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Ainat [17]
2 years ago
7

Write an equation in point-slope form of the line through the point (-1, 2) and with slope m= 2.

Mathematics
1 answer:
sashaice [31]2 years ago
3 0

Answer: y-2=2(x+1)

Step-by-step explanation: You get the point slope formula and simply put in the information given

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Consider the function f(x)= 2/5x-4
Gre4nikov [31]

Answer: a) \frac{5}{2}x+10=f^{-1}(x)=g(x)

Step-by-step explanation:

Since we have given that

f(x)=\frac{2}{5}x-4

a.) Find the inverse of f(x) and name it g(x).

Let f(x) = y

So, it becomes

y=\frac{2}{5}x-4

Switching x to y , we get

x=\frac{2}{5}y-4

5x=2y-20\\\\5x+20=2y\\\\\frac{5x+20}{2}=y\\\\\frac{5}{2}x+10=y\\\\\frac{5}{2}x+10=f^{-1}(x)=g(x)

b) . Use composition to show that f(x) and g(x) are inverses of each other.

\mathrm{For}\:f=\frac{2}{5}x-4\:\\\\\mathrm{substitute}\:x\:\mathrm{with}\:g\left(x\right)=\frac{5}{2}x+10\\\\=\frac{2}{5}\left(\frac{5}{2}x+10\right)-4\\\\=x

Similarly,

\mathrm{g\left(x\right)=\frac{5}{2}x+10,\:f\left(x\right)=\frac{2}{5}x-4,\:g\left(x\right)\circ \:f\left(x\right)}\\\\\mathrm{For}\:g=\frac{5}{2}x+10\:\mathrm{substitute}\:x\:\mathrm{with}\:f\left(x\right)=\frac{2}{5}x-4\\\\=\frac{5}{2}\left(\frac{2}{5}x-4\right)+10\\\\=x

so, both are inverses of each other.

c) Draw the graphs of f(x) and g(x) on the same coordinate plane.

As shown below in the graph , Since for inverse function we need an axis of symmetry i.e. y=x

And both f(x) and g(x) are symmetry to y=x.

∴ f(x) and g(x) are inverses of each other.


5 0
3 years ago
A tree initially measured 3812 feet tall. Over the next 512 years, it grew to a final height of 4912 feet. During those 512 year
Arlecino [84]

Answer:

2 feet per year

Step-by-step explanation:

I think you meant 38 1/2

and 5 1/2

but if you didn't then its

2.1484375

because

4912-3812=1100

1100÷512= 2.1484375

3 0
3 years ago
Simplify (1+tan^2y)(cos2y-1)
Reil [10]
1+tan^2(y)=1/cos^2(y)
cos 2y -1=cos^2(y) -sin^2(y)-cos^2(y) -sin^2(y)


8 0
3 years ago
Need help!!!! Asap I’ll Mark Brainly
antiseptic1488 [7]

Answer:

I think 9 and 12 are paraellograms. the others are not paraellograms. dunno if im right. but I tried my best

Step-by-step explanation:

7 0
2 years ago
Express the product of (x + 3)<br> and<br> (3+5) as a trinomial in simplest form.
ch4aika [34]

Answer:

<em>The answer would be 8x + 24</em>. And it's not a trinomial form. Why? Maybe the given is not just (3+5), it's (3x+5). So that we can get trinomial product.

Sol.

(x + 3) (3x + 5)

Each parenthesis has a binomial (two numbers)

A. Note that whenever you have two parenthesis next to each other like this, it implies factoring. So let's factor.

3x^2 + 5x + 9x + 15

We get a quartnomial (containing 4 numbers), but we're looking for a trinomial. Can we reduce this?

B. Yeah, so we reduce

3x^2 + 14x + 15

There you go, this is a trinomial.

8 0
3 years ago
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