Answer:
Find the ratio of hops to distance traveled (1: 1.5), then multiply 150 by 1.5.
Step-by-step explanation:
A child is hopping along a sidewalk. The ratio table below shows the comparison between the number of hops and the distance traveled. Hopping Number of hops Distance traveled (ft) 20 30 50 75 80 120 150 ?
Which statement correctly explains how to find the distance traveled after 150 hops? Subtract 120 – 75 to get 45, then add that number to 120. Add 30 + 75 + 120. Find the ratio of hops to distance traveled (1:1.5), then multiply 150 by 1.5. Find the ratio of hops to distance traveled (1:1.5), then divide 150 by 1.5.
Solution:
The table is:
No. of hops Distance traveled
20 30
50 75
80 120
150 ?
From the table, for every 30 increase in the number of hops, the distance travelled increase by 45 feet
Find the slope of the line:
m = (y2-y1) / (x2-x1)
m=slope of the line
y2-y1 = change in distance travelled
x-2 - x1 = Change in number of hops
m = (y2-y1) / (x2-x1)
m = (75-30) / (50-20)
=45 / 30
m = 1.5
Then, the line is:
y = 1.5x
We substitute x = 150
y = 1.5x
y = 1.5 × 150
y = 225
1 equals 0.3
2 equals 1.25
The length is 10 and the area is 100 because 6,8,10 is a pythagorean triple. 36 + 64 = 100 and the square root of 100 is 10. 10 ^ 2 is the area which is 100. If this is right could you possibly give me brainliest? Hope this helped.
Answer:
6
Step-by-step explanation:
Cost per item is found by dividing the cost by the number of items. If the woman bought n items for $120, the cost of each item is $120/n. If the woman bought 24 more items, n+24, at the same price, then the cost per item is $120/(n+24). The problem statement tells us this last cost is $16 less than the first cost:
120/(n+24) = (120/n) -16
Multiplying by n(n+24) gives ...
120n = 120(n+24) -16(n)(n+24)
0 = 120·24 -16n^2 -16·24n . . . . . . subtract 120n and collect terms
n^2 +24n -180 = 0 . . . . . . . . . . . . . divide by -16 to make the numbers smaller
(n +30)(n -6) = 0 . . . . . . . . . . . . . . factor the quadratic
The solutions to this are the values of n that make the factors zero: n = -30, n = 6. The negative value of n has no meaning in this context, so n=6 is the solution to the equation.
The woman bought 6 items.
_____
Check
When the woman bought 6 items for $120, she paid $120/6 = $20 for each of them. If she bought 6+24 = 30 items for the same money, she would pay $120/30 = $4 for each item. That amount, $4, is $16 less than the $20 she paid for each item.
Answer:
The constant of variation in a direct variation is the constant (unchanged) ratio of two variable quantities. The formula for direct variation is. y = k x (or y = k x ) where k is the constant of variation . Example 1: If y varies directly as x and y = 15 when x = 24 , find x when y = 25 .
Step-by-step explanation:
Hope this helps, mark brainliest
