A boat is heading towards a lighthouse, whose beacon-light is 148 feet above
the water. The boat's crew measures the angle of elevation to the beacon, 8°.
What is the ship's horizontal distance from the lighthouse (and the shore)?
Round your answer to the nearest hundredth of a foot if necessary.
Answer:
feet
Submit Answer
attempt 1 out of 2 / problem 2 out of max 4
Answer:
x = 1053.07 ft
Step-by-step explanation:
So if you look at the diagram I drew it might become a bit more apparent what you have to do. For this problem you'll need to use one of the six trigonometric functions. In this case you know the angle and the opposite side of the angle, and you need the adjacent side. The trigonometric function tan is defined as [tex]\frac{oppposite}{adjacent}[/tex]. So let's plug in the known values:
[tex]tan(8) = \frac{148}{x}[/tex]
multiply both sides by x
[tex]tan(8) * x = 148[/tex]
Divide both sides by tan(8)
[tex]x=\frac{148}{tan(8)}[/tex]
Calculating tan of 8 degrees using a calculator
[tex]x=\frac{148}{0.141}[/tex]
Simplify
x = 1053.07 ft
What is the value of x if e³x+6 - 87
Write a compound inequality that represents the given graph
Answer:
A
Step-by-step explanation:
The graph is composed of two different rays.
Eliminate B and C.Also, when x = -2, there is an open hole.
Eliminate D.This leaves A as the answer.
The price of an item has been reduced by 85%. The original price was $33.
Answer:
4.95
Step-by-step explanation:
85% of 33 = 28.5
33 - 28.5 = 4.5
Use the function below to find F(-4)
F(x) = 2^x
Answer:
1/16
Step-by-step explanation:
F(-4) = 2^-4
= 1/(2^4) = 1/16
Do you know the answer to 8+(10-4)-3*2 and how to solve it?
Answer:
8
Step-by-step explanation:
10 minus 4 goes first because of BODMAS so thats 6
then 3 times 2 because again bodmas to thats 6
so then its 8 + 6 - 6
can be done in any order not affected by bodmas
6-6 cancels out so the answer is 8
comment if you want an in depth explanation on bodmas lol
Lee put $5,000 into a stock market index mutual fund that grew at an average of 6.5% per year for 10 years. without any added deposits or withdrawals, about how much is in lee's mutual fund account after only 8 years, if you ignore compounding?
The amount in lee's mutual fund account after 8 years will be $7600
Given: Principal amount (P) = $5000,
Time (t) = 10 years,
Rate of interest (r) = 6.5% per year
To find: lee's mutual fund account after only 8 years
We know that Simple interest (SI) is given by:
[tex]S.I = \frac{PTR}{100}[/tex].......(1)
So, by using equation (1) money (P') in a mutual fund account after 8 years will be
[tex]P'=P+\frac{PTR}{100}[/tex]
[tex]=5000+\frac{5000*6.5*8}{100}[/tex]
[tex]= 5000+50*6.5*8[/tex]
= 5000+2600
= 7600
Hence, the amount in lee's mutual fund account after 8 years will be $7600
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Find the coordinates of the circumcenter of DEF.
11. D (6,0), E (0,6), F (-6,0)
12. D (0,0) E (6,0), F (0,4)
In order to determine the coordinates of the circumcenter of triangle DEF with the given vertices, let its circumcenter be P(x, y). Hence, PD = PE = PF.
By squaring all sides of triangle DEF, we have:
PD² = PE² = PF²
From PD² = PE², we have:
(x - 6)² + (y - 0)² = (x - 0)² + (y - 6)²
x² - 12x + 36 + y² = x² + y² - 12y + 36
-12x + 12y = 0 ..........equation 1.
From PE² = PF², we have:
(x - 0)² + (y - 6)² = (x - (-6))² + (y - 0)²
x² + y² - 12y + 36 = (x + 6)² + y²
x² + y² - 12y + 36 = x² + 12x + 36 + y²
-12x - 12y = 0 ..........equation 2.
Solving eqn. 1 and eqn. 2 simultaneously, we have:
x = 0 and y = 0.
Therefore, the coordinates of the circumcenter of triangle DEF with the given vertices are (0, 0).
At D (0,0) E (6,0), F (0,4).From PD² = PE², we have:
(x - 0)² + (y - 0)² = (x - 6)² + (y - 0)²
x² + y² = x² - 12y + 36 + y²
12y = 36
y = 3.
From PE² = PF², we have:
(x - 6)² + (y - 0)² = (x - 0)² + (y - 4)²
x² - 12x + 36 + y² = x² + y² - 8y + 16
-12x - 8y = -20
-12x - 8(3) = -20
-12x - 24 = -20
12x = -4
x = -1/3.
Therefore, the coordinates of the circumcenter of triangle DEF with the given vertices are (-1/3, 3).
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The current salaries in Sasha’s department are $42,000, $32,000, $33,000, $38,000, and $50,000. Sasha wants to adjust the lowest salary up to $40,000. If Sasha gives every employee a $1,000 raise in addition to adjusting the lowest salary, Find the total cost for the increment?
The total cost for the increment is $13,000.
What is the total cost for the increment?There are 5 employee's in Sasha's department. The total amount of increment is $5000. (5 x $1000).
The lowest salary is 32,000. If it is increased to $40,000. The total cost of the increment is $8000 (40,000 - 32,000)
Total cost of the increment = $8000 + $5000 = $13,000
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Select the correct answer.
Here's another plant stand. It has 2 rows, each holding 4 plants. Suppose this plant stand is turned upright.
Choose the number sentence that represents the plants on the upright plant stand.
8 × 1 = 8
4 × 2 = 8
2 × 2 = 4
4 × 4 = 16
The number sentence that gives the best representation of the plants on the upright stand is 8 × 1 = 8.
How to solve for the plant on the upright stand.Given that the plant is said to be upright, then the number of row would be seen as 1.
The rows of the plants are made up of 2 and the plants in them are said to be 4. Hence we would have 4 x 2 = 8
From here we would conclude that 8 × 1 = 8 is the plants on the upright stand.
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2. A shop owner raises the price of a $150 pair of shoes by 40%. After a few weeks, because of falling sales, the owner reduces the price of the shoes by 40%. A customer then says that the shoes are back at the original price.
a. What is the mistaken assumption here?
b. Why is that assumption incorrect?
c. What do the shoes actually cost now? show calculation
d. By what percent should the shoes be decreased in order to have the price back at $150? Round to the nearest 10th percentage. (for example if your decimal answer is .058267 your answer would be 5.8267% round to nearest 10th percent answer is 5.8%) show calculation
The mistaken assumption is that the customer thinks the shoes are back to their original price.
The assumption is wrong because the price of the shoe is now lower than $150.
The cost of the shoe now is $126.
In order to retain the price of $150, the percentage decrease should have been 28.6%.
What is the cost of the shoe now?Price of the shoe after it was increased : 1.4 x 150 = 210
Price of the shoe after it was decreases: (1 - 0.4) x 210
0.6 x 210 = $126
The percentage the price should be decreased for the price to be back to $150 = (150 / 210) - 1 = 28.9%
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The volume of a fish tank is 50 cubic feet. if the density is 0.2 fish over feet cubed, how many fish are in the tank? 5 10 125 250
Answer: 10
Step-by-step explanation:
I just took the test!! :)
Find data on the increase in consumer credit card debt in the U.S.A. Based on your findings, do you think the extent of the consumer debt is (a) a crisis, (b) a significant occurrence but nothing to worry about or (c)a good thing?
Justify your conclusion.
Increase in Consumer Credit Card Debt is a debt Crisis , Option A is the correct answer.
What is Consumer Credit Card Debt ?
It is the debt which has been accumulated due to the consumers buying products and services out of the credit card and not paying them back in the period of 90 days.
In USA , the credit card balance is $841 billion in the first quarter of 2022 , which is $15 billion less form the last year but at a significant peak.
