Can you me on my math homework

QUESTION 1

The given equation is

Split the middle term to get;

Factor to get,

We factor further to obtain,

Apply the zero product property to get,

QUESTION 2

The given equation is

Split the middle term to get;

Factor to get,

We factor further to obtain,

Apply the zero product property to get,

QUESTION 3

The length of the photo is

The width of the photo is

The length of the frame is

The width of the frame is

The area  total area of the frame is

The total of the frame of the photo must be 120.

This implies that,

We rearrange and simplify to get,

We divide through by 4 to obtain;

Split the middle term

Factor

Since x is length,

The dimensions of the frame are

QUESTION 4

Equate the function to zero

Split the middle term

Factor

Hence the other zero is 5

1. w = -6, -7

2. v = -3, 11

3. Frame's width all around is same, x, and x = 1 inch

4. The other zero of the function is 5 ( x = 5 )

Step-by-step explanation:

1.

For the question given   , we need to find 2 numbers such that their sum is equal to the number before x (which is 13) and their product is equal to the constant (which is 42) AND THEN replace 13w with those 2 numbers(and w).

Such two numbers are 7 and 6

Now we can write:

Then we can group the first 2 terms and last 2 terms and take common, then solve.

Since two expressions' product is equal to 0, either w+6 = 0 or w+7 = 0

w+6=0

w = -6

and

w+7 = 0

w= -7

Hence, w = -6, -7

2.

This is similar to Question #1, so we need two numbers that multiplied gives us -33 and added gives us -8.

Such two numbers are -11 and +3

Thus we can replace -8 with this and take common and then solve for v:

So either v-11 =0 or v+3 = 0

v - 11 = 0

v = 11

and

v+3=0

v = -3

Hence, v = -3, 11

3.

Since total area of frame & photo is 120, we need an expression for frame & photo and equate that to 120.

If picture's width is 10 and two sides there is frame of x inches each, so width of whole this is 10 +2x

Similarly, the length is 8 and two sides there is frame of x inches each, so length of whole is 8 +2x

Area of rectangle is length * width

Thus, we have  

We need to find x, so we solve the equation above:

Since length cannot be negative, x = 1 only

4.

Factoring the original equation as we did earlier, we see "what two numbers multiplied gives us -35 and added gives us +2?"

Those 2 numbers are +7 and -5

Thus we can write, group, and solve for x:

So x-5 =0 or x+7 = 0

x+7=0

x = -7 (already given in the problem)

and

x-5=0

x=5

Hence, the other zero of the function is 5