Solve for x please thanks

Mathematics

1 answer:

N76 [4]3 years ago

6 0

Answer:

Step-by-step explanation:

So, lets go over what we know:

The equation to find x is the same on both sides.

Now, lets find this equation:

So, the total area of the two lines on the left side of the triangle are 24.

Lets first subtract the first line from the total of the two lines to find the value of the second line:

24-3

21.

Now that we know the value of the 2nd line is 21. lets divide it by the first line(3) to find the scale factor:

21/3

So the scale factor is 7!

Lets plug this in for x.

We know that the first line is 4.

The second line is 7x bigger than 4.

So we can calculate this as:

7x4

So x is 28!

This is your answer!

Hope it helps! :)

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3 years ago

Find the area of the region that lies under the parabola y=5x - x^2, where 1≤x≤4. I would definitely like to see some work :)

Elena L [17]

Answer:

16.5 square units

Step-by-step explanation:

You are expected to integrate the function between x=1 and x=4:

$\displaystyle\text{area}=\int_1^4{(5x-x^2)}\,dx=\left.\left(\dfrac{5}{2}x^2-\dfrac{1}{3}x^3\right)\right|_{x=1}^{x=4}\\\\=\dfrac{5(4^2-1^2)}{2}-\dfrac{4^3-1^3}{3}=37.5-21=\boxed{16.5}$

<em>Additional comment</em>

If you're aware that the area inside a (symmetrical) parabola is 2/3 of the area of the enclosing rectangle, you can compute the desired area as follows.

The parabolic curve is 4-1 = 3 units wide between x=1 and x=4. It extends upward 2.25 units from y=4 to y=6.25, so the enclosing rectangle is 3×2.25 = 6.75 square units. 2/3 of that area is (2/3)(6.75) = 4.5 square units.

This region sits on top of a rectangle 3 units wide and 4 units high, so the total area under the parabolic curve is ...

area = 4.5 +3×4 = 16.5 . . . square units