Reasoning A ship is sighted from the top of a lighthouse.
The angle of depression from the lighthouse to the ship is 45°
The distance from the top of the lighthouse directly to the ship is 4 miles.
Calculate the horizontal distance of the ship from the bottom of the lighthouse
Give your answer correct to 2 decimal places.

Answer:

see the explanation

Step-by-step explanation:

we have the points

(4,7) and (4,-3)

we know that

The x=coordinate of both points are the same

so

the line that goes through those two points is a vertical line (parallel to the y-axis)

The slope is undefined

Because

The formula to calculate the slope between two points is equal to

[tex]m=\frac{y2-y1}{x2-x1}[/tex]

substitute the values

[tex]m=\frac{7+3}{4-4}[/tex]

[tex]m=\frac{10}{0}[/tex]

Is undefined (the denominator is equal to zero)

see  the attached figure to better understand the problem

Answer:

Step-by-step explanation:

Sample Response: Since both points have the same x-coordinate, the line would be vertical. A vertical line has no slope because the run of the graph, which is the denominator, is zero and therefore an undefined fraction.

Answer:

$17.35

Step-by-step explanation:

86.74*.2

Answer: [tex]\frac{(x+4)(x+1)}{x+2}[/tex]

Step-by-step explanation:

The area of a rectangle [tex]A[/tex] is given by the multiplication of its base [tex]b[/tex] by its height [tex]h[/tex]:

[tex]A=(b)(h)=x^{2}+5x+4[/tex] (1)

In addition we are told the length of one of the sides (let's choose [tex]b[/tex]) is:

[tex]b=x+2[/tex] (2)

Substituting (2) in (1):

[tex](x+2)h=x^{2}+5x+4[/tex] (3)

Isolating [tex]h[/tex]:

[tex]h=\frac{x^{2}+5x+4}{(x+2)}[/tex]

Factoring in the numerator:

[tex]h=\frac{(x+4)(x+1)}{x+2}[/tex] This is the length of the other side of the rectangle

The portion of cake Mike ate is 1/6.

The numbers given are expressed as fractions. Fractions are numbers that consist of numerators and denominators. For example, in the fraction 2/3, 2 is the numerator and 3 is the denominator.

The first step is to determine which portion of the cake that was stored in the freezer.

Portion kept in the freezer = 2/3 x 3/4 = 1/2

The second step is to determine the amount of cake Mike ate.

2/3 - 1/2

[tex]\frac{4 - 3}{6}[/tex] = [tex]\frac{1}{6}[/tex]

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The portion of the cake that Mike ate is [tex]\frac{1}{6}[/tex].

The given parameters:

The portion of the cake that Mike wrapped and stored in the freezer is calculated as follows;

[tex]= \frac{3}{4} \times \frac{2}{3} \\\\= \frac{1}{2}[/tex]

The portion of the cake that Mike ate is calculated as follows;

[tex]remaining = original - portion \ stored\\\\remaining = \frac{2}{3} - \frac{1}{2} = \frac{4 - 3}{6} = \frac{1}{6}[/tex]

Thus, the portion of the cake that Mike ate is [tex]\frac{1}{6}[/tex].

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the two solutions are approximately [tex]\( x_1 \approx 2.95 \) and \( x_2 \approx -0.042 \).[/tex]

To find the value of x that satisfies the equation [tex]\( 32x^2 - 93x - 4 = 0 \)[/tex], we can use the quadratic formula:

[tex]\[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}} \][/tex]

Where:

- a = 32

- b = -93

- c = -4

Now, let's plug these values into the quadratic formula:

[tex]\[ x = \frac{{-(-93) \pm \sqrt{{(-93)^2 - 4 \cdot 32 \cdot (-4)}}}}{{2 \cdot 32}} \]\[ x = \frac{{93 \pm \sqrt{{8649 + 512}}}}{{64}} \]\[ x = \frac{{93 \pm \sqrt{{9161}}}}{{64}} \]\[ x = \frac{{93 \pm 95.7}}{{64}} \][/tex]

Now, we have two possible solutions:

[tex]\[ x_1 = \frac{{93 + 95.7}}{{64}} \]\[ x_2 = \frac{{93 - 95.7}}{{64}} \]\[ x_1 \approx \frac{{188.7}}{{64}} \]\[ x_2 \approx \frac{{-2.7}}{{64}} \]\[ x_1 \approx 2.95 \]\[ x_2 \approx -0.042 \][/tex]

Therefore, the two solutions are approximately [tex]\( x_1 \approx 2.95 \) and \( x_2 \approx -0.042 \).[/tex]

The probable question maybe:

What are the solutions for x in the equation [tex]\( 32x^2 - 93x - 4 = 0 \)[/tex]?

