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3 years ago

-7z - 7 ≤ -5z + 5 need help sloving

Mathematics

2 answers:

V125BC [204]3 years ago

7 0

-7z - 7 ≤ -5z + 5

- 7 - 5 ≤ -5z + 7z
-12 ≤ 2z
-12/2 ≤ z
-6 ≤ z or z>= -6

Lostsunrise [7]3 years ago

6 0

This is an inequality problem. The way to solve this is to treat the inequality sign (<, >, etc) like an equal sign (=).

-7z - 7 = -5z + 5

first, you get rid of the constants (the numbers that don't have variables with them)
the way to do that is to perform reverse operations (when there is a negative, add. when positive, subtract. same for multiplying and dividing)

-7z - 7 = -5z + 5
+ 7    + 7
------------------------
-7z = -5z + 12

the sevens are cancelled out because of the + and the - on both of them, and 5+7 is 12.
now, for the coefficients. you do the same process.

-7z - 7 = -5z + 5
+ 7    + 7
------------------------
  -7z = -5z + 12
+5z +5z
-------------------------
-2z = 12

now that you have combined all the alike terms, you divide until the variable is by itself. (/ is divide)

-7z - 7 = -5z + 5
+ 7    + 7
------------------------
  -7z = -5z + 12
+5z +5z
-------------------------
-2z = 12
/-2 /-2
-----------------------
z = -6

twelve divided by -2 is -6. so, z = -6.
now all you have to do is switch out the inequality sign: z < -6

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3 years ago

Al factorizar el trinomio cuadrado perfecto, obtenemos el siguiente resultado: (que no se como resolver) xd algun pro que sepa r

PolarNik [594]

Answer:

$\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2$

Step-by-step explanation:

<u>Trinomio Cuadrado Perfecto</u>

El producto notable llamado cuadrado de un binomio se expresa como:

$(a-b)^2=a^2-2ab+b^2$

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:

$\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8$

Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:

$\displaystyle a=\sqrt{\frac{100}{81}m^8p^{12}q^{16}z^2}$

$\displaystyle a=\frac{10}{9}m^4p^{6}q^{8}z$

Calculamos el valor de a como la raiz cuadrada del primer término del trinomio:

$\displaystyle b=\sqrt{\frac{1}{49}m^2p^2z^8$

$\displaystyle b=\frac{1}{7}mpz^4$

Nos cercioramos de que el término central es 2ab:

$\displaystyle 2ab=2\frac{10}{9}m^4p^{6}q^{8}z\frac{1}{7}mpz^4$

Operando:

$\displaystyle 2ab=\frac{20}{63}m^5p^7q^8z^5$

Una vez verificado, ahora podemos decir que:

$\displaystyle \frac{100}{81}m^8p^{12}q^{16}z^2-\frac{20}{63}m^5p^7q^8z^5+ \frac{1}{49}m^2p^2z^8=\left(\frac{10}{9}m^4p^{6}q^{8}z-\frac{1}{7}mpz^4\right)^2$

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2 years ago

In a 30-60-90 triangle, what is the length of the hypotenuse when the shorter leg is 5 cm?

zheka24 [161]

Shorter Leg=x

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3 years ago

Identify the vertex for the graph of y = −3x^2 + 6x − 4

algol [13]

Answer:

the vertex is (1,-1)

Step-by-step explanation:

y = −3x^2 + 6x − 4

the vertex is at

h= -b/2a where ax^2 +bx+c

h= -6/2(-3)

h= -6/-6

h=1

substitute this in to find the y value

y = -3(1)^2 +6(1)-4

y = -3+6-4

y = -1

the vertex is (1,-1)

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3 years ago

The equation of line A is y = 7x + 12. Line B is perpendicular to line A and passes through the point . What would be the soluti

max2010maxim [7]

Since B is perpendicular to A. We can say that the gradient of B will be -1/7 (product of the gradients of 2 perpendicular lines has to be -1).
Now we know that the equation for B is y=-(1/7)x + c with c being the y intercept.
Since the point isnt specified in the question, we could leave the equation like this.
But if there is a given point that B passes through, just plug in the x and y values into their respective places and solve to find c. That should give you the equation for b.
Now, to find the solution of x, we have 2 equations:
1) y=7x+12
2)y=-(1/7)x+c

In this simultaneous equation we see that y is equal to both the expressions. So,
7x+12=-(1/7)x+c

Now, since the value of c is not found, we cannot actually find the value of x, but if we would find c, we could also find x since it would only be a matter of rearranging the equation.
And there you go, that is your solution :)

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3 years ago