Explain please .................

The distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.

Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.

We have:

A boat is heading towards a lighthouse, where Mason is watching from a vertical distance of 122 feet above the water. Mason measures an angle of depression to the boat at point A to be 16°.

We can draw the above situation as a form of a right-angle triangle.

From the figure, the distance between AB is x ft

From the right angle triangle DBC:

tan66 = 122/CB

CB = 54.31 ft

From the right angle triangle DAC

tan16 = 122/AC

AC = 425.46 ft

x = AC - CB

x = 425.46 - 54.31

x = 371.15 ft ≈ 371 ft

Thus, the distance between point A and point B is 371 ft if the Mason measures an angle of depression to the boat at point A to be 16°.

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Answer:

p = 39       f = 44    

Step-by-step explanation:

p = $ 1.73

f = $ 1.44

equation

p + f = 83

1.73 p + 1.44 (83 - p) = $ 130.83

p = 39 (amount of times fruit pies were sold).

Therefore,

p = 39

f = 44

Answer:

the interest for 100 in 5 years us 12.5

Answer:

0.00790625

Step-by-step explanation:

499.9997656975

Astronomical unit

=

0.00790625

Light-year

Formula

for an approximate result, divide the length value by 63240

Answer:

Human coastal development has also helped jellyfish thrive. The structures and construction that we have placed in the water, such as piers, marinas, oil platforms, artificial reefs, refuse, rubble, aquaculture pens and structures, etc. provide an abundance of habitats for polyps to settle on.

The rules describes the transformation is (x, y)(x, y).

The correct option is (B)

A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure.

If the figure is rotated 360 degrees then the coordinates remains unchanged.

This is because when from where it started it stops there again.

As the 360 degree rotation is complete circle rotation.

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The equation that shows the relationship between the variables are T = 0.112N, D = 54A and T = 62.5A

An equation is an expression that shows the relationship between two or more numbers and variables.

Let k represent the constant of proportionality

3) T = kN

28 = 250k

k = 0.112

i) T = 0.112N

ii) T = 0.112(300) = 33.6

iii) 98 = 0.0112N

N = 875

4) D = kA

270 = 5k

k = 54

i) D = 54A

ii) D = 54(4.5) = 243

iii) 324 = 54A

A = 6

5) T = kA

150 = 2.4k

k = 62.5

i) T = 62.5A

ii) T = 62.5(1.8) = 112.5

iii) 3(60) = 62.5A

A = 2.88

The equation that shows the relationship between the variables are T = 0.112N, D = 54A and T = 62.5A

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Considering the slope of the lines, it is found that the lines going through the points are neither parallel nor perpendicular.

The slope, given by change in y divided by change in x, determines if the lines are parallel, perpendicular, or neither, as follows:

In this problem, the slopes are given as follows:

The multiplication is of 1, not -1, hence they are neither parallel nor perpendicular.

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Peter's gross pay will be 1820.9.He put in 32 hours of work two weeks ago, and the tip money came to $1587.30.

Before taxes, benefits, and other payroll deductions are taken out of an employee's paycheck, that amount is known as their gross pay.

Given data;

Peter earn per hour = 7.30

Gratuities = 7 %

Given condition;

No of hour person work = 32

Gratitutes = 1587.30

Let the gross pay will be x;

x = gratuities + no of hoy\ur work × money earned per hour;

x =  1587.30 + 32 × 7.30

x = 1820.9

Hence,Peter's gross pay will be 1820.9.

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The standards that use 2.4 GHz are:

A wifi standard defines two characteristics of the wi-fi network, which are speed and frequency.

Such that there are two common frequencies, 2.4 GHz (usually with larger speed) and 5 GHz (usually with lower speed)

The standards that use 2.4 GHz are:

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Answer:

3x^2+ 13x + 12

Step-by-step explanation:

Multiply the length and width:
(3x+4) * (x+3)
FOIL method:
3x^2 + 9x + 4x + 12
Combine like terms
3x^2+ 13x + 12

Assuming that both lines are parallel, we conclude that C = 74°.

Here we can see that both of the lines that go upwards are parallel lines. This means that C and the 74° angles are opposite angles.

Then if we say that x is the angle at the right of the 74°, we must have that:

x + 74° = 180°

x = 180° - 74° = 106°

And we also must have that:

x + C = 106° + C = 180°

Solving for C:

C = 180° - 106° = 74°

C = 74°.

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Answer:

sorry i dont know the answer .

The school store is in $42 loss , Option B is the correct answer.

When the sales is more than the expenses then it is called profit and vice versa is called Loss.

The sales and expenses for three months are given

To calculate overall Profit/Loss

Total Expenses = $125 + $0 +$ 57 = $182

Total Sales = $47 +$65 + $28 = $140

Therefore as sales is less than the expense , The school is in loss

Loss = $ 182 -$ 140 = $42

Thus Option B is the correct answer.

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Answer:

  2

Step-by-step explanation:

Corresponding sides are proportional in these similar triangles.

__

  short side/long side = k/4 = 4/8

  k = 4(4/8) . . . . multiply by 4

  k = 2

_____

Additional comment

The lengths of the hypotenuses can be found the same way, or using the Pythagorean theorem. Using side ratios, we have ...

  l² = k(k+8) = 2(10) = 20 . . . . from MN/MO = ML/MN

  l = 2√5

  m² = 8(8+2) = 80 . . . . from LN/LO = LM/LN

  m = 4√5

The similarity statements are ...

  ΔLMN ~ ΔLNO ~ ΔNMO

The measure of angle x will be 88 degrees. Then the correct option is C.

The complete question is attached below.

Let there is a triangle ABC such that |AB| = a units, |AC| = b units, and |BC| = c units and the internal angle A is of θ degrees, then we have:

2ab cos θ = a² + b² – c²

The triangle is shown below.

Then the value of the variable x will be

2 · 7 · 10 · cos x = 7² + 10² – 12²

       140 · cos x = 49 + 100 – 144

                cos x = (149 – 144) / 140

                       x = 87.95 ≈ 88°

Then the correct option is C.

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The statements that are true about circle Q are:

The measure of the central angle is 45°.  The measure of the entire circle is 360°.  This makes the ratio of the central angle to the entire circle 45/360 = 9/72 = 1/8

To find the area of the shaded sector, this will be:

A = πr² = π(6²) = 36π

1/8(36π) = 36π/8 = 18π/4 = 9π/2 = 4.5π square units.  This is not 4 square units.

The ratio of the area of the shaded sector to the area of the circle would not be the same as the ratio of the length of the arc to the area of the circle.

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Answer:

1,3,4

Step-by-step explanation:

The area of the trapezoid is calculated as 45.5 feet squared.

What does Area of Trapezoid mean?

The entire area occupied by the sides of a trapezoid is its area. It's important to notice that if we know the lengths of all the sides, we can divide the trapezoid into smaller polygons, such as triangles and rectangles, calculate their areas, and then sum them all together to determine the area of the trapezoid.

If the parallel sides of the trapezoid are known, along with their height, it is possible to determine their area. It is expressed as,

A=[tex]1/2[/tex](a+b) h

where, A= the area of the trapezoid

h= height

'a' & 'b' = parallel side bases

a=5.5 feet , b= 8.5 feet & h=6.5 feet

A=[tex]1/2[/tex](a+b)h

∴A=[tex]1/2[/tex](5.5+8.5)*6.5

⇒A=[tex]1/2[/tex](14)*6.5

⇒A=7*6.5

⇒A=45.5 feet squared

Therefore, the solution is  (b) 45.5 feet squared.