Answer:

$5100 would be $76.50

$4876 would be $73.14

$5215 would be $78.23

$6225 would be $93.38

$5235 would be $78.53

Step-by-step explanation:

To find commissions take your sale price and multiply it by your percentage and divide by 100

Answer: $399.77

Step-by-step explanation:

Answer:

Step-by-step explanation:

P = 2(L + W).....perimeter of a rectangle formula

P = 20

L = 2W + 1

20 = 2(2W + 1 + W)

20 = 2(3W + 1)

20 = 6W + 2

20 - 2 = 6W

18 = 6W

18/6 = W

3 = W <==== the width is 3 inches

L = 2W + 1

L = 2(3) + 1

L = 6 + 1

L = 7 <===== the length is 7 inches

Answer:

Width = 3 inches

Length = 7 inches

Step-by-step explanation:

L = 1 + 2W

P = 20 inches

P = 2L + 2W

2L + 2W = 20 inches

Fill in known value (length)

2(1 + 2W) + 2W = 20 inches

Solve

2 + 4W + 2W = 20 inches

6W = 18 inches

Simplify

W = 3 inches

Width = 3 inches

Length = 2(3) + 1 = 7 inches

:)

[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ 4^{-\frac{11}{3}}\div 4^{-\frac{2}{3}}\implies \cfrac{4^{-\frac{11}{3}}}{4^{-\frac{2}{3}}}\implies 4^{-\frac{11}{3}}\cdot 4^{\frac{2}{3}}\implies 4^{-\frac{11}{3}+\frac{2}{3}} \\\\\\ 4^{-\frac{9}{3}}\implies 4^{-3}\implies \cfrac{1}{4^3}\implies \cfrac{1}{64}[/tex]

Answer:A

Step-by-step explanation:

The equation that best set up the quadratic formula is [tex]x = \frac{ -(-2) |+-| \sqrt{(-2)^2-4(1)(4)} }{2(1)}[/tex].

Hence, option A is the correct answer.

Quadratic equation is simply an algebraic expression of the second degree in x. Quadratic equation in its standard form is;

ax² + bx + c = 0

Where x is the unknown

Using the quadratic formula

x = (-b±√(b² - 4ac)) / (2a)

Given that;

x² + 1 = 2x – 3

First we re-arrange the the equation.

x² + 1 = 2x - 3

x² - 2x + 1 + 3 = 0

x² - 2x + 4 = 0

Hence;

Next we input this values into the quadratic formula

x = (-b±√(b² - 4ac)) / (2a)

x = (-(-2)±√((-2)² - 4(1)(4))) / (2(1))

[tex]x = \frac{ -(-2) |+-| \sqrt{(-2)^2-4(1)(4)} }{2(1)}[/tex]

The equation that best set up the quadratic formula is [tex]x = \frac{ -(-2) |+-| \sqrt{(-2)^2-4(1)(4)} }{2(1)}[/tex].

Hence, option A is the correct answer.

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                                                    Question # 4

Answer:

Total number of cameras left to bid on = 3/5

Step-by-step Explanation:

To determine:

What fraction of the total number of cameras is left to bid on?

Solution Steps:

Total number of cameras left to bid on = 10/10 - 4/10

                                                                  = 6/10

                                                                   = 3/5   ∵ As 6/10 = 3/5

Hence, total number of cameras left to bid on = 3/5

                                               Question # 5

Answer:

The remaining portion of tickets = 17/100

Step-by-step Explanation:

To determine:

What portion of the tickets remain?

Solution Steps:

The remaining portion of tickets = 100/100 - 83/100

                                                       = 17/100

Hence, the remaining portion of tickets = 17/100

Keywords: fraction, number

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Answer:

A. [tex]\displaystyle 10\:units[/tex]

Step-by-step explanation:

Use the Distance Formula:

[tex]\displaystyle \sqrt{[-x_1 + x_2]^2 + [-y_1 + y_2]^2} = D \\ \\ \sqrt{[-3 + 2]^2 + [-6 - 4]^2} = \sqrt{[-1]^2 + [-10]^2} = \sqrt{1 + 100} = \sqrt{101} ≈ 10,04987562 ≈ 10[/tex]

Since we are talking about distance, we ONLY want the NON-NEGATIVE root.

I am joyous to assist you anytime.

Final answer:

The approximate length of a line segment connecting points A(3, 6) and B(2, -4) is found using the distance formula and it is approximately 10 units.

