A person is watching a boat from the top of a lighthouse. The boat is approaching the lighthouse directly. When first noticed, the angle of depression to the boat is 14°52'. When the boat stops, the angle of depression is 45°10'. The lighthouse is 200 feet tall. How far did the boat travel from when it was first noticed until it stopped? Round your answer to the hundredths place.

Step-by-step explanation:

area of shaded area = area of larger circle - area of smaller circle

a = pi * (r+7)^2 - pi * r^2

a = pi * r^2 + 14pi*r + 49* pi - pi * r^2

pi r^2 cancels

a = 14*pi*r + 49 *pi

a = 7pi(2r + 7)

Answer:

14πr + 49π

Step-by-step explanation:

Logically, to find the area of the border of a circle, we need to find both the area of the inner circle [not including border] and the area of the outer circle [including border]

Once we have found these two areas,  we find the difference (difference meaning subtraction) between the two values.

We know that the area of a circle = πr²

We can use this formula to find the area of both circles.

Inner circle:

πr²

(cannot be simplified further)

Outer circle:

π(r + 7)²

(r + 7)² = (r + 7)(r + 7) = r² + 7r +7r +49 {FOIL method}

  outer       -   inner

π(r² + 14r + 49) - πr²

π (r² +14r +49)= πr² + 14πr + 49π

πr² + 14πr + 49π - πr²

πr² - πr² = 0

So, the area of our border is: 14πr + 49π

hope this helps!!

(also, you don't have to, but marking brainliest gives you some of your points back anyway)

Answer:

5/6

Step-by-step explanation:

cuz there's 6 sides and there are 5 more sides than the 1

The correct answer is :  [tex]\frac{5}{6}[/tex]

Step-by-step explanation:

a die has 6 sides.

each side has a number 1-6

The chance of it rolling a number greater than one is 5 chances per 6 options or 5/6

A function assigns the values. The inverse of the function is y = (x+5)/2.

A function assigns the value of each element of one set to the other specific element of another set.

To find the inverse of the function, the function is needed to be solved for x, and then replace x with y and vice versa. Therefore, the inverse of the function will be,

f(x) = y = 2x - 5

y = 2x - 5

y + 5 = 2x

x = (y+5)/2

y = (x+5)/2

Hence, the inverse of the function is y = (x+5)/2.

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Answer:

49(17 + 3)

Step-by-step explanation:

The Distributive Law says [tex]a(b+c)=ab+ac[/tex].  But it can be used in the other direction,  [tex]ab+ac=a(b+c)[/tex].  That way, you look at ab and ac to find the common factor a.  What's playing the role of  a  in the expression 49 x 17 + 49 x 3?  It's 49, the factor that shows up twice.  That's the factor that can be taken outside the parentheses.

49 x 17 + 49 x 3 = 49(17 + 3)

Answer:

Step-by-step explanation:

Ratio and proportion:

   [tex]\sf \dfrac{x}{3}=\dfrac{6}{9}\\\\ x = \dfrac{6*3}{9}\\\\x = 2[/tex]

[tex]\sf \dfrac{8}{y}=\dfrac{6}{9}\\\\Cross \ multiply,\\\\y*6=9*8\\\\y=\dfrac{9*8}{6}\\\\y=3*4\\\\\bf y = 12[/tex]

[tex]\sf \dfrac{a}{15}=\dfrac{6}{9}\\\\a =\dfrac{6}{9}*15\\\\a=2*5\\\\\bf a = 10[/tex]

Answer:

the answer would be 23/13 - 15/13i

Step-by-step explanation:

The result of the complex expression (10 – 4i) ÷ (5 + i) is [tex]\frac{23}{13} - i\frac{15}{13}[/tex] .

Given, complex expression  (10 – 4i) ÷ (5 + i)

Complex roots: When the roots are complex in nature then they appear in complex conjugate pair.

Complex roots: a ± ib

Complex number pair : a ± ib

i = iota(imaginary number)

a = real part

b = imaginary part

Value of iota :

[tex]i = \sqrt{-1}\\ i^2 = -1[/tex]

Complex expression :  (10 – 4i) ÷ (5 + i)

Apply rationalization,

Use formula [tex](a^2 - b^2) = (a+b)(a-b)[/tex].

[tex]\frac{ (10 - 4i) }{(5 + i)} \times \frac{5-i}{5-i} \\\\= \frac{(10 - 4i) \times (5-i) }{(5+i)(5-i)} \\\\=\frac{50 -30i -4}{5^2 - i^2}\\ \\= \frac{46 - 30i}{25 +1 } \\\\= \frac{46 - 30i}{26} \\\\[/tex]

[tex]= \frac{23}{13} - i\frac{15}{13}[/tex]

The real part is positive and imaginary part is negative.

