Casey is in Florida when a Zombie Apocalypse suddenly breaks out in his area. He needs to help his family and friends cross a sinkhole to escape the marauding herd. Help Casey calculate the amount of rope he will need to zipline his family and friends to safety … don’t mess this up!
(a) Choose a point on the graph (using whole numbers) and use this point to form a triangle, making the red line one side of this triangle. Calculate the three midsegments of the triangle you created, these will stabilize the zipline. Show all of your calculations below and draw in your work in the image above.
(B) Calculate the perimeter of the triangle and the lengths of each midsegment. Add these together so that Casey knows just how much rope he will need to create this lifeline to safety. Show all of your work below. Only round off at the end of the problem. Round to the nearest hundredth digit.
Pleaseeee help 50 points I don't know how to make you brainliest but include that with the answer and I will make you brainliest plzz
Answers
Attaching ropes to the midsegment of the triangle formed ensures that the
zipline can more safely cross the family and friends to safety.
The amount of rope needed to create a lifeline to safety is approximately 46.56Reasons:
The coordinates of the endpoints of the redline = A(4, 3), and B(-8, -2)
The point selected, P = (4, -3)
[tex]\displaystyle Mid \ point \ of AB, \ D = \left(\frac{4 + (-8)}{2}, \ \frac{3 + (-2)}{2} \right) = \left(-2, \, 0.5\right)[/tex]
[tex]\displaystyle Mid \ point \ of AP, \ E = \left(\frac{4 +4}{2}, \ \frac{3 + (-3}{2} \right) = \left(4, \ 0 \right)[/tex]
[tex]\displaystyle Mid \ point \ of\, BP, \ F = \left(\frac{-8 +4}{2}, \ \frac{-2+ (-3}{2} \right) = \left(-2, \ -2.5\right)[/tex]
The lengths of the midsegments are found as follows
Length of DE = √((4 - (-2))² + (0 - (0.5))²) = 0.5·√(145)
Length of DF = √(((-2) - (-2))² + ((-2.5) - (0.5))²) = 3
Length of EF = √(((-2) - 4)² + ((-2.5) -0)²) = 6.5
(b) The length of side AB = √((4 - (-8))² + (3 - (-2))²) = 13
The length of side BP = √((4 - (-8))² + (-3 - (-2))²) = √(145)
The length of side AP = √((4 - 4)² + (-3 - 3)²) = 6
The perimeter of the triangle ΔABP = 13 + 6 + √(145) = 19 + √(145)
The amount of rope needed to create a lifeline to safety is therefore;
19 + √(145) + 0.5·√(145) + 3 + 6.5 = 28.5 + 1.5·√(145) ≈ 46.56
The amount of rope needed to create a lifeline to safety = 46.56
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Related Questions
how much water should be added to 5 gallons of 50% acid solution to get a 20% solution?
ASAP!!! PLS
Answers
Answer:
22.5
Step-by-step explanation:
50%of5+20%=22.5
50/100×5=2.5
2.5+20=22.5%
Answer:
3 gallons
Step-by-step explanation:
10=100 percent
10/5 =2
5-2=3
3 gallons
sets if 98% of households have at least one television set and 4 households are selected, find the probability that at least one household has a television set.
Answers
Using the binomial distribution, it is found that there is a 0.99999984 = 99.999984% probability that at least one household has a television set.
For each household, there are only two possible outcomes, either it has at least one television set, or it does not. The probability of a household having at least one television set is independent of any other household, which means that the binomial distribution is used to solve this question.
Binomial probability distribution
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes. n is the number of trials. p is the probability of a success on a single trial.In this problem:
4 households are selected, hence [tex]n = 4[/tex].98% have at least one television set, hence [tex]p = 0.98[/tex]The probability that at least one household has a television set is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.98)^{0}.(0.02)^{4} = 0.00000016[/tex]
Then:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.00000016 = 0.99999984 [/tex]
0.99999984 = 99.999984% probability that at least one household has a television set.
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Find the slope and y-Intercept of the line in the graph. Drag and drop each number into the correct box
to complete the statement.
