Answer:
D. 216 cubic centimetres.
Step-by-step explanation:
The answer is D, because 6 to the 3rd power is 216. therefore, if the side length is 6, the answer is 216.
Answer: the small bottle holds 15 ounces while the large bottle holds 23 ounces.
Step-by-step explanation:
Let x represent the number of ounces that a small bottle holds.
Let y represent the number of ounces that a large bottle holds.
He drank 2 small bottles and 2 large bottles, for a total of 76 ounces. It means that
2x + 2y = 76 - - - - - - - - - - - - 1
The day before, he drank 4 small bottles and 1 large bottle, for a total of 83 ounces. This means that
4x + y = 83 - - - - - - - - - - - - -2
Multiplying equation 1 by 2 and equation 2 by 1, it becomes
4x + 4y = 152
4x + y = 83
Subtracting, it becomes
3y = 69
y = 69/3 = 23 ounces
Substituting y = 23 into equation 1, it becomes
2x + 2 × 23 = 76
2x + 46 = 76
2x = 76 - 46 = 30
x = 30/2 = 15 ounces
Answer:
Rate of change = -12
Step-by-step explanation:
y − 3 = −12(x + 4)
Expanding, we have;
y - 3 = -12x - 48
y = -12x - 48 + 3
y = -12x - 45
Now, formula for rate of change is;
Rate of change = (y(x + h) - y)/h
y(x + h) is; y = -12(x + h) - 45
This gives;
Rate of change = (-12(x + h) - 45 + 12x + 45)/h
Rate of change = (-12x - 12h - 45 + 12x + 45)/h
Rate of change = -12h/h
Rate of change = -12
Answer:
Five x squared plus two
Step-by-step explanation:
An exponent of two is always pronounced as "squared"
Answer:
1a. y-intercept: 12
1b. slope: -3/2
1c. equation: y = -3/2x +12
2a. y-intercept: -9
2b. slope: 2
2c. equation: y = 2x -9
Step-by-step explanation:
<h3>1.</h3>
A) We observe the pattern to be <em>x-values in the table increase by 2, while y-values in the table decrease by 3</em>. We notice the first x-value is 2, so extending the table upward to x=0 would tell us the y-intercept. That is, adding 3 to the first y-value will give the y-intercept as (x, y) = (0, 12).
B) We have already observed that the "rise" (change in y) is -3 for each "run" (change in x) of 2. The slope is the ratio of these changes:
slope = m = rise/run = -3/2
C) From the above, we know that m=-3/2 and b=12. Putting these values into the equation for the line gives ...
y = -3/2x +12
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<h3>2.</h3>
A) We observe the pattern to be <em>y-values increase by 2 while x-values increase by 1</em>. As before, we can find the point that would go before the first one shown in the table. It will have an x-value of 0 and a y-value of -9.
the y-intercept is -9
the slope is 2/1 = 2
the equation is y = 2x -9
