A pole 7 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, Rashaad 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.

Given:

Required:

To solve the given equation by factoring method.

Explanation:

Consider

And

Final Answer:

2 is the numerical expression when  2 to the power of five sixths.

What are power and exponent?

 [tex]2^{5/6} * 2^{1/6}[/tex]

 [tex]2^{6/6}[/tex]

  2¹

 = 2

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To find the value of x, we can work the two triangles separately; as follows:

So, according to the figures above:

x = y + z, and we can find y and z using Pythagoras theorem:

Then:

The cost of 19 bottles of juice is $19.76.

The "Unit Price" tells us the cost per litre, per kilogram, per pound, etc, of what we want to buy.

Given that, Abigail buys 12 bottles of grapefruit juice at the corner store for a total cost of $12.48 and each bottle costs the same amount,

Cost of one bottle = 12.48/12 = $1.04

Cost of 19 bottles = $1.04*19 = 19.76

Hence, The cost of 19 bottles of juice is $19.76.

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Answer:

Let the number of bags be 3 and the amount, x

1 bag = $4.75

1 bag = $4.753 bags = x

cross-multiply

x = $4.75 × 3

x = $14.25

hence,

3 bags = $14.25

Equation he can use:

Equation he can use:Since the amount for 1 bag is already stated, the number of bags sold is multiplied by the amount for 1 bag to get the amount.

Answer:y=4.72

Step-by-step explanation:

A)The actual distance between towns K and L is 10 cm .

B) The bearing of town L from town k is 117 degree

The length of the line segment connecting the two sites is used to measure distance between them. The shortest line segment between a point and a line will have a length equal to the distance between them.

The following list includes four distance metrics that are maybe the most often employed in machine learning: the Hamming Distance. Distance in Euclid. New York City distance

The distance a number is from 0 on the number line is its absolute value. Because -7 is 7 units away from 0, its absolute value is 7. Because it is 5 units away from 0, the number 5 has an absolute value of 5. Any number that is less than zero is considered to be negative.

Given ,

A)The actual distance between towns K and L is 10 cm .

B) check the photo of my work

C) The bearing of town L from town k is 117 degree

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In order to evaluate the sequences, let's find the ratio of each one by subtracting the second term and the first one.

1)

Since the ratio is negative, the sequence is decrescent.

2)

The ratio is positive, so we have a crescent sequence.

3)

The ratio is positive, so we have a crescent sequence.

ANSWER

Given;

Firstly, convert to decimal

we have;

"Percent" means "per 100" or divide by 100

Hence, we have;

now, converting to the nearest thousandth

The answer to the nearest thousandth is

Answer:

The answer is -4 as the correct slope for Find the slope:

(-1, 5), (2, -7)

Step-by-step explanation:

SOLUTION

Given the question in the image, the following are the solution steps to answer the question

STEP 1: Write the given equation

STEP 2: Complete the table

Hence, the table for the equation will be:

From the information available, the initial population was 16,007. That figure was taken as at the year zero which is January 1, 2014.

This means

This trend would be used until we get to January 1, 2030, when we would calculate as follows;

Note that the years count from Jan 1 to Jan 1.

The function that models the yearly growth is;

Using the first year, 2014 which is year zero, the result would remain 16,007. That is;

For the 16th year, which is year 2030, we woud now have the following;

Rounded to the nearest whole number, this figure becomes;

ANSWER:

The domain of the given situation is 0≤t≤10.

The elements that make up a function are its domain and range. A function's domain is the set of all potential input values, while its range is the range of possible output values. Range, Function, and Domain. If a function f: A B exists that maps each element of A to an element of B, then A is the domain, and B is the co-domain. When (a, b) ∈ R, the image of element 'a' under the relation R is supplied by 'b'.

Given, the average hiking rate is 3 miles per hour.

The number of hours you plan hiking for is 10 hours.

Now, as we know that time can't be negative so we know that the domain must have t≥0.

And it is given that you plan to hike for 10 hours so the domain must also have t≤10.

Therefore, the domain of the given situation is 0≤t≤10.

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The solution set of the given equation is {(-1,-8),(3,4),(8,19)}.

The set of ordered pairs that make up the solution to an equation with two variables is referred to as the solution set.

