Answer: 691
<u>Step-by-step explanation:</u>
There are 3 different ways to find the remainder. I am not sure which method you are supposed to use, so I will solve using all 3 methods.
Long Division:
<u> 10x³ + 24x² + 77x + 230 </u>
x - 3 ) 10x⁴ - 6x³ + 5x² - x + 1
- <u>(10x⁴ - 30x³) </u> ↓ ↓ ↓
24x³ + 5x² ↓ ↓
- <u>(24x³ - 72x²) </u> ↓ ↓
77x² - x ↓
- <u>(77x² - 231x) </u> ↓
230x + 1
- <u>(230x - 690)</u>
691 ← remainder
Synthetic Division:
x - 3 = 0 ⇒ x = 3
3 | 10 -6 5 -1 1
|<u> ↓ 30 72 231 690</u>
10 24 77 230 691 ← remainder
Remainder Theorem:
f(x) = 10x⁴ - 6x³ + 5x² - x + 1
f(3) = 10(3)⁴ - 6(3)³ + 5(3)² - (3) + 1
= 810 - 162 + 45 - 3 + 1
= 691
$1.35 x 10 = $13.50 for 10 gallons
$23.50 - $13.50 = $10.00
$1.35 x 7 = $9.45 for 7 more gallons
17 gallons is $22.45
17/27 = 459 miles but I'm missing the last bit of change so round it up to 460 for a total of miles
(0,50)(5,100)
slope = (100 - 50) / 5 - 0) = 50/5 = 10
y = mx + b
slope(m) = 10
(0,50)...x = 0 and y = 50
now we sub and find b, the y int
50 = 10(0) + b
50 = b
equation is : y = 10x + 50
Angel has 50 and she saves 10 a week <===
Answer:
slope of the parallel line = 8
Step-by-step explanation:
Parallel lines have the same slope. To determine the equation of the other line, you need to transform the given linear equation into its slope-intercept form, y = mx + b:
-8x + y = 2
Add 8x to both sides to isolate y:
-8x + 8x + y = 8x + 2
y = 8x + 2 (this is the slope-intercept form where the slope (m) = 8, and the y-intercept (b) = 2).
Given that the slope of the first equation is 8, then we can assume that the slope of line parallel to -8x + y = 2 will also be 8.
