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Define x:
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Let x be the number of students in the second class:
⇒second class = x
There are 3 more students in the first class than in the second class:
⇒first class = x + 3
There are 2 more students in the third class than in the second class:
⇒third class = x + 2
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Expression for each class:
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First class = x + 3
Second class = x
Third class = x + 2
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Expression for total number of students:
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Total = x + 3 + x + x + 2
Total = 3x + 5
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Find x:
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There are 80 students in total, so
3x + 5 = 80
3x = 75
x = 25
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Find the number of students in each class:
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First class = x + 3 = 25 + 3 = 28
Second class = x = 25
Third class = x + 2 = 25 + 2 = 27
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Answer: There are 25 students in the second class.
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Here we need to find the last angle , that will be 21 so The answer is b
the equation of a vertically opening parabola is
(x - h)² = 4p(y - k)
where (h, k) are the coordinates of the vertex and p is the distance of the focus and directrix from the vertex. If 4p is positive parabola opens up and if 4p is negative parabola opens down
rearrange 12y = (x - 1)² - 48 into this form
(x - 1)² = 12y + 48
(x - 1)² = 12( y + 4) ← in standard form
Vertex = (1, - 4 )
4p = 12 ⇒ p = 3 ⇒ parabola opens upwards
the focus is above the vertex and the directrix is below the vertex in a vertically opening up parabola
Focus = (1, - 4 + 3 ) = (1, - 1)
Directrix has equation y = - 4 - 3 ⇒ y = - 7
87 and 93
45 and 135
74 and 106
x-12=30
In the problem it states <u>a number (x) decreased (-) by 12. </u> So with that information you're equation should look like x-12. The next part of the problem says that it is <u>equal (=) to 30</u> So now you're equation should be set up as x-12=30. To find "x" you must isolae "x". To do that you would add 12 from the left hand side leaving x and then you would also add 12 to 30. And with that you're left with what x is.
x=42
Hope it helps!
