The graph of y=f(x) is shown below. what are all of the real solutions of f(x)=0

Mathematics

1 answer:

Ksju [112]3 years ago

7 0

The solutions are x=-4 ; x=1 ; x=8

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A triangle with a height of 12

Sidana [21]

The area of a triangle is 1/2*base*height

So make your equation: 1/2*b*12=42

6*b=42

b=7

So the base is 7 inches long

Hope that helped!

6 0

3 years ago

⚠️ Help I don’t know how todo this and I’d appreciate it if someone could help me ⚠️

Blababa [14]

1. Henry is wrong to say both equations are I correct because they are indeed correct: 12=12 is equivalent to x=x and vise versa. This is because x is a variable and can stand for any number including 12. The ratios of both equations are 1:1 which also makes them equal, because you can simplify them down to 1=1 or 0=0 for example. I hope that makes sense...

6 0

3 years ago

Find the area of the region (CALCULUS HELP I WILL VOTE BEST ANSWER)

kogti [31]

I'm not sure what is meant by "partitioning the x-axis" - partition is a term more often used with computing Riemann sums. So either partitioning has a special meaning for you, or you have to approximate the area with a Riemann sum.

I'm going to assume you just want the exact area of the given region. Notice that the two curves y = 4e ˣ and y = -x + 4 intersect when x = 0 at the point (0, 4). Both curves then meet the vertical line x = 4. The exponential function is increasing while the linear one is decreasing, so 4e ˣ ≥ -x + 4.

The region is then the set of points,

R = {(x, y) | 0 ≤ x ≤ 4 and -x + 4 ≤ y ≤ 4e ˣ}

so the area is given by the integral,

$\displaystyle\int_0^4 (4e^x-(-x+4))\,\mathrm dx=\int_0^4(4e^x+x-4)\,\mathrm dx=\left(4e^x+\frac{x^2}2-4x\right)\bigg|_0^4=\boxed{4e^4-12}$