To answer this, I set up a system of equations for each sentence mentioned (B=3A for Betty, A - 390 for Ann, and B = (A - 390) + 1330 to show the relationship between Betty and Charles's amounts. The way to answer this is to replace the B with the 3A that represents Betty's amount. This creates 3A= (A-390) + 1330. By having only one variable you can then solve the equation to find Ann's amount. If you know Ann's amount, you can figure out Charles' amount. To solve the equation add 1330 and -390 which is the same as subtracting 390 from 1330. This leaves you with 3A= A + 940. Subtract 1A from both sides, to leave you with 2A = 940. Solve for a by dividing both sides by 2. This leaves you with A= 470. Take this value of a and substitute it in to Charles's equation which is C = A - 390. 470 - 390 equals 80. This is Charles' amount saved.
Answer:
x = 12 hours
Step-by-step explanation:
If one pipe fills store pool in 12 hours in 1 hour will fill 1/12 of the pool
If one pipe fills a store pool in 6 hours in 1 hour will fill 1/6 of the pool
Let call " x " number of hours needed by the third pipe to fills the pool
then in 1 hour will fill 1/x
The three pipes working together in 1 hour will fill
1/12 + 1/6 + 1/x
Now we know that the three pipes take 3 hours to fill the pool then in 1 hour three pipes will fill 1/3 of the pool, therefore
1/12 + 1/6 + 1/x = 1/3
( x + 2*x + 12) /12*x = 1/3 ⇒ ( 3*x +12 )/ 12*x = 1/3
9*x + 36 = 12*x
- 3*x = - 36
x = 36/3
x = 12 hours
Answer: Store B
Step-by-step explanation: Divide the price by the pound. That gets your price per pound. So, 12.95÷5=2.59
7.50÷3=2.50
Store B has the better deal because their chicken is 9¢ cheaper per pound.
Answer:
The vertex is at (-3/2, 33/4)
x=-3/2
Step-by-step explanation:
y= -x^2 -3x+6
Factor out a negative from the first two terms
y = -(x^2 +3x) +6
Complete the square
Take 3 /2 and square it (3/2)^2 = 9/4
The - on the outside of the parentheses means we really are subtracting it so we need to add it on the outside
y = -(x^2 + 3x + 9/4) +9/4 +6
= -(x+3/2)^2 + 9/4 +6
Get a common denominator of 4
= -(x+3/2)^2 + 9/4 +6*4/4
y =- (x+3/2)^2 + 9/4 +24/4
y = -(x+3/2)^2 + 33/4
y = a(x-h)^2 +k where (h,k) is the vertex
y = -(x - -3/2)^2 + 33/4
The vertex is at (-3/2, 33/4)
The axis of symmetry is at the x coordinate of the vertex
x=-3/2
Answer:
A man travels 600km partly by train and partly by car. If he covers 400km by train and the rest by car, it takes him 6 hours and 30 minutes. But if he travels 200 km by train and rest by car, he takes half an hour longer.find the speed of the train and that of the car
Step-by-step explanation:
