What is the product of 5 7/10 - 5/18

244/45

Step-by-step explanation:

Simplify the following:

5 + 7/10 - 5/18

Put 5 + 7/10 - 5/18 over the common denominator 90. 5 + 7/10 - 5/18 = (90×5)/90 + (9×7)/90 + (5 (-5))/90:

(90×5)/90 + (9×7)/90 + (5 (-5))/90

90×5 = 450:

450/90 + (9×7)/90 + (5 (-5))/90

9×7 = 63:

450/90 + 63/90 + (5 (-5))/90

5 (-5) = -25:

450/90 + 63/90 + (-25)/90

450/90 + 63/90 - 25/90 = (450 + 63 - 25)/90:

(450 + 63 - 25)/90

| 1 | |  

| 4 | 5 | 0

+ | | 6 | 3

| 5 | 1 | 3:

(513 - 25)/90

| | 10 |  

| 4 | 0 | 13

| 5 | 1 | 3

- | | 2 | 5

| 4 | 8 | 8:

488/90

The gcd of 488 and 90 is 2, so 488/90 = (2×244)/(2×45) = 2/2×244/45 = 244/45:

 244/45

Our x-intercepts are at:

Our y-intercept is (0, -10).

Step-by-step explanation:

We have the function:

And we know that one factor is:

Since we know one factor, we can use synthetic division to find the depressed polynomial, then continue factoring to find the remaining zeros (x-intercepts).

To find the y-intercept, we can simply substitute 0 for x and evaluate. This can be done anytime.

We can apply synthetic division for a polynomial P(x) divided by a binomial in the form (x-a).

Since our factor is (x-5), a=5.

Please refer to the attachment below for the synthetic division.

So, we are left with:

The remaining factor is now a quadratic. This can be easily factored:

To find our zeros, set our function f(x) to 0:

Then by the Zero Product Property:

Hence, our x-intercepts are:

To find our y-intercept, we can substitute 0 for x and evaluate. Hence:

Evaluate:

So, our y-intercept is at (0, -10).