7
(0,5)
4 3
2
1
0
(3,-1)
-1
-2
3
TO
de
8 7
0 1 2
55
The slope is m
and they-intercept is b =
Answers
Answer:
slope = - 2, y- intercept = 5
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 5) and (x₂, y₂ ) = (3, - 1) ← 2 points on the line
m = [tex]\frac{-1-5}{3-0}[/tex] = [tex]\frac{-6}{3}[/tex] = - 2
The y- intercept is the point on the y- axis where the line crosses
The y- intercept = 5
If an amount of $25,000 is deposited into a saving account at an interest rate 4%, compounded semi-annually, how long will it take to accumulate on this account $28,500? The function describing your balance is M(n) =25,000(1+0.04/2)^2n, where n is time in years. Round up your answer to the next period.
Answers
It will take 3 years and 4 months to accumulate $ 28,500.
To determine, if an amount of $ 25,000 is deposited into a saving account at an interest rate 4%, compounded semi-annually, how long will it take to accumulate on this account $ 28,500, the following calculation must be performed:
25,000 x (1 + 0.04 / 2) ^ (2X) = 28500 25000 x 1.02 ^ 2X = 28500 1.02 ^ 2X = 28500/25000 1.02 ^ 2X = 1.14 1.02 ^ 6.62 = 1.14 6.62 / 2 = X 3.33 = X
Therefore, it will take 3 years and 4 months to accumulate $ 28,500.
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What is the slope of a line perpendicular to the line whose equation is
3x + 3y = –27. Fully simplify your answer.
Answers
Answer:
1
Step-by-step explanation:
Perpendicular lines always have the opposite slope (meaning that you have to switch the numerator and denominator) and sign when comparing to the given equation.
To start off, convert the equation to be formatted into y=. You do this by first subtracting the 3x from both sides of the equation so that it now reads 3y=-3x-273y=−3x−27 . Now, divide the whole equation by three in order to get rid of the value attached to the y. The equation should now read to be: y=-x-9y=−x−9 . Now, just switch the the slope into its opposite (which is the reciprocal) and switch the negative sign into a positive.
what you've learned from it. Was it a success or a challenge?
Answers
which is the correct answer??
geometry
Answers
Answer:
SAS || Side - Angle - Side
Step-by-step explanation:
You have 2 sets of congruent sides, and one set of congruent angles between them. (SAS)
That angle is congruent because ∠QRP and ∠TRS are vertical angles, and vertical angles have the same measurement.
22 divided by 2,737 include the remainder
Answers
Answer:
124.409
Step-by-step explanation:
sana makatulong sa inyong lahat
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks.
A pair of kids and a pair of adults decided to compete in a three-legged race. The kids got to start 15 yards ahead of the adults, since they had shorter legs. When they were told to start, the kids hobbled forward at a rate of 1 yard per second, and the adults hobbled after them at a rate of 4 yards per second. Soon they were side-by-side. How long did that take? How far did the adults go?
It took seconds for the adults to go yards and catch up to the kids?
Answers
A system of equations is simply a system that contains related equations of multiply variables
It took 5 seconds for the adults to go 20 yards and catch up to the kids
Let x represents the time of the race
The kids started 15 yards ahead, and they raced at 1 yard per second.
So, the kids' equation is represented as: [tex]\mathbf{k =15 + x}[/tex]
The adults' raced at 4 yards per second.
So, the adults' equation is represented as: [tex]\mathbf{a =4x }[/tex]
When they are side by side, we have the following equivalent equation
[tex]\mathbf{4x = 15 + x}[/tex]
Subtract x from both sides
[tex]\mathbf{3x = 15}[/tex]
Divide both sides by 3
[tex]\mathbf{x = 5}[/tex]
It means that, it took the adults 5 seconds to catch up with the kids
Substitute 5 for x in any of the equations to calculate the distance travelled.
[tex]\mathbf{a =4 \times 5}[/tex]
[tex]\mathbf{a =20}[/tex]
It means that, the adults catch up with the kids at 20 yards
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Answer:
The adults went 123 yards and caught up to the kids in 41 seconds
Step-by-step explanation:
ixl :)
The total cost of going to the theatre for 18 people is £803.16.
How much will each person need to pay to cover the total cost?
Answers
You and your best friend are both on the swim team. You want to beat your friend at the next swim meet so you decide to swim 151515 minutes longer than she does one day at practice.
Answers
Answer:
45
Step-by-step explanation:
15+15+15=45
that would increase her practice time by 45 minutes
just add 15’s
3
Roy and David both play football for the same team. A football match is 90 minutes long.
In one match, Roy plays for 70% of the 90 minutes and David plays for of the 90 minutes.
Who plays for the longer time and by how many minutes?
Answers
Answer:
27 minutes
Step-by-step explanation:
please check the image it has all the steps to solve it . Thank you.