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Answer:

The answer would be 125, because 1*1 = 1 2*2*2= 8 and so forth

Step-by-step explanation:

I hope this helps

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{Your equation:}[/tex]

[tex]\mathsf{1, 8, 27, 64, ?}[/tex]

[tex]\huge\textbf{LET'S CONVERT IT TO FOR EASIER}\\\\\huge\textbf{TO UNDERSTAND A WHOLE LOT}\\\\\huge\textbf{BETTER.}[/tex]

[tex]\mathsf{1^3, 2^3, 3^3, 4^3, ?}[/tex]

[tex]\huge\textbf{Notice the pattern?}\\\\\\\\\huge\textbf{So, that means your mystery number}\\\\\huge\textbf{has to be squared (also known as to the}\\\\\huge\textbf{power of 3}[/tex]

[tex]\huge\textbf{Breaking down the exponents}[/tex]

[tex]\mathsf{1^3}\\\mathsf{= 1\times1\times1}\\\mathsf{= 1\times1}\\\mathsf{= \bf 1}[/tex]

[tex]\mathsf{2^3}\\\mathsf{= 2\times2\times2}\\\mathsf{= 4\times2}\\\mathsf{= \bf 8}[/tex]

[tex]\mathsf{3^3}\\\mathsf{= 3\times3\times3}\\\mathsf{= 9\times3}\\\mathsf{= \bf 27}[/tex]

[tex]\mathsf{4^3}\\\mathsf{= 4\times4\times4}\\\mathsf{= 16\times4}\\\mathsf{= \bf 64}[/tex]

[tex]\huge\textbf{If you didn't notice that your}\\\\\huge\textbf{exponents went like 1,2,3,4.}\\\\\\\\\huge\textbf{so that your mystery number has to}\\\\\huge\textbf{be 5 squared}[/tex]

[tex]\mathsf{5^3}\\\\\huge\textbf{That is what I meant \& this should give}\\\\\huge\textbf{you your result to this question.}[/tex]

[tex]\mathsf{5^3}\\\mathsf{= 5\times5\times5}\\\mathsf{= 25\times5}\\\mathsf{=125}[/tex]

[tex]\huge\textbf{The result:}[/tex]

[tex]\huge\boxed{\mathsf{Option\ B. \ 125}}\huge\checkmark[/tex]

[tex]\huge\textbf{The outro}[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

[tex]\huge\textbf{Signature}[/tex]

Answer:

[tex]\sf \dfrac{11}{20} \quad or \quad 0.55[/tex]

Explanation:

[tex]\rightarrow \sf \dfrac{3}{4} - \dfrac{1}{5}[/tex]

make the denominators same by lcm

[tex]\rightarrow \sf \dfrac{5(3)}{20} - \dfrac{4(1)}{20}[/tex]

expand the following

[tex]\rightarrow \sf \dfrac{15}{20} - \dfrac{4}{20}[/tex]

Join the fractions together

[tex]\rightarrow \sf \dfrac{15-4}{20}[/tex]

Subtract the integers

[tex]\rightarrow \sf \dfrac{11}{20} \quad or \quad 0.55[/tex]

Answer:

11/20 or 0 whole 11/20 or 0.55

Step-by-step explanation:

Find the least common multiple (LCM) of 4 and 5 at first:

We can't do the LCM of 5 and 4,so just multiply them, 5*4 = 20

Now,

For 3/4 : divide 20 by 4,then multiply the result by 3.For 1/5 : divide 20 by 4, then multiply the result by 1. Simple!

Subtracting the numerators,

As a whole number:

As a decimal:

The parabola with the minimum at (4, -3) is the third option:

[tex]y = 0.5*x^2 - 4x + 5[/tex]

Remember that for a parabola of the form:

[tex]y = a*x^2 + b*x + c[/tex]

If a > 0, the minimum is at the x-value of the vertex:

[tex]x = \frac{-b}{2a}[/tex]

If a < 0, there is no minimum (so we discard option 2).

Taking the third option:

[tex]y = 0.5*x^2 - 4x + 5[/tex]

The x-value of the vertex is:

[tex]x = \frac{-(-4)}{2*0.5} = 4[/tex]

As expected.

To get the y-value of the vertex (and minimum) we just evaluate the parabola equation in x = 4.

[tex]y = 0.5*(4)^2 - 4*4 + 5 = -3[/tex]

So the minimum is at (4, -3), as expected, so that is the correct option.

