An anchor cable supports a vertical utility pole forming a 51 degree angle with the ground. The cable is attached to the top of the pole. If the distance from the base of the
pole to the base of the cable is 5 meters, how tall is the pole? (Round to the nearest hundredth.) PLS HELP

The height of an isosceles triangle can be found by using the Pythagorean Theorem to calculate the length of the hypotenuse, subtracting the lengths of the other two sides, and taking the square root of the difference.

To find the height of an isosceles triangle given three sides, you can use the Pythagorean Theorem. Begin by calculating the length of the hypotenuse (the longest side of the triangle). To do this, square the lengths of the two other sides and add them together. Then, take the square root of that sum. This is the length of the hypotenuse. Next, subtract the lengths of the other two sides from the hypotenuse and take the square root of the difference. The result is the length of the altitude, which is also the height of the triangle.

Learn more about height here

brainly.com/question/27996736

#SPJ4

Answer:218

explanation: 162 divided by 9 = 18 and 18 multiplied by 12 =218

a) The given relation is function.

b) The function is, $x = 18.5 y

c) The value of (f+ g)(9) is 5.

d) The he original amount of her loan is 6000.

A function with one or two variables and no exponents is referred to as a linear function. It is a function with a straight line as its graph.

Given:

a) The given relation is function because is input have have output, no two outputs have same input.

b) After 8 hours, a person earned $148 in wages.

So, the unit rate change = 148/ 8

                                        = 18.5

So, if y represents the number of hour and $x the wages, then the function is $x = 18.5 y.

c)  Let f(x)=x and g(x)=x-13

(f+ g)(9)

= (x+  x-13) (9)

= 2x -13

= 2(9)- 13

= 5

d) The modeled function. P(m) = 6000 - 300m.

so, the original amount of her loan is 6000.

Learn more about linear function here:

brainly.com/question/20286983

#SPJ1

Answer: 108000

Step-by-step explanation: Here's how I got my answer:

So, first, we need to know something. Whenever there's a fraction, you need to do this. I'll show you the numbers for this problem:

(60^3) / 2

So, the numerator goes in parentheses, and the denominator is what we are dividing by. So, 60^3 is the same as 60 x 60 x 60. You'd get 216000. Then, divide by 2 to get 108000. I hope this helps!

TIP: do NOT turn 3/2 into an improper fraction; 1 1/2. You would get a completely different answer.

x + 2y = 3x + 4

2y = 3x + 4 - x

y = (2x + 4)/2

y = x + 2

Answer: y=x+2

Step-by-step explanation:

you subtract x on the left on both sides then you'll have 2y=2x+4 we have to get y by itself so divide it by 2 on both side and when you do that on the right you divide both 2x and 4 by 2 thus giving y=x+2

To translate a triangle with vector (-5/2), you need to subtract 5/2 from the x-coordinate and add 2 to the y-coordinate of each vertex of the triangle. This will move the triangle 5 units to the right and 2 units up.

A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric shapes. The name given to a triangle containing the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. 180 degrees is the result of multiplying three triangle angles.

To translate a triangle with a vector, you can use the vector to adjust the coordinates of the triangle's vertices.

For example, if the triangle has vertices at (x1, y1), (x2, y2), and (x3, y3), you can translate it by the vector (-5/2) by subtracting 5/2 to the x-coordinates of the vertices. The new coordinates of the translated triangle would be (x1-5/2, y1), (x2-5/2, y2), and (x3-5/2, y3).

This will move the triangle 5/2 units to the left along the x-axis.

It is important to note that the translation vector you provided only has one component, which is -5/2. Since the vector only has x component, the translation will only occur along the x-axis and the y-coordinate of the vertices will not change.

To know more about triangle visit:

brainly.com/question/2773823

#SPJ4

Answer:

The answer is D) 5, the number of eggs on the charts never exceeds that number.

The common factors and the greatest common integer for each pair of numbers are:

               Common prime factors        Greatest common factor

30, 45        3 and 5                                     5

40, 70         2 and 5                                    5

63, 42         3 and 7                                     7

81, 54          3                                               3

33, 99         3 and 11                                    11

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

30 and 45

3 x  5 x 2 = 30

3 x 3 x 5 = 45

Common prime factors = 3 and 5

Greatest common factor = 5

40 and 70

2 x 5 x 4 = 40

2 x 7 x 5 = 70

Common prime factors = 2 and 5

Greatest common factor = 5

63 and 42

3 x 3 x 7 = 63

2 x 3 x 7 = 42

Common prime factors = 3 and 7

Greatest common factor = 7

81 and 54

3 x 3 x 3 x 3 = 81

2 x 3 x 3 x 3 = 54

Common prime factors = 3

Greatest common factor = 3

33 and 99

3 x 11 = 33

3 x 3 x 11 = 99

Common prime factors = 3 and 11

Greatest common factor = 11

Thus,

Common prime factors are given above.

