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Rainbow [258]
3 years ago
9

What is the y-intercept of the line?

Mathematics
2 answers:
AleksAgata [21]3 years ago
6 0

Answer:

b = 11

Step-by-step explanation:

Using this formula y - y₁ = m(x - x₁) we can figure out the y-intercept (<em>and slope!</em>)<em> </em>

Plugging the numbers in, we get y - 9 = -1/4(x - 8)

We can then simplify that into y = -1/4x + 11

Akimi4 [234]3 years ago
5 0

Answer:

a. 11

Step-by-step explanation:

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This is finding exact values of sin theta/2 and tan theta/2. I’m really confused and now don’t have a clue on how to do this, pl
Lostsunrise [7]

First,

tan(<em>θ</em>) = sin(<em>θ</em>) / cos(<em>θ</em>)

and given that 90° < <em>θ </em>< 180°, meaning <em>θ</em> lies in the second quadrant, we know that cos(<em>θ</em>) < 0. (We also then know the sign of sin(<em>θ</em>), but that won't be important.)

Dividing each part of the inequality by 2 tells us that 45° < <em>θ</em>/2 < 90°, so the half-angle falls in the first quadrant, which means both cos(<em>θ</em>/2) > 0 and sin(<em>θ</em>/2) > 0.

Now recall the half-angle identities,

cos²(<em>θ</em>/2) = (1 + cos(<em>θ</em>)) / 2

sin²(<em>θ</em>/2) = (1 - cos(<em>θ</em>)) / 2

and taking the positive square roots, we have

cos(<em>θ</em>/2) = √[(1 + cos(<em>θ</em>)) / 2]

sin(<em>θ</em>/2) = √[(1 - cos(<em>θ</em>)) / 2]

Then

tan(<em>θ</em>/2) = sin(<em>θ</em>/2) / cos(<em>θ</em>/2) = √[(1 - cos(<em>θ</em>)) / (1 + cos(<em>θ</em>))]

Notice how we don't need sin(<em>θ</em>) ?

Now, recall the Pythagorean identity:

cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1

Dividing both sides by cos²(<em>θ</em>) gives

1 + tan²(<em>θ</em>) = 1/cos²(<em>θ</em>)

We know cos(<em>θ</em>) is negative, so solve for cos²(<em>θ</em>) and take the negative square root.

cos²(<em>θ</em>) = 1/(1 + tan²(<em>θ</em>))

cos(<em>θ</em>) = - 1/√[1 + tan²(<em>θ</em>)]

Plug in tan(<em>θ</em>) = - 12/5 and solve for cos(<em>θ</em>) :

cos(<em>θ</em>) = - 1/√[1 + (-12/5)²] = - 5/13

Finally, solve for sin(<em>θ</em>/2) and tan(<em>θ</em>/2) :

sin(<em>θ</em>/2) = √[(1 - (- 5/13)) / 2] = 3/√(13)

tan(<em>θ</em>/2) = √[(1 - (- 5/13)) / (1 + (- 5/13))] = 3/2

3 0
2 years ago
I need help with question 1, 2, 6, 7 and 8.
olga2289 [7]

Answer:

Step-by-step explanation:

Q1) 15+15+15+15+15+15=90

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Q2) 2 over 2

Q6) 13 over 52

6 0
3 years ago
A garden has an area of 32 square feet what is the smallest possible perimeter
stepan [7]

Answer:

24 feet

Step-by-step explanation:

factors that produce an area of 32:

1x32  Would give a perimeter of 66

2x16  Would give a perimeter of 36

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6 0
3 years ago
In the set of real numbers, the first number less than -3 is -4. True False
mariarad [96]
True, -4 seems bigger because 4 is bigger than 3 but it's negative and is further away from 0 
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3 years ago
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Can someone help or show me how to simplify this equation 22.5+7(n-3.4)
Scorpion4ik [409]
<span>22.5+7 (n-3.4)=19.8n

We simplify the equation to the form, which is simple to understand
<span>22.5+7(n-3.4)=19.8n

Reorder the terms in parentheses
<span>22.5+(+7n-23.8)=19.8n

Remove unnecessary parentheses
<span>+22.5+7n-23.8=+19.8n

We move all terms containing n to the left and all other terms to the right.
<span>+7n-19.8n=-22.5+23.8

We simplify left and right side of the equation.
<span><span>-12.8n=+1.3

</span>We divide both sides of the equation by -12.8 to get n.
<span>n=-0.1015625</span></span></span></span></span></span></span>
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3 years ago
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