Answer:
A.) 2752.8 feet
B.) 5044.3 feet
C.) 6182.9 feet
Step-by-step explanation:
A.) Given that the camp to the base of the mountain is 2,000 feet. And the angle of elevation is 54 degrees
Using SohCahToa, to calculate the height
Tan 54 = height/2000
Height = 2000 tan54 = 2752.8 feet
B.) Given that the base of the mountain is 2600 feet wide.
Let use pythagorean theorem to find the slant length
Adjacent = 2600/2 = 1300 feet
Slant length = root ( 1300^2 + 2752.8^2)
Slant length = 3044.3 feet
The total distance that Jacob and his dad hiked from their campsite to the top of the mountain will be
3044.3 + 2000 = 5044.3 feet
C.) Given that the angle of depression is 24 degrees while the height is 2752.8 feet
Using pythagorean theorem again
Tan 24 = 2752.8/distance
Distance = 2752.8/tan24
Distance = 6182.9 feet
The height of the mountain for the following conditions are as follows:
A.) 2752.8 feet
B.) 5044.3 feet
C.) 6182.9 feet
What is Angle of Elevation?The angle of elevation is an angle that is formed between the horizontal line and the line of sight.
A.) Given that the camp to the base of the mountain is 2,000 feet. And the angle of elevation is 54⁰
To calculate the height
Tan 54⁰ = height/2000
Height = 2000 X tan54⁰ = 2752.8 feet
B.) Given that the base of the mountain is 2600 feet wide.
Let use pythagorean theorem to find the slant length
Adjacent = 2600/2 = 1300 feet
Slant length = √ ( 1300^2 + 2752.8^2)
Slant length = 3044.3 feet
The total distance that Jacob and his dad hiked from their campsite to the top of the mountain will be
3044.3 + 2000 = 5044.3 feet
C.) Given that the angle of depression is 24⁰ while the height is 2752.8 feet
Using Pythagorean theorem again
Tan 24⁰ = 2752.8/distance
Distance = 2752.8/tan24⁰
Distance = 6182.9 feet
Thus, the height of the mountain for the following conditions are as follows:
A.) 2752.8 feet
B.) 5044.3 feet
C.) 6182.9 feet
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1) Which of the equivalent expressions for P(x) reveals the price which gives a profit of
zero without changing the form of the expression?
P(x) = -3x? + 432x - 1680
b) P(x) = -3(x-4)(x - 140)
P(x) = -3(x - 72)2 + 13872
2) Find a price, which gives a profit of zero.
Answer:
1. (B)P(x) = -3(x-4)(x - 140)
2. $140
Step-by-step explanation:
(1) Given the profit function, P(x) where x is the price, the expression which reveals the price which gives a profit of zero without changing the form of the expression is:
P(x) = -3(x-4)(x - 140)
This is as a result of the fact that equating it to zero immediately yields the zeros of the quadratic polynomial.
(2)When the profit, P(x)=0, then using the expression above we have:
[tex]P(x) = -3(x-4)(x - 140)\\Since -3\neq 0, then:\\x-4=0$ or x-140=0\\x=4 or x=140[/tex]
A price of $4 or $140 as the case may be gives a profit of zero.
Write an expression in simplest form for the perimeter of a right triangle with leg lengths of 12a to the power of 5 and 9a to the power of 5.
Answer:
[tex]36a^5[/tex].
Step-by-step explanation:
In a right angle triangle,
Length of one leg [tex]=12a^5[/tex]
Length of other leg [tex]=9a^5[/tex]
According to the Pythagoras theorem,
[tex]Hypotenuse^2=leg_1^2+leg_2^2[/tex]
Using Pythagoras theorem,
[tex]Hypotenuse^2=(12a^5)^2+(9a^5)^2[/tex]
[tex]Hypotenuse^2=144(a^5)^2+81(a^5)^2[/tex]
[tex]Hypotenuse=\sqrt{225(a^5)^2}[/tex]
[tex]Hypotenuse=15a^5[/tex]
Perimeter of right angle triangle is the sum of all sides of the triangle.
[tex]Perimeter=12a^5+9a^5+15a^5[/tex]
[tex]Perimeter=36a^5[/tex] units.
Therefore, the required expression is [tex]36a^5[/tex].
Justin played a game with 24 floating plastic ducks each with a colored sticker on the bottom. There are an equal number of red blue and green stickers on the set of ducks. What is the probability that one duck chosen at random will have a red or blue sticker
Answer:
Because there are 24 ducks total and they are separated equally into three categories, we can figure out that there are 24 / 3 = 8 ducks of each color. This makes the probability of pulling a red/blue duck would be (8*2)/24 or 16/24. If we want this to be a percentage we can just solve 16/24*100 and it will give us 66.66...%
A baseball coach purchased a total of 28 helmets and caps. Each helmet cost $21.50, and each cap cost $8.25. If the coach spent a total of $363.50, how many helmets did the coach purchase?
