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Measuring a Pond: A surveyor is measuring the width of a pond. The transit is setup at point C and forms an angle of 37° from point A to point B. The distance from point C to point A is 54 feet and the distance from point C to point B is 72 feet. How wide is the pond from point A to point B?
Answers
Answer:
43.47 feet (2 d.p.)
Step-by-step explanation:
Points A, B and C form a triangle.
We have been given sides a and b, and their included angle C.
The distance between points A and B is side c of triangle ABC.
Therefore, we can solve this problem using the Law of Cosines, which relates the lengths of the sides of a triangle to the cosine of one of its angles.
[tex]\boxed{\begin{minipage}{6 cm}\underline{Law of Cosines (for finding sides)} \\\\$c^2=a^2+b^2-2ab \cos (C)$\\\\where:\\ \phantom{ww}$\bullet$ $a, b$ and $c$ are the sides.\\ \phantom{ww}$\bullet$ $C$ is the angle opposite side $c$. \\\end{minipage}}[/tex]
Given values:
a = side CB = 72 ftb = side CA = 54 ftC = angle ACB = 37°Substitute the given values into the Law of Cosines formula and solve for side c:
[tex]\implies c^2=72^2+54^2-2(72)(54)\cos(37^{\circ})[/tex]
[tex]\implies c^2=8100-7776\cos(37^{\circ})[/tex]
[tex]\implies c=\sqrt{8100-7776\cos(37^{\circ})}[/tex]
[tex]\implies c=43.4719481...[/tex]
[tex]\implies c=43.47\; \sf ft\;(2\; d.p.)[/tex]
Therefore, the width of the pond from point A to point B is 43.47 feet, to two decimal places.
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Step-by-step explanation:
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For the equation: D = -0.306c + 0.9979, what is the value of D when c= 1.67? Express answer with the correct number of sig figs?
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Answer:
0.48688Step-by-step explanation:
Let's solve your equation step-by-step.
d=(−0.306)(1.67)+0.9979
Step 1: Simplify both sides of the equation.
d=(−0.306)(1.67)+0.9979
d=−0.51102+0.9979
d=(−0.51102+0.9979) (Combine Like Terms)
d=0.48688
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For each graph, decide whether or not it is a function.
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I've already answered this but
1. it is a function
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What is 4•(5+3)=4•8=
Answers
Answer:
32
Step-by-step explanation:
Answer:
32
Step-by-step explanation:
I hope this helps, and have a great day! :)
One last stop before you head home. You and your friends are worn out, but you can’t help but stop for a candy apple to eat on the ride home from Snack Centra. Yum! You would like to take some home to your family, so what’s the best deal? You can purchase 5 apples for $6.25 or 8 apples for $9.25. What’s the best way to spend your last few bucks?
Answers
Answer:
the 8 for 9.25
Step-by-step explanation:
that is the best deal because 1.25 dollars per apple for for the 5 apples for 6.25 dollars rather than 1.15 dollars per apple for the 8 apples for 9.25 dollars so therfore 8 for 9.15 is overall a better for the price per apple
bonjour,pouvez vous m’aider ;)
a. calculer DC
b.en déduire que ED =1,60 m
c.une fillette mesure 1,10 m
elle passe a 1,40m derrière la camionnette.
Le conducteur peut-il la voir ? expliquer
Données :
(AE) // (BD)
AE = 1,50 m
BD = 1,10 m
EC = 6 cm
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Answer:
je suis super nul en math desolee
Goran makes 8 dollars for each hour of work. Write an equation to represent his total pay p after working h hours.
Answers
Answer:
P=H(8)
Step-by-step explanation:
P equals Pay.
H equals Hours.
Gorans pay is whatever his hours are times 8.
P=H(8)
I hope this helps!
Linda Pearl purchased a new computer for $3,500 using the stores installment credit plan. if he is required to make a 30% down payment and finances the remaining amount what is the total amount that he will finance
Answers
Answer:
$2450 is the remaining amount
Step-by-step explanation:
i divided 3500 into 10th because its usually easier to do when you are working with percents, then so every 10 is $350. so he put down $1050 or the 30% because 350x3 is 1050 then you subtract 1050 from 3500 which then you get 2450.
Answer:
2450
Step-by-step explanation:
70% of 2450
HELPPP PLS ILL GIVE BRAINLESS DIE SOON
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Answer:
C nnnnnnnnñnnnnn
Step-by-step explanation:
That is the answer C
Three car brands A, B, and C have all the market share in a certain city. Brand A has 20% of the market share, brand B has 30%, and brand C has 50%. The probability that a brand A car needs a major repair during the first year of purchase is 0.05, the probability that a brand B car needs a major repair during the first year of purchase is 0.10, and the probability that a brand C car needs a major repair during the first year of purchase is 0.15. a. What is the probability that a randomly selected car in the city needs a major repair during its first year of purchase? b. If a car in the city needs a major repair during its first year of purchase, what is the probability that it is a brand A car?