Explanation:

To calculate the approximate length of a line segment connecting points A and B, we use the distance formula. The distance formula is derived from the Pythagorean theorem and is:

d = \/((x2 - x1)² + (y2 - y1)²)

Given points, A(3, 6) and B(2, -4), we can plug these coordinates into the formula:

d = \/((2 - 3)² + (-4 - 6)²)

Now, calculate the squares and sum:

d = \/((-1)² + (-10)²)

d = \/(1 + 100)

d = \/(101)

The square root of 101 is approximately 10.05, which is close to 10 units.
Therefore, the approximate length of the line segment connecting points A and B is 10 units, which corresponds to option A.

Answer:

The correct answer is A. 12 minutes.

Step-by-step explanation:

Let's solve for y, when x = 12, as follows:

y = 175 - 15x

y = 175 - 15 * 12

y = 175 - 180

y = - 5

This result means that after 12 minutes the fish tank would be completely drained and if it's needed 5 additional gallons of water could also be drained. It's not necessary to continue making more calculation with the the other options given because this is the right answer.

The correct answer is A. 12 minutes.

Answer:

[tex]S = P(1.08)^{t}[/tex]

Step-by-step explanation:

A $10,000 deposit at the bank will double in value in 9 years.

If the interest is r% and it is compounded each year, then we can write from the formula of compound interest that

[tex]20000 = 10000(1 + \frac{r}{100})^{9}[/tex]

⇒ [tex]2 = (1 + \frac{r}{100})^{9}[/tex]

⇒ [tex]1 + \frac{r}{100} = 1.08[/tex]

⇒ r = 8%

Therefore, the formula for the accumulated amount t years after the investment is made will be  

[tex]S = P(1 + \frac{8}{100})^{t} = P(1.08)^{t}[/tex]  

where, P is the invested principal and S is the accumulated sum. (Answer)

Answer:

n= (-m-13)/2

Step-by-step explanation:

look @ photo

Answer: m=-2n-13

               ↗️⬆️↖️

To complete the Venn diagram, calculate that 48 out of 60 farms grow potatoes and the remaining 16 grow sugar beets, since the potato farms number is three times the sugar beet farms.

The question asks us to complete a Venn diagram with information about how many farms grow potatoes vs sugar beets, given that 60 farms grow one or the other, not both. 4/5 of the 60 farms grow potatoes, which is 48 farms.

Since the number of farms that grow potatoes is three times the number that grow sugar beets,

we can determine the number of sugar beet farms by dividing the number of potato farms by 3, giving us 16 farms growing sugar beets.

Here's the step-by-step solution:

Answer:

Step-by-step explanation:

Simplifying

h(x) = x2 + 3x + -18

Multiply h * x

hx = x2 + 3x + -18

Reorder the terms:

hx = -18 + 3x + x2

Solving

hx = -18 + 3x + x2

Solving for variable 'h'.

Move all terms containing h to the left, all other terms to the right.

Divide each side by 'x'.

h = -18x-1 + 3 + x

Simplifying

h = -18x-1 + 3 + x

Reorder the terms:

h = 3 + -18x-1 + x

Answer:

h(x)= (x+3/2 ) ^2  −  81/4

​

Step-by-step explanation:

Its correct :)

Answer:

The final amount in the account after 6 years at compound interest is $1568.78 .

Step-by-step explanation:

Given as :

The principal amount in account = p = $1500

The rate of compound interest = r = 0.75 %

The time period of the loan = t = 6 years

Let The Amount in account after 6 years = $A

From Compound Interest method

Amount = Principal × [tex](1+\dfrac{\textrm rate}{100})^{\textrm time}[/tex]

I.e A = p × [tex](1+\dfrac{\textrm r}{100})^{\textrm t}[/tex]

Or, A = $1500 × [tex](1+\dfrac{\textrm 0.75}{100})^{\textrm 6}[/tex]

Or, A = $1500 × [tex](1.0075)^{6}[/tex]

Or, A = $1500 × 1.04585

Or, A = $1568.775

So, The final amount= A = $1568.78

Hence The final amount in the account after 6 years at compound interest is $1568.78 . Answer

Answer:

The distance of base of wire to the base of tower is 13.27 ft

Step-by-step explanation:

Given as :

The measure of wire connected between base ad antenna top = 20 ft

The wire is connected to the  antenna on tower at height h = 15 ft above the ground

Let The distance of base of wire to the base of tower = x ft

Let the angle drawn on ground = Ф

Now, According to question

In figure AOB

Sin angle = [tex]\dfrac{\textrm perpendicular}{\textrm hypotenuse}[/tex]

i.e SinФ = [tex]\dfrac{\textrm AB}{\textrm BO}[/tex]