Answer:
5 helmets
31 caps
8.25, 16.50 24.75 33 x 10 = 330
330/2 = 165 = 20 helmets
363.50 - 165 = 198.50
5 x 21.50 = 107.50 (+ 11 x 8.25 = 16.50+24.75 +24.75+24.75 = 49.50+41.25) =£91 + 107.50 = 198.50
20+11 = 31
31 caps
5 helmets
Step-by-step explanation:
There are 10 helmets did the coach purchase.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
A baseball coach purchased a total of 28 helmets and caps.
And, Each helmet cost $21.50, and each cap cost $8.25. and the coach spent a total of $363.50.
Let number of helmets = x
And, Number of caps = y
Here, A baseball coach purchased a total of 28 helmets and caps.
Hence, We get;
⇒ x + y = 28 ..(i)
And, Each helmet cost $21.50, and each cap cost $8.25. and the coach spent a total of $363.50.
Hence, We get;
⇒ 21.50x + 8.25y = 363.50
⇒ 5 (4.30x + 1.65y) = 5 × 72.7
⇒ 4.30x + 1.65y = 72.7 .. (ii)
Multiply by 4.30 in (i) ad subtract from (ii);
⇒ 4.30x + 4.30y - 4.30x - 1.65y = 120.4 - 72.7
⇒ 2.65y = 47.7
⇒ y = 18
And, From (i);
⇒ x + y = 28
⇒ x + 18 = 28
⇒ x = 10
Hence, Number of helmets = 10
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f(n) = 41 – 5n
Complete the recursive formula of f(n).
f(1) =
f(n) = f(n − 1)+
Answer:
f(1) = 36
f(n) = f(n-1) - 5.
Step-by-step explanation:
f(1) = 41 - 5 = 36.
f(n) = f(n - 1) - 5.
I need help with this math problem please
Answer:
x=12
Step-by-step explanation:
90 = x + 42 + 3x
48 = x + 3x
48 = 4x
12 = x
Answer:
x = 12
Step-by-step explanation:
Since we are given a right angle, we can say that:
sum of all angles = 90 degrees
x + 42 + 3x = 90
4x = 48
x = 12
So, x is equal to 12 degrees!
Hope this helps))) ^‿^
1. Warp coils, like those found on my new spaceship, are manufactured in groups of 36 (as everyone
knows). If there is a 4% rate of defect in manufacturing,
a) find the mean number of defects per group.
a)
Answer:
1.44
Step-by-step explanation:
No. of warp coils manufactured in one group = 36
defect rate = 4%
That is 4 out of every 100 warp coil is defective
No. of defective warp coil in one group = 4% of warp coil in one group
= 4% of 36 =4/100 *36
= 1.44
Thus, there are 1.44 defective coil in each group.
Since, mean number is average number of defect.
So if each group has 1.44 defective coils then mean for all the group will remain same i.e 1.44
Find the probability that a point chosen at random will lie in the shaded region.
I don't understand what to do here :(
Step-by-step explanation:
In the 1st question
Total boxes = 6
Shaded boxes = 2
Probability = 2/6 = 1/3
PLZZZ HELP ME I NEED HELP AND I HAVE A TIMER AND I WILL GIVE YOU BRAINLEST
On a coordinate plane, 2 lines intersect around (3.8, negative 1.5).
Given the graph of a system of equations, which statements are true about the solution? Check all that apply.
The x-value is an integer.
The x-value is between 3 and 4.
The y-value is between –2 and –1.
The x-value is positive.
The x- and y-values have the same sign
Answer:
b,c,d
Step-by-step explanation:
I just did the assignment
Answer:
b, c. d
Step-by-step explanation:
Can someone help me with questions 2 and 3 pls?
1 cup = 1/2 pint, so where it says 4 cups we'll just read 2 pints.
1. In one show we serve 30 × 2 pints of small and 42 × 6 pints of regular.
Total = 30 × 2 + 42 × 6 = 60 + 252 = 312 pints
Answer: 312 pints
2. 8 pints per gallon, 2 gallons per container makes 16 pints per container.
312 pints / 16 pints per container = 19.5 containers
We round up since we need a whole number of containers.
Answer: 20 containers
We can't really see question 3.
Von mixes tomato sauce and milk to make soup. First he puts 150 milliliters of
tomato sauce in a pot. Next he adds the milk that is in the measuring cup. How
many milliliters of soup does he make?