In mathematics, a function's domain is the collection of possible inputs it will accept.

Given equation is 2y = 6x - 10 and domain is {-1, 3, 8}

We can also write the given equation is

y =(6x-10)/2      ------------equation 1

As we know, domain is considered as the value of x,

Consequently, if we enter x = -1 in equation 1, we will receive

y = (-16)/2

y = -8

Similarly put x = 3 in equation 1, we will get

y = 8/2

y = 4

Similarly put x = 8 in equation 1, we will get

y = 38/2

y = 19

By combining the values of x and y, we get

The solution set of the given equation is {(-1,-8),(3,4),(8,19)}.

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In the triangle LMN angle N is 76 degree.

Given,

In the question:

There is two isosceles triangle in the figure:

Triangle JKL and Triangle LMN

Angle J = 64 degree

To find the angle Angle N

Now, According to the question:

The triangle is isosceles.

<J = 64 degrees

All triangles have 180

<JLK = 180 - 64 - 64

Angle JLK = 52degree.

Angle JLK = MLN  = 52 degree (Vertical opposite angle )

M is the left over from the 2 equal angles.

N = 180 - <M - < MLN                      

N = 180 - 52 - 52

N = 76 degree

Hence, In the triangle LMN angle N is 76 degree.

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the z value needed to conduct a two tail test in a statistical inference problem, specifying a 90% level of confidence is 1.65

A confidence interval is based on the sample statistics and is used to estimate a population parameter.

For example, a sample mean is used to build a confidence interval to estimate the population mean.

the z value needed to conduct a two tail test in a statistical inference problem, specifying a 90% level of confidence is 1.65

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Since the player makes 95 out of 140 free throws, the probability that he makes the next free throw is:

Answer: 67.86%

Answer: She will need 1239 cm^3 of foil

Explanation:

Surface area of square pyramid = base area of square + area of 4 triangular faces

Area of square base = l^2

where

l is the length of each side of the square base

From the information given,

l = 8

Area of square base = 8^2 = 64

Area of each triangular face = 1/2 x base x height

We would find the height of each face by applying Pythagorean theorem to the right triangle formed below. It is ex[ressed as

hypotenuse^2 = one leg^2 + other leg^2

hypotenuse = 10

one leg = 4

other leg = h

4^2 + h^2 = 10^2

36 + h^2 = 100

h^2 = 100 - 36 = 64

h = √64

h = 8

base = 8

Area of 4 triangular faces 4 x 1/2 x 8 x 8 = 128

Surface area of square base pyramid = 128 + 64 = 192 in^2

We would convert 192 in^2 cm^2

Recall,

1 inch^2 = 6,4516 cm^2

192 inch^2 = 192 x 6.4516

= 1239 cm^2

She will need 1239 cm^3 of foil

Answer:

Multiply each term in the parentheses by a²b

2a⁵b²- 5a³b²

Answer:

Step-by-step explanation:

[tex]a^2b(2a^3b-5ab)=\\\\2a^3ba^2b-5aba^2b=\\\\2a^{3+2}b^{1+1}-5a^{1+2}b^{1+1}=\\\\2a^5b^2-5a^3b^2[/tex]

The complement of the smaller angle of supplementary angles in ratio 4:5 is given by 10 degree.

Given that the supplementary angles are in ratio 4:5.

Let the angles be 4x and 5x respectively.

We know that the sum of supplementary angles is 180 degree.

So, 4x+5x = 180

9x = 180

x = 180/9

x = 20

So the angles are = (20*4),(20*5) = 80,100.

So the smaller angle is 80 degree.

So the complement of the smaller angle is = 90-80 = 10 degree.

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You have to calculate the probability of obtaining an odd number after rolling the die and obtaining tail after tossing a coin, symbolically:

Where

"O" represents the event " rolling an odd number"

"T" represents the event "tossing a coin and obtaining tail"

The events are independent, which means that the intersection between both events is equal to the product of the individual probability of each event:

So, first, we have to calculate the probabilities of "rolling an odd number" P(O) and "tossing a coin and obtaining tail" P(T)

-The die is six-sided and numbered from 1 to 6, assuming that each possible outcome has the same probability, we can calculate the probability of rolling one number (N) as follows:

The possible outcomes when you roll a die are {1, 2, 3, 4, 5, 6}

Out of these six numbers, three are odd numbers {1, 3, 5}, this is the number of favorable outcomes of the event "O", and the probability can be calculated as follows:

So, the probability of rolling an odd number is P(O)=1/2

-When you toss a coin, there are two possible outcomes: "Head" and "Tail", assuming that both outcomes are equally possible.

