Answer:
y = x² - 4x - 21
Step-by-step explanation:
The equation of a parabola in vertex form is
y = a(x - h)² + k
where (h, k) are the coordinates of the vertex and a is a multiplier
Here (h, k) = (2, - 25), thus
y = a(x - 2)² - 25
To find a substitute (7, 0) into the equation
0 = a(7 - 2)² - 25 = a(5)² - 25 = 25a - 25 ( add 25 from both sides )
25a = 25 ( divide both sides by 25
a = 1, thus
y = (x - 2)² - 25 ← in vertex form
Expand and simplify
y = x² - 4x + 4 - 25
y = x² - 4x - 21 ← in standard form
Answer:
A) The relative frequencies in the table are reasonably close; C) The relative frequency of rolling an even number is 0.51.
Step-by-step explanation:
The relative frequencies given are at most 0.02 apart. This means they are reasonably close.
The theoretical probability for each outcome would be 1/4, or 0.25; this means the theoretical probability of rolling an even number would be 0.50, not 0.51.
However, the relative frequency of rolling an even number would be 0.24+0.27 = 0.51.
Since the relative frequencies are reasonably close, the number cube is likely to be fair.
9514 1404 393
Answer:
1 solution
Step-by-step explanation:
The coefficients of d are different on the two sides of the equation (3d vs 6d), so the equation has one solution.
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Dividing by 3 gives ...
d +11 = 2(d +33)
d + 11 = 2d + 66
Adding -d-66 to both sides gives ...
-55 = d . . . . . . the one solution
Answer: x=3
Step-by-step explanation:
3x + 5 = 14
Subtract 5 from both sides
3x=9
Divide both sides by 3 to get x alone
x=3
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