a keyboard is on sale for $676. If this price represents a 20% discount from the original price, what is the original price to the nearest cent?

Answer:

t=(a+by)/(y-1)

Step-by-step explanation:

(t-b)y =t+a

ty-by = t+a

ty-by=t+a

ty-by=a+by

t(y-1)=a+by

thus,

t=(a+by)/(y-1)

Answer:  D) Add 64 to both sides

Why do this?

Because we want to be able to factor the left hand side into the form p^2, where p is some algebraic expression. This will help us ultimately solve for x.

Currently, the left hand side is x^2+16x which does factor to x(x+16), but that isn't in the form p^2. We want something like (x+1)^2 or (x+2)^2. The general form is (x+k)^2 where k is some fixed constant.

Let's expand out (x+k)^2 using the FOIL rule and we get x^2+2kx+k^2

The x coefficient is 2k. If we cut that in half, we get k. Squaring that result leads to k^2.

So we have this order: 2k cuts in half to k then square it to get k^2

For x^2+16x, we have the x coefficient as 16. That cuts in half to 8, then that squares to 64. We add 64 to both sides

Note how

x^2+16x = 9

x^2 + 16x + 64 = 9+64

(x+8)^2 = 73

From here, we apply the square root to both sides and then subtract 8 from both sides to fully isolate x. You would get two different solutions.

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I recommend you use the FOIL rule to confirm that (x+8)^2 expands out to x^2+16x+64, to help check your work.

Plug in 12 for j

12/3 +3

4+3= 7

Answer: i think 3

Step-by-step explanation:

To find the missing digit in the multiplication problem 34 x □5, we need to determine what number should replace the blank space.

To solve this, we can use basic multiplication principles.

First, let's look at the units digit. When multiplying any number by 5, the units digit of the product will always be either 0 or 5. Therefore, the units digit of the missing number is either 0 or 5.

Next, let's consider the tens digit. In this case, it's 4. To find the tens digit of the product, we need to multiply the tens digit of the multiplicand (3) by the missing digit. If we multiply 3 by 5, we get 15, which means the tens digit of the product is 5. However, if we multiply 3 by 0, we get 0, which means the tens digit of the product is 0.

Therefore, we have two possible answers: 305 and 345. Both of these numbers are valid options for the missing digit in the multiplication problem 34 x □5.

I hope this helps! Let me know if you have any further questions.