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Answer:

julie

Step-by-step explanation:

12 x 4 +=48

19x 6 = 114

The values of x that would result in the given expression being equal to 0 is -2, 6

Given the following expression

f(x) = (x-6)(x+2)

If the function f(x) = 0, then;

(x-6)(x+2) = 0
x - 6 = 0 and x + 2 = 0

Determine the value of  x

x = 6 and x = -2

Hence the values of x that would result in the given expression being equal to 0 is -2, 6

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Answer:

-8 or -1

Step-by-step explanation:

x*2+9x+8=0

(x+8)(x+1)=0

x+8=0 or x+1=0

x= -8 or x= -1

the required perimeters are 26 inch, 48 inch, 34 inch and 64 inch respectively.

Perimeter, is the measure of the figure on its circumference.

1. perimeter for a cross section parallel  to base of right rectangular prisms that is 10 inches long, 3 inches wide and 14 inches high:
length = 10 inches and width = 3 inch
The perimeter of that cross section is given by.
= 2 x length + 2 x width
=  2 x 10 + 2 x 3
= 20 + 6
= 26 inches

2.  perimeter of cross section  perpendicular to the base of a cube with 12 inch edge is given by.
= 4 x length
= 4 x 12
= 48 inches

3. perimeter of a cross section perpendicular to the base and passing through the diagonal of the base the right rectangle is given by.
length = 5; width = 12; height = 4; diagonal = 13;
perimeter = 2 x height + 2 x diagonal
                 = 2 x 4 + 2 x 13
                 =  34  inches

4. perimeter of a cross section of a cube having edges of 16 inches each.
   perimeter = 4 x edge
                    =  4 x 16

                    =  64

Thus, The required perimeter of the cross section are 26, 48, 34, 64 all in inches.

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Answer:

x = 4

Step-by-step explanation:

Use order of operations (PEMDAS) to simplify and solve algebraic equations:

P - Parentheses: Simplify all parentheses in the equation first.
E - Exponents: Evaluate all exponential expressions in the equation next.
M/D - Multiplication/Division: After P and E, Multiplication in the equation comes next. These are interchangeable, so if these are the only operations left, calculate in the direction left to right.
A/S - Addition/Subtraction: After everything else has been done, move on to Addition/Subtraction.  These two are also interchangeable, so you must also calculate in the direction left to right.

First, implement the order of operations to simplify the equation:

2²(x + 3) + 9 - 5 = 32 --- Evaluate the exponent.

4(x + 3) + 9 - 5 = 32 --- Use the Distributive Property to multiply.

4x + 12 + 9 - 5 = 32 --- Add/Subtract (Combine like terms).

4x + 16 = 32

Next, isolate the variable x to solve for its value:

4x + 16 = 32 --- Subtract 16 from both sides of the equation.

4x = 16 --- Divide both sides of the equation by 4 to get the value of x.

x = 4

To confirm that x = 4, you can substitute x for 4 in the original equation and see if both sides of the equation are equal:

2²[(4) + 3] + 9 - 5 = 32 --- Simplify the parentheses.

2²(7) + 9 - 5 = 32 --- Evaluate the exponent.

4(7) + 9 - 5 = 32 --- Multiply.

28 + 9 - 5 = 32 --- Simplify the equation using Addition/Subtraction.

32 = 32

After using substitution, we can confirm that x = 4.

To solve for the x-variable in a linear equation, we will need to isolate it on one side of the equation. If the x-variable is inside a parenthesis, we will need to open the parenthesis first, then isolate the variable. To solve/simplify the equation, we will need to use PEMDAS. It is a common method used to simplify equations and inequalities through priorities.

The word "PEMDAS" is a shortened word of "Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction". We follow this order (left-right) to simplify algebraic terms. Since parenthesis is the first priority, we would simplify the expression inside the parentheses. There are two exceptions to this priority in PEMDAS. (1) One of the terms in the expression is a variable, so the expression cannot be simplified, or (2) if there was no parenthesis in the first place. The next priority is "Exponents". This priority is used if there are any exponents used in the equation. The only exception to this priority is when there are no exponents used in the equation. The next priority is "Multiplication". This means that you have to simplify any products "multiplying terms" first. The only exception to this is when there are no terms being multiplied. The next priority is "Division". This priority tells that we need to simplify any division occurring the equation next. There is only one exception to this priority. Only possible if there is no division occurring in the equation. Then, we have "addition" as our 5th priority. This priority states that simplifying any expression that is being added next. The only exception to this priority is when there are no terms being added. The last and final priority is subtraction. This priority states that simplify any expression that is being subtracted. There is no exception to this priority.