What is the equation of this line?
Answers
Answer:
y = x
Step-by-step explanation:
The equation of a line passing through the origin is
y = mx ( m is the slope )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (1, 1) ← 2 points on the line
m = [tex]\frac{1-0}{1-0}[/tex] = [tex]\frac{1}{1}[/tex] = 1 , then
y = x ← equation of line
help ??? on edu math review
Answers
Answer:
It must be C.
Step-by-step explanation:
x² - 9 = 16
=> 16 + 9 = x²
=> 25 = x²
=> x = 5
Referring to the options, C is the only one that is accurate to me. Hoped this helped.
find the gcf of 27 and 3
Answers
Answer:
Step-by-step explanation:
27x3=81
Answer:
It's 3 hope it's help....
Help help help help help help help help help
Answers
Answer:
8
Step-by-step explanation:
4+4 =8
Answer:
y = 8
Step-by-step explanation:
To find this simply you have to put values instead of x and y,
For an example,
If the value of x is 1, you have to put 1 instead of x to the equation to find the value of y,
x = 1,
y = x + 4
y = 1 + 4
y = 5
In the same way, you can find the value of y when the value of x is 4.
x = 4,
y = x + 4
y = 4 + 4
y = 8
Hope this helps you.
Let me know if you have any other questions :-)
A man is 32 years older than his son ten year ago he was three times as old as his son was then find the present age of each?
Answers
Answer:
son 26 age
Father 58 age .........
a grower wishes to mix a one peso per gram chemical with 80 centavo per gram chemical to produce mixture of 200 grams chemical which he can sell for 84 centavo a gram. how many grams of each price of chemical should he use
Answers
40 grams of $ 1 per gram and 160 grams of $ 0.80 per gram should be used.
Since a grower wishes to mix a one peso per gram chemical with 80 cent per gram chemical to produce mixture of 200 grams chemical which he can sell for 84 cent a gram, to determine how many grams of each price of chemical should he use you must perform the following calculation:
(150 x 1 + 50 x 0.8) / 2 = 95 (140 x 1 + 60 x 0.8) / 2 = 94 (100 x 1 + 100 x 0.8) / 2 = 90 (50 x 1 + 150 x 0.8) / 2 = 85 (40 x 1 + 160 x 0.8) / 2 = 84
Therefore, 40 grams of $ 1 per gram and 160 grams of $ 0.80 per gram should be used.
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If an amount of $25,000 is deposited into a saving account at an interest rate 4%, compounded semi-annually, how long will it take to accumulate on this account $28,500? The function describing your balance is M(n) =25,000(1+0.04/2)^2n, where n is time in years. 20 points and WILL GIVE BRAINLIEST!
Answers
It will take 3.3 years to accumulate $28,500 on this account
According to the compound amount formula expressed as:
[tex]A=P(1+\frac{r}{n} )^{nt}[/tex]
P is the principal = $25,000
A is the amount = $28,500
r is the rate in decimal = 4% = 0.04
n = 2 (semi annualy)
Substitute the given parameters into the formula as shown:
[tex]28,500=25,000(1+\frac{0.04}{2} )^{2t}\\1.14=(1+0.02)^{2t}\\1.14 = (1.02)^{2t}\\ln1.14 = 2tln1.02\\2t=\frac{ln1.14}{ln1.02}\\2t= \frac{0.13103}{0.01980}\\2t= 6.6177\\t = 3.30yrs[/tex]
Hence it will take 3.3 years to accumulate $28,500 on this account
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How many solutions for
55l=50l+5
Answers
Answer:
Zero
Step-by-step explanation:
The question is impossible to answer. 501+5 does not equal 551, 501+5 equals 506.
f (x)= -3x+10 and g (x) = x^2-7x
f(-5)=
g(2)=
f(4m)=
Answers
we have f (x)= -3x + 10
so f(-5)= (-3)(-5) +10 = 15 + 10 = 25
we have g (x) = x^2 - 7x
so g(2)= 2^2 - 7.2 = 4 - 14 = -10
we have f (x)= -3x + 10
so f(4m)= -3(4m)+10 = -12m + 10
ok done. Thank to me :>
2. Find the simple interest paid to borrow $4800 for 6 years at 7%.
Answers
1% is 48
7% 336 [1 year]
6 years is 2016
Answer:
$2016
Step-by-step explanation:
Simple Interest equation: I = Prt
So,
P = $4800
r = [tex]\frac{7}{100}[/tex] = 0.07
t = 6
I = (4800) · (0.07) · (6)
Thus,
The simple interest is $2016.