Answers
Answer:
a.) 0.115
b.) 0.087
Step-by-step explanation:
Given,
P(A) = 20% = 0.20
P(B) = 30% = 0.30
P(C) = 50% = 0.50
Let M - major repairing during first year
P(M/A ) = 0.05
P(M/B) = 0.10
P(M/C) = 0.15
a.)
P(M) = P(M∩A) + P(M∩B) + P(M∩C)
= P(M/A).P(A) + P(M/B).P(B) + P(M/C).P(C)
= (0.05)(0.20) + (0.30)(0.10) + (0.15)(0.50)
= 0.01 + 0.03 + 0.075
= 0.115
⇒P(M) = 0.115
b.)
P(A/M) = P(A∩M)/ P(M) = P(M/A).P(A)/P(M)
= (0.05)(0.20) / 0.115
= 0.01 / 0.115 = 0.087
⇒P(A/M) = 0.087
Sophia is a salesperson at a home improvement center. She is paid a monthly commission that is 7.5% of her first $1,000 in sales and
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Answers
Write a whole number that round to 2000 if we are rounding to the nearest thousaand
Answers
Answer:2200
Step-by-step explanation:
Easy peesy lemon squezzy
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Answer:
Step-by-step explanation:
5. You are asked to write an equation of the line in slope-intercept form, so you need to determine the slope of the line and the y-intercept.
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7. When x = 0, function A = 0 and function B = 3, so function B has a greater initial value.
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Answers
Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Valerie and Seth are measuring the outside walls of a house using two different instruments. They want to find the house's perimeter. Valeria measured the north and east sides while Seth measured the west and south sides. Their results are listed in the table.
Part A
Use decimal numbers to write an expression that represents the length of the walls that Valerie measured.
Part B
Now use decimal numbers to write an expression that represents the length of the wall that Seth measured.
Part C
Write an expression for the perimeter of the house. Use the work you completed in part A & B to guide you.
Part D
Simplify the expression from part C to find the perimeter of the house in feet.
Part E
Suppose that you evaluate the expression for Valerie's wall and the expression for Seth's wall separately. Then you add the two expressions together. Will you get the same answer that you arrived at in part D? Why or why not? Show your work to prove your case.
PLEASE PLEASE PLEASE HELP I REALLY NEED HELP IN THIS WORK, THANK YOU.
Answers
Answer:
A)
Valerie measured 4 walls at 2 1/2 feet. In decimal form, each wall is 2.5 feet long. So, the total length of the 4 walls is (2.5 × 4) feet.
Valerie measured 3 walls at 21 1/4 feet. In decimal form, each wall is 21.25 feet long. So, the total length of the 3 walls is (21.25 × 3) feet.
Valerie measured 1 wall at 32 feet.
The expression that gives the total length of the walls that Valerie measured is (2.5 × 4) + (21.25 × 3) + 32.
B)
Seth measured 1 wall at 3.5 feet.
Seth measured 2 walls at 22.75 feet. So, the total length of the 2 walls is (22.75 × 2) feet.
Seth measured 1 wall at 58 feet.
The expression that gives the total length of the walls that Seth measured is 3.5 + (22.75 × 2) + 58.
C)
The total length of Valerie’s walls is (2.5 × 4) + (21.25 × 3) + 32.
The total length of Seth’s walls is 3.5 + (22.75 × 2) + 58.
To find the expression for the perimeter of the house, add Valerie’s expression to Seth’s:
(2.5 × 4) + (21.25 × 3) + 32 + 3.5 + (22.75 × 2) + 58.
D)
(2.5 × 4) + (21.25 × 3) + 32 + 3.5 + (22.75 × 2) + 58
= 10 + 63.75 + 32 + 3.5 + 45.5 + 58
= 212.75
The perimeter of the house is 212.75 feet.
E)
The total length of Valerie’s walls is 105.75 feet:
(2.5 × 4) + (21.25 × 3) + 32 = 10 + 63.75 + 32 = 105.75 feet.
The total length of Seth’s walls is 107 feet:
3.5 + (22.75 × 2) + 58 = 3.5 + 45.5 + 58 = 107 feet.
