Answer:
<h2>14mph</h2>
Step-by-step explanation:
Given the gas mileage for a certain vehicle modeled by the equation m=−0.05x²+3.5x−49 where x is the speed of the vehicle in mph. In order to determine the speed(s) at which the car gets 9 mpg, we will substitute the value of m = 9 into the modeled equation and calculate x as shown;
m = −0.05x²+3.5x−49
when m= 9
9 = −0.05x²+3.5x−49
−0.05x²+3.5x−49 = 9
0.05x²-3.5x+49 = -9
Multiplying through by 100
5x²+350x−4900 = 900
Dividing through by 5;
x²+70x−980 = 180
x²+70x−980 - 180 = 0
x²+70x−1160 = 0
Using the general formula to get x;
a = 1, b = 70, c = -1160
x = -70±√70²-4(1)(-1160)/2
x = -70±√4900+4640)/2
x = -70±(√4900+4640)/2
x = -70±√9540/2
x = -70±97.7/2
x = -70+97.7/2
x = 27.7/2
x = 13.85mph
x ≈ 14 mph
Hence, the speed(s) at which the car gets 9 mpg to the nearest mph is 14mph
<span>Each paper clip can be traded for three matches.
Each pencil can be traded for six paper clips which can be traded for (6 x 3 = 18) eighteen matches.
</span><span>Two pencils and two paper clips are worth (2 x 18 + 2 x 3 = 36 + 6 = 42) which is greater than thirty-eight matches.
Therefore, </span><span>Two pencils and two paper clips are worth thirty-eight matches.</span>
Answer:
x = 10, y = 
Step-by-step explanation:
The opposite sides of a parallelogram are congruent.
For LMNO to be a parallelogram then
ON = LM and OL = NM, that is
ON = LM
7x - 6 = 6x + 4 ( subtract 6x from both sides )
x - 6 = 4 ( add 6 to both sides )
x = 10 , then
NM = x - 9 = 10 - 9 = 1 and
OL = NM , that is
3y - 3 = 1 ( add 3 to both sides )
3y = 4 ( divide both sides by 3 )
y =
Answer:
2<7
Step-by-step explanation:
-7<=-2
-7+9<-2+9
2<7
