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xz_007 [3.2K]
3 years ago
14

( show your work ) The banner that football players run through is 18 feet high and 30 feet long. How much paper is needed to

Mathematics
1 answer:
Virty [35]3 years ago
3 0

Answer:

540 square feet worth of paper

Step-by-step explanation:

This is an area problem. Area is length multiplied by width. The provided length is 30 feet and the provided width is 18 feet. When they are multiplied, you get 540 square feet. Note that the height is the width in this context because if you laid the banner down, 18 would be the width. The banner is being held up, so the 18 feet is called the height.

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Find all solutions to the equation in the interval [0, 2π).
ANEK [815]

Answer:

x = π/6, π/2, 5π/6, 3π/2

Step-by-step explanation:

cos x = sin(2x)

Use double angle formula.

cos x = 2 sin x cos x

Move everything to one side and factor.

cos x − 2 sin x cos x = 0

cos x (1 − 2 sin x) = 0

Set each factor to 0 and solve.

cos x = 0

x = π/2, 3π/2

1 − 2 sin x = 0

sin x = 1/2

x = π/6, 5π/6

The total solution is:

x = π/6, π/2, 5π/6, 3π/2

6 0
3 years ago
Choose the set of three sides that correctly matches each description. Each option will be used only once.
34kurt

Answers:

  • 30-60-90 triangle = 4, 8, 4*sqrt(3)
  • 45-45-90 triangle = 6, 6, 6*sqrt(2)
  • Right triangle, but not special right triangle =  6, 8, 10
  • Triangle but not a right triangle = 7, 8, 10
  • Not a triangle = 7, 12, 19

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

Explanation:

The template for a 30-60-90 triangle is that the short leg x leads to hypotenuse 2x, and longer leg x*sqrt(3). If x = 4, then we get the sides 4, 8, 4*sqrt(3) which are the short leg, hypotenuse, and long leg in that order.

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

The template for a 45-45-90 triangle is that we have x as the leg length and x*sqrt(2) as the hypotenuse. If x = 6, then we end up with the sides 6, 6, 6*sqrt(2)

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

The triangle with sides 6, 8, 10 is a right triangle because a = 6, b = 8, c = 10 makes a^2+b^2 = c^2 true. I'm using the converse of the pythagorean theorem. We don't have a special right triangle because these sides do not fit the templates mentioned in the previous two sections above.

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

The triangle with sides a = 7, b = 8, c = 10 on the other hand will not make a^2+b^2 = c^2 true. Note that a^2+b^2 = 7^2+8^2 = 113 which is not the same as 10^2 = 100. However, a triangle is possible because adding any two sides leads to a sum larger than the third side (triangle inequality theorem).

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

We cannot form a triangle with sides 7, 12, 19 because the sides 7 and 12 add to 7+12 = 19 but that's not longer than the third side 19.

The triangle inequality theorem says that if you want to form a triangle with sides a,b,c then the following three inequalities must all be true

a+b > c

a+c > b

b+c > a

6 0
3 years ago
NEED HELP ALGEBRA 1
tigry1 [53]
<h3>Answer: E) 1/5</h3>

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

Method 1

Use your calculator to find the decimal version of each fraction

  • 4/10 = 0.40
  • 12/25 = 0.48
  • 14/20 = 0.70
  • 28/50 = 0.56
  • 1/5 = 0.20

We see that 0.20 is the smallest decimal of the list, so 1/5 is the smallest fraction of the list.

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

Method 2

To compare fractions, we need to get all of the denominators to the same value. A good target is the lowest common denominator (LCD)

In this case, the LCD is 100

  • 4/10 = 40/100 .... multiply top and bottom by 10
  • 12/25 = 48/100 .... multiply top and bottom by 4
  • 14/20 = 70/100 .... multiply top and bottom by 5
  • 28/50 = 56/100  .... multiply top and bottom by 2
  • 1/5 = 20/100  .... multiply top and bottom by 20

The last fraction has the smallest denominator, so 1/5 is the smallest.

4 0
3 years ago
Read 2 more answers
(Need help urgently)<br> Pictures of problems attached
murzikaleks [220]

Answer: m=-3

Explanation: When a line is parallel to another, they both have the same slope.

4 0
3 years ago
Sam is sitting in a boat on a lake. She can get sunburned from the sunlight that hits her directly and from
Nina [5.8K]

An absolute function is represented as: y = a|x - h| + k where the vertex is (h,k).

<em>The function that describes the path of the sunlight is: </em>y= 2|x - 4|<em />

We have:

<em />(h,k) = (4,0)<em> --- the vertex i.e. the point where the sun hits the water</em>

(x,y) =(5.5,3)

Recall that:

y = a|x - h| + k

Substitute (h,k) = (4,0)

y = a|x - 4| + 0

y = a|x - 4|

Substitute (x,y) =(5.5,3) to solve for a

3 = a|5.5 - 4|

3 = a|1.5|

Take absolute value of 1.5

3 = 1.5a

Solve for a

a = \frac 3{1.5}

a = 2

Recall that:

y = a|x - 4|

Substitute a = 2

y= 2|x - 4|

Hence, the function that describes the path of the sunlight is: y= 2|x - 4|

See attachment for the graph of y= 2|x - 4|

Read more absolute functions at:

brainly.com/question/1389494

8 0
2 years ago
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