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Roman55 [17]
3 years ago
6

Write the SLOPE-INTERCEPT FORM equation given a slope of -1/2 and the point (6,-1).

Mathematics
1 answer:
pochemuha3 years ago
3 0

Answer:

The answer is

<h2>y =  -  \frac{1}{2} x + 2</h2>

Step-by-step explanation:

To find an equation of a line when given the slope and a point we use the formula

y -  y_1 = m(x -  x_1)

where

m is the slope

( x1 , y1) is the point

From the question the point is (6 , - 1) and slope - 1/2

So we have

y + 1 =  -  \frac{1}{2} (x - 6) \\ y + 1 =  -  \frac{1}{2} x + 3 \\ y =   - \frac{1}{2} x +  3 - 1 \\

We have the final answer as

y =  -  \frac{1}{2} x + 2 \\

Hope this helps you

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X = 11/3 this answer is finding x in this problem
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henley needs to calculate the base of a trapezoid, b, given the area, a, in inches. She need to rearrange the formula a=16(b+4).
yKpoI14uk [10]

Answer:

b = (a/16) - 4

Step-by-step explanation:

a = 16(b + 4)

a = 16b + 64

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b = (a/16) - 4

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The floor of the cage measures 11 yardyard wide by 66 feetfeet long. One bag of shavings covers 55 square feetfeet. How many bag
bazaltina [42]

Answer:

3 3/5 bags

Step-by-step explanation:

We have to find the surface area of the floor of the cage first.

The cage measures 1 yard wide by 6 feet long.

1 yard = 3 feet

The floor of the cage is rectangular, so, the surface area of the floor of the cage is therefore:

3 * 6 = 18 square feet

One bag of shavings covers 5 square feet.

To find the number of bags we need to cover the floor, we divide the surface area of the floor by the number of bags per square feet.

The number of bags needed for the floor of the cage is therefore :

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5 0
3 years ago
NO LINKS!!
dexar [7]

Answer: Anything between 0 and 10, excluding both endpoints.

In terms of symbols we can say 0 < w < 10 where w is the width.

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

Explanation:

You could do this with two variables, but I think it's easier to instead use one variable only. This is because the length is dependent on what you pick for the width.

w = width

2w = twice the width

2w-5 = five less than twice the width = length

So,

  • width = w
  • length = 2w-5

which lead to

area = length*width

area = (2w-5)*w

area = 2w^2-5w

area < 150

2w^2 - 5w < 150

2w^2 - 5w - 150 < 0

To solve this inequality, we will solve the equation 2w^2-5w-150 = 0

Use the quadratic formula. Plug in a = 2, b = -5, c = -150

w = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\w = \frac{-(-5)\pm\sqrt{(-5)^2-4(2)(-150)}}{2(2)}\\\\w = \frac{5\pm\sqrt{1225}}{4}\\\\w = \frac{5\pm35}{4}\\\\w = \frac{5+35}{4} \ \text{ or } \ w = \frac{5-35}{4}\\\\w = \frac{40}{4} \ \text{ or } \ w = \frac{-30}{4}\\\\w = 10 \ \text{ or } \ w = -7.5\\\\

Ignore the negative solution as it makes no sense to have a negative width.

The only practical root is w = 10.

If w = 10 feet, then the area = 2w^2-5w results in 150 square feet.

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

Based on that root, we need to try a sample value that is to the left of it.

Let's say we try w = 5.

2w^2 - 5w < 150

2*5^2 - 5*5 < 150

25 < 150 ... which is true

This shows that if 0 < w < 10, then 2w^2-5w < 150 is true.

Now try something to the right of 10. I'll pick w = 15

2w^2 - 5w < 150

2*15^2 - 5*15 < 150

375 < 150 ... which is false

It means w > 10 leads to 2w^2-5w < 150  being false.

Therefore w > 10 isn't allowed if we want 2w^2-5w < 150 to be true.

4 0
2 years ago
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motikmotik

Answer:

32

Step-by-step explanation:

f(x)= 3(x-2)² + 5

Let x = -1

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Parentheses first

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Exponents

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Multiply

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Add

f(-1) = 32

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