How many stripes does each zebra have if there are 6 zebras at the zoo, 162 stripes in all, and all the zebras have the same num
2 answers:
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Problem 13a
Each column of the table represents an (x,y) pairing. The first column has x = 0 and y = 2 so (0,2) is one point on this line. Since x = 0 here, this means that we have the y intercept. The y intercept is 2. We'll use this later.
Another point on this line is (3,8) which is drawn from the second column.
Use the two points (0,2) and (3,8) to find the slope m
m = (y2-y1)/(x2-x1)
m = (8-2)/(3-0)
m = 6/3
m = 2
Since the slope is 2 and the y intercept is 2 (see above), this means m = 2 and b = 2
Plug those into y = mx+b and we get y = 2x+2
Answer: y = 2x+2
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Problem 13b
(0,20) is on the line as the first column shows. The y intercept is 20 since x = 0 here. So b = 20
Another point on this line is (3,8) as drawn from the second column
Slope:
m = (y2-y1)/(x2-x1)
m = (8-20)/(3-0)
m = -12/3
m = -4
Use the slope (m = -4) and the y intercept (b = 20) to get...
y = mx+b
y = -4x+b ... replace m with -4
y = -4x+20 ... replace b with 20
Answer: y = -4x+20
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Problem 13c
(2,5) and (4,8) are on the line. These two points are drawn from columns 1 and 2 respectively.
Slope
m = (y2-y1)/(x2-x1)
m = (8-5)/(4-2)
m = 3/2
m = 1.5
Note: the fraction 3/2 is equivalent to the decimal form 1.5
Use the slope m = 1.5 along with (x,y) = (2,5) to find the value of b
y = mx+b
y = 1.5x+b ... m is replaced with 1.5
5 = 1.5*2+b ... plug in (x,y) = (2,5)
5 = 3+b
5-3 = 3+b-3
2 = b
b = 2
So we can now update y = mx+b to y = 1.5x+2
Answer: y = 1.5x+2
Note: If your teacher wants a fraction instead of a decimal (for the slope), then you would write
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Problem 13d
(0,20) is on the line. So the y intercept is 20, indicating that b = 20
(3,11) is also on the line
Again as done with 13a-13c, I'm only looking at the first two columns.
Slope
m = (y2-y1)/(x2-x1)
m = (11-20)/(3-0)
m = -9/3
m = -3
Therefore
y = mx+b
turns int
y = -3x+20
after replacing m and b with the values we found earlier
Answer: y = -3x+20
Each column of the table represents an (x,y) pairing. The first column has x = 0 and y = 2 so (0,2) is one point on this line. Since x = 0 here, this means that we have the y intercept. The y intercept is 2. We'll use this later.
Another point on this line is (3,8) which is drawn from the second column.
Use the two points (0,2) and (3,8) to find the slope m
m = (y2-y1)/(x2-x1)
m = (8-2)/(3-0)
m = 6/3
m = 2
Since the slope is 2 and the y intercept is 2 (see above), this means m = 2 and b = 2
Plug those into y = mx+b and we get y = 2x+2
Answer: y = 2x+2
==============================================
Problem 13b
(0,20) is on the line as the first column shows. The y intercept is 20 since x = 0 here. So b = 20
Another point on this line is (3,8) as drawn from the second column
Slope:
m = (y2-y1)/(x2-x1)
m = (8-20)/(3-0)
m = -12/3
m = -4
Use the slope (m = -4) and the y intercept (b = 20) to get...
y = mx+b
y = -4x+b ... replace m with -4
y = -4x+20 ... replace b with 20
Answer: y = -4x+20
==============================================
Problem 13c
(2,5) and (4,8) are on the line. These two points are drawn from columns 1 and 2 respectively.
Slope
m = (y2-y1)/(x2-x1)
m = (8-5)/(4-2)
m = 3/2
m = 1.5
Note: the fraction 3/2 is equivalent to the decimal form 1.5
Use the slope m = 1.5 along with (x,y) = (2,5) to find the value of b
y = mx+b
y = 1.5x+b ... m is replaced with 1.5
5 = 1.5*2+b ... plug in (x,y) = (2,5)
5 = 3+b
5-3 = 3+b-3
2 = b
b = 2
So we can now update y = mx+b to y = 1.5x+2
Answer: y = 1.5x+2
Note: If your teacher wants a fraction instead of a decimal (for the slope), then you would write
==============================================
Problem 13d
(0,20) is on the line. So the y intercept is 20, indicating that b = 20
(3,11) is also on the line
Again as done with 13a-13c, I'm only looking at the first two columns.
Slope
m = (y2-y1)/(x2-x1)
m = (11-20)/(3-0)
m = -9/3
m = -3
Therefore
y = mx+b
turns int
y = -3x+20
after replacing m and b with the values we found earlier
Answer: y = -3x+20
Answer:
Approximately 22.97 years
Step-by-step explanation:
Use the equation for continuously compounded interest, which uses the exponential base "e":
Where P is the principal (initial amount of the deposit - unknown in our case)
A is the accrued value (value accumulated after interest is compounded), in our case it is not a given value but we know that it triples the original deposit (principal) so we write it as: 3 P (three times the principal)
k is the interest rate : 5% which translates into 0.05
and t is the time in the savings account to triple its value (what we need to find)
The formula becomes:
To solve for "t" we divide both sides of the equation by P (notice it cancels P everywhere), and then to solve for the exponent "t" we use the natural logarithm function: