Answer:
a
Step-by-step explanation:
12x - 5y = 2
12x - 12x - 5y = -12x + 2
-5y = -12x + 2
-5 -5
y = 2.4x - 0.4
y - 3 = 2.4(x - 3)
y - 3 = 2.4(x) - 2.4(3)
y - 3 = 2.4x - 7.2
+ 3 + 3
y = 2.4x - 4.2
Answer:
50 boxes
Step-by-step explanation:
first we can find how many apples there are
42*12=504
then subtract 4 of the rotten apples
504-4=500
then find how many boxes there can be
500/10=50
<u>vertex</u>
y = 3(x - 2)² - 4
y = 3((x - 2)(x - 2)) - 4
y = 3(x² - 2x - 2x + 4) - 4
y = 3(x² - 4x + 4) - 4
y = 3(x²) - 3(4x) + 3(4) - 4
y = 3x² - 12x + 12 - 4
y = 3x² - 12x + 8
3x² - 12x + 8 = 0
x = <u>-(-12) +/- √((-12)² - 4(3)(8))</u>
2(3)
x = <u>12 +/- √(144 - 96)</u>
6
x = <u>12 +/- √(48)
</u> <u> </u> 6<u>
</u>x =<u> 12 +/- 6.93</u>
<u /> 6
x = 2 +/- 1.155
x = 2 + 1.155 x = 2 - 1.155
x = 3.155 x = 0.845
y = 3x² - 12x + 8
y = 3(3.155)² - 12(3.155) + 8
y = 3(1.334025) - 3.786 + 8
y = 4.002075 - 3.786 + 8
y = 0.216075 + 8
y = 8.216075
(x, y) = (3.155, 8.216075)
or
y = 3x² - 12x + 8
y = 3(0.845)² - 12(0.845) + 8
y = 3(0.714025) - 10.14 + 8
y = 2.142075 - 10.14 + 8
y = -7.857925 + 8
y = 0.142675
(x, y) = (0.845, 0.142675)
<u>y-intercept</u>
y = 3x² - 12x + 8
y = 3(0)² - 12(0) + 8
y = 3(0) - 0 + 8
y = 0 - 0 + 8
y = 0 + 8
0 = -y + 8
y = 8
(x, y) = (0, 8)
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<u>vertex</u>
y = 4(x - 5)² = 1
y = 4(x - 5)² - 1
y = 4((x - 5)(x - 5)) - 1
y = 4(x² - 5x - 5x + 25) - 1
y = 4(x² - 10x + 25) - 1
y = 4(x²) - 4(10x) + 4(25) - 1
y = 4x² - 40x + 100 - 1
y = 4x² - 40x + 99
4x² - 40x + 99 = 0
x = <u>-(-40) +/- √((-40)² - 4(4)(99))</u>
2(4)
x = <u>40 +/- √(1600 - 1584)</u>
8
x = <u>40 +/- √(16)</u>
8
x = <u>40 +/- 4</u>
8
x = 5 +/- 1/2
x = 5 + 1/2 x = 5 - 1/2
x = 5 1/2 x = 4 1/2
y = 4x² - 40x + 99
y = 4(5 1/2)² - 40(5 1/2) + 99
y = 4(30 1/4) - 220 + 99
y = 121 - 220 + 99
y = -99 + 99
y = 0
(x, y) = (5 1/2, 0)
or
y = 4x² - 40x + 99
y = 4(4 1/2)² - 40(4 1/2) + 99
y = 4(20 1/4) - 180 + 99
y = 81 - 180 + 99
y = -99 + 99
y = 0
(x, y) = (4 1/2, 0)
<u>y-intercept</u>
y = 4x² - 40x + 99
y = 4(0)² - 40(0) + 99
y = 4(0) - 0 + 99
y = 0 - 0 + 99
y = 0 + 99
y = 99
(x, y) = (0, 99)
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<u>vertex</u>
y = (x - 1)² = 2
y = (x - 1)² - 2
y = ((x - 1)(x - 1)) - 2
y = (x² - x - x + 1) - 2
y = x² - 2x + 1 - 2
y = x² - 2x - 1
x² - 2x - 1 = 0
x = <u>-(-2) +/- √((-2)² - 4(1)(-1))</u>
2(1)
x = <u>2 +/- √(4 + 4)</u>
2
x = <u>2 +/- √(8)</u>
2
x = <u>2 +/- 2.83</u>
2
x = 1 +/- 1.415
x = 1 + 1.415 x = 1 - 1.415
x = 2.415 x = 0.415
y = x² - 2x - 1
y = (2.145)² - 2(2.145) - 1
y = 4.60125 - 4.029 - 1
y = 0.57225 - 1
y = 0.42775
(x, y) = (2.415, 0.42775)
or
y = x² - 2x - 1
y = (0.415)² - 2(0.415) - 1
y = 0.172225 - 0.83 - 1
y = -0.657775 - 1
y = -1.657775
(x, y) = (0.415, -1.657775)
<u>y-intercept</u>
y = x² - 2x - 1
y = (0)² - 2(0) - 1
y = 0 - 0 - 1
y = 0 - 1
y = -1
(x, y) = (0, -1)
Probability is expressed as
number of favourable outcomes/total number of possible outcomes
Looking at the given scenario, the number os students that earned a grade of A is 5. Since we are concerned with these students, then, the number of favourable outcomes is 5.
The total number of students for all grades is 35. This means that the total number of possible outcomes is 35
Thus, the probability that a student earns a grade of A is
5/35
= 0.14
