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3 years ago

What is the slope of the line that passes through the points (1, -6)(1,−6) and (-8, 9) ?(−8,9)?

Mathematics

1 answer:

Monica [59]3 years ago

4 0

Answer:

The answer to your question is m = -5/3

Step-by-step explanation:

Data

Point 1 = (1, -6)

Point 2 = (-8, 9)

Process

To find the slope just substitute the values in the formula and simplify.

Formula

slope = m = (y2 - y1) / (x2 - x1)

-Identify x1, y1, x2 and y2

x1 = 1 y1 = -6 x2 = -8 y2 = 9

-Substitution

m = (9 + 6) / (-8 - 1)

-Simplification

m = 15/-9

-Result

m = -5/3

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3p + 7 = -4(4 - 6p) + 2

zvonat [6]

p=1

Step-by-step explanation:

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$\frac{ - 21p}{ - 21} = \frac{ - 21}{ - 21} \\ p = 1$

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gladu [14]

Answer:

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Step-by-step explanation:

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3 years ago

A recipe for cake needs ¾ of a cup of milk. You are making ½ of the recipe. How much milk do you need?

Bad White [126]

Multply across the fraction so
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3 years ago

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Prove that sin^4x + cos^4x= sinxcosx

yKpoI14uk [10]

Answer:

(the relation you wrote is not correct, there may be something missing, so I will simplify the initial expression)

Here we have the equation:

$sin^4(x) + cos^4(x)$

We can rewrite this as:

$(sin^2(x))^2 + (cos^2(x))^2$

Now we can add and subtract cos^2(x)*sin^2(x) to get:

$(sin^2(x))^2 + (cos^2(x))^2 + 2*cos^2(x)*sin^2(x) - 2*cos^2(x)*sin^2(x)$

We can complete squares to get:

$(cos^2(x) + sin^2(x))^2 - 2*cos(x)^2*sin(x)^2$

and we know that:

cos^2(x) + sin^2(x) = 1

then:

$1 - 2*sin(x)^2*cos(x)^2$

This is the closest expression to what you wrote.

We also know that:

sin(x)*cos(x) = (1/2)*sin(2*x)

If we replace that, we get:

$1 - \frac{sin^2(2*x)}{2}$

Then the simplification is:

$cos^4(x) + sin^4(x) = 1 - \frac{sin^2(2*x)}{2}$

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3 years ago

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

maks197457 [2]

F(g(x)) = [(-7x-8)/(x-1) - 8} / [(-7x - 8)/(x-1) + 7] =

[(-7x - 8 - 8(x-1)) / (x-1)] / [(-7x - 8 + 7(x-1)) / (x-1)] = (-15x) / (-15) = x.

g(f(x)) = [-7*(x-8)/(x+7) - 8] / [(x-8)/(x+7) - 1] =

[(-7x + 56 -8*(x+7)) / (x+7)] / [(x - 8 - (x + 7)) / (x+7)] = (-15x) / (-15) = x.

So since f(g(x)) = g(f(x)) = x we can conclude that f and g are inverses.

5 0

3 years ago