The greatest common factor is given above.

Learn more about expressions here:

https://brainly.com/question/3118662

#SPJ1

Answer: 2 2/3

Step-by-step explanation:

Scrooge sees out of his window when Marley's ghost leaves as all the spirits of people whom Scrooge has not met before in his life. Thus, option B is correct.

Although ghosts are typically thought of as lone, human-like essences, and there have been reports of ghostly battalions, ghosts that resemble animals instead than people.

Here, we have,

Scrooge discovers "the air filled with phantoms" outside s windowsill after Marley's Apparition hath left it. Some of these imprisoned spirits were people Scrooge had indeed known. It resembles an incredible image of the metropolis that Scrooge has already been familiar with. Scrooge is compelled to agree.

Scrooge responds with the ghost's request to peek out just the balcony. He observes a mass of ghosts, each one imprisoned in bonds. As both they and Marley vanish into darkness, they sob at their failure to live noble, compassionate lives and their incapacity to help other people in need.

Therefore, option B is the correct option.

Learn more about ghosts, here:

brainly.com/question/11648302

#SPJ1

Answer:

Step-by-step explanation:

55 times 25, making Angel attempt 1375 free throws

Answer:

Step-by-step explanation:

The correct option for the given linear equation is option (B).

What is a linear equation?

An equation is said to be linear if the maximum power of the variable is always 1. A linear equation with two variables has the conventional form Ax + By = C. Here, the variables x and y, the coefficients A and B, and the constant C are all present.

The given equation is y =20x + 35

       y = total amount of money

       x = number of months the customer has been renting the storage unit

A) If x = 355

        y = 20 * 355 + 35 = $7135

    This is not the correct option.

B) If x = 16

      y = 20*16 + 35 = $355

     This is the correct option.

C) if x = 320

      y = 20 * 320 + 35 = $6435

      This is not the correct option.

D) If x = 16

       y = 20*16 + 35 = $355

      This is not the correct option.

Therefore the correct option for the given linear equation is option (B).

To learn more about linear equations, follow the link.

https://brainly.com/question/2030026

#SPJ1

The annual state tax withheld for Kelly Waxman would be 1,662.50 dollars.

Therefore the answer is d) $1,662.50.

Here is the breakdown of the calculation:

Kelly's salary of $30,000 minus the married exemption of $3,000 = $27,000

The first $3,500 are taxed at 3%, which is

= 0.03×3500

= $105

The next $3,500 are taxed at 4.5%, which is

= 0.045×3500

= $157.50

The remaining $27,000 - $3,500 - $3,500 = $20,000 are taxed at 7%, which is

= 0.07×20000

= $1,400

Adding all three amounts together: $105 + $157.50 + $1,400 = $1,662.50. It is the annual state tax withheld.

To know more on tax

https://brainly.com/question/10114457

#SPJ4

To write an equation for a parabola with the vertex and y-intercept, the equation of vertex form y=a(x-h)^2+k is used.

What is a parabola?

A parabola is an approximately U-shaped, mirror-symmetrical plane curve in mathematics. It corresponds to a number of seemingly unrelated mathematical descriptions, all of which can be shown to define the same curves.

Consider an example where vertex is (2,1) and y-intercept is (0,-3).

The equation of parabola needs to be deduced using these points.

The equation of a parabola in vertex form is -

y=a(x-h)^2+k

Here, a is a constant and (h ,k) are the coordinates of the vertex.

So, (h,k)=(2,1)

⇒y=a(x−2)^2+1

To obtain the value of a, substitute (0,−3) into the equation -

-3=4a+1

4a=-4

a=-1

⇒y=-1(x−2)^2+1

Now, distribute and simplify -

y=-1(x−2)^2+1

y=-(x^2-4x+4)+1

y=-x^2+4x-4+1

y=-x^2+4x-3

On, graphing this equation a parabola is obtained.

Therefore, to write an equation of parabola vertex form is used.

To learn more about parabola from the given link

https://brainly.com/question/64712

#SPJ4

Let x equal the x³-1 coefficient. Thus, x=1 is the coefficient of the given function.

Coefficient definition.

A number or symbol that multiplies another number or symbol is referred to as a "coefficient" (used as a mathematical variable).

Give a co-efficient example in writing.

A coefficient is a result of multiplying an amount by a variable. 6z, for instance, is short for six times z. 6 is a coefficient since z is a variable. The coefficient is one for variables that don't have a value.

Let x equal the x³-1 coefficient. Thus, x=1 is the coefficient of the given function.

The expression's coefficient is the term multiplied by x³. Since x³ is not a word, the answer is 1.

