- Factor the indicated expression:
- Simplified the index, the root and also the exponent using the number 2.
<h3><em><u>MissSpanish</u></em> </h3>
We are given the following:
- parabola passes to both (1,0) and (0,1)
<span> - slope at x = 1 is 4 from the equation of the tangent line </span>
<span>First, we figure out the value of c or the y intercept, we use the second point (0, 1) and substitute to the equation of the parabola. W</span><span>hen x = 0, y = 1. So, c should be equal to 1. The</span><span> parabola is y = ax^2 + bx + 1 </span>
<span>Now, we can substitute the point (1,0) into the equation,
</span>0 = a(1)^2 + b(1) + 1
<span>0 = a + b + 1
a + b = -1 </span>
<span>The slope at x = 1 is equal to 4 which is equal to the first derivative of the equation.</span>
<span>We take the derivative of the equation ,
y = ax^2 + bx + 1</span>
<span>y' = 2ax + b
</span>
<span>x = 1, y' = 2
</span>4 = 2a(1) + b
<span>4 = 2a + b </span>
So, we have two equations and two unknowns,<span> </span>
<span>2a + b = 4 </span>
<span>a + b = -1
</span><span>
Solving simultaneously,
a = 5 </span>
<span>b = -6</span>
<span>Therefore, the eqution of the parabola is y = 5x^2 - 6x + 1 .</span>
<span>If 3 is added to the number: x + 3
b) ...and the sum is tripled..
"The sum" is "x + 3" so: 3(x+3)
c) ...the result is 27 more than the number.
27 more than the number is x + 27
d) Put it all together:
3(x + 3) = x + 27
Solve for x:
1) Distribute the left side of the equation:
3x + 9 = x + 27
2) Subtract x from each side of the equation:
2x + 9 = 27
3) Subtract 9 from each side of the equation:
2x = 18
4) Solve for x:
x = 9
Check:
1) x = 9
2) 3(x + 3) = x + 27
3) 3 ([9] + 3) = [9] + 27
4) 3(12) = 9 + 27
5) 36 = 36
So, therefore The answer is correct</span>
Answer:
What statements are you talking about
Step-by-step explanation:
