Evaluate the expression when a = 3, b = 2, and c= -3: (a³ + 2bc)/( c² -5)

Mathematics

1 answer:

natta225 [31]2 years ago

4 0

((3*3*3)+2(-6))/((-3*-3)-5)
(27-12)/9-5
15/4

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zhenek [66]

Answer:

Step-by-step explanation:

$(\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{x+2}$

$\frac{3^6}{4^6} \cdot \frac{16^5}{9^5}=\frac{4^{x+2}}{3^{x+2}}$

$\frac{3^6}{4^6} \cdot \frac{(4^2)^5}{(3^2)^5}=\frac{4^{x+2}}{3^{x+2}}$

$\frac{3^6}{4^6} \cdot \frac{4^{10}}{3^{10}}=\frac{4^{x+2}}{3^{x+2}}$

$\frac{3^6}{3^{10}} \cdot \frac{4^{10}}{4^6}=\frac{4^{x+2}}{3^{x+2}}$

$3^{-4} \cdot 4^{4}=4^{x+2}3^{-(x+2)}$

This implies

x+2=4

and

-(x+2)=-4.

x+2=4 implies x=2 since subtract 2 on both sides gives us x=2.

Solving -(x+2)=-4 should give us the same value.

Multiply both sides by -1:

x+2=4

It is the same equation as the other.

You will get x=2 either way.

Let's check:

$(\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{2+2}$

$(\frac{3}{4})^6 \times (\frac{16}{9})^5=(\frac{4}{3})^{4}$

Put both sides into your calculator and see if you get the same thing on both sides:

Left hand side gives 256/81.

Right hand side gives 256/81.

Both side are indeed the same for x=2.

4 0

3 years ago

How to combine like terms

aev [14]

Example: $1x+2y+3z+4a+5x+6y+7z+8+9$

We can see that there is more than one number with the variable x, therefore, we say they're ''like terms'' and because of that they can be summed. We do this with all of the other numbers with similar variables. If no numbers with similar variables are left, like 4a, you don't do anything but write them as they are. You can also see that 8 and 9 can also be summed because neither of them has a variable, therefore they're similar.

In this step, you just do the operation with the numbers and keep the same variable.

$(1x+5x)+(2y+6y)+(3z+7z)+4a+(8+9)$