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3 years ago

Write the slope-intercept form of the equation of the line described. Through (-1,-1) parallel to y=6x-2

Mathematics

1 answer:

Alex17521 [72]3 years ago

7 0

Answer:

$\boxed {\boxed {\sf y= 6x+5}}$

Step-by-step explanation:

We are asked to find the slope-intercept equation of a line. Slope-intercept form is one way to write the equation of a line. It is:

$y=mx+b$

Where m is the slope and b is the y-intercept.

We are given a point (-1, -1) and the line is parallel to the line y= 6x-2. Since the line is parallel to the other line, they have the same slope, which is 6. We have a point and a slope, so we should use the point-slope formula to find the equation of the line.

$y-y_1= m (x-x_1)$

Here, m is the slope and (x₁, y₁) is the point. We know the slope is 6 and the point is (-1, -1). Therefore:

m= 6
x₁= -1
y₁= -1

Substitute the values into the formula.

$y- -1 = 6(x- -1) \\y+1= 6(x+1)$

Distribute the 6. Multiply each value inside the parentheses by 6.

$y+1 = (6*x)+ (6*1) \\y+1= 6x+6$

Slope-intercept form requires y to be isolated. 1 is being added to y. The inverse of addition is subtraction. Subtract 1 from both sides.

$y+1-1=6x+6-1 \\y= 6x+5$

The equation of the line in slope-intercept form is <u>y=6x+5</u>

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Need help with AP CAL

anzhelika [568]

Answer: Choice C

$\displaystyle \frac{1}{2}\left(1 - \frac{1}{e^2}\right)$

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

Explanation:

The graph is shown below. The base of the 3D solid is the blue region. It spans from x = 0 to x = 1. It's also above the x axis, and below the curve $y = e^{-x}$

Think of the blue region as the floor of this weirdly shaped 3D room.

We're told that the cross sections are perpendicular to the x axis and each cross section is a square. The side length of each square is $e^{-x}$ where 0 < x < 1

Let's compute the area of each general cross section.

$\text{area} = (\text{side})^2\\\\\text{area} = (e^{-x})^2\\\\\text{area} = e^{-2x}\\\\$

We'll be integrating infinitely many of these infinitely thin square slabs to find the volume of the 3D shape. Think of it like stacking concrete blocks together, except the blocks are side by side (instead of on top of each other). Or you can think of it like a row of square books of varying sizes. The books are very very thin.

This is what we want to compute

$\displaystyle \int_{0}^{1}e^{-2x}dx\\\\$

Apply a u-substitution

u = -2x

du/dx = -2

du = -2dx

dx = du/(-2)

dx = -0.5du

Also, don't forget to change the limits of integration

If x = 0, then u = -2x = -2(0) = 0
If x = 1, then u = -2x = -2(1) = -2

This means,

$\displaystyle \int_{0}^{1}e^{-2x}dx = \int_{0}^{-2}e^{u}(-0.5du) = 0.5\int_{-2}^{0}e^{u}du\\\\\\$

I used the rule that $\displaystyle \int_{a}^{b}f(x)dx = -\int_{b}^{a}f(x)dx$ which says swapping the limits of integration will have us swap the sign out front.

--------

Furthermore,

$\displaystyle 0.5\int_{-2}^{0}e^{u}du = \frac{1}{2}\left[e^u+C\right]_{-2}^{0}\\\\\\= \frac{1}{2}\left[(e^0+C)-(e^{-2}+C)\right]\\\\\\= \frac{1}{2}\left[1 - \frac{1}{e^2}\right]$

In short,

$\displaystyle \int_{0}^{1}e^{-2x}dx = \frac{1}{2}\left[1 - \frac{1}{e^2}\right]$

This points us to choice C as the final answer.

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2 years ago

Leon charged $75 at an interest rate of 12.5%. How much will Leon have to pay after one month if he makes no payments

pav-90 [236]

I believe that the question is assuming this is taking place over one month here is what I think you would do.

1) 75/12.5 = 6
2) add that answer to 75, so 75+6, and you get 81

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3 years ago

Seclect all the sets of numbers that are possible values for x in the inequalit, x > - 8. { -10, -8, -6}. { -8, 0, 8}. { -9,

Sauron [17]

Answer:

{ -6, -4, -2}

Step-by-step explanation:

Since x > - 8, x can be any number greater than - 8.

x = -7, -6, -5, -4,...

BUT, it can't be equal because it's not using this sign $\geq$

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

1. { -10, -8, -6} can't be an inequality of x because it has -10, -8.

2.{ -8, 0, 8} can't be an inequality of x because of -8.

3.{ -9, 1, 7} can't be an inequality of x because -9 isn't greater than x.

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3 years ago

3/4^2 + 1^2 = x2<br><br> solve for x with work shown! pls help!

photoshop1234 [79]

Answer:

X=19/32

Step-by-step explanation:

3/4^2+1^2=2*x

3/4^2+1=2x

3+(4^2)/4^2=2x

3+16/4^2=2x

19/4^2=2x

19/(2^2)^2=2x

19=16(2x)

19=16*2x

32x=19

32x/32=19/32

x=19/32

This took alot of time goodluck!

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2 years ago

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What is the answer to, - (-x - 3)?

bekas [8.4K]

Step-by-step explanation:

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