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Answer:

consistent and dependent

consistent and independent

Step-by-step explanation:

If a system of equations has no solutions, it is said to be inconsistent.

If a system of equations has at least one solution, it is said to be consistent.

If there is just one solution to a system of equations, it is said to be independent.

If a system of equations has an unlimited number of solutions, it is dependent.

A 3 x 3 system of equations is a three-variable system of equations. That is correct (x, y, z)

A three-by-three-equation system might be dependent, independent, or inconsistent.

A 3 x 3 system of equations can be written as follows:

consistent and self-sufficient (This indicates that there is just one answer.)

Dependable and consistent (It has infinite solutions)

If it is inconsistent, it can neither be dependent nor independent

Answer:

1. 570 mL = 0.57 L

2. 623 cm3 = 0.000623 m3

3. 38 gal. = 608 cups

4. 585mL = 39.5624 tbsp

5. 20 fl. oz. = 120 tsp

6. 12 hrs = 720 min

Step-by-step explanation:

1. 570 mL to L

divide the volume value by 1000, 570 / 1000 = 0.57

2. 623 cm3 to m3

divide the volume value by 623/10^6 = 0.000623

3. 38 gal. to c

1 gallon is 16 cups,  

multiply the volume value by 16, 38 x 16 = 608c

4. 585mL to tbsp

for an approximate result, divide the volume value by 14.787

14.787 x 585 = 39.5624

5. 20 fl. oz. to tsp

multiply the volume value by 6, 20 x 6 = 120

6. 12 hrs to min

1 hour is 60 minutes

multiply the time value by 60

12 x 60 = 720

The rate of interest of the instalment is 13%

The part payment of a loan is called Instalment

It is given that

The Cash price is $540

Instalment of $42

Time = 15 month = 15/12 = 1.25 years

Total Amount paid = 42 * 15 =$630

Interest Paid is $90

90 = 540 * 1.25 *Rate

Rate = 13%

The rate of interest of the instalment is 13%

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Regarding the proportional connection that Peter's equation simulates, claim C is accurate. Peter moves along at a 13/4 mph walking pace.

An equation is a mathematical statement that uses an equal sign to join two algebraic expressions having the same value.

The complete question is

"Peter uses the equation Y=13/4x to model the number of miles that he has walked in x hours. Which statement is true about the proportional relationship that is modeled by the peat there's the equation?

A:Peter walks a rate of 4/13 miles per hour.

B: Peter walks at a  rate of 4 miles per hour.

C: Peter walks at a rate of 13/4 miles per hour.

D: Peter walks at a rate of 13 miles per hour."

Provided equation

Y=13/4x

where y is the distance traveled and x denotes the amount of time.

According to the equation, Peter moves along at a speed of 13/4 miles per hour.

As a result, the proportional connection represented by Peter's equation is valid as stated in assertion C.

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Answer:

1/7 + r = 1/3

Step-by-step explanation:

Rocco takes 7 hours to do the job.
In 1 hour, Rocco does 1/7 of the job.

Rocco's rate is 1/7 job per hour.

It takes Giulia x hours to do the job.

In 1 hour, Giulia does 1/x of the job.

Let r = 1/x. Giulia's rate is r part of the job per hour.

Together, Rocco and Giulia take 3 hours to do the job.

In 1 hour, Rocco and Giulia do 1/3 of the job.

Together, their rate is 1/3 of the job per hour.

1/7 + r = 1/3

Step-by-step explanation:

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The range and domain of the graphs have been determined .

Domain is the value that can be an input to the function and the range is all the value a function can obtain.

From the given graphs ,

For Graph 1

It can be seen that the line extends from x = -5 to +4

where -5 is not included

therefore the domain is given by

D = { x| -5 < x ≤4}

and the range is

R = {y | -3 < y≤4}

For Graph 2

The input value x extends from -∞ to +∞

so the domain is

D = { x| - ∞ ≤ x ≤ +∞ }

and the range is given by

R = {y | - ∞ ≤ y ≤ 3}

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