What is the equation of the parabola passing through the points(0,6). (3, 15.6), and (10,-4)?
1 answer:
Answer:
y = -0.6x^2 + 5x + 6
Step-by-step explanation:
First, find the equation of a linear line that passes through the points (0,6) and (3, 15.6) in the slope intercept form, y = mx + b. We know that the line has a y-intercept of 6, so b = 6. Substitute 3 for x, 15.6 for y, and 6 for b to find m.
y = mx + b
15.6 = 3m + 6
9.6 = 3m
m = 3.2
y = 3.2x + 6
y = a(x - 0)(x - 3) + 3.2x + 6
y = a(x)(x - 3) + 3.2x + 6
Finally, substitute 10 for x and -4 for y in the equation above to find a.
-4 = a(10)(10 - 3) + 3.2*10 + 6
-4 = a(10)(7) + 32 + 6
-4 = 70a + 38
-42 = 70a
a = -0.6
Simplify to write in standard form.
y = -0.6(x)(x - 3) + 3.2x + 6
y = -0.6x^2 + 5x + 6
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The <em><u>correct answer</u></em> is:
She can make 2 loaves of bread and 4 batches of muffins.
Explanation:
Let b represent bread and m represent muffins.
The equation for the amount of flour she needs is 3.5b+2.5m=17.
The equation for the amount of sugar she needs is 0.75b+0.75m=4.5.
To solve this, we will want to eliminate one of the variables. To do this, we will make the coefficients of one of the variables the same. If we multiply 2.5 by 0.3, we get 0.75; this is what we will do to the first equation:
She can bake two loaves of bread.
Substituting 2 for b in the first equation, we have
3.5(2)+2.5m=17
7+2.5m=17
Subtract 7 from each side:
7+2.5m-7=17-7
2.5m=10
Divide both sides by 2.5:
2.5m/2.5 = 10/2.5
m = 4
She can bake 4 batches of muffins.