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Delicious77 [7]
3 years ago
15

Let f be a linear function such that f(1) = 5 and f(3) = 9. Find an equation for f(x).

Mathematics
1 answer:
sleet_krkn [62]3 years ago
4 0

Answer:

f(x)=2x+3

Step-by-step explanation:

So we know that:

f(1)=5 \text{ and } f(3)=9

In other words, we have 2 coordinates: (1,5) and (3,9).

With this, we can figure out the slope. Let (1,5) be x₁ and y₁ and let (3,9) be x₂ and y₂. The slope formula is:

m=\frac{y_2-y_1}{x_2-x_1}

Substitute:

m=\frac{9-5}{3-1}\\m=4/2=2

So, the slope is 2.

Now, use the point-slope form to figure out the y-intercept. The point-slope form is:

y-y_1=m(x-x_1)

For consistency, let's continue to use (1,5) as x₁ and y₁. Now, we can use 2 as m. Thus:

y-(5)=2(x-1)

Distribute:

y-5=2x-2

Add 5 to both sides:

y=2x+3

So:

f(x)=2x+3

And that's our equation :)

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Calculate the total area of the shaded region.
LUCKY_DIMON [66]

so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check

\stackrel{f(x)}{2x^3-x^2-5x}~~ = ~~\stackrel{g(x)}{-x^2+3x}\implies 2x^3-5x=3x\implies 2x^3-8x=0 \\\\\\ 2x(x^2-4)=0\implies x^2=4\implies x=\pm\sqrt{4}\implies x= \begin{cases} 0\\ \pm 2 \end{cases}

so f(x) = g(x) at those points, so let's take the integral of the top - bottom functions for both intervals, namely f(x) - g(x) from -2 to 0 and g(x) - f(x) from 0 to +2.

\stackrel{f(x)}{2x^3-x^2-5x}~~ - ~~[\stackrel{g(x)}{-x^2+3x}]\implies 2x^3-x^2-5x+x^2-3x \\\\\\ 2x^3-8x\implies 2(x^3-4x)\implies \displaystyle 2\int\limits_{-2}^{0} (x^3-4x)dx \implies 2\left[ \cfrac{x^4}{4}-2x^2 \right]_{-2}^{0}\implies \boxed{8} \\\\[-0.35em] ~\dotfill

\stackrel{g(x)}{-x^2+3x}~~ - ~~[\stackrel{f(x)}{2x^3-x^2-5x}]\implies -x^2+3x-2x^3+x^2+5x \\\\\\ -2x^3+8x\implies 2(-x^3+4x) \\\\\\ \displaystyle 2\int\limits_{0}^{2} (-x^3+4x)dx \implies 2\left[ -\cfrac{x^4}{4}+2x^2 \right]_{0}^{2}\implies \boxed{8} ~\hfill \boxed{\stackrel{\textit{total area}}{8~~ + ~~8~~ = ~~16}}

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2 years ago
What is the equivalent fraction of 4/10?
VashaNatasha [74]
Divide both sides by 2.
2/5
:)
8 0
3 years ago
Read 2 more answers
Help me pleaseee (10 points )
Gemiola [76]

Answer:

m<T = , m<M =  and m<Z =

Step-by-step explanation:

From the given ∆TMZ, let the measure angle T be represented by T.

So that,

m<M = 2T + 6°

m<Z = 5T - 50°

Sum of angles in a triangle =

T + (2T + 6°) + (5T - 50°) =

8T - =

8T =  +

   =

T =

  =

Therefore,

i. m<T =

ii. m<M = 2T + 6°

       = 2 x  + 6°

       =

m<M =

iii. m<Z = 5T - 50°

           = 5 x  - 50°

           =  - 50°

           =

m<Z =

5 0
3 years ago
Simplify:
liubo4ka [24]

Answer:

78.5÷3.14=25

56.272×41.2=2318.4064

429×338×712=103241424

447÷513=0.8713450292

Step-by-step explanation:

hope it will help!

8 0
3 years ago
What is the product of 2 numbers of 1 2 3 4 5 6 10 20 30​
Zanzabum

Answer:

ekena la pernina de la abobo Kot Sa Rita kolos talas 8

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