Or,  SinФ = [tex]\dfrac{\textrm h}{\textrm 20}[/tex]

Or,  SinФ = [tex]\dfrac{\textrm 15}{\textrm 20}[/tex]

Or, SinФ = [tex]\dfrac{\textrm 3}{\textrm 4}[/tex]

or, Ф = [tex]sin^{-1}(\frac{3}{4})[/tex]

∴ Ф = 48.5°

Now, Again from figure

Tan angle = [tex]\dfrac{\textrm perpendicular}{\textrm base}[/tex]

i.e TanФ = [tex]\dfrac{\textrm AB}{\textrm OA}[/tex]

Or, Tan 48.5° = [tex]\dfrac{\textrm h}{\textrm x}[/tex]

Or, 1.13 = [tex]\dfrac{\textrm 15}{\textrm x}[/tex]

∴ x = [tex]\dfrac{\textrm 15}{\textrm 1.13}[/tex]

i.e x = 13.27 feet

So, The distance of base of wire to the base of tower = x = 13.27 ft

Hence, The distance of base of wire to the base of tower is 13.27 ft Answer

Final answer:

The other end of the wire will be located approximately √175 ft away from the base of the tower.

Explanation:

To find the distance from the base of the tower to the other end of the wire, we can use the Pythagorean theorem. The wire forms the hypotenuse of a right triangle, with one leg being the height of the antenna and the other leg being the distance from the base of the tower. Let's call this distance 'x'.

Using the Pythagorean theorem, we have:

x² + 15² = 20²

Simplifying this equation, we get:

x² = 20² - 15²

x² = 400 - 225

x² = 175

Taking the square root of both sides, we find:

x = √175

So the other end of the wire will be located approximately √175 ft away from the base of the tower.

Answer:

Step-by-step explanation:

1,115.625 miles in 21 hrs and 15 min.....

15 minutes = 15/60 = 0.25 hrs......so they did it in 21.25 hrs

1,115.625 / 21.25 = 52.5 miles per hr <===

Answer:

The word sum corresponds to addition, which means:

d + 12 = 20

:)

Answer: d + 12 = 20

Step-by-step explanation: In this problem, we are asked to write an algebraic expression that represents the sentence.

The key to understanding this problem is by looking at the keyword "sum." The word sum means addition so reading this problem from left to right, the sum of d and 12 that's d + 12 "is 20" = 20.

So, d + 12 = 20 will be our algebraic expression.

Answer:

Step-by-step explanation:

it equals -19

Answer:

The value of the given expression [tex]-16-3=-19[/tex]

Step-by-step explanation:

Given expression is [tex]-16-3[/tex]

To find the value of the given expression:

[tex]-16-3=-16-3[/tex]

Now taking the negative sign (-) outside the terms of the above equation we get,

[tex]-16-3=-(16+3)[/tex]

Now apply the algebraic sum to  the above expression we get,

[tex]=-19[/tex]

Therefore [tex]=-19[/tex]

The value of the given expression is [tex]-16-3=-19[/tex]

The waffle cone has a larger radius compared to the sugar cone.

The radius of a cone can be found using the formula:

radius = volume / height / pi

Both cones have the same volume of 12 ounces, so we can use this formula to compare their radii:

For the waffle cone: radius = 12 / 5 / pi = 0.766

For the sugar cone: radius = 12 / 8 / pi = 0.477

Therefore, the waffle cone has a larger radius compared to the sugar cone.

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The waffle cone has a larger radius of approximately 2.03 inches compared to the sugar cone's radius of approximately 1.61 inches.

To determine which cone has a larger radius, we need to calculate the radius of each cone using the volume formula for a cone. Since both cones hold the same volume (12 ounces), we'll convert this to cubic inches (since 1 ounce is approximately 1.8 cubic inches, 12 ounces is roughly 21.6 cubic inches).

The volume formula for a cone is:

V = (1/3)πr²h

Where V is the volume, r is the radius, and h is the height.

Waffle Cone:

Volume (V) = 21.6 cubic inches
Height (h) = 5 inches

Therefore, we have:

21.6 = (1/3)πr²(5)

Solving for r, we get:

21.6 = (5/3)πr²
r² = 21.6 / ((5/3)π)
r² = 12.97 / π
r ≈ sqrt(4.13)
r ≈ 2.03 inches

Sugar Cone:

Volume (V) = 21.6 cubic inches
Height (h) = 8 inches

Therefore, we have:

21.6 = (1/3)πr²(8)

Solving for r, we get:

21.6 = (8/3)πr²
r² = 21.6 / ((8/3)π)
r² = 8.1 / π
r ≈ sqrt(2.58)
r ≈ 1.61 inches

Comparing the two radii, the waffle cone has a larger radius of approximately 2.03 inches, while the sugar cone has a smaller radius of approximately 1.61 inches.

