of functions.

Subtraction of functions

The subtraction of function involves the creation of a new function through the addition of two other functions.

Subtraction of one real-valued function from another.

Let h: X → and p: X → be any two real functions, where X ⊆ Real numbers. Then, we can define h - p: X → by h - p x = h(x) – p(x), for all x ∈ X.

Given that:-

f(x) = 2x + 1

g(x) = 27

We have to find the value of (f- g)(x)

We know that,

(f- g)(x) = f(x) - g(x)

Hence, we can write,

(f- g)(x) = 2x + 1 - 27 = 2x - 26

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The average cost of each book that Nancy got is $32

Cost refer to the amount or value of a product. cost is usually valued in money hence one has to pay some money to h]]get the commodity of choice

In the question, the commodity is mundane books

given that

Nancy had 209 dollars to spend

number of books = 6

amount remaining after buying = $17

The question can be represented mathematically as

6x + 17 = 209

where x is the cost of the each book

6x + 17 = 209

6x = 209 - 17

6x = 192

dividing through by 6

6x / 6 = 192 / 6

x = 32

hence each book costs $32

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The points that he average on the last two tests will be 93 points.

A mean is the average of the set of numbers that are given.

On the first five tests that he took, he averaged 86 points. The total points will be:

= 86 × 5

= 430 points

He averaged 88 points on all seven tests. The total will be:

= (88 × 7)

= 616 points

The point average on the last two tests will be:

= (616 - 430)/2

= 186/2

= 93 points

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Answer:

6.25 weeks

Step-by-step explanation:

Take 18.75 ÷ 3. The construction crew finishes 3 km per week. You should receive 6.25 by solving the equation. So, this is the answer.

Answer:

They should play music

Step-by-step explanation:

They should play music obviously because the sales were higher

1) Gathering the data

Strategy:

Running : 2x As he swims

Biking: 4x Runs

Runs = 3 miles

Then

2) Runs = 3 miles Swims = 6 miles Biking = 12 miles

The Total distance will be the sum of those activities:

3+6+12=21 miles

⇒Given that the general rule to find the nth term is

[tex]T_{n} =-2+6(n-1)[/tex]

⇒To find the 11th term this means that they need a term which is in the position 11

⇒To get the number we plug in the 11 which is the position in the place of n and simplify.

[tex]T_{11} =-2+6(11-1)\\T_{11} =-2+6(10)\\T_{11} =-2+60\\T_{11} =58[/tex]

The 11th term is 58

Goodluck!!!

In linear equation,  R = 4c is an equation to represent the amount R Natalia and her friends raised after selling c cakes.

What are a definition and an example of a linear equation?

The equation that will represent the amount raised after selling the cakes to be written in slope-intercept form is given as .

Where,

y = R (amount of cake sold in dollars)

x = c (cakes sold)

m = slope

b = y-intercept.

The equation would look like

R = mc + b

We need to find the value of m and b, to get an equation to represent the situation.

The first point we have from the information given is (15, 60) => 15 cakes sold for $60.

The second point is (22, 88) => 22 cakes sold for $88.

Slope(m) = 88 - 60/22 - 15 = 28/7 = 4

To find b, substitute c = 15, R = 60 and m = 4, into R = mc + b

  60 = 4(15) + b

  60 = 60 + b

   b = 0

Since b = 0, this means there is a proportional relationship between R and c.

Substitute m = 4 and b = 0 into   R = mc + b to derive an equation to represent the amount R Natalia and her friends raised after selling c cakes.

    R = 4c + 0

    R = 4c

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Using concepts of statistics, we got 7% people are from age 18-24,and 15% for criminal arrests,65 and older are in 13% population and cover less than 1% crime rate.

The topic of crime in the United States is very large, technically covering any action that is punishable under a state or federal law. Any analysis of the topic  requires division into further sub-categories. One common way to do this is  by limiting analysis to crimes involving jail time (i.e. misdemeanors and felonies, which generally differ via the length of jail time involved), then differentiate between violent crimes or property crimes. Violent crimes are described as offenses which involve force or the threat of force, while property crime majorly includes offences involving the taking of money or property, but where there is not any  force or threat of force against the victims. Property crimes are outnumbering violent crimes in the U.S. in 2020, numbering 6.45 million and 1.31 million respectively. Larceny was the actually most common property crime with 4.6 million incidents, while the aggravated assaults accounted for around two thirds of violent crimes.

Hence, percentage of people whose age is in between 18-24 is 7%,

people from age 18-24 engaged in illegal work=15%,

percentage of people whose age is 65 or more than =13%,

people involved in crime having age more than or equal to 65=1%

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The given scatterplot has no correlation. This is because there is no pattern among the dots on the scatterplot.

Correlation is a measure that is used in statistics to measure the linear relationship that exists between two variables. Correlation can either be positive, negative or zero. The closer the correlation coefficient is to one, the higher the correlation.

Positive correlation is when two variables move in the same direction. When drawn on a scatterplot, the line of best fit is upward sloping. The coeffect of correlation for positive correlation is always positive.

Negative correlation is when two variables move in different directions.  When drawn on a scatterplot, the line of best fit is downward sloping. The coeffect of correlation for negative  correlation is always negative.

Zero correlation or no correlation is when there is no relationship between the variables. When drawn on a scatterplot, there is no discernible patterns among the variables.

