9514 1404 393
Answer:
13 cm, 39 cm, 39 cm
Step-by-step explanation:
If x is the short side, then the other two sides are 3x and 3x. The perimeter is the sum of side lengths:
x +3x +3x = 91
x = 91/7 = 13
3x = 3(13) = 39
The length of the short side is 13 cm; the other two sides are 39 cm.
Answer:
![\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B100%7D%7B81%7Dm%5E8p%5E%7B12%7Dq%5E%7B16%7Dz%5E2-%5Cfrac%7B20%7D%7B63%7Dm%5E5p%5E7q%5E8z%5E5%2B%20%5Cfrac%7B1%7D%7B49%7Dm%5E2p%5E2z%5E8%3D%5Cleft%28%5Cfrac%7B10%7D%7B9%7Dm%5E4p%5E%7B6%7Dq%5E%7B8%7Dz-%5Cfrac%7B1%7D%7B7%7Dmpz%5E4%5Cright%29%5E2)
Step-by-step explanation:
<u>Trinomio Cuadrado Perfecto</u>
El producto notable llamado cuadrado de un binomio se expresa como:
![(a-b)^2=a^2-2ab+b^2](https://tex.z-dn.net/?f=%28a-b%29%5E2%3Da%5E2-2ab%2Bb%5E2)
Si se tiene un trinomio, es posible convertirlo en un cuadrado perfecto si cumple con las condiciones impuestas en la fórmula:
* El primer término es un cuadrado perfecto
* El último término es un cuadrado perfecto
* El segundo término es el doble del proudcto de los dos términos del binomio.
Tenemos la expresión:
![\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B100%7D%7B81%7Dm%5E8p%5E%7B12%7Dq%5E%7B16%7Dz%5E2-%5Cfrac%7B20%7D%7B63%7Dm%5E5p%5E7q%5E8z%5E5%2B%20%5Cfrac%7B1%7D%7B49%7Dm%5E2p%5E2z%5E8)
Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:
![\displaystyle a=\sqrt{\frac{100}{81}m^8p^{12}q^{16}z^2}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%3D%5Csqrt%7B%5Cfrac%7B100%7D%7B81%7Dm%5E8p%5E%7B12%7Dq%5E%7B16%7Dz%5E2%7D)
![\displaystyle a=\frac{10}{9}m^4p^{6}q^{8}z](https://tex.z-dn.net/?f=%5Cdisplaystyle%20a%3D%5Cfrac%7B10%7D%7B9%7Dm%5E4p%5E%7B6%7Dq%5E%7B8%7Dz)
Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:
![\displaystyle b=\sqrt{\frac{1}{49}m^2p^2z^8](https://tex.z-dn.net/?f=%5Cdisplaystyle%20b%3D%5Csqrt%7B%5Cfrac%7B1%7D%7B49%7Dm%5E2p%5E2z%5E8)
![\displaystyle b=\frac{1}{7}mpz^4](https://tex.z-dn.net/?f=%5Cdisplaystyle%20b%3D%5Cfrac%7B1%7D%7B7%7Dmpz%5E4)
Nos cercioramos de que el término central es 2ab:
![\displaystyle 2ab=2\frac{10}{9}m^4p^{6}q^{8}z\frac{1}{7}mpz^4](https://tex.z-dn.net/?f=%5Cdisplaystyle%202ab%3D2%5Cfrac%7B10%7D%7B9%7Dm%5E4p%5E%7B6%7Dq%5E%7B8%7Dz%5Cfrac%7B1%7D%7B7%7Dmpz%5E4)
Operando:
![\displaystyle 2ab=\frac{20}{63}m^5p^7q^8z^5](https://tex.z-dn.net/?f=%5Cdisplaystyle%202ab%3D%5Cfrac%7B20%7D%7B63%7Dm%5E5p%5E7q%5E8z%5E5)
Una vez verificado, ahora podemos decir que:
![\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Cfrac%7B100%7D%7B81%7Dm%5E8p%5E%7B12%7Dq%5E%7B16%7Dz%5E2-%5Cfrac%7B20%7D%7B63%7Dm%5E5p%5E7q%5E8z%5E5%2B%20%5Cfrac%7B1%7D%7B49%7Dm%5E2p%5E2z%5E8%3D%5Cleft%28%5Cfrac%7B10%7D%7B9%7Dm%5E4p%5E%7B6%7Dq%5E%7B8%7Dz-%5Cfrac%7B1%7D%7B7%7Dmpz%5E4%5Cright%29%5E2)
Answer:
going horizontally, 15, 3, 9, then 1, 3, 6, then 20, then, 40, 60
Step-by-step explanation:
Answer:
D
Step-by-step explanation:
![A = P(1 + \frac{r}{n})^{nt}\\](https://tex.z-dn.net/?f=A%20%3D%20P%281%20%2B%20%5Cfrac%7Br%7D%7Bn%7D%29%5E%7Bnt%7D%5C%5C)
[5000* (1+0.125)]/12 =234.375, rounds up to $234.38
Answer:
![\frac{15y-10}{15y-3}](https://tex.z-dn.net/?f=%5Cfrac%7B15y-10%7D%7B15y-3%7D)
Step-by-step explanation:
First at all, we need to use
to convert this expression into a fraction, like:
to convert into
.
Expand the fraction to get the least common denominator, like
![\frac{3y}{3*1}-\frac{2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3y%7D%7B3%2A1%7D-%5Cfrac%7B2%7D%7B3%7D)
Write all numerators above the common denominator, like this:
![\frac{3y-2}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B3y-2%7D%7B3%7D)
The bottom one used the same way to became simplest form, like this:
![y+\frac{1}{5}](https://tex.z-dn.net/?f=y%2B%5Cfrac%7B1%7D%7B5%7D)
![\frac{y}{1} +\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7By%7D%7B1%7D%20%2B%5Cfrac%7B1%7D%7B5%7D)
![\frac{5y}{5*1}+\frac{1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B5y%7D%7B5%2A1%7D%2B%5Cfrac%7B1%7D%7B5%7D)
![\frac{5y+1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B5y%2B1%7D%7B5%7D)
And it became like this:
![\frac{3y-2}{3}/\frac{5y+1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B3y-2%7D%7B3%7D%2F%5Cfrac%7B5y%2B1%7D%7B5%7D)
Now, we are going to simplify this complex fraction. We can use cross- multiply method to simplify this fraction.
![\frac{3y-2}{3}*\frac{5y+1}{5}](https://tex.z-dn.net/?f=%5Cfrac%7B3y-2%7D%7B3%7D%2A%5Cfrac%7B5y%2B1%7D%7B5%7D)
3y-2(5) and 5y-1(3)
and it will becomes like this in function form:
![\frac{3y-2(5)}{5y+1(3)}](https://tex.z-dn.net/?f=%5Cfrac%7B3y-2%285%29%7D%7B5y%2B1%283%29%7D)
Then, we should distribute 5 through the parenthesis
![\frac{15y-10}{5y+1(3)}](https://tex.z-dn.net/?f=%5Cfrac%7B15y-10%7D%7B5y%2B1%283%29%7D)
![\frac{15y-10}{15y+3}](https://tex.z-dn.net/?f=%5Cfrac%7B15y-10%7D%7B15y%2B3%7D)
And.... Here we go. That is the answer.