Hello!
To find the line parallel to the line x + 2y = 6 and passing through the point (1, -6), we will need to know that if two lines are parallel, then their slopes are equivalent to each other.
Since the given equation is written in standard form, we will need to change it to slope-intercept form to get the slope. Slope-intercept form is: y = mx + b.
x + 2y = 6 (subtract x from both sides)
2y = 6 - x (divide both sides by 2)
y = 6/2 - x/2
y = -1/2x + 3 | The slope of parallel lines are -1/2.
Since we are given the slope, we need to find the y-intercept of the line that goes through the point (1, -6) by substituting that point into a new equation with a slope of m equalling to -1/2.
y = -1/2x + b (substitute the given point)
-6 = -1/2(1) + b (simplify - multiply)
-6 = -1/2 + b (add 1/2 to both sides)
b = -11/2 | The y-intercept of the parallel line is -13/2.
Therefore, the line parallel to x + 2y = 6 and goes through the ordered pair (1, -6) is y = -1/2x + -11/2.
Answer:
a. -216, 0 real roots
Step-by-step explanation:
The discriminant of ...
ax² + bx + c = 0
is ...
d = b² -4ac
When we put your equation into the standard form shown above, we get ...
7n² +8n +10 = 0
Then we can identify a=7, b=8, c=10. The discriminant is then ...
d = 8² - 4·7·10 = 64 -280 = -216
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The interpretation of the discriminant is ...
- < 0; no real roots (2 complex roots)
- = 0; one real root (multiplicity 2)
- > 0; 2 real roots
Your discriminant is -216, so there are 0 real roots.
Answer:
The medium-sized can is the cheaper by the oz, and is $0.005 per oz. cheaper.
Step-by-step explanation:
Medium can: $0.92/(46 oz) = $0.020/oz
Large can: $3.60 / (144 oz) = $0.025/oz
Surprisingly, the medium can price per oz. is lower than that of the large can. The difference is $0.005 per oz.
