Step-by-step explanation:
in such cases we always try to split the complex figure into non-overlapping simple figures, calculate their areas and add them up.
what simple figures can we see here ?
I see a rectangle 80m × 130m.
and that leaves for me a right-angled triangle in the upper right corner with the legs of
250-80 = 170 m and 130-50 = 80 m
the area of a rectangle is
length × width
the area of a right-angled triangle is
leg1 × leg2 / 2
the individual areas are
80×130 = 10,400 m²
170×80/2 = 170×40 = 6,800 m²
and that gives us a total for the whole area
10400 + 6800 = 17,200 m²
Answer:
Explanation:
To simplify a polynomial, we have to do two things: 1) combine like terms, and 2) rearrange the terms so that they're written in descending order of exponent.
First, we combine like terms, which requires us to identify the terms that can be added or subtracted from each other. Like terms always have the same variable (with the same exponent) attached to them. For example, you can add 1 "x-squared" to 2 "x-squareds" and get 3 "x-squareds", but 1 "x-squared" plus an "x" can't be combined because they're not like terms.
Let's identify some like terms below.
f(x)=−4x+3x2−7+9x−12x2−5x4
Here you can see that -4x and 9x are like terms. When we combine (add) -4x and 9x, we get 5x. So let's write 5x instead:
f(x)=5x+3x2−7−12x2−5x4
Let's do the same thing with the x-squared terms:
f(x)=5x+3x2−7−12x2−5x4
f(x)=5x−9x2−7−5x4
Now there are no like terms left. Our last step is to organize the terms so that x is written in descending power:
f(x)=−5x4−9x2+5x−7
Step-by-step explanation:
Answer:
x = 5, y = 4
Step-by-step explanation:
![\left\{\begin{array}{ccc}4x+5y=40\\x-y=1\end{array}\right\\\\A=\left[\begin{array}{ccc}4&5\\1&-1\end{array}\right]\\\\detA=\left|\begin{array}{ccc}4&5\\1&-1\end{array}\right|=(4)(-1)-(1)(5)=-4-5=-9\\\\A^D=\left[\begin{array}{ccc}-1&-1\\-5&4\end{array}\right]\\\\\left(A^D\right)^T=\left[\begin{array}{ccc}-1&-5\\-1&4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5C%7B%5Cbegin%7Barray%7D%7Bccc%7D4x%2B5y%3D40%5C%5Cx-y%3D1%5Cend%7Barray%7D%5Cright%5C%5C%5C%5CA%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D4%265%5C%5C1%26-1%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5CdetA%3D%5Cleft%7C%5Cbegin%7Barray%7D%7Bccc%7D4%265%5C%5C1%26-1%5Cend%7Barray%7D%5Cright%7C%3D%284%29%28-1%29-%281%29%285%29%3D-4-5%3D-9%5C%5C%5C%5CA%5ED%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-1%5C%5C-5%264%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Cleft%28A%5ED%5Cright%29%5ET%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-5%5C%5C-1%264%5Cend%7Barray%7D%5Cright%5D)
![A^{-1}=\dfrac{1}{detA}\left(A^D\right)^T\\\\A^{-1}=\dfrac{1}{-9}\left[\begin{array}{ccc}-1&-5\\-1&4\end{array}\right]=\left[\begin{array}{ccc}\dfrac{1}{9}&\dfrac{5}{9}\\\dfrac{1}{9}&-\dfrac{4}{9}\end{array}\right]](https://tex.z-dn.net/?f=A%5E%7B-1%7D%3D%5Cdfrac%7B1%7D%7BdetA%7D%5Cleft%28A%5ED%5Cright%29%5ET%5C%5C%5C%5CA%5E%7B-1%7D%3D%5Cdfrac%7B1%7D%7B-9%7D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D-1%26-5%5C%5C-1%264%5Cend%7Barray%7D%5Cright%5D%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cdfrac%7B1%7D%7B9%7D%26%5Cdfrac%7B5%7D%7B9%7D%5C%5C%5Cdfrac%7B1%7D%7B9%7D%26-%5Cdfrac%7B4%7D%7B9%7D%5Cend%7Barray%7D%5Cright%5D)
