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satela [25.4K]
3 years ago
8

A circus performer walks on a tightrope 25 feet above the ground. The tightrope is supported by two beams and two support cables

. If the distance between each beam and the base of its support cable is 15 feet, what is the length of the support cable? Round to the nearest foot.
Mathematics
1 answer:
miv72 [106K]3 years ago
5 0
The length of the support cable is about 29 feet.

If you sketch out the question, you will see that it will form a right triangle with the cable as the hypotenuse.

Just set up and use the Pythagorean Theorem.

15^2 + 25^2 = c^2
850 = c^2
29.15 = c
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The student council is selling cupcakes at the school play. ​The cost to ​make the cupcakes is a fixed $75 plus $0.17 per cupcak
dedylja [7]

Answer:

C = 75 + 0.17x and R = 2x

2x - (75 + 0.17x) > 0

x ≥ 41

Step-by-step explanation:

The cost to make the cupcakes is a fixed $75 plus $0.17 per cupcakes made and the selling price of each cupcake is $2.00.

Part A: Now, the equation for the cost, C, for making x cupcakes is  

C = 75 + 0.17x ......... (1)

Again the equation for the revenue, R, from selling x cupcakes is

R = 2x ............ (2)

Part B: So, the inequality that could be solved to find the number of cupcakes, x, that must be made and sold to make a profit is  

R - C > 0

2x - (75 + 0.17x) > 0 ......... (3)

Part C: Solving inequality (3) we get

(2 - 0.17)x > 75

⇒ x > 40.98

⇒ x ≥ 41 {Since, x can not be a fraction}

(Answer)

3 0
3 years ago
Two lines have a slope of 3 and different y-intercepts how many solutions will this system have
Taya2010 [7]

Answer:

0 solutions / no solutions

Step-by-step explanation:

If two lines have the same slope but different y-intercepts, it means that they are parallel.

For example, we have two lines:  

y = x

y = x + 1

Both lines have the same slope of 1, but different y - intercepts. Because each equation increases the x and y at the same right (slope) but started at different points, the two equations will never touch.

It's similar to two runner who run at the same pace. If one runner started 50 meters ahead, that runner will always be ahead 50 meters (y-intercept) because they both run at the same rate.

6 0
3 years ago
Write an explicit formula for the arithmetic sequence whose common difference is -18
drek231 [11]

Let the first term be a(0).  Then the formula for a(n) is a(0)-18(n-1).

Check:  What's the first term?  Let n = 1:  a(1) = a(0)-18(1-1) = a(0) (correct)

What's the second term?    Let -n =2:  a(2) = a(0)-18(2-1) = a(0) - 18

and so on.

7 0
2 years ago
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Im desperate like most of my question-
kvv77 [185]
<h3>Answer: 9.75 dollars</h3>

===========================================================

Explanation:

There are two ways to solve this problem.

Method 1:

35% = 35/100 = 0.35

35% of 15 = 0.35*15 = 5.25

So you save $5.25, which is the discount amount.

The sale price is 15 - 5.25 = 9.75 dollars

---------------

Method 2:

If you save 35%, then you still need to pay the remaining 65%

35% + 65% = 100%

The sale price is 65% of original price

sale price = 65% of original price

sale price = 0.65*15

sale price = 9.75 dollars

---------------

Extra info (optional section)

The benefit of method 2 is that we can chain multiple discounts together. Consider that on top of the 35% discount, the store then decides that members (people who pay monthly) will get an extra 10% off. The natural thinking is that the total discount is 35%+10% = 45% off, but that's not correct.

We can see this if we say that the original price is say $100 and 35% off would lead to a price of 0.65*100 = 65 dollars. Then an extra 10% off means we pay 90% of that new price (65 dollars) to get 0.90*65 = 58.50

As a shortcut, we can just multiply the values of 0.65*0.90 = 0.585

Then note how 100*0.585 = 58.50 showing us a fairly fast way to compute the final sale price even if multiple discounts are applied. This can be extended to more discounts. Again, we do not add the percentages when it comes to figuring out how much the total discount percentage would be.

Since the item was $100 but now it's 58.50, this means we saved 100-58.50 = 41.50 dollars. The discount is therefore 41.50/100 = 41.50% which is close to the 45% calculated earlier, but not quite there.

7 0
3 years ago
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max2010maxim [7]

Answer:

The car is going 45 mph

Step-by-step explanation:

Since the speed limit is 35 mph and the car is 10 mph over the speed, we can add them to find out how fast the car is going. We can solve 35+10 which will give us 45. So it is not a sum of 0 but instead a sum of 45.

(hope this helped)

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3 years ago
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