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MrRa [10]
3 years ago
7

Jim and his dad are building a rectangular flower bed. They have a total of 35 feet of landscaping timber to use, and they want

to use all of it. However, they are not sure what width and length they want the flower bed to be. In this activity, you will write a function in which the width of the flower bed, w, is the input, and the length, l, is the output. The perimeter of a rectangle is given by the equation 2l + 2w = p.If the width of the flower bed is 15 feet, what is its length? Write your answer as an evaluation of a function.
Mathematics
1 answer:
Katyanochek1 [597]3 years ago
6 0

Step-by-step explanation:

the answer is in the image above

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Find the exact value of cot(15degrees) using half angle formulas?
liubo4ka [24]

Double angle (or half angle, depending how you look at it) identities:

\cos^2\dfrac x2=\dfrac{1+\cos x}2

\sin^2\dfrac x2=\dfrac{1-\cos x}2

\implies\cot^2\dfrac x2=\dfrac{\cos^2\frac x2}{\sin^2\frac x2}=\dfrac{1+\cos x}{1-\cos x}

So we have

\cot^215^\circ=\dfrac{1+\cos30^\circ}{1-\cos30^\circ}=\dfrac{1+\frac{\sqrt3}2}{1-\frac{\sqrt3}2}

\implies\cot^215^\circ=7+4\sqrt3

\implies\cot15^\circ=\sqrt{7+4\sqrt3}=2+\sqrt3

Note that when taking the square root, we should take into account that that could yield two possible solutions, but we know \cos15^\circ>0 and \sin15^\circ>0, so it's also the case that \cot15^\circ>0.

Also, the reason we have equality in the last step can be explained like so:

7+4\sqrt3=4+4\sqrt3+3=4+4\sqrt3+(\sqrt3)^2=(2+\sqrt3)^2

(not unlike the process used to complete the square)

8 0
4 years ago
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If BD bisects angle ABC, measure of DBC = 79 degrees, and measure of angle ABC= 9x-4, find the value of x.
saul85 [17]

Try this option:

answer is 18.

For more information see the attached picture.

6 0
3 years ago
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How do I multiply? What is 1 times 3? I have no clue
rosijanka [135]

Answer:

<u>It is 3</u>

Step-by-step explanation:

Multiplication is one of the four basic operations in arithmetic, along with addition, subtraction, and division. Multiplication can actually be considered repeated addition, and you can solve simple multiplication problems by adding repeatedly. For larger numbers, you'll want to do long multiplication, which breaks the process down into repeated simple multiplication and addition problems. You can also try a shortcut version of long multiplication by splitting the smaller number in the problem into tens and ones, but this works best when the smaller number is between 10 and 19.

  • <u>Restate the problem as an addition problem. </u>
  • <u>Add the repeated number together to get your answer. </u>
  • <u>Switch to long multiplication when multiplying 2-digit or larger numbers.</u>

<u> </u>

<u />

8 0
4 years ago
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What is the answer to my question
Vedmedyk [2.9K]
672 cm³
Step-by-step explanation:
10x7x9=630
2x3x7=42
630+42=672
5 0
3 years ago
Write the equation for the line passing through (- 6, 0.5) and (2, 6.5) .​
AURORKA [14]

Answer:

y=3/4x+5.2

Step-by-step explanation:

y2-y1/x2-x1

6.5-0.5-=6

2--6=2+6=8 (2 negatives make a positive)

6/8 (simplify)=3/4

crosses y at 5.2

3 0
3 years ago
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