Answer:
B
Step-by-step explanation:
Although this problem is quite long and exhausting, it is deceptively simple.
We know that his 12-gallon fuel tank is only half full, so we know that the car needs 6 more gallons of fuel.
If he turns in the car late, he will have to pay y = 2.59x + 32.00, where x is the number of empty gallons (in this case, 6)
In this case, he will pay 2.59(6) + 32.00 = $47.54
If he turns in the car on time, he will have to pay y = 4.50x + 5.00, where x is the number of empty gallons (still 6).
In this case, he will pay 4.50(6) + 5.00 = $32.00
Using these results, we know that B must be true.
<span>6x + 7y = 11 . . . . (1)
5x + 2y = 13 . . . . (2)
</span><span>
6x + 7y = 11 (multiply through by 2) </span>→ 12x + 14y = 22 (
)
<span>
5x + 2y = 13 (multiply through by 7) </span>→ 35x + 14y = 91 (
)
by subtracting (
) from (
)
⇒ (35x + 14y) - (12x + 14y) = 91 - 22
⇒ 35x - 12x + 14y - 14y = 91 - 22
⇒ 23x = 69
⇒ 23x ÷ 23 = 69 ÷ 23
∴ x = 3
By substituting found value of x into (2),
⇒ 5(3) + 2y = 13
⇒ 15 + 2y = 13
⇒ 2y = 13 - 15
2y = -2
∴ y = -1
Thus the solution to the system is (3 , -1)
Answer: y - 5 = 2/3(x - 0)
Explanation:
Point slope form:
y - y1 = m(x - x1)
Given information:
y1 = 5
x1 = 0
m = 2/3
We can write the equation using the form:
y - 5 = 2/3(x - 0)
Let's say the shorter side is x.
So, the longer side would be ( 7 + x )
Now we have to use the Pythagorean Theorem to find the value of x.
a² + b² = c²
( 7 + x )² + x² = 13
7² + x² + x² = 13²
49 + 2x² = 169
2x² = 169 - 49
2x² = 120
x² = 60
x = √60
So the longer side is ( 7 + √60 ) and the shorter side is √60
Answer:
The volume of a right circular cylinder with a base diameter of 17.5 ft and a height of 24.5 ft is:
5889.95 ft³
Step-by-step explanation:
We are given a base diameter of a right circular cylinder as :
d = 17.5 ft.
hence radius of cylinder i.e. r =d/2 = 8.75 ft.
height of the cylinder = 24.5 ft.
now we know that volume of cylinder i.e. V is given by :
V = πr²h
putting the value of r and h in the given formula to obtain the volume
V = 3.14×(8.75)²×24.5
= 5889.95 ft³
hence, the volume of a right circular cylinder with a base diameter of 17.5 ft and a height of 24.5 ft is:
5889.95 ft³