Answer:

$6

The drawings will help

Answer: [tex]A(t)=-8t+52[/tex]

Step-by-step explanation:

The  equation of the line in Slope-Intercept form is:

[tex]y=mx+b[/tex]

Where "m" is the slope and "b" is the y-intercept.

According to the data given in the exercise, you know that:

- [tex]A(t)[/tex] represents the area to paint the Hiros' romm as a function of time.

- The rate he painted the room was 8 square meters per hour.

- The area left to paint after 3 hours was 28 m².

Therefore, based on this, you can idenfity that:

1. The slope of the line is:

[tex]m=-8[/tex]

2. One of the point on the line is:

[tex](3,28)[/tex]

So you must substitute the slope and the coordinates of that point into [tex]y=mx+b[/tex] and then solve for "b" in order to find its value:

[tex]28=-8(3)+b\\\\28+24=b\\\\b=52[/tex]

Therefore, you can determine that the function [tex]A(t)[/tex] is:

[tex]A(t)=-8t+52[/tex]

Answer:

D

Step-by-step explanation:

The function of the x in the table is not having a specific pattern apart from repeating 3's.

Choice A: pattern for x +1

pattern for y +1

Choice B:pattern of x -1

pattern for y +1

Choice C: pattern for x +1

pattern for y -0

Choice D:pattern for x -0

pattern for y +1

Therfore D would be the answer.

Answer:

A) The total feet needed for the fence total perimeter is 54 feet

B) The total cost of fence is $432

C) The square feet of grass needed foe the total area is 180 square feet

D) The total cost of the project is $572

Step-by-step explanation:

Given as :

The dimension of rectangular field

Length of rectangular field = L = 12 feet

width of rectangular field = w = 15 feet

The cost of grass per square foot = 50 cents = $0.5    ( ∵ 1 cents = $0.01 )

The cost of small fence = $8 per linear foot

Now, According to question

A ) Let The total feet needed for the fence total perimeter = A feet

∵ Perimeter of rectangular field = 2 × Length + 2 × width

Or, A = 2 × L + 2 × w

Or, A = 2 × 12 feet + 2 × 15 feet

Or, A = 24 feet + 30 feet

∴ A = 54 feet

So, The total feet needed for the fence total perimeter = A = 54 feet

B ) Let The total cost of fence = $B

So, The total cost of fence = The cost of small fence × perimeter of fence

i.e B = $8 × 54 feet

∴ B = $432

So,The total cost of fence = B = $432

C) Let the square feet of grass needed foe the total area = C square feet

∵The Area of rectangular fence = Length × width

Or, The square feet of grass needed foe the total area = Area of rectangular fence = L × w

i.e C = 12 feet × 15 feet

Or, C = 180 feet²

So,The square feet of grass needed foe the total area = C = 180 square feet

D) Let The total cost of grass = $D

∵ The cost of grass per square foot = $0.5

So,Total cost of grass = $0.5 × Area of fence

i.e D = $0.5 ×  180 feet²

Or, D = $90

So, The Total cost of grass = D = $90

E) Let the total cost of the project = $E

∵Mr. Jones spend additional $50 for tools

So, The total cost of the project =  money spent on tools + total cost of fence + Total cost of grass

i.e E = $50 + B + D

Or, E = $50 + $432 + $90

∴ E = $572

So, The total cost of the project = E = $572

Hence,

A) The total feet needed for the fence total perimeter is 54 feet

B) The total cost of fence is $432

C) The square feet of grass needed foe the total area is 180 square feet

D) The total cost of the project is $572  Answer

Answer:

B

Step-by-step explanation:

(x-6)(x+6)

The -6x cancels out the other 6x

x^2 - 36

Answer:

Graph 3.

Step-by-step explanation:

Since they need to earn $240 by selling $3 candy bars, they must sell at least 80 candy bars since 240/3 = 80.

With this in mind, selling more than 80 candy bars would be acceptable, but selling less would not which is why the third graph is correct.

Answer:

c

Step-by-step explanation:

Answer:

The first choice.

Step-by-step explanation:

We only need to know one part of this step function to figure out the answer. The first step is y=-1 if -6<x<=-4, this knocks out the 2nd and 3rd answer choices as they don't follow this equation.