A. 400 milliliters
B. 460 mill
C. 350 mill
D. 500 mill
Answer:
500 milliliters or ml
Step-by-step explanation:
First, we find the amount of milk is in the measuring cup which is 350 ml and then add 350 ml of milk to the 150 ml of tomato sauce to get 500 ml.
Hope it helped :)
The amount of soup made by Von is equal to 500 milliliters. Hence, option D is correct.
What are arithmetic Operations?The four fundamental operations of arithmetic are addition, subtraction, multiplication, and division of two or even more items.
Included in them is the study of integers, especially the order of operations, which is important for all other areas of mathematics, notably algebra, data management, and geometry.
As per the data given in the question,
Von mixes tomato sauce and milk to make soup.
Initially, the amount of tomato sauce added in the pot = 150 milliliters.
Then, milk is added that is in the measuring cup that is 350 milliliters.
So,
The total amount of soup made by him,
= 150 + 350
= 500 milliliters.
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What is the volume of this rectangular prism?
Answer:
volume = 5/8 cm^3
Step-by-step explanation:
v=lwh
(5/2)(1/3)(3/4)=15/24=5/8
Therefore, volume = 5/8 cm^3
I hope this helped and have a good rest of your day!
I need help plzzzz I’m nearly done
Answer:
≈ 70.4 cm
Step-by-step explanation:
The circumference (C) of a circle is calculated as
C = 2πr ( r is the radius ) , thus
C = 2 × 3.142 × 11.2 ≈ 70.4 ( to 1 dec. place )
HELP ASAP
table
———————————————
Radius (ft) Bushels of corn
500 2705
1000 10818
1500 24341
2000 43273
2500 67613
What type of function best models the given data set?
A. Constant
B. Exponential
C. Linear
D. Quadratic
Answer:
Linear would be fine as it doesn't decrease to under zero
and a curve graph would represent this data fine at 10818 turning point.
Step-by-step explanation:
-4b - 5 + 2b =10. Can I have some help solving this.
Answer:
-7.5
Step-by-step explanation:
Simplify
-4b - 5 + 2b = 10
-2b - 5 = 10
-2b = 15
b = -7.5
Answer:
-7.5
Step-by-step explanation:
-4*- 7.5 =30
2*-7.5= -15
30-5-15=10
The graph shows the rate that Tom travels
on his bicycle, with the line traveling through
the point (5,45)
Use this graph to answer questions 1 and 2.
What is the constant of proportionality in the graph?
Answer:
The constant of proportionality is 9.
Step-by-step explanation:
k=y/x This is the formula.
k=45/5 Plug in the x and y coordinates of a point on the line (5,45).
k=9 Here's your answer!
Ginger is taking a cab in Washington D.C. The taxi fare includes a base charge of $3.00 as soon as you enter the cab, plus an additional $2.50 per mile traveled. If Ginger starts off with a $50 bill, takes a cab for 8 miles and leaves a $2 tip. How much money will she be left with?
Answer:
she will be left with 25 dollars
Step-by-step explanation:
2.50 x 8=20
20+3+2=25
Answer:
Answer is 25 dollars.
Step-by-step explanation:
3$- 50 dollars= 47.
2.50 x 8= 20 dollars.
20$ -47 = 27.
2$- = 25
What is the total area, in square units, of the
figure shown below?
a. 6
b. 12
c. 24
d. 30
Answer:
30 !
Both are right triangles so you can do 4*3= 12 and then 12/2= 6
then 6*8=48 and 48/2=24
24+6 =30!
hope this helps ! :)
Find the 76th term of the arithmetic sequence 17, 19, 21, ...
Answer: 167
Step-by-step explanation: To find the 76th term of this arithmetic sequence, we will be using our explicit formula which is shown below.
[tex]^{a}n = ^{a}1 (n - 1)d[/tex]
Since we want to determine the 76th term, we are going
to substitute 76 in for n in our explicit formula.
Then, [tex]^{a}1[/tex] will be our first term in our sequence which is 17.
Lastly, d is our common difference or the difference between each of the terms in our arithmetic sequence which is 2.
So we have [tex]^{a} 76 = 17 + (76 - 1)(2)[/tex].
Now we have all the information we need. Just simplify from here.
Make sure to apply order of operations because this is where many
students make mistakes. Inside the parentheses first!
(76 - 1) is going to be 75.
So we have [tex]^{a} 76 = 17 + (75)(2)[/tex].
Then, we have to make sure we multiply before we add.
So (75)(2) is going to give us 150.
So we have [tex]^{a} 76 = 17 + 150[/tex].