Kayla drives her new car to work every day. It uses 1 3/5 gallons of gas for each round trip. How many round trips to work can Kayla drive on a 16-gallon full tank of gas?
Answers
Answer:
16 road trips
Step-by-step explanation:
Is (x + 6) a factor of f(x) = x3 − 3x2 + 2x − 8? Show how to use either the remainder theorem or the factor theorem to explain your reasoning.
Answers
Answer:
x + 6 is not a factor of f ( x ) = x³ - 3x² + 2x - 8 because when -6 is substituted into the function, the answer is not 0.
Step-by-step explanation:
→ Substitute x = -6 into f ( x )
( 6 )³ - 3 × ( 6 )² + ( 2 × 6) - 8
→ Simplify
216 - 108 + 12 - 8
→ Simplify further
112
Simplify the following and write your answer in simplest radical form:
√-14*√-22
Answers
Steps are in the attachment.
Note :-
=》2 is taken as negative & also taken out of the square root as it's the common factor.
______
⚜ Hope it helps :))
how many prime numbers are multiples of 5 please
Answers
Answer:
the only number would be 5
Step-by-step explanation:
5 is the first and only prime multiple of 5
There are only ''one'' prime number are multiples of 5.
What is Prime number?
Prime numbers are number that have only two factors, 1 and themselves.
Given that;
The prime numbers multiples of 5.
Now,
The multiples of 5 = 5, 10, 15, 20, 25, ...
But there are only one prime number (that is; 5) which are multiple of 5.
Thus, There are only ''one'' prime number are multiples of 5.
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9,962÷41. What dose it =
Answers
Answer:
242.975609756
Step-by-step explanation:
Answer:
242.975
Step-by-step explanation:
TIP: u can use a calculator if your teacher allows you, it would be faster :)
Please Help! I don't understand how the Alabama paradox works. I will give you a lot of points!
--PLEASE show all work
The table shows the populations, in thousands, of the three states in a country with a population of 3760 thousand. Use Hamilton's method to show that the Alabama paradox occurs if the number of seats in congress is increased from 24 to 25
Answers
Answer:
State A loses a seat to State B when the total is increased
Step-by-step explanation:
The "work" is most easily done by a spreadsheet, as the calculations are easily defined and very repetitive.
The "fair share" of seats is the fraction the population is of the total, multiplied by the total number of seats. It will generally be a mixed number (integer plus fraction).
If the whole number is 1 or greater, the number of seats allocated at least that whole number.
If not all seats are allocated, the fractions are sorted in decreasing order, and 1 additional seat is added to the allocation for each state, working down the list, until all of the seats are allocated.
__
The attachment shows State A has the highest fraction when the number of seats is 24. Only one additional seat needs to be allocated in that case. State A gets that extra seat.
When the number of seats is 25, States B and C have the highest fractions. Each of them gets one additional seat, and State A gets no additional seats. This results in the appearance of State A giving up a seat to State B.
_____
Additional comment
Hamilton's apportionment method was used for a number of years in the US. The method now in use is substantially different. The current method would divide the 24 seats so that A=3, B=6, C=15. The 25th seat would be given to State A.
determine x+3 is a factor of P(x)=-2x^3-4x^2-7
Answers
Answer:
p(0)= -7
Step-by-step explanation:
Cliff earns $15 for each hour that he works as a television sales person plus an additional $10 for each television that he sells which of the following represents the amount cliff earns , in dollars, if he sells n television and works h hours ?
Answers
Answer:
15h+10n
Step-by-step explanation:
You forgot to list the equations.
10 * n = 10n = $ paid for amount of televisions sold
15 * h = 15h = $ paid for hours worked
15h + 10n = Total amount paid
The answer for n television sold and h hours working is 15h +10n.
Expression:
An expression is an algebraic or mathematical statement in which some variable and constant are arranges with any algebraic operations
Given that
Cliff earned for one hour = $15
Therefore for h hours = 15h
Also he earned additional for each television sold = $10
Therefore for n television sold = 10n
How to add the algebraic terms?Here 15h and 10n are two algebraic numbers because there is constants 15 and 10 and variables h and n are multiplied simultaneously.
Therefore the total earning is the addition of both
15h + 10n
The final answer is 15h + 10n
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