For the event "toss a coin and obtain tail" there is only one favorable outcome out of the two possible ones, so the probability can be calculated as:

The probability of tossing a coin and obtaining a tail is P(T)=1/2

Once calculated the individual probabilities you can determine the asked probability:

Current price of go-kart = $2,589

Price of go-kart next month = $2,119

If Rafael decides to buy the go-kart next month,

He will save $2,589 - $2,119 = $470

By definition of estimation

Estimation is an approximate calculation or judgment of the value, number, quantity, or extent of something

Approximating to the nearest hundred

$470 = $500

Therefore, Rafael will save an estimate of $500 if he wants to buy the go-kart next month

Answer:

$22.50 for 5 bags of cat food

Step-by-step explanation:

$13.50 divided by 3 equals $4.50. Multiply this by 5 and you will end up with $22.50 for 5 bags of cat food

Answer:

slope = - 14

Step-by-step explanation:

calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 92, 21 ) and (x₂, y₂ ) = (- 93, 35 )

m = [tex]\frac{35-21}{-93-(-92)}[/tex] = [tex]\frac{14}{-93+92}[/tex] = [tex]\frac{14}{-1}[/tex] = - 14

Given:

Principal Amount, P = $4,400

Interest rate, r = 90%

Here, Camilla needs to create an exponential equation that allows her tract the interest earned over time.

This is a Compound interest problem.

To find create an exponential equation, apply the formula below:

WHere:

P is the principal amount = $4,400

r is the rate = 90% = 0.90

t is the time (number of years)

Input values into the equation above:

Therefore, the exponential equation that allows her to track the interest earned over time is:

Plugging the value for the number of years for t, you will get the interest earned over time, t.

ANSWRER:

The given information is:

- They surveied 164 pet owners

- 61 own a dog

- 66 own a cat

- 11 own both a dog and a cat

We have to find how many owned neither a cat nor a dog.

We can represent this survey in the following diagram:

To find the solution we need to subtract the number of people who said they own a dog, own a cat, and own both, from the total number of people in the survey, so:

The people who own neither a dog nor a cat are 26.

By using properties of angles, it is obtained that

x = 20°,

What is an Angle?

When two straight lines intersect, an angle is formed. The point of intersection is called the vertex of the angle and the lines are called the arms of the angle.

Here,

[tex]m\angle DOB =m\angle DOE +m\angle EOB[/tex] [ Addition of two angles]

[tex]m\angle DOB =90+x[/tex] [ Substitution]

[tex]m\angle AOC = m\angle DOB[/tex] [Vertically opposite angle]

[tex]110 = 90 + x[/tex] [ Substitution]

[tex]x = 20^{\circ}[/tex] [Algebra]

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The scale factor is always the ratio of new image with respect to the old image.

6) The scale factor as per the image is 3:1 or 3.

7) The New image is P'Q'R'S' and old image is PQRS so the scale factor is given by:

Q'R':QR=3:6 or 1:2.

The scale factor is 1/2.

8) Here the pair of congruent angles is:

The proportional sides are:

So FG corresponds to RS, GH corresponds to TS, HF corresponds to TR.

Since f is the number of female cousins and the number of male cousins is 4 less than the number of female cousins, we can write the following expression to represent the number of male cousins:

For example, if the number of female cousins is 7, we can use this value (f = 7) in the expression above to find the number of male cousins:

So if the number of female cousins is 7, the number of male cousins is 3.

Therefore the expression for the number of boy cousins is f - 4.

To evaluate f(x) at x = -4 we substiitute x in the equation with -4. Doing this gives

which is our answer!

We find the surface area of the figure by dividing the figure into smaller ones. This is:

Area 1, rectangle:

Area 2, triangle:

Area 3, rectangle:

Area 4, triangle:

Area 5, rectangle:

Therefore, the surface area of the ramp is:

Substitute the corresponding values:

Answer: 9.96 m^2