Answer:
Step-by-step explanation:
Cindy is correcy because on "Step 1:" the multiplication was correctly distributed over the subtraction in paranthesis 5(x-2) = 5*x- 5*2 = 5x-10.
Henry was wrrong because he distributed 5 only over x and not over -2 as well 5(x-2) ≠ 5*x-2
Answer:
c.0.13
Step-by-step explanation:
From clue 3, we know that the three numbers average to 15. This means we add up the three numbers x,y and z and divide by 3 to get 15. So one equation is (x+y+z)/3 = 15 which turns into x+y+z = 45 after multiplying both sides by 3.
Let's say that x < y < z. In other words x is the smallest number, y is the middle and z is the largest. Based on clue 2, this would tell us that z = 8*x (since largest is 8 times the smallest). We can replace the 'z' in the equation x+y+z = 45 with 8x like so
x+y+z = 45
x+y+8x = 45 ... replace z with 8x
9x+y = 45
Now onto clue #1. The smallest number x is a prime number and it is 1/6 times the size of the middle number y. Put another way, the middle number y is 6 times larger than the smallest number. We have this equation y = 6*x
9x+y = 45
9x+6x = 45 ... replace ywith 6x
15x = 45
x = 45/15
x = 3 which is a prime number
Now that we know x = 3, we can use it to find y
y = 6*x = 6*3 = 18
and then use x = 3 to find z
z = 8*x = 8*3 = 24
Therefore the three mystery numbers are 3, 18, and 24. Note how these three values add to 3+18+24 = 45 which you then divide over 3 to get 45/3 = 15. So the average of the values 3, 18, 24 is the number 15. This helps confirm the answer.
Answer:
$6.00
Step-by-step explanation:
Use the formula for simple interest: Interest = Principle x Rate x Time
so I = $60.00 x .1 x 1 = $6.00
Answer:
(x - 3)^2 + (y - 4)^2 = 3^2
Step-by-step explanation:
Notice that both endpoints are on the vertical line x = 3. Thus, to determine the diameter of this circle, we need only subtract 1 from 7, obtaining 6. The diameter is 6, so the radius is 3.
The center is on the vertical line x = 3 and is halfway between the endpoints of the diameter, that is, at y = 4. (3, 4) describes this point.
Then we insert the known quantities into the general equation for a circle with center at (h, k) and radius r: 3 for h, 4 for k and 3 for r:
(x - 3)^2 + (y - 4)^2 = 3^2 is the desired equation.