This extent of the consumer debt is a debt crisis.
The debt on the bank increases as the debt on the consumer increases , causing in bank recession and a recession brings harm to the economy , It is a crisis situation and need to be handled before it affects the market.
Therefore increase in Consumer Credit Card Debt is a debt Crisis , Option A is the correct answer.
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Write an inequality, in slope-intercept form, for the graph below. If necessary,
use "<=" for < or ">=" for >.
-5
(1,1)
(0, -2)
5
The inequality of the given graph in Slope Intercept Form is;
y ≥ 3x - 2
How to write an inequality in slope intercept form?From the attached graph, we see that the boundary line passes through the points (0,-2) and (1,1), and as such the equation of the boundary line is gotten from the general formula;
(y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)
Thus, we have;
(y + 2)/(x - 0) = (1 + 2)/(1 - 0)
(y + 2)/x = 3
y + 2 = 3x
y = 3x - 2
Now, the boundary line is a solid line and the shaded area lies above the boundary line, therefore the sign of inequality must be ≥.
The inequality of the given graph in Slope Intercept Form is;
y ≥ 3x - 2
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En la feria el juego de gusano da 5 vueltas y equivale a 150 metros, calcula a cuento equivale lo siguiente: 8/4 de vuelta =_____3 4/6 de vuelta =_____1 4/6 de vuelta= _____3/4 de vuelta= ___4/6 de vuelta= ____7/9 de vuelta =___
las ecuaciones con fracciones dan:
8/4 de vuelta = 60m(3 + 4/6) de vuelta = 110m4/6 de vuelta = 20m3/4 de vuelta = 22.5m7/9 de vuelta= 23.33 m¿Cuanto vale cada una de las expresiones?Sabemos que 5 vueltas es igual a 150 metros, entonces cada vuelta es equivalente a:
v = 150m/5 = 30m
Es decir, cada vuelta equivale a 30 metros.
Ahora simplemente podemos resolver las ecuaciones con fracciones:
8/4 de vuelta = (8/4)*30m = 60m(3 + 4/6) de vuelta = (3 + 4/6)*30m = 110m4/6 de vuelta = (4/6)*30m = 20m3/4 de vuelta = (3/4)*30m = 22.5m7/9 de vuelta = (7/9)*30m = 23.33 mSi quieres aprender más sobre fracciones:
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How can you determine the measure of an angle if you know the opposite side of the angle and the hypotenuse?
Answer:
Use sine rule.
Explanation:
[tex]\begin{tabular}{|c|c|c|c|} \cline{1-2} \multicolumn{2}{|c|}{\bf {SOH CAH TOA Formula's}} \\ \cline{1-2} \cline{1-2} \rm{sine rule} & sin(\theta) \sf = opposite/hypotenuse \\ \cline{1-2} \rm{cosine rule} & cos(\theta) \sf = adjacent/hypotenuse \\\cline{1-2} \rm{tan rule} & tan(\theta) \sf = opposite/adjacent \\ \cline{1-2}\end{tabular}[/tex]
If opposite side of an angle and hypotenuse is given.
Use sine rule: sin(θ) = opposite/hypotenuse
For example:
Given that opposite of the angle is 10 cm and hypotenuse is 20 cm.
To find the angle:
sin(θ) = 10/20
θ = sin⁻¹(10/20)
θ = sin⁻¹(1/2)
θ = 30°
Several ways
You can use sin directly
As
sinØ=Opposite/HypotenuseThen you can find Ø from it
Otherwise
You may find adjacent using Pythagorean theorem
Then you can use cos
cosØ=Adjacent/HypotenuseYou may use tan even
tanØ=Opposite/Adjacentthe cost c(x) for a taxi ride is given by c(x) =2x + 3.00, where x is the number of minutes. on a piece of paper graph c(x) =2x + 3.00. then determine which answer matches the graph you drew, including the correct axis
A function assigns the values. The correct option is D.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
The complete options of the question are mentioned in the below image.