Now just add to find that [tex]^{a} 76 = 167[/tex].
So the 76th term is 167.
In the figure angle a measures 41 degrees and angle d measures 32. What is the measurement of angle E?
Answer:
it is c
Step-by-step explanation:
Find the volume of this cylinder. Give your answer to 1 decimal place when the radius is 11 cm and the length is 14 cm
Answer:
5324
Step-by-step explanation:
volume of cylinder=πr^2l=22/7×11^2×14=5324
Pls answer quickly, this is due today !!!!!!
Mrs. Rappa has decided to take her $2,000 and go check out the savings accounts at Circle Bank of PI Haven. She picks up a flyer in the lobby. There are a couple of savings accounts to choose from. Look at the copy of the information from the flyer below. Write a letter to Mrs. Rappa and offer your advice to her about her options. Be sure to tell Mrs. Rappa your reasoning (using sentences and showing calculations for each account) to decide which account is best. If you have additional advice for Mrs. Rappa about the number of years she is investing her funds - you may do so.
Savings Accounts Interest Rate Years in account
Sleepy Savings 5% 7
Centsational Savings 10% 3
Answer:
Step-by-step explanation:
Dear Mrs.Rappa,
I don't know much about this but i do know that saving accounts are risky and she should just set up a checking. Because it's proven that you'll take the risk of losing value in your money. And you take a risk, but to help you more i need to know about what the 5% 7 means. if i do know what it's means, but the 5% is good, it's compound interest which means you get more money on that interest It grows, but as far as the 7 goes, IDK. but the saving %"s are good like yay money, but she takes the risks. So why the risk is there is because of the stock market, and also because the bank takes other clients money for them to pay other client's. So a risk in 7yrs.
Sincerely,
First name Last name Here
a rectangular field has side lengths that measure 9/10 mile and 1/2 mile. What is the area of the field
Answer:
9/20, or 0.45 mile.
Step-by-step explanation:[tex]\\[/tex]
To find the area of a rectangle, multiply length times width. In this problem we are given both the length and width.
[tex]\frac{9}{10}[/tex] × [tex]\frac{1\\}{2}[/tex] is just 9/20, which is 0.45.
I need the right answer please
Answer:
a) i) x = 6, y = 9
ii) 20
iii) -5
b) -40
Step-by-step explanation:
3(6) - 2(9)
18 - 18 = 0
greatest
3(10) - 2(5)
30 - 10
20
least
3(5) - 2(10)
15 - 20
-5
5(a - 4b)
5[-7 - 4(¼)]
5(-7 - 1)
5(-8)
-40
What is the solution to this system of equations?
Negative 3 x + 5 y = negative 2. 3 x + 7 y = 26.
(4, 2)
(2, 3 and one-third)
no solution
infinitely many solutions
Answer:
4,2
Step-by-step explanation:
did the test
The solution of the system of equation is (4, 2) which is correct option(A).
What is equation?Equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.
Given the two systems of equations,
-3x + 5y = -2
3x + 7y = 26
Adding the both equations
-3x + 5y + 3x + 7y = -2+26
12y = 24
y = 2
Substitute the value of y in any one of the equations,
3x + 7 y = 26
3x + 7(2) = 26
3x = 26-14
3x = 12
x = 4
Hence, the solution of the system of equation is (4, 2).
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12. For angle A it is known that sin(A)>0 and tan (A) <0. If A is drawn in standard position, in which quadrant
does its terminal ray lie?
Answer:
Quadrant 2
Step-by-step explanation:
Sin = opp/hyp and opp is positive in quadrants 1 & 2.
Tan = opp/adj - we need one of these values to be positive and the other negative. adj is negative in quadrants 2 & 3.
Quadrant 2 is found in both of the scenarios that we need to occur.
find the term independent of x in the expansion of x^9(2-1/x^3)^6
(it's also pictured)
Answer:
20
Step-by-step explanation:
how do i solve this?
Answer:
idk
Step-by-step explanation:
idk
Answer:
that is to hard
Step-by-step explanation:
What is the value of x in the equation below?
40x + 120 = 720
21
18
15
12.5
Answer:
The answer would be 15.
Step-by-step explanation:
The first thing that you have to do is subtract 120 on both sides
40x + 120 = 720
-120 -120
40x = 600
Then you have to divide by 40.
40x= 600
600 ÷ 40 = 15
x = 15.
I hope I helped
Answer:
15
Step-by-step explanation:
40×15=600+120=720
Big ideas math 6th grade chapter 5 test
Answer:
I'm not sure if you need help but...
Step-by-step explanation:
6+6=12