Simplifying the equation using PEMDAS:

We have the following equation: 2²(x + 3) + 9 - 5 = 32

Let us simplify using our first priority. Unfortunately, there is a variable inside the parenthesis. Therefore, we can't simplify the expression inside the parenthesis. Let us now simplify using out second priority. We can see a term outside the parenthesis "2²". Since that term has an exponent, let us simplify that term! Eventually, the term will simplify to 4.

Before we move onto the next priority, let us open the parenthesis as we need to isolate the x-variable. This basically means that we need to simplify the distributive property. To simplify the distributive property, we need to multiply the term outside the parenthesis to all the terms inside the parenthesis. So, we have the following simplified equation:

Our next priority is multiplication. So, let us simplify any products occurring in the equation. We can see 4 being multiplied to 3. Therefore, let us simplify that term! Simplifying that term basically gives us 12. So:

Now, our next priority is division. However, we do not see any division occurring in the equation. Therefore, this follows the exception of the division priority in PEMDAS. So, let us move on to the next priority.

The next priority is addition. We can see 12 being added to 9. Therefore, let us simplify the expression. Simplifying that expression gives us 21. So:

The last and final priority is subtraction. We can see 5 being subtracted from 21. Therefore, let us simplify the expression, which gives us 16. So:

Solving for the x-variable by isolating it:

Now, let us isolate the x-variable to determine its value. This can be done by subtracting 16 on both sides of the equation. Then, we can divide 4 both sides to cancel out the coefficient of x.

Therefore, the value of x in the equation is 4.

Answer:

120°

Step-by-step explanation:

x = angle       supplement = 180-x

x = 4(180-x) -120

x = 720 -  4x - 120

5x = 600°

x =120°

Answer:

245 +4.9m = 2000

Step-by-step explanation:

so 245 is what he has and he puts it where he gets 2 percent monthly so 4.9 is 2 percent of 245. 2000 is there because that's how much he wants to save.

Answer:

40 miles

Step-by-step explanation:

10X4

The answer is 40 miles

-------------------------------------------------------

If he consistently rides ten mph (miles per hour) for 4 hours (4*10) he would have ridden 40 miles.

Answer:

1(x - 2xz - 2xy + 4y²)

Step-by-step explanation:

I notice that no term all of them have. which means itbwill be factorised via 1.

1(x - 2xz - 2xy + 4y²)

The equation which represent the problem is 14.5 = 469.8k.

An equation is a mathematical statement with an 'equal to =' symbol between two expressions that have equal values.

Here, As given in question

The number of gallons of gas Connie’s car, g, uses is directly proportional with the number of miles she drives, m.

                                    g α m

                                     g = km     ............(i)

g = 14.5 gallons of gas          m = 469.8 miles

                                  14.5 = k X 469.8

                                  14.5 = 469.8k

Thus, the equation which represent the problem is 14.5 = 469.8k.

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Answer:

  1/4

Step-by-step explanation:

The change of base formula for logarithms is ...

  [tex]\log_b(a)=\dfrac{\log(a)}{\log(b)}[/tex]

__

Using this with the given values, we have ...

  [tex]\log_x(y)=\dfrac{\log_p(y)}{\log_p(x)}=\dfrac{5}{20}\\\\\boxed{\log_x(y)=\dfrac{1}{4}}[/tex]

Answer:

A

Step-by-step explanation:

Givens

y2 = 15

y1 = 0

x2 = 3

x1 = 0

Equation

slope = (y2 - y1) / (x2 - x1)

Solution

The question is a bit unfair. It looks like you should be answering one. It's not true. What makes it not so is that the axis (x and  y) have different intervals.

Substitute the givens into the equation

slope = (15 - 0) / (3 - 0)

slope = 15 / 3

slope = 5

Answer Slope = 5 or A

Answer:

it's A

Step-by-step explanation:

that's what i put on that question

Answer:

x = -2y

y-intercept: ( 0, 0 ) and slope: [tex] \frac{1}{2} [/tex]

Answer: 48

Step-by-step explanation:

We need to find the least common multiple of 12 and 16.

Finding the prime factorizations of 12 and 16,

[tex]12=2^{2} \times 3\\\\16=2^{4}[/tex]

Thus, the least common multiple is [tex]2^{4} \times 3=\boxed{48}[/tex]

Answer:

True

Step-by-step explanation:

Step 1: We can plug 106 into x in the equation x - 62 = 44.

Step 2: Check if 106 - 62 = 44. It’s correct, so the answer is TRUE!!

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \:True [/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: x - 62 = 44[/tex]

[ add 62 on both sides ]

[tex]\qquad \tt \rightarrow \: x - 62 + 62 = 44 + 62[/tex]

[tex]\qquad \tt \rightarrow \: x = 106[/tex]

The proved value is same as that of statement, hence the statement is correct.