![A\cdot\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}40\\1\end{array}\right] \\\\A^{-1}A\cdot\left[\begin{array}{ccc}x\\y\end{array}\right] =A^{-1}\cdot\left[\begin{array}{ccc}40\\1\end{array}\right] \\\\\left[\begin{array}{ccc}x\\y\end{array}\right] =A^{-1}\cdot\left[\begin{array}{ccc}40\\1\end{array}\right]](https://tex.z-dn.net/?f=A%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D40%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5CA%5E%7B-1%7DA%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3DA%5E%7B-1%7D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D40%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3DA%5E%7B-1%7D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D40%5C%5C1%5Cend%7Barray%7D%5Cright%5D)
![\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}\dfrac{1}{9}&\dfrac{5}{9}\\\dfrac{1}{9}&-\dfrac{4}{9}\end{array}\right]\cdot\left[\begin{array}{ccc}40\\1\end{array}\right] \\\\\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}\left(\frac{1}{9}\right)(40)+\left(\frac{5}{9}\right)(1)\\\\\left(\frac{1}{9}\right)(40)+\left(-\frac{4}{9}\right)(1)\end{array}\right]\\\\\left[\begin{array}{ccc}x\\y\end{array}\right] =\left[\begin{array}{ccc}5\\4\end{array}\right]\Rightarrow x=5,\ y=4](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cdfrac%7B1%7D%7B9%7D%26%5Cdfrac%7B5%7D%7B9%7D%5C%5C%5Cdfrac%7B1%7D%7B9%7D%26-%5Cdfrac%7B4%7D%7B9%7D%5Cend%7Barray%7D%5Cright%5D%5Ccdot%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D40%5C%5C1%5Cend%7Barray%7D%5Cright%5D%20%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D%5Cleft%28%5Cfrac%7B1%7D%7B9%7D%5Cright%29%2840%29%2B%5Cleft%28%5Cfrac%7B5%7D%7B9%7D%5Cright%29%281%29%5C%5C%5C%5C%5Cleft%28%5Cfrac%7B1%7D%7B9%7D%5Cright%29%2840%29%2B%5Cleft%28-%5Cfrac%7B4%7D%7B9%7D%5Cright%29%281%29%5Cend%7Barray%7D%5Cright%5D%5C%5C%5C%5C%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7Dx%5C%5Cy%5Cend%7Barray%7D%5Cright%5D%20%3D%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D5%5C%5C4%5Cend%7Barray%7D%5Cright%5D%5CRightarrow%20x%3D5%2C%5C%20y%3D4)
Group A:
1 dot at 9: 1 x 9 = 9
7 dots at 10: 7 x 10 = 70
8 dots at 15: 8 x 15 = 120
8 dots at 17: 8 x 17 = 136
6 dots at 19: 6 x 19 = 114
Mean: (9+70+120+136+114) / (1+7+8+8+6) = 449/30 = 14.97
Group B:
6 dots at 10: 6 x 10 = 60
5 dots at 14: 5 x 14 = 70
6 dots at 18: 6 x 18 = 108
5 dots at 25: 5 x 25 = 125
4 dots at 28: 4 x 28 = 112
4 dots at 29: 4 x 29 = 116
mean: (60+70+108+125+112+116) / (6+5+6+5+4+4) = 591 / 30 = 19.70
The group that has a lower mean age of painting students is Group A. Its mean is 14.97 or 15 years of age.
Answer:
18550 - 10x
Step-by-step explanation:
Given that :
Cost of admission in Advance = $25
Cost of admission at the door = $35
Number of people who paid in advance = x
Total number of tickets sold = 530
Total amount made from ticket sales will be :
(Number who paid in advance * cost) + (number who paid at the door * cost)
(25 * x) + (530 - x) * 35
25x + 18550 - 35x
18550 - 10x
