Please help and please explain this question step by step

The length of the guy wire to the nearest foot would be = 10 ft.

The relationship between the tower, guy wire and pole forms the shape of a right angle triangle.

The distance from the stake to the pole (opposite) =a = 5 ft

The distance from the pole to the tower (adjacent) =b= 9ft

The length of the guy wire= c = X

Using the Pythagorean formula:

c² = a² + b²

c² = 5² + 9²

c² = 25+81

c² = 106

C = √106

C= 10 ft ( to the nearest foot)

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Complete question:

A guy wire runs from the top of a cell tower to a metal stake in the ground. Sophie places a 7 ft tall pole to support the guy wire. After placing the pole, Sophie measures the distance from the stake to the pole to be 5 ft. She then measures the distance from the pole to the tower to be 9 ft. Find the length of the guy wire, to the nearest foot.

Answer:

\(\textsf{B)} \quad f(x) = 5 \sin (16x) + 7}\)

Step-by-step explanation:

The sine function is periodic, meaning it repeats forever.

\(\boxed{f(x) = A \sin (B(x + C)) + D}\)

where:

Given values:

Calculate the value of B:

\(\dfrac{2\pi}{B}=\dfrac{\pi}{8}\implies 16\pi=B\pi\implies B=16\)

Substitute the values of A, B C and D into the standard formula:

\(f(x) = 5 \sin (16(x + 0)) + 7\)

\(f(x) = 5 \sin (16x) + 7\)

Therefore, the sine function with an amplitude of 5, a period of π/8, and a midline at y = 7 is:

\(\Large\boxed{\boxed{f(x) = 5 \sin (16x) + 7}}\)

After the transformation point A will be at (5, 6.586), point B will be at (5.121, 7.121) and point C will be at (6.121, 5.121).

The coordinates of a triangle after rotation and translation can be found using the following steps:

       x' = (x - a) * cos(θ) - (y - b) * sin(θ) + a

       y' = (x - a) * sin(θ) + (y - b) * cos(θ) + b

        x' = x + dx

        y' = y + dy

       x' = (1 - 2) * cos(45) - (3 - 4) * sin(45) + 2 = -1.121 + 1.121 + 2 = 2.000

       y' = (1 - 2) * sin(45) + (3 - 4) * cos(45) + 4 = -0.707 - 0.707 + 4 = 2.586

      x' = 2 + 3 = 5

      y' = 2.586 + 4 = 6.586

     similarly for point B(2,5) will be (5.121,7.121)

     and for point C(3,3) will be (6.121,5.121)

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Answer:

\(FG = 7\)

Step-by-step explanation:

Given

\(EG = 5x + 7\)

\(EF = 5x\)

\(FG = 2x - 7\)

Required

Determine the length of FG

Since, F is on segment EG, then

\(EG= EF + FG\)

Substitute values for EG, EF and FG

\(5x + 7 = 5x + 2x - 7\)

Collect Like Terms

\(5x - 5x - 2x = -7 - 7\)

\(- 2x = -14\)

Solve for x

\(x = -14/-2\)

\(x = 7\)

Substitute 7 for x in \(FG = 2x - 7\)

\(FG = 2 * 7- 7\)

\(FG = 14- 7\)

\(FG = 7\)

Answer:

Step-by-step explanation:

P(BA)=P(B)+P(A)-P(AnB)

= 0.51+0.8-0.468

=1.31-0.468

=0.842

P(BA) = 0.842

Answer:

60 km

Step-by-step explanation:

the line is constant around 3

Answer:

they filter the air coming into the body

The probability of drawing a marble that is green or even-numbered is  28/35

The total number of marbles in the jar is 35, of which 10 are blue, 12 are green, and 13 are red.

We need to find the probability of drawing a marble that is green or an even number.

First, let's find the number of even-numbered marbles.

Out of 35 marbles, 17 of them are even-numbered (2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34).

There are 12 green marbles, and 17 even-numbered marbles,

Therefore, there are 12 + 17 - 1 = 28 marbles that are either green or even-numbered.

The probability of drawing a marble that is green or even-numbered is

28/35

So the probability of drawing a marble that is green or even-numbered is  28/35

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a) The value of x is 21

b) The value of the expression is 135.

c) The value of the expression is 135.

Here we know that the lines G and M are parallel, meaning that the two shown angles are alternarte exterior angles, and thus, have the same measure, then we can write:

5*(x + 6) = 9*(x - 6)

We can solve that linear equation for x:

5x + 30 = 9x - 54

30 + 54 = 9x - 5x

84 = 4x

84/4 = x

21 = x

Then the measures of the angles are:

a1 = 5*(21 + 6) = 135°

a2 = 9*(21 - 6) = 135°

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Answer:

The sum of the interior angle measures of a regular hexagon is 720°.