Answer:

x=8

Step-by-step explanation:

4x+10 = 2x+26

4x-2x+10=2x-2x+26  [Subtract 2x from both sides]

2x+10=26

2x + 10 - 10 = 26 - 10  [Subtract 10 from both sides]

2x = 1

2x/2 = 16/2  [Divide both sides by 2]

x = 8

CHECK:

Does 4x+10 = 2x+26 when x is 8?

4(8)+10 = 2*(8)+26  ?

32+10 = 16+26    ?

42 = 42   YES

Answer:

[tex]\large \boxed{\sf x =8}[/tex]

Explanation:

[tex]\sf \rightarrow 4x + 10 = 2x + 26[/tex]

collect like terms

[tex]\sf \rightarrow 4x -2x = 26-10[/tex]

subtract like terms

[tex]\sf \rightarrow 2x = 16[/tex]

divide both sides by 2

[tex]\sf \rightarrow x = 8[/tex]

Let's see

Answer:

53 the correct answer off your question.

Firstly, let’s assume the the whole capacity the work requires is 1.

Then, let’s see how 1 man can do in 50 days: 1/5.

Further, let’s see how 1 man can do in 1 day : 1/(5×50) = 1/250.

Similarly, let’s see how 1 woman can do in 1 day: 1/(10×50) = 1/500.

Now, we have 8 men, and they can do 8*1/250 in 1 day, which is 4/125.

Besides, we have 4 women, and they can do 4×1/500 in 1 day, which is 1/125.

Therefore, all people we have can do 4/125 + 1/125 of the work in 1 day, which is 1/25.

As a result, the work takes 1/(1/25)= 25 days.

Answer:

x1 = 4 y x2= 2

Step-by-step explanation:

escuchame

x2 - 5x -6 = 0

(4)^2 - 5(2) - 6 = 0

16 - 10 - 6 = 0

6 - 6 = 0

de nade :)

Step-by-step explanation:

[tex]f(x) = 2 {x}^{2} [/tex]

[tex] \: [/tex]

[tex] = (f \circ f)(x)[/tex]

[tex] = f(f(x))[/tex]

[tex] = 2 {x}^{2} [/tex]

[tex] = 2 {(2 {x}^{2} )}^{2} [/tex]

[tex] = 2( {2}^{2} {x}^{2 + 2} )[/tex]

[tex] = 2(4 {x}^{4} )[/tex]

[tex] = 8 {x}^{4} [/tex]

The answer is A.

[tex]\large\displaystyle\text{$\begin{gathered}\sf 4x-3+5=2x+7-8x \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{Simplify \ both \ sides \ of \ the \ equation. } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{4x+2=-6x+7 } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{Add \ 6x \ to \ both \ sides.} \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{Subtract \ 2 \ from \ both \ sides. } \end{gathered}$}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \boldsymbol{Divide \ both \ sides \ by \ 10.} \end{gathered}$}[/tex]

↓

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Verification} \end{gathered}$}[/tex]

[tex]\sf{4\times\dfrac{1}{2}-3+5=2\times\dfrac{1}{2}+7-8\times\dfrac{1}{2} }[/tex]

[tex]\sf{\dfrac{4}{2}-3+5=2\times\dfrac{1}{2}+7-8\times\dfrac{1}{2} }[/tex]

[tex]\sf{2-3+5=2\times\dfrac{1}{2}+7-8\times\dfrac{1}{2} }[/tex]

Cancel 2

[tex]\sf{2-3+5=1+7-8\times\dfrac{8}{2} }[/tex]

[tex]\sf{2-3+5=1+7-\dfrac{8}{2} }[/tex]

[tex]\sf{2-3+5=1+7-4 }[/tex]

[tex]\sf{-1+5=1+7-4}[/tex]

[tex]\sf{4=1+7-4}[/tex]

[tex]\sf{4=8-4}[/tex]

[tex]\sf{4=4}[/tex]

[tex]\large\displaystyle\text{$\begin{gathered}\sf \bf{Checked} \end{gathered}$}[/tex]

[tex]\huge \red{\boxed{\green{\boxed{\boldsymbol{\purple{Pisces04}}}}}}[/tex]

Answer:

2y + 3 = 4y + 2; y = 1/2

Step-by-step explanation:

to find this equation we can use the ys and the 1s to create an equation

so

in the left side

there are 2 ys and 3 1s

your equation is

2y + 3

on the other side

it is

4 ys and 2 1s

so

4y + 2 is your equation

then yo uset them equal to each other

2y + 3 = 4y + 2

if you must solve

subtract 2y and 2 from both sides

1 = 2y

then divide both sides by 2

y = 1/2 is your answer