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weqwewe [10]
3 years ago
14

Omar and Mackenzie want to build a pulley system by attaching one end of a rope to their 8-foot-tall tree house and anchoring th

e other end to the ground 28 feet away from the base of the treehouse. How long, to the nearest foot, does the piece of rope need to be?
a. 26ft
b. 27ft
c. 28ft
d. 29ft
Mathematics
1 answer:
Ilia_Sergeevich [38]3 years ago
6 0

Answer:

d. 29ft

Step-by-step explanation:

Using pythagoras theorem which states that

a^2 + b^2 = c^2

where a and b are the opposite and adjacent sides of a right angled triangle and c is the hypotenuse side

From the attached image, Let the length of the rope be x

x^{2} = 8^{2}+ 28^{2} \\

x^{2} = 64 + 784

x^{2} = 848

x =\sqrt{848}

x = 29.12

x≈29

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x= infinity; 9x to the power of 3 + x to the power of 2 - 5 divided by 3x to the power of 4 + 4x to the power of 2
Delvig [45]

Answer:

here n Hope it helps. goodluck

5 0
2 years ago
What is the effect on the graph of the function f(x) =5x when f(x) is replaced with f(x) + 9?
Nimfa-mama [501]

Answer:

When we add 9 to the function we are shifting the function up 9 units.


Step-by-step explanation:

If it were added inside the function, it woulds shift it left or right.

But since it is outside the function, we will shift it up or down

When we add 9 to the function we are shifting the function up 9 units.

5 0
3 years ago
Todd wants to make a snack of a number of grapes and slices of cheese. He knows that each grape has 2 calories. The slice of che
Viefleur [7K]

Answer:

The answer to your question is:

a) C = 2g + 155c

b) g = 25 grapes

c) c = 3

Step-by-step explanation:

Data

grapes = g = 2 calories

cheese = c = 155 calories

a) Equation, we consider the amount of grapes and the calores given.

Total calories = C = 2g + 155c

b) We consider that the slices of cheese stays the same

                       2g + 155 = 205

                       2g = 205 -155

                        2g = 50

                        g = 50/2 = 25 grapes

c) Then the number of grapes stays the same

                       2(25) + 155c = 515

                       50 + 155c = 515

                       155c = 515 - 50

                        155c = 465

                        c = 465/155

                        c = 3 slices of cheese

4 0
3 years ago
The amount of time that a customer spends waiting at an airport check-in counter is a random variable with mean 8.0 minutes and
strojnjashka [21]

Answer:

P ( 5 < X < 10 ) = 1

Step-by-step explanation:

Given:-

- Sample size n = 49

- The sample mean u = 8.0 mins

- The sample standard deviation s = 1.3 mins

Find:-

Find the probability that the average time waiting in line for these customers is between 5 and 10 minutes.

Solution:-

- We will assume that the random variable follows a normal distribution with, then its given that the sample also exhibits normality. The population distribution can be expressed as:

                                   X ~ N ( u , s /√n )

Where

                            s /√n = 1.3 / √49 = 0.2143

- The required probability is P ( 5 < X < 10 ) minutes. The standardized values are:

                        P ( 5 < X < 10 ) = P (    (5 - 8) / 0.2143 <  Z  <  (10-8) / 0.2143   )

                                                 = P ( -14.93 < Z < 8.4 )

- Using standard Z-table we have:

                        P ( 5 < X < 10 ) = P ( -14.93 < Z < 8.4 ) = 1        

7 0
3 years ago
the average rate of change of the function f(x) on the interval -3≤x≤3 is -2.5. If (-3)=14 then which of the following is the va
oksian1 [2.3K]

The average rate of change of <em>f(x)</em> on -3 ≤ <em>x</em> ≤ 3 is given to be

(<em>f</em> (3) - <em>f</em> (-3)) / (3 - (-3)) = -2.5

If <em>f</em> (-3) = 14, then

(<em>f</em> (3) - 14) / (3 + 3) = -2.5

(<em>f</em> (3) - 14) / 6 = -2.5

<em>f</em> (3) - 14 = -15

<em>f</em> (3) = -1

4 0
3 years ago
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