Step-by-step explanation:

To find the sum of the interior angle measures of a regular hexagon, we can use the fact that any polygon can be divided into triangles. The formula to find the sum of the interior angles of any polygon with n sides is:

Sum of interior angles = (n - 2) × 180°

In the case of a hexagon, n = 6. So, we can plug this value into the formula:

Sum of interior angles = (6 - 2) × 180° = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

To explain this using triangles, let's divide the hexagon into triangles. A hexagon can be divided into four triangles by drawing three diagonals from one vertex to the three non-adjacent vertices. Since the sum of the interior angles of each triangle is 180°, and we have four triangles:

Sum of interior angles of hexagon = 4 × 180° = 720°

The sum of the interior angle measures of a regular hexagon is 720°.

Answer:

I don't understand this question, try rephrasing

The sale price of coat is $180 and the sale price of boot is $284 when 20% off a coat and a pair of boots are now  on sale.

Given that,

20% off a coat and a pair of boots are now  on sale. The coat normally sells for $225. The boots cost $130 on the open market.

We have to find the coat's sale price and what is the cost of the boots on sale.
We know that,

The formula for the sales price is S = P - PD

Where, S is sales price, P is the original price and D is the discount percent.

P = 225 and D = 20%

S = 225 - 225 × 20%

S = 225 - 45

S = $180 is the sale price of coat.

Now,

Total regular price = 225 + 130 = 355

S = 355 - 355 × 20%

S = $284 is the sale price of boots.

Therefore, The sale price of coat is $180 and the sale price of boot is $284.

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The required derivative of the given function g(z) = ln√(16- z² / 16+z²) is

\(g'(z) =-\dfrac{32z}{\left(z^2+16\right)\left(-z^2+16\right)}\)

The outside-inside rule, the composite function rule, and the function of a function rule are all synonyms for this chain rule in differentiation. It is exclusively used to calculate the derivatives of composite functions.

The chain rule formula as shown below

d/dx ( f(g(x) ) = f' (g(x)) · g' (x)

The function is given in the question

g(z) = ln√(16- z² / 16+z²)

We have to differentiate g(z) = ln√(16- z² / 16+z²)

Differentiation with respect to z in the given function,

\(\frac{d}{dz}\left(\ln \left(\sqrt{\left(\left(\frac{16-z^2}{16+z^2}\right)\right)}\right)\right)\)

We have to apply the chain rule of differentiation for finding derivatives,

\(\dfrac{1}{\sqrt{\dfrac{16-z^2}{16+z^2}}}\dfrac{d}{dz}\left(\sqrt{\dfrac{16-z^2}{16+z^2}}\right)\)

\(-\dfrac{32z}{\left(z^2+16\right)\left(-z^2+16\right)}\)

Therefore, the required derivative of the given function g(z) = ln√(16- z² / 16+z²) is

\(g'(z) =-\dfrac{32z}{\left(z^2+16\right)\left(-z^2+16\right)}\)

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Answer:

a. \(\frac{8}{9}\) b. 216

Step-by-step explanation:

Answer:

Team A: 0

Team B: 0.3889

Team C: 0.5

Team D: 0.1111

Step-by-step explanation:

The relative frequency is given by:

The division of the number of people in an interval by the total number of people.

In this question:

18 track members.

None ran between 0 and 4.9 seconds. So the frequency of Team A is 0/18 = 0

7 ran between 5 and 9.9 seconds. So the frequency of Team B is 7/18 = 0.3889

9 ran between 10 and 14.9 seconds. So the frequency of Team C is 9/18 = 0.5

2 ran between 15 and 19.2 seconds. So the frequency of Team D is 2/18 = 0.1111

Answer: combine like terms and you get −2x

Step-by-step explanation:

\(\rm\red{\overbrace{\underbrace{\tt\color{gold}{\:\:\:\:\:\:\:\:Answer:\:\:\:\:\:\:\:\:\:}}}}\)

\( - 2x\)

\(\huge\color{gold}{\boxed{{\colorbox{black}{ChaEunWoo2009}}}}\)

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The answer is - 17

here, we have to apply BODMAS rule

given ,- 22 + (10) = 15

            = - 22 - 10 + 15

           = -32 + 15

           = - 17

BODMAS is an acronym for the sequence of operations to be performed while simplifying the mathematical expressions.

