The rate of change of function A is 7 more than the rate of change of function B.
Distribute
remember a(b+c)=ab+ac
we can actually divide both sides by x
5(4x+8)=4(6x-10)
distribute
20x+40=24x-40
minus 20x both sides
40=4x-40
add 40 both sides
80=4x
divide by 4
20=x
Area of square = 24cm²
⇒ Length = √24
Find the diagonal of half the square:
a² + b² = c²
c² = (0.5√24)² + (√24)²
c² = 6 + 24
c² = 30
c = √30
The diagonal of half of the square is the radius of the circle.
⇒ radius = √30
Area of the semicircle = 1/2πr² = 1/2π(√30)² =15π
Answer: 15π²
Answer:
7/24
Step-by-step explanation:
7/8 x 1/3= 7x1=7; 8x3=24
Question 1
Simplify the following expression: (5x2 + 3x + 4) − (2x2 − 6x + 3). If
the final answer is written in the form Ax2 + Bx + C, what is the value
of B?
Solution:
5x^2 + 3x + 4 - 2x^2 + 6x - 3 = 3x^2 + 9x + 1
Then, B = 9
Question 2
Simplify: (3x2 − 2) + (2x2 − 6x + 3)
5x2 − 6x + 1
5x2 − 6x − 1
x2− 6x + 1
5x2 − 8x + 3
Solution:
3x^2 - 2 + 2x^2 - 6x + 3 = 5x^2 - 6x + 1
Question 3
A sports company conducted a road test of a new model of a geared bike.
The test rider cycled (3x - 2) miles on a flat road, (x2 - 5) miles
uphill, and (2x + 7) miles downhill. Which simplified expression is
equivalent to the total distance, in miles, for which the bike was
tested?
x2 - x
x2 + 5x
x2 − x + 14
x2 + 5x + 14
(3x - 2) + (x2 - 5) + (2x + 7) = 3x - 2 + x^2 - 5 +2x + 7 = x^2 + 5x
Question 4
Simplify: (4x − 6) − (5x + 1)
x + 7
−x + 7
x − 7
−x − 7
(4x − 6) − (5x + 1) = 4x - 6 - 5x - 1 = -x -7
Question 5
Simplify the following expression: (x + 6y) - (3x − 10y). If the final
answer is written in the form Ax + By, what is the value of A?
(x + 6y) - (3x − 10y) = x + 6y - 3x + 10y = -2x + 16y
A = -2
Question 6
Simplify: (3x − 5) + (3x + 6)
6x − 1
1
6x − 11
(3x − 5) + (3x + 6) = 3x - 5 + 3x + 6 = 6x + 1
