Answer: She babysat 7 hours
Step-by-step explanation:if you take the knowledge you have; she charges 6$ per hour. and lily mad 42$ you can divide 42 by 6 to get the answer of 7
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>
Answer:
Javier can buy <em>at maximum</em> about 3.7 gallons of oil.
Step-by-step explanation:
Let g represent the amount of gasoline in galloons.
We know that Javier has at most $15.00 to spend. In other words, the total cost after buying the snacks and gasoline must be <em>less than or equal to </em>15.
He already bought a snack and a drink for a total of $2.59.
And each gallon of gasoline costs $3.39.
So, we can write the following inequality:
To find how many galloons of gasoline Javier can buy, we will need to solve for g.
So, subtract 2.59 from both sides. This yields:
Divide both sides by 3.39:
So, Javier can buy <em>at maximum</em> about 3.7 gallons of oil.
And we're done!
Solution:
100<em>x</em>^2-58<em>x</em>-16
~Add x to both sides
~Subtract 4 from both sides
~Divide both sides by 5
~Simplify
~M=
~B=