B=Brackets

O=Off

D=Division

M=Multiplication

A=Addition

S=Subtraction

The four basic Mathematical rules are addition, subtraction, multiplication, and division.

Basic math skills are those that involve making calculations of amounts, sizes or other measurements. Core concepts like addition, subtraction, multiplication and division provide a foundation for learning and using more advanced math concepts.

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Step-by-step explanation:

The attachment above is a table summarizing everything.

so the answer should be - 0.5

Answer: 35

Step-by-step explanation: i first divided 12 and 125 since there is 125 cards in total and 12 different cards which gives you 10 point something. There is 3 multiples of 4 so i multiplied 3x10 which gives you 30 and the closest answer is 35. You're welcome

Answer:

35

Step-by-step explanation:

got it right

Answer:

Step-by-step explanation:

Use SAS congruency; AD=DC, and they both share side BD. Also, BD is the perpendicular bisector to AC, so it also forms 2 right angles. Proof using SAS.

Or, if you don’t know SAS congruency, you may use SSS congruency;

Use the Pythagorean theorem. Side length AB^2 = AD^2 + BD^2
BC^2 = DC^2 + BD^2.

AD=DC, so therefore AB = BC. Use SSS congruency, and there you go.

A plane is an undefined term of geometry.

The statement that explains the difference is (c) A plane does not have a formal definition, and a ray is described through undefined terms.

In geometry, a plane do not have a particular definition.

The definition of a plane is depedent on the example or concept that is being describe.

A ray on the other hand is defined as a function of the undefined terms of geometry.

Hence, the statement that explains the difference between a plane and a ray is (c)

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Answer:

15

Step-by-step explanation:

When you see something like f (18), this means 18 needs to be plugged in for x

let's plug in 18

f (18) = \(\frac{2}{3} (18) + 3\)

Let's solve

(18 × 2) ÷ 3 = 12

12 + 3 = 15

f (18) = 15

An equation for the total cars and trucks for dealership A is: x + y = 164.

An equation for the total cars and trucks for dealership B is: 2x + 0.5y = 229.

The number of cars that dealership A sold is: 98 cars.

The number of trucks that dealership B sold is: 66 trucks.

In order to write a system of linear equations to describe this situation, we would assign variables to the number of cars sold and number of trucks sold, and then translate the word problem into an algebraic equation as follows:

Since the first dealership sold a total of 164 cars and trucks, a linear equation to model this situation is given by;

x + y = 164.

Additionally, the second dealership sold twice as many cars and half as many trucks as the first dealership, with a total of 229 cars and trucks;

2x + 0.5y = 229.

By solving the systems of linear equations simultaneously, we have:

2x + 0.5(164 - x) = 229

1.5x + 82 = 229

x = 98 cars.

For the y-value, we have;

2(98) + 0.5y = 229

0.5y = 229 - 196

y = 33/0.5

y = 66 trucks.

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Answer and Step-by-step explanation:

To find out how many more yards of red fabric Reuben used, we need to subtract the amount of yellow fabric from the amount of red fabric. Since the two fractions have different denominators, we need to find a common denominator before subtracting them. The least common multiple of 8 and 4 is 8, so we can rewrite both fractions with a denominator of 8:

7/8 - 1/4 = 7/8 - (1/4) * (2/2) = 7/8 - 2/8 = (7 - 2)/8 = 5/8

So, Reuben used 5/8 yards more red fabric than yellow fabric.

Answer:

0.920

Step-by-step explanation:

To calculate this, we proceed to the t-table

Using degree of freedom 5 and significance level of 0.2, the t-value is 0.920

If you can buy 1 bunch of seedless green grapes for $2, then $18 we can buy 9 bunches.

The concept used here is a simple division to find out how many bunches of seedless green grapes can be purchased with a given amount of money.

In this case, we know the cost of one bunch of seedless green-grapes ($2) and we are given a total amount of money ($18) that we can spend on grapes. We can use division to find out how many bunches we can buy with that amount.

⇒ Number of bunches = ($18)/($2) per bunch,

⇒ Number of bunches = 9 bunches;

Therefore, with $18, you can buy 9 bunches of seedless green grapes.

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Answer: b = 11.62

Step-by-step explanation:

We can use this formula to solve for b:

\(b^{2} =\) \(\sqrt{c^{2}-a^{2} }\)

\(b^{2} =\) \(\sqrt{12^{2}-3^2 }\)

\(b^2= \sqrt{144-9}\)

= 11.61895004

We can round that to 11.62.

Hope this helped!