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Step-by-step explanation:

x + 3y = 1

x = 1 - 3y-(i)

7x + 8y = 11

x= 11-8y/7-(ii)

substituting eqn (i) in eqn (ii)

11-8y/7= 1-3y

11-8y=7-21y

13y=-4

y=-4/13

putting the value of y in eqn (i)

x=1-(-12/13)

x=25/13

The given polynomials are as ,

We have to subtracrt these given polynomials,

Option D is correct.

Answer:

B. Opposite angles in a parallelogram are congruent.

Explanation:

The figure shows a parallelogram. In this parallelogram, ∠R and ∠T are opposite angles and ∠Q and ∠S are opposite angles.

Since the information says that ∠R is congruent to ∠T and ∠Q is congruent to ∠S, the theorem is opposite angles in a parallelogram are congruent.

So, the answer is B. Opposite angles in a parallelogram are congruent.

The angle measures in this problem are given as follows:

1. Angle SVT: 79º.

2. Angle BEC: 65º.

Angles SVT and SVR are vertical, meaning that they have the same measure, hence we can find the value of y as follows:

8y - 33 = 5y + 9

3y = 42

y = 42/3

y = 14.

Hence the measure of the angle SVT is of:

m<SVT = 5y + 9 = 5(14) + 9 = 79º.

The two angles given in this problem are also vertical, meaning that we can solve for x as follows:

5x - 10 = 3x + 40

2x = 50

x = 50/2

x = 25º.

Then the bottom angle is:

3 x 25 + 40 = 115º.

The bottom angle is supplementary with angle BEC, hence we can find the measure of angle BEC as follows:

115 + m<BEC = 180

m<BEC = 180 - 115

m<BEC = 65º.

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The equation of the perpendicular line will be y = –(1/3)x + d. Then the correct option is B.

Let the equation of the line be y = ma + c. Then the equation of the perpendicular line that is perpendicular to the line y = mx +c is given as y = -(1/m)x + d. If the slope of the line is m, then the slope of the perpendicular line will be negative 1/m.

The equation is given below.

3x – y = 10

y = 3x – 10

Then the equation of the perpendicular line is given as,

y = –(1/3)x + d

The equation of the perpendicular line will be y = –(1/3)x + d. Then the correct option is B.

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Answer:

3500

Step-by-step explanation:

split 7000 in half for stocks and treasury= 3500 each.

7 percent on 3500 is 3724, 7 percent of 3500 is 245 dollors. 535 x 7 is 3745 = 3500 invested in treasury.

The number of ways to plan her schedule of menus for the 20 school days is 10^20.

To calculate combinations, we will use the formula nCr = n! / r! * (n - r)!, where n represents the total number of items, and r represents the number of items being chosen at a time. To calculate a combination, you will need to calculate a factorial.

For each day, there are ten different choices for what she will cook that day. 20 decisions are made, one for each day with ten different possibilities for each choice.

The complete question is: A school cook plans her calendar for the month of February in which there are 20 school days. She plans exactly one meal per school day. Unfortunately, she only knows how to cook ten different meals.

How many ways are there for her to plan her schedule of menus for the 20 school days if there are no restrictions on the number of times she cooks a particular type of meal?

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The slope of the points has a value of 97/16

From the question, the line passes through the following points

(64, 94) and (48, -3).

The slope of the line that passes through the points is then calculated using

Slope = (y₂ - y₁)/(x₂ - x₁)

Where x and y are the coordinates above

Substitute the known values in the above equation

So, we have the following equation

Slope = (94 + 3)/(64 - 48)

Evaluate the difference and the sum

Slope = 97/16

Hence, the slope is 97/16

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To identify the inequality of the given graph:

1. Identify the equation of the borderline in slope-intercept form (y=mx+b)

- Find the slope (m): Use two points in the line in the next formula:

- Identify the y-intercept (b): the value of y where the line cross the y-axis (when x is 0)

b= -1

Equation of the border line:

2, Identifify the inequality sing:

-When the inequality is < or > the borderline is a dotted line

-When the inequality is ≥ or ≤ the border line is a full line

-When the inequality is < or ≤ the shaded area is under the borderline

-When the inequality is > or ≥ the shaded are is over the borderline

In this case you have a dotted borderline and a shaded area under the borderline, then, the inequality is:

The equivalent expression of  4(8g + 5) + 6 is 4(5 + 8g) + 6

Equivalent expressions are expressions that work the same even though they look different.

In other words, two expressions are said to be equivalent if they have the same value irrespective of the value of the variable(s) in them.

Therefore, let's find the equivalent expression of 4(8g + 5) + 6.

Hence,

4(8g + 5) + 6

32g + 20 + 6

32g + 26

Hence, the equivalent expression is 32g + 26 or 4(5 + 8g) + 6

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Step-by-step explanation:

the midpoint coordinates between 2 points A and B are

((xa + xb)/2, (ya + yb)/2)

xa = 3

ya = 0

and so we get

(3 + xb)/2 = 0

3 + xb = 0

xb = -3

(0 + yb)/2 = 5

yb = 10

therefore, S = (-3, 10)

3x^2 + 1 = 5x

3x^2 - 5x + 1 = 0

quadratic formula

where ax^2 + bx + c = 0

so

You can see that the 25 - 12 = 13 so the answers are A and B