The sum of 105.75 feet and 107 feet is 212.75 feet. The Commutative Property allows me to add numbers in any order. This is why the answers in parts D and E match.
edmentum answers :)
Question 1
Which set of numbers below can be used to make a triangle?
10, 1,9
4,8,5
1,1,5
O 2, 6, 12
Answers
Answer:
The Ans is 4,8,5
Step-by-step explanation:
As 8 is the base and 4,5 are sides
Hope it helps you
Divide the product of 22 and 27 =
Answers
Find the surface area of this net.
square centimeters
Answers
Answer:
Step-by-step explanation:
area of blue triangle = 0.5×8×3 = 12 cm²
area of A = 5×12 = 60 cm²
area of C = area of A
area of B = 8×12 = 96 cm²
total surface area = 2×12 + 2×60 + 96 = 240 cm²
Answer:
240cm²
Step-by-step explanation:
Describe or show two different ways to find the volume of a right rectangular prism with dimensions of 9 centimeters by 7 centimeters by 12 centimeters.
Answers
Answer:
9×7×12=756 is the dimensions
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Answers
Answer:
7/10
Step-by-step explanation:
Brainliest?!?!?!?!
Answer: 7/10
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Identify the digit with the given place value. 0.27845 hundredths
Answers
Answer:
7.
Step-by-step explanation:
Place value can be defined as the numerical value representing a digit owing to its position in a number. Some examples of the various place values used in representing each digit are tenths, hundredths, thousandths, unit, tens, hundreds, thousands etc.
For example, in the number 0.27845;
The place value of 0 is units.The place value of 2 is tenths.The place value of 7 is hundredths. The place value of 8 is thousandths. The place value of 4 is ten thousandths. The place value of 5 is hundred thousandths.Therefore, given the number 0.27845.
The digit representing hundredths in 0.27845 is 7.
How many total outcomes of desserts are possible?
A) 4
B) 14
C) 24
D) 34
Answers
Answer:
the answear is C because if you multiply the last two boxes you get 24
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the pizza
Answers
Answer:
2.12in
Step-by-step explanation:
Pizza is circular in nature
Area of a circle = πr²
r is the radius
Given
A = 14.13in²
14.12 = 3.14r²
r² = 14.12/3.14
r²= 4.49
r = 2,12in
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Answers
Answer:
0.5
Step-by-step explanation:
Answer:
1/5
Step-by-step explanation:
It's okay, you're not dum, you might have just not payed attention in online class or you might have forgotten.
We can find the slope by using 2 coordinates that are on a line.
We can choose any of the coordinates from this table. I'm gonna use (0, 4) and (2, 5)
The formula for find the slope is the rise over the run or
y1 - y2 / x1 - x2
4 - 5 / 0 - 5
-1 / -5
1/5
The slope is 1/5
0.9 (13) - 1.7 (3) =
Answers
Answer:
6.6
Step-by-step explanation:
HELP! Question down below
Answers
Answer:
B. Both are correct
Step-by-step explanation:
The graph correctly shows y=2x and the table is right.
Answer:
Your answer is.....
Both are correct
Mark it as brainlist answer . follow me for more answer.
Step-by-step explanation:
Darby bought a rare baseball card for $2,000. Three years later, the value of the card had increased 35% of its original value. By how much did the value of Darby’s baseball card increase?
$___
Answers
================================================
Work Shown:
35% = 35/100 = 0.35
35% of 2000 = 0.35*2000 = 700
Since the card increased by 700 dollars, this means the card is now worth 2000+700 = 2700 dollars.
2(x+5)=3x+1
How do I solve this
Answers
Answer:
x = 9
Step-by-step explanation:
2(x+5)=3x+1
Distributive Property
2x+10=3x+1
Subtract 2x from both sides
10=x+1
Subtract 1 from both sides
9=x
Correct form: x=9
in math what does the word "of" mean
Answers
Answer:
Multiplication
Step-by-step explanation:
The word 'of', in Math, simply means multiplication. Generally, whenever you encounter this word, put a multiplication sign in your equation at that point. The word 'of' is used very simply in percentage problems, and usually you just have to replace 'of' with a multiplication sign to get rid of it!
Answer:
"In mathematics, “of” means ”a part of something”. Mostly, “of” means “to multiply”. In other context, mathematical expressions like “f of x”, where “of” means “depending on” or “involving” or “defined in terms of” “x”; it also refers to the act of applying the function to its argument".
Step-by-step explanation:
Yw. Plz mark brainliest
H(x)= -x^2+ 3x + 5 What is the average rate of change from x = 3 to x = 5
Answers
Answer:
f(x)=x^(2),[2,3]
-2x-h+3
Step-by-step explanation: