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Elodia [21]
3 years ago
9

Find the equation of the line. Use exact numbers. y=__x + __

Mathematics
2 answers:
Natalija [7]3 years ago
6 0

\tt Step-by-step~explanation:

In order to solve, we need to know the formula for slope-intercept: y = mx + b. M stands for the slope, and b stands for the y-intercept, or where the line crosses the y-axis.

\tt Step~1:

Let's solve for the slope first. In order to find the slope, we need to find the rise and run of the line. The line rises 3 units before intersecting with a point, so that is the rise. The line goes across 1 unit, so that is the run of the line. Slope = rise/run. Slope = 3/1 = 3.

\tt Step~2:

Now that we have the slope, we can solve for the y-intercept. We can see clearly that the line passes through 3 on the y-axis, so that is our y-intercept, or b. y = mx + b → y = 3x + 3

\Large\boxed{\tt Our~final~answer:~y=3x+3}

never [62]3 years ago
3 0
Y= 3/1 x + 3 ///////////
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Exercise 3.5. For each of the following functions determine the inverse image of T = {x ∈ R : 0 ≤ [x^2 − 25}.
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a. The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

b. The inverse image of g(x) is g^{-1}(x) = e^{x}

c. The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

<h3 /><h3>The domain of T</h3>

Since T = {x ∈ R : 0 ≤ [x^2 − 25} ⇒ x² - 25 ≥ 0

⇒ x² ≥ 25

⇒ x ≥ ±5

⇒ -5 ≤ x ≤ 5.

<h3>Inverse image of f(x)</h3>

The inverse image of f(x) is f⁻¹(x) = ∛(x/3)

f : R → R defined by f(x) = 3x³

Let f(x) = y.

So, y = 3x³

Dividing through by 3, we have

y/3 = x³

Taking cube root of both sides, we have

x = ∛(y/3)

Replacing y with x we have

y = ∛(x/3)

Replacing y with f⁻¹(x), we have

So,  the inverse image of f(x) is f⁻¹(x) = ∛(x/3)

<h3>Inverse image of g(x)</h3>

The inverse image of g(x) is g^{-1}(x) = e^{x}

g : R+ → R defined by g(x) = ln(x).

Let g(x) = y

y =  ln(x)

Taking exponents of both sides, we have

e^{y} = e^{lnx} \\e^{y} = x

Replacing x with y, we have

y = e^{x}

Replacing y with g⁻¹(x), we have

So, the inverse image of g(x) is g^{-1}(x) = e^{x}

<h3>Inverse image of h(x)</h3>

The inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

h : R → R defined by h(x) = x − 9

Let y = h(x)

y = x - 9

Adding 9 to both sides, we have

y + 9 = x

Replacing x with y, we have

x + 9 = y

Replacing y with h⁻¹(x), we have

So, the inverse image of <u>h</u>(x) is h⁻¹(x) = x + 9

Learn more about inverse image of a function here:

brainly.com/question/9028678

5 0
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Answer:

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Step-by-step explanation:

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Area:

A=(x+7)(2x-3)

A=2x^2+11x-21

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Answer:

1.3.6

Step-by-step explanation:

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