Answer:
11.17 ft
Step-by-step explanation:
Since the swing hangs from a beam 10 feet high with the seat hanging 2 feet above the ground, the swing moves in an arc of radius r = 10 ft - 2 ft = 8 ft.
Now, since the swing moves back and forth from -130° to -50° to the horizontal, the length of arc L it moves in is given by
L = Δθ/360 × 2πr where Δθ = change in angle of the swing = θ₂ - θ₁ where θ₁ = -50° and θ₂ = -130°. So, Δθ = θ₂ - θ₁ = -130° -(-50°) = -130° + 50° = -80°.
Substituting r and Δθ into L, we have
L = -80°/360° × 2π(8 ft)
= -8/36 × 16π ft
= -32π/9 ft
= -100.53/9 ft
= -11.17 ft
Ignoring the negative sign, the length of arc L = 11.17 ft. So, the swing moves back and forth 11.17 ft
HELP ME QUICK
Consider the Pythagorean Theorem and its converse. Which statements are correct?
A)
6, 8, and 10 are possible side lengths for a right triangle.
B)
10, 15, and 20 are possible side lengths for a right triangle.
The Pythagorean Theorem works only for sides of a right triangle.
D)
If the sides of a right triangle are of length 8 and 15. its hypotenuse is 17
E)
The Converse of the Pythagorean Theorem allows us to calculate side
lengths of right triangles.
Answer:
Step-by-step explanation:
A-Yes
B-No
C-Yes
D-Yes
E-Yes
If consider the Pythagorean Theorem and its converse. A, C, D, and E are correct statements.
What is Pythagoras's theorem?Pythagoras's theorem states that in a right-angled triangle, the square of one side is equal to the sum of the squares of the other two sides.
In this case, statement A is correct because 6, 8, and 10 are possible side lengths for a right triangle.
Statement B is incorrect because 10, 15, and 20 are not possible side lengths for a right triangle.
Statement C is correct because the Pythagorean Theorem works only for sides of a right triangle.
Statement D is correct because if the sides of a right triangle are of lengths 8 and 15, its hypotenuse is 17.
Statement E is correct because the converse of the Pythagorean Theorem allows us to calculate the side lengths of right triangles.
Thus, the correct statements would be options A, C, D, and E.
Learn more about Pythagoras's theorem here:
brainly.com/question/343682
#SPJ2
1. Lynn is tracking the progress of her plant's growth. Today the plant is 5 cm high. The plant grows 1.5 cm per day. A. Find an equation that represents the plants height after any given number of days. B. How tall is the plant after 9 days?
Answer:
the anwer is C
Step-by-step explanation:
I hope its help
Freddy earns $750.00/week, he is single and has 3 dependents. He lives in a state with a tax rate of 3%. What does he pay in state income taxes every week?
Answer:
$17.88
Step-by-step explanation:
Freddy earns = $750 per week
Has 3 dependents
and he is single
Tax rate = 3%
Lets calculate Freddy's Annual Taxes and Taxable income
Freddy's Annual income = 750 *52 = $39,000
Annual Allowance for a single person = $2000
Annual allowance for 3 dependents = $2000 * 3 = $6000
Hence Freddy's Annual Taxable Income = ( 39000 - 8000 ) = $31,000
Annual withheld tax = 3% * $31,000 = $930
Therefore Freddy's weekly withheld tax = 930 / 52 = $17.88
The initial temperature of the mixture was +20 °C. The mixture froze at –1.5 °C.
A total of 165 kJ of internal energy was transferred from the mixture to cool and
freeze it.
specific heat capacity of the mixture = 3500 J/kg °C
specific latent heat of fusion of the mixture = 255 000 J/kg
Calculate the mass of the mixture.
Give your answer to 2 significant figures.
Answer:
Step-by-step explanation:
Meredith invests $18,200 in an account that earns
3.25% simple interest. What will the balance in
Meredith's account be after 15 years?
How to factorise
a²b² - 6abc + 9c²
can anyone explain it by step-by-step
pls
Answer:
here is the step by step factorization process
How can sample data be used to from an estimate about the population?
Answer: A proportion can be solved to relate the sample to the population and solved to form an estimate.
Step-by-step explanation:
What is the sum of 5+ 12^2
Answer:
169
Step-by-step explanation:
5² + 12²
25 + 144
169
Natalie had 20 lbs. of cat food. If she feeds
her cat 6 of a pound daily, how many days
will the food she has last?
Answer:
3 days
Step-by-step explanation:
20/6 is 3.333
Answer:
3 days
Step-by-step explanation:
cuz after three days you will have two pounds left so you cant go another day
Please help with #28 I’m really struggling to figure this answer out!
Answer:
cant help you i dont one suck
What is the approximate diameter of a tire that will make 775 complete rotations in one mile? (Note: there are 5280 feet
in 1 mile)
Answer:
About 2.17 feet.
Step-by-step explanation:
Let d represent the diameter of the tire.
