Answer:
Option B.
Step-by-step explanation:
The given quadratic equation is
We need to find the solution of given quadratic equation.
Divide both sides by 9.
Taking square root on both sides.
The solution of given equation are 
and 
.
Therefore, the correct option is B.
Answer:
Find the ratio of hops to distance traveled (1: 1.5), then multiply 150 by 1.5.
Step-by-step explanation:
A child is hopping along a sidewalk. The ratio table below shows the comparison between the number of hops and the distance traveled. Hopping Number of hops Distance traveled (ft) 20 30 50 75 80 120 150 ?
Which statement correctly explains how to find the distance traveled after 150 hops? Subtract 120 – 75 to get 45, then add that number to 120. Add 30 + 75 + 120. Find the ratio of hops to distance traveled (1:1.5), then multiply 150 by 1.5. Find the ratio of hops to distance traveled (1:1.5), then divide 150 by 1.5.
Solution:
The table is:
No. of hops Distance traveled
20 30
50 75
80 120
150 ?
From the table, for every 30 increase in the number of hops, the distance travelled increase by 45 feet
Find the slope of the line:
m = (y2-y1) / (x2-x1)
m=slope of the line
y2-y1 = change in distance travelled
x-2 - x1 = Change in number of hops
m = (y2-y1) / (x2-x1)
m = (75-30) / (50-20)
=45 / 30
m = 1.5
Then, the line is:
y = 1.5x
We substitute x = 150
y = 1.5x
y = 1.5 × 150
y = 225
Answer:
(a) Profit function P(x) = 0.02x^2+60x-80
(b) Average profit P(x)/x = P/x = 0.02x+60-80/x
Marginal profit dP/dx = 0.04x+60
Step-by-step explanation:
Cost function: C(x) = -0.02x^2+40x+80
Price function: p(x) = 100
(a) The profit function P(x) = x*p(x)-C(x) can be expressed as:
(b)Average profit function: P(x)/x
Marginal profit function: dP/dx
This is because when we do verification of an
identity, we must work separately on both sides, and to see in the end
if we can get an equality. Because if we square both sides, that already means
that we assume that the equality exist in the beginning, so no need to
verify the identity.
Answer: The first equation should be multiplied by 9 and the second equation by −4, to eliminate the y-terms and solve for x in the fewest steps.
Step-by-step explanation:
Given : Equation (1) 5x − 4y = 28
Equation (2) 3x - 9y = 30
to eliminate the y-terms and solve for x in the fewest steps, we should multiply equation (1) by 9 and equation (2) by -4 such that
9(5x − 4y) =9 (28)⇒45x-36y=252
-4(3x - 9y) = -4(30)⇒ -12x+36y= -120
Now adding both equations, y-term eliminated and we get, 45x-12x=132
⇒33x=132⇒x=4.