To learn more about co-efficient visit the link:

brainly.com/question/1038771

#SPJ4

The full question should be:

What is the coefficient form of X³ 2 *?

The area of the shaded regions is 4π + 4, which can be obtained by subtracting 2π - 4 from 3π. This is an exact value, with no further simplification required.

Step 1: Calculate the area of the entire circle.

A = πr^2

A = π(5)^2

A = 25π

Step 2: Calculate the area of the unshaded region.

A = πr^2

A = π(2)^2

A = 4π

Step 3: Subtract the area of the unshaded region from the area of the entire circle.

A = 25π - 4π

A = 21π

Step 4: Calculate the area of the shaded region.

A = 21π - (2π - 4)

A = 21π - 2π + 4

A = 19π + 4

A = 4π + 4

The area of the shaded regions can be found by subtracting the area of the unshaded region from the area of the entire circle. To find the area of the entire circle, we use the formula A = πr^2, where r is the radius of the circle. Plugging in r = 5, we get A = 25π. To find the area of the unshaded region, we use the same formula, but now with r = 2. This gives us A = 4π. Subtracting the area of the unshaded region from the area of the entire circle gives us A = 21π. We then subtract 2π - 4 from 21π to get the area of the shaded region, which is 4π + 4. This is an exact value, with no further simplification required.

Learn more about area here

https://brainly.com/question/13194650

#SPJ4

A value of 20 would fit the best in the table's empty cell to imply that there is no proof of a link between the variable and the outcome.

Option c is accurate.

The pattern between the supplied series must be found in order to determine the missing number. Verify that the series only shows increases, decreases, or both. The difference between two numbers should then be checked; this will help you discover the pattern.

To locate the missing numbers, the candidate must first identify the pattern or relationship between these numbers and then apply it.

To know more about missing number visit:-

https://brainly.com/question/12750881

#SPJ1

The vertex of V' had a preimage of V(0, 3) as V' has a dilation of 3.

Two-dimensional figures can be transformed mathematically in order to travel about a plane or coordinate system.

Dilation: The preimage is scaled up or down to create the image.

Reflection: The picture is a preimage that has been reversed.

Rotation: Around a given point, the preimage is rotated to create the final image.

Translation: The image is translated and moved a fixed amount from the preimage.

Given, On a coordinate plane, polygon S'T'U'V' has points (- 2, 4), (- 4, 1),

(- 2, - 2), and (0, 1) with a dilation rule  DO,1/3 (x, y) to [(1/3)x, (1/3)y].

Therefore, The coordinates of the vertex V had a preimage of,

3(V'), which is 3(0, 1) = (0, 3).

learn more about transformations here :

https://brainly.com/question/11709244

#SPJ1

Answer:

6.2 < x < 26.6

Step-by-step explanation:

The length of a side of a triangle is between the difference and the sum of the lengths of the other two sides.

16.4 - 10.2 = 6.2

16.4 + 10.2 = 26.6

Let x = length of third side.

6.2 < x < 26.6

On solving the provided question, we can say that vectors are -  4 miles E: <4, 0>; 4 miles SE: <2√2, -2√2>; 7 miles S: <0, -7>; 6 miles SW: <-3√2, -3√2>; 2 miles E: <2, 0>

In mathematics, a vector is a quantity with magnitude and direction but no location. Acceleration and velocity are two examples of such numbers. A thing with both magnitude and direction is called a vector. A vector can be conceptualised geometrically as a directed line segment, the length of which corresponds to the magnitude of the vector, and the direction of which is denoted by an arrow. Size and direction are two independent characteristics of a quantity or phenomena known as a vector. The phrase also describes how these numbers are represented mathematically or geometrically. In nature, vectors may be found in electromagnetic fields, weight, momentum, force, and velocity.

4 + 4 + 7 + 6 + 2 = 23 miles.

vectors are -

4 miles E: <4, 0>

4 miles SE: <2√2, -2√2>

7 miles S: <0, -7>

6 miles SW: <-3√2, -3√2>

2 miles E: <2, 0>

To know more about vector visit:

https://brainly.com/question/30202103

#SPJ4

Wilbur drove for 5 hours before Jack caught up with him.

Based on the information, the distance = (Wilbur's speed) x (time) = (Jack's speed) x (time + (time Wilbur drove))

We know that Jack's speed is 75 mph, and that he caught up with Wilbur after 2 hours. We also know that the distance covered by Jack is the same as the distance covered by Wilbur.

So we can write:

distance = (Wilbur's speed) x (time) = (Jack's speed) x (2 hours)

We are given that the Wilbur's speed is 30 mph, so we can substitute that in the above equation:

distance = 30 mph x (time) = 75 mph x 2 hours

Then we can solve for time by dividing both sides of the equation by 30:

time:

= (75 mph x 2 hours) / 30 mph

= 5 hours

Learn more about distance on:

https://brainly.com/question/26046491

#SPJ1

On solving the provided question, we cans ay that - the value of the each unit in this time will be from unitary method is 85.

