Hello from MrBillDoesMath!
Answer:
n = 5
Discussion:
Let the original number be "n" Translating the problem statement to mathematical symbolism:
n + 4 = 19 - 2n => add 2n to both sides
n + 2n + 4 = 19 - 2n + 2n => combine like terms
3n + 4 = 19 => subtract 4 from both sides
3n = 19 -4 = 15 => divide both sides by 3
n = 15/3 =5
Check: Does 5 +4 = 19 - 2(5)? Does 9 = 9? Yes. so the value for n is confirmed correct.
Thank you,
MrB
We need to compute the diagonal of yhe square.
d²=7²+7²=49×2cm²
d=7×sqrt(2)=7×1.41=9.87cm.
The diagonal we just computed is the diameter of the circle that contains the square.
Since d=9.87 < 11, then indeed, the square fits inside the circle, without touching it.
I don’t think I just want points
The measure of angle A is 144.3 degrees and the angle to cut the molding is 54.3 degrees
<h3>How to solve for angle A?</h3>
Start by solving the acute part of angle A using the following sine function
sin(Ax) = (30 - 4)/32
Evaluate the quotient
sin(Ax) = 0.8125
Take the arc sin of both sides
Ax = 54.3
The measure of angle A is then calculated as:
A = 90 + Ax
This gives
A = 90 + 54.3
Evaluate
A = 144.3
Hence, the measure of angle A is 144.3 degrees
<h3>The angle to cut the molding</h3>
In (a), we have:
Ax = 54.3
This represents the angle where the molding would be cut
Hence, the angle to cut the molding is 54.3 degrees
Read more about angles at:
brainly.com/question/1592456
#SPJ1
so hmmm seemingly the graphs meet at -2 and +2 and 0, let's check
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.
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![\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}}](https://tex.z-dn.net/?f=%5Cstackrel%7Bg%28x%29%7D%7B-x%5E2%2B3x%7D~~%20-%20~~%5B%5Cstackrel%7Bf%28x%29%7D%7B2x%5E3-x%5E2-5x%7D%5D%5Cimplies%20-x%5E2%2B3x-2x%5E3%2Bx%5E2%2B5x%20%5C%5C%5C%5C%5C%5C%20-2x%5E3%2B8x%5Cimplies%202%28-x%5E3%2B4x%29%20%5C%5C%5C%5C%5C%5C%20%5Cdisplaystyle%202%5Cint%5Climits_%7B0%7D%5E%7B2%7D%20%28-x%5E3%2B4x%29dx%20%5Cimplies%202%5Cleft%5B%20-%5Ccfrac%7Bx%5E4%7D%7B4%7D%2B2x%5E2%20%5Cright%5D_%7B0%7D%5E%7B2%7D%5Cimplies%20%5Cboxed%7B8%7D%20~%5Chfill%20%5Cboxed%7B%5Cstackrel%7B%5Ctextit%7Btotal%20area%7D%7D%7B8~~%20%2B%20~~8~~%20%3D%20~~16%7D%7D)
