Answer:
Student A and Student B both answered 2 questions correctly.
See explanation below
Step-by-step explanation:
Note: that answers in the form:
ARE ALL EQUIVALENT.
First of all, 4/5 is equivalent to 0.8 if we do long division.
and 19/20 is 0.95 if we do long division.
Now, <u>Student A:</u>
Both of the fractions are correct and the negative sign is equivalent and makes the answer correct, so both are correct.
For <u>Student B:</u>
Similarly, both answers are correct for this student as well, looking at the equivalence we showed first.
Also, "-" (negative) in front of the parenthesis and inside parenthesis here doesn't matter.
Hence,
Student A and Student B both answered 2 questions correctly.
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
Given:
There are 4 quarts in a gallon.
She wants to convert 6 quarts to a gallon.
To find:
Whether she should multiply 6 by 4 or divide 6 by 4 to find her answer.
Solution:
We have,
Here, 6 quarts is equal to 
gallon. It means we need to multiply 6 by 4 in to find the answer.
Well since we know that the perimeter of a square is four times the length of one of its sides. We just have to divide 5 by 4 to get the length of one side:
5feet /4 sides = 1.25 feet
And to finish off, we have to convert feet to inches:
<u>1 foot </u>= <u>12 inches</u>
1.25 feet x inches
x inches = 12 inches x 1.25 feet ÷ 1 foot
x inches = 15 inches
Therefore, each side is 15 inches long.
Hope this helps!
Answer:
Value of expression in single logarithm is 
.
Step-by-step explanation:
Given expression is,
Now using logarithmic rule to solve the expression as follows,
Applying product rule of logarithmic,
Therefore,
Applying power rule of logarithmic,
Therefore,
Applying quotient rule of logarithmic,
Therefore,
Simplifying,
Therefore value of expression is
