Answer:
X = - 5
Step-by-step explanation:
The above word problem is mathematically interpreted thus:
-1X - 4X = -4 - 4X + 4 + 5
-5X = - 4 - 4X + 4 + 5
-5X = - 4 - 4X + 9
Collect like terms
-5X + 4X = - 4+ 9
-X = 5
X = - 5
Answer:
There are 20 ducklings.
Step-by-step explanation:
For every group of 6 ducks, 5 would be ducklings.
24 / 6 = 4
There are 4 groups of ducks.
5 * 4 = 20
Answer:
Option (2)
Step-by-step explanation:
ΔDEF is a dilation image of ΔABC.
Rule for the dilation,
Scale factor = 
= 
= 
= 
Therefore, scale factor by which ΔABC is dilated is .
Option (2) will be the correct option.
Step-by-step explanation:
First, we define the variables:
x: number of years after 1950
f (x): amount of vinyl sold.
Then, with the variables defined, we have:
68594 vinyl records were sold in 1958 ---------> f (8) = 68594
91299 vinyl records were sold in 1961 ---------> f (11) = 91299
38720 vinyl records were sold in 1952 ---------> f (2) = 38720
161743 vinyl records were sold in 1967 ---------> f (17) = 161743
First find the slope of the given line:
4x +2y = 1
Subtract 4x from each side:
2y = -4x + 1
Divide both sides by 2:
y = -2x +1/2
The slope is -2.
Now use the slope to find the y-intercept. Because the line is perpendicular, you need to use the negative inverse of the slope.
The negative inverse of -2 is 1/2
Now using the point-slope form y - y1 = m(x-x1)
Use the inverse slope for m, and the given point(-4,3) to get:
y - 3 = 1/2(x+4)
Simplify:
y - 3 = x/2 +2
Add 3 to each side:
y = x/2 + 5
Reorder the terms to get y = 1/2x +5
The answer is D.