The cost cost c(x) for a taxi ride is given by c(x) =2x + 3.00, where x is the number of minutes. Therefore, the graph of the equation can be drawn as shown below.
Hence, the correct option is D.
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Given: -2x^(2)-3x+4=0, use the quadratic formula to solve for the roots
The roots of the quadratic equations are -4 and -1
How to determine the roots-2x^(2)-3x+4=0
Expand the equation first
[tex]-2(x^2 - 3x + 4) = 0[/tex]
Find two factor that are multiples of -8 and sum up to give -3, the facors are -4 and -1
Replace -3x with 4x and -x
[tex]-2(x^2 -4x + x + 4) = 0[/tex]
Factorize the equation
[tex]-2 (x (x + 4) + 1 (x + 4)[/tex]
We have
2(x + 1) = 0 and 2(x+ 4) = 0
2(x + 1) = 0
2x + 2 = 0
x = -1
2(x+ 4) = 0
2x + 8 = 0
x = -8/2
x = -4
Therefore, the roots of the quadratic equations are -4 and -1
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!!HELP!! PLEASE I NEED THIS DONE IN AN HOUR IF ANYONE CAN HELP
Answer:
the 1st answer is x = 5, the 2nd answer is x = 7, the 3rd answer is x = 4, the 4th answer is: x = 4, the 5th answer is the exact form: x = - 1/3 but the decimal form is: x = - 0.3, the 6th answer is x = 3.
Brainliest?
Wrote an expression gor
m < RST
The expression for the angle m∠RST from the given bisctor is; 6x - 18
How to find the expression for a given angle?From the given image in the attachment we are given that;
SQ bisects ∠TSR
m ∠RSQ = 3x - 9
Now, since SQ is a bisector of ∠TSR, we can say that
m∠RST = 2 * m∠RSQ
Thus angle RST is expressed as;
m∠RST = 2(3x - 9)
m∠RST = 6x - 18
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Simplify the expression: 2 * | 12 - 14 | =
[tex]2 \times |12-14|=2 \times |-2| =2\times 2=\boxed{4}[/tex]
Joyce has as much money as George; then they bet 5 cents each and George lost. If, after the bet, George has x cents, how much does Joyce have ?
PLS HELP ASAP! will mark brainliest and 20 points
Answer:
x + 10
Step-by-step explanation:
You want to know how much money Joyce has if she won a bet with George in which they both started with the same money, both bet 5 cents, and George ended up with x cents.
BetWe assume that both Joyce and George put 5 cents in the pool. After doing that, each had x cents. If Joyce won the 10-cent pool, she now has ...
x + 10 cents
__
Additional comment
If they both bet against a house, or in a situation where a third party was involved, the amount Joyce ends with depends on the odds of the game, or the percentage collected by the house.
Given that the game is not specified, we have made up the rules.
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You are 22 years old and are starting a savings plan and will deposit $200 every 2 months until you retire. The account will give you 7% interest. How much do you expect your account to be worth when you retire at 67 years old?
Answer:
Formulae can be searched for confirmation : compounding interest with regular payments
Step-by-step explanation:
Calculations do it by yourself
Answer:
clchjtdjgdtklgdlnajajhbshsjzsnnjdndmqjsnsn him
Henry begins a savings account with $500. The savings account accumulates 2.5% annual interest based on the equation Vh=500(1.025)^t , where Vh is the value of the account after t years. Andres begins a savings account three years later with the same initial amount of money at the same interest rate. Which equations represent the value of Andres’s account after t years?
A) Va=500(1.025)^t-3 and Va=464.30(1.025)^t
B) Va=500(1.025)^t+3 and Va=538.45(1.025)^t
C)Va=500(1.025)^t-3 and Va=538.45(1.025)^t
D)Va=500(1.025)^t+3 and Va=464.30(1.025)^t
The exponential function that represents the value of Andres’s account after t years is:
A) Va=500(1.025)^t-3 and Va=464.30(1.025)^t
What is the equation for the value of Andres's account?For Henry, it is given by:
[tex]Vh = 500(1.025)^t[/tex]
Andres starts 3 years later than Henry, hence the equation is:
[tex]Va = 500(1.025)^{t - 3}[/tex]
Applying an exponential simplification, we have that:
[tex]Va = 500\frac{1.025^t}{1.025^3} = 464.3(1.025)^t[/tex]
Hence option A is correct.