The unit technique is an approach to problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value. The unit method, to put it simply, is used to extract a single unit value from a supplied multiple. For instance, 40 pens would cost 400 rupees, or the price of one pen. The process for doing this may be standardized. a single country. anything that has an identity element. (mathematics, algebra) (Linear algebra, mathematical analysis, mathematics of matrices or operators) Its adjoint and reciprocal are equivalent.

here,

value of the 20 unit is 1700

value of the each unit will be 1700/20 = 85

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1

The expected mass of the sample in the year of 2021 is given as follows:

9 mg.

An exponential function is defined as follows:

y = a(b)^x.

For which the parameters are given as follows:

The initial mass was of 130 mg, hence the parameter a is given as follows:

a = 130.

In two years, the mass decayed to 80 grams, hence the parameter b can be obtained as follows:

b² = 80/130

b = square root(80/130)

b = 0.78446454055.

This means that the exponential function for the mass of the sample in x years after 2010 is given as follows:

y = 130(0.78446454055)^x.

2021 is 11 years after 2010, hence the expected mass is obtained as follows:

y = 130(0.78446454055)^11

y = 9 mg.

More can be learned about exponential functions at https://brainly.com/question/25537936

#SPJ1

Different types of algorithms are:

As a very general approach to problem solving and an algorithmic paradigm, brute-force search or exhaustive search—also referred to as generate and test—involves iteratively listing all potential candidates for the solution and determining whether each one satisfies the problem's statement.

A brute-force algorithm would count all integers from 1 to n and determine whether each one divides n without a remainder in order to find the divisors of a natural number n.

For the eight queens puzzle, a brute force method would look at all possible configurations of 8 pieces on the 64-square chessboard and determine whether each queen piece could engage in mutually exclusive attacks for each configuration.

Learn more about Brute Force algorithm

https://brainly.com/question/20115984

#SPJ4

Sally can solve minimum of 35 calculus problem and maximum of 50 calculus problem.

Calculus is a branch of mathematics that focuses on rates of change, to put it simply. For instance, you might want to determine how quickly a car will slow down as it approaches a stop sign. Calculus can assist you in calculating that change. Calculus introduces movement into math, that's correct!

Calculus is useful in many different fields, including engineering, medicine, biological research, economics, architecture, space science, electronics, statistics, and pharmacology.

minimum = 35

maximum=50

To know more about calculus visit:-

brainly.com/question/6581270

#SPJ4

Answer:

<1=75°[corresponding angles are equal]

<2=180-<1=(180-75)°=105°[sum of st.angles is supplementary]

<3=<2=105°[Vertically opposite angles are equal]

<4=75°[Alternate angles are equal]

<6=<2=105°[Corresponding angles are equal]

<7=<6=105°[Vertically opposite angles are equal]

<8=75°[Vertically opposite angles are equal]

*mark me brainliest

The measure of angle TQW from the given figure is 25°.

A perpendicular is a straight line that makes an angle of 90° with another line. 90° is also called a right angle and is marked by a little square between two perpendicular lines as shown in the figure. Here, the two lines intersect at a right angle, and hence, are said to be perpendicular to each other.

Given that, QT⊥PQR at Q, QW⊥QS at Q, and m∠SQP=25°.

From the given figure, m∠SQP+m∠SQT=90° -------(I)

m∠TQW+m∠SQT=90° -------(II)

Here, equation (I)=(II), we get

m∠SQP+m∠SQT=m∠TQW+m∠SQT

m∠SQP=m∠TQW

25°=m∠TQW

Therefore, the measure of angle TQW from the given figure is 25°.

To learn more about the perpendicular lines visit:

https://brainly.com/question/18271653.

#SPJ1

The third term of the arithmetic sequence will be negative 14.

A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.

Let a₁ be the first term and d be a common difference.

Then the nth term of the arithmetic sequence is given as,

aₙ = a₁ + (n - 1)d

The first term is 20 and the common difference is calculated as,

aₙ = aₙ₋₁ - 17

aₙ - aₙ₋₁ = - 17

d = - 17

Then the third term is calculated as,

a₃ = 20 + (3 - 1) (-17)

a₃ = 20 + 2 (-17)

a₃ = 20 - 34

a₃ = - 14

The third term of the arithmetic sequence will be negative 14.

More about the arithmetic sequence link is given below.

https://brainly.com/question/12373434

#SPJ1

Answer: Trapezoid

Step-by-step explanation:

Answer:

Step-by-step explanation:

Trapezoid square and the down right all the way