Then the circumference of the tire will be:
[tex]C=d\pi[/tex]
So, the tire will travel dπ miles after one rotation.
After 775 rotations, the total miles traveled should be 5280 feet. Thus:
[tex]775(d\pi)=5280[/tex]
Solve for d:
[tex]\displaystyle d=\frac{5280}{775\pi}[/tex]
Approximate:
[tex]d=2.1686...\approx2.17[/tex]
The circumference of the tire should be about 2.17 feet.
this is really easy i just dont get it
Answer:
x=1
Step-by-step explanation:
We wanna have the same amount on both sides
There are 3 circles on the left and 7 circles on the right. There are also 4 triangles. Turn into numbers...
4x+3=7
4x=7-3
x=1
We can check by substituting one
7=7
Cups are sold in packages of 8. Napkins are sold in packages of 12.
What is the fewest number of packages of cups and the fewest number of packages of napkins that can be purchased so there will be the same number of cups as napkins?
Answer:
2 Packages of Napkins, 3 Packages of Cups
Step-by-step explanation:
12 * 2 = 24
8 * 3 = 24
Answer:
3 packages of cups and 2 packages of napkins
-30=p-17
help pleaseee
Answer:
p = -13
Step-by-step explanation:
2^5*2^negative 3 simplify
Answer:
4
Step-by-step explanation:
Simplify the following:
2^5/2^3
Hint: | For all exponents, a^n/a^m = a^(n - m). Apply this to 2^5/2^3.
Combine powers. 2^5/2^3 = 2^(5 - 3):
2^(5 - 3)
Hint: | Subtract 3 from 5.
5 - 3 = 2:
2^2
Hint: | Evaluate 2^2.
2^2 = 4:
Answer: 4
An item is regularly priced at $30. It is now priced at a discount of 30% off the regular price. What is the price now?
1. Which equation represents a line that is parallel to the line y = 4x – 1?
Find the value of x degrees.
Answer:
X=25°
Step-by-step explanation:
[tex]x = \frac{1}{2} (t2 - 22) [/tex]
[tex] = \frac{1}{2} (50)[/tex]
[tex] = 25[/tex]
[tex]x = 25[/tex]
hope it helps u
Write the unit rate per video game. $78 for 4 video games. $ for video game. 100 points question better not be wrong or else
Answer:
78:4
Step-by-step explanation:
Noah randomly selects one of his eight different pairs of shoes to wear each day. Of his eight pairs of shoes, Noah has two pairs of boots and one pair of loafers. For how many days of the next 264 is it expected that Noah will wear either boots or loafers?
Answer: I’m pretty sure it’s 11/264 days
Step-by-step explanation:
Evaluate ba+cd if a=7/8 , b=−7/16 , c=0.8 , and d=1/4 . Write your answer as a mixed number in simplest form.
Answer:
-117/640
Step-by-step explanation:
ba + cd
b= -7/16
a= 7/8
c= 08.(4/5)
d= 1/4
Hence it can be calculated as follows
-7/16×7/8 + 4/5×1/4
-49/128 + 1/5
-246+128/640
= -117/640
Answer: -2 11/20
Step-by-step explanation I did this and it is correct
(8x- 1) (11X - 25) (15y - 48)
1320xyX−4224xX−165yX−3000xy+528X+9600x+375y−12001320xyX-4224xX-165yX-3000xy+528X+9600x+375y-1200
Write the slope-intercept form of the equation of the line.
Answer:
1
Step-by-step explanation:
the line is y = x+2
x is greater than or equal to -1 and less than or equal to 4
Use x only once in your inequality.
Answer:
x ≥ -1 ≤ 4
Step-by-step explanation:
This would be your inequality.
true or false: the diagonals of a rectangle bisect opposite angles
Answer:
False
Step-by-step explanation:
diagonals don't have to be congruent or bisect each other. The diagonals of a rectangle bisect its angles.
HURRY NEED HELP ASAP
The following information is known about a loan.
Time = 8 years
Interest rate = 14%
Principal = $1,010
What is the total amount of simple interest that is earned?
$113.20
$1,131.20
$11,311.20
$113,112.00
Answer:
1,131.20
Step-by-step explanation:
I=prt
1,010*0.14*8
A contractor rents a trailer truck to
haul materials. The inside of the
trailer is 20 feet long, 7 feet wide,
and 8 feet high. Find the storage
capacity of the trailer in cubic feet.
Answer:
1120ft^3
Step-by-step explanation:
A spinner for a game has 5 equal sections labeled 1-5. why is the probability of spinning a 1 or a 4?
Answer:
40%
Step-by-step explanation:
5 shots 20% for each you have 2 so 20+20=40
help asap i need to know if the property is a b c or d
Answer:
B
Step-by-step explanation:
In steps 1 and 2 there is only addition occuring to both sides of the equation.
6. Place the decimals in order from
least to greatest.
2.12 2.21 2.14 2.41
4.51 45.1 54.1 4.15 41.5
Answer:
2.12
2.14
2.21
2.41
4.15
4.51
41.5
45.1
54.1