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QUESTION 4
.
1 POINT
The sum of eight times a number and four is ninety-two. Find the number.
Provide your answer below:
Answer:
The missing number is 11
Step-by-step explanation:
Step-by-step explanation:
x is the number
8x + 4 = 92 (8 times the number plus 4 is 92).
8x = 88
x = 11
the number is 11.
A rectangular sheet of metal has a perimeter of 82 inches. Its area is 348 square inches. What are the dimensions of the sheet?
The area of a 2D form is the amount of space within its perimeter. The length of the rectangle is 29 inches and the width of the rectangle is 12 inches.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
Let the width of the sheet be represented by x and the length be represented by y.
Area = x × y
348 = xy
x = 348/y
Perimeter = 2(x+y)
82 = 2(x+y)
41 = x + y
41 = (348/y) + y
0 = y² - 41y + 348
y = 29, 12
Therefore, the length of the rectangle is 29 inches and the width of the rectangle is 12 inches.
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The area of the parallelogram below is ____ square meters. A parallelogram with height labeled with 7 meters. The top horizontal side is labeled 6 meters. The base of the left triangle formed by the height is 2 meters. Numerical Answers Expected
The area of the parallelogram in the image given is: 42 m².
What is the Area of a Parallelogram?Area of a parallelogram = base × height
Given the parameters:
Base = 6 metersHeight = 7 metersArea of the parallelogram = (6)(7)
Area of the parallelogram = 42 m²
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using this diagram, find x and y
Answer:
x=13
y=11
Step-by-step explanation:
3y+5+52=90
3y=90-57
3y=33
y=33/3=11
4x=52
x=52/4=13
3y+5 and 52 are complementary
3y+5+52=903y+57=903(y+19)=90y+19=30y=11Apply angle sum property
4x+3(11)+5+90=1804x+33+5=904x+38=904x=52x=13Please help!!! Rationalize the denominator and simplify the following expression:
Rationalizing the denominator and simplifying the expression, the result is 6√5 + 13.
Option C is the correct answer.
What is the simplified form of this expression?Given that;
[tex]\frac{4+\sqrt{5} }{\sqrt{5} -2}[/tex]
To rationalize the denominator, we multiply the expression by [tex]\frac{\sqrt{5} +2 }{\sqrt{5} +2}[/tex]
Hence
[tex]\frac{4+\sqrt{5} }{\sqrt{5}-2 } *\frac{\sqrt{5} +2 }{\sqrt{5} +2}\\\\\\\frac{(4+\sqrt{5}) }{(\sqrt{5}-2) } \frac{(\sqrt{5} +2) }{(\sqrt{5} +2)}\\\\\\\frac{(4+\sqrt{5})(\sqrt{5}+2) }{\sqrt{5}^2+\sqrt{5}*2-2\sqrt{5} -4 } \\\\\\\frac{(4+\sqrt{5} )(\sqrt{5}+2 )}{1}\\ \\(4+\sqrt{5} )(\sqrt{5}+2 )\\\\4\sqrt{5}+4*2+\sqrt{5}\sqrt{5}+\sqrt{5}*2\\ \\ 4\sqrt{5}+8+5+2\sqrt{5}\\ \\ 6\sqrt{5}+13[/tex]
Rationalizing the denominator and simplifying the expression, the result is 6√5 + 13.
Option C is the correct answer.
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If 12 +22+ 32 +
+ 5122
= m, then 22 +42 +62+ 10242 is
equal to:
4m
2m
3m
M2
M4
Answer:
m2
Step-by-step explanation:
the 2nd equation is double the first one and the first one is 1