We can take the two points given and plug them into the slope formula.
(-3, 3), (1, -5)
x1 y1 x2 y2
Subtract:
Divide:
(-3, 3), (1, -5)
x1 y1 x2 y2
Subtract:
Divide:
3 A trainer for a soccer team keeps track of the amount of water players consume during practice. The trainer observes that the
average amount of water consumed by the team is a linear function of the temperature. The graph and equation for this function are shown. Choose True or False for each statement. True у 7.8 a. For every degree increase in temperature, the average amount of water consumed increases by 0.0875 gallons. False 7.2 b. When the temperature is below 74 degrees, the team consumes no water. Water (gal) True 6.6 64 False 6.0 0 X True 0 74 76 78 80 82 84 86 88 90 92 94 C. When the temperature is 86 degrees, the team consumes somewhere between 7 gal and 7.2 gal of water. Temperature (°F) False w = 0.0875t – 0.45, where w represents the average amount of water consumed, and t represents the temperature on that day. True d. The amount of water consumed by the team decreases by 0.45 gallons for every degree the temperature falls, False S
1 answer:
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<h2>Steps:</h2>
So firstly, to factor this we need to first find the potential roots of this polynomial. To find it, the equation is , with p = the factors of the constant and q = the factors of the leading coefficient. In this case:
Next, plug in the potential roots into x of the equation until one of them ends with a result of 0:
Since we know that 3 is a root, this means that one of the factors is (x - 3). Now that we know one of the roots, we are going to use synthetic division to divide the polynomial. To set it up, place the root of the divisor, in this case 3 from x - 3, on the left side and the coefficients of the original polynomial on the right side as such:
- 3 | 1 - 10 + 25 - 40 + 84
- _________________
Firstly, drop the 1:
- 3 | 1 - 10 + 25 - 40 + 84
- ↓
- _________________
- 1
Next, multiply 3 and 1, then add the product with -10:
- 3 | 1 - 10 + 25 - 40 + 84
- ↓ + 3
- _________________
- 1 - 7
Next, multiply 3 and -7, then add the product with 25:
- 3 | 1 - 10 + 25 - 40 + 84
- ↓ + 3 - 21
- _________________
- 1 - 7 + 4
Next, multiply 3 and 4, then add the product with -40:
- 3 | 1 - 10 + 25 - 40 + 84
- ↓ + 3 - 21 + 12
- _________________
- 1 - 7 + 4 - 28
Lastly, multiply -28 and 3, then add the product with 84:
- 3 | 1 - 10 + 25 - 40 + 84
- ↓ + 3 - 21 + 12 - 84
- _________________
- 1 - 7 + 4 - 28 + 0
Now our synthetic division is complete. Now since the degree of the original polynomial is 4, this means our quotient has a degree of 3 and follows the format . In this case, our quotient is
.
So right now, our equation looks like this:
However, our second factor can be further simplified. For the second factor, I will be factoring by grouping. So factor x³ - 7x² and 4x - 28 separately. Make sure that they have the same quantity inside the parentheses:
Now it can be rewritten as:
Since the polynomial cannot be further simplified, your answer is: