Remark
Answer: The second one. The second step removes the brackets on the right. It uses the <em><u>distributive property</u></em> which puts back the common factor that was taken out of the two terms 6x and 24. Quite often the distributive property is useful when presenting a problem to be solved.
The associative property is more of an order thing and that is very useful sometimes as well what it says is that if you have three numbers a + b + c the order which you combine things does not matter.
For example 3 + 4 + 5 could be combined as 3 + 4 = 7; 7 + 5 = 12 or 3 + 5 = 8, 8 + 4 = 12.
The associative property is useful when adding fractions.
17 + 0 = 17
additive identity property....which basically states if u add a number to 0, it results in the original number
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-16 * -1 = -16
multiplicative identity property...which basically states if u multiply a number by 1, it results in the original number
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10 * 1/10 = 1
inverse property of multiplication...which states that any number multiplied by its reciprocal will equal 1. The reciprocal of a number can be found by just flipping the number.
examples :
10 (or 10/1)...its reciprocal is 1/10
4/5...its reciprocal is 5/4
-2 (or -2/1)...its reciprocal is -1/2
Answer: D) 10 sin (πx) - 5
<u>Step-by-step explanation:</u>
The range (maximum - minimum) is 5 - (-15) = 20
The amplitude (A) is range (20) ÷ 2 = 10
The vertical shift (D) is maximum (5) - amplitude (10) = -5
Of the given options, only A & D are candidates. Now we need to decide if it is a cos graph (A) or a sin graph (D). If we shift the graph up 5 units (to eliminate the vertical shift) , the graph would pass through the origin. Thus it is a sin graph and the answer must be option D.
For line A,
if we increase x by 1 unit then y increases by 4 units i.e. (1,3) and similarly another point becomes
(2,7).
For line B,
if we increase x by 1 uni then y also increases by 1 unit i.e ( 1,1) and similarly another points becomes (2,2),(3,3),(4,4), etc.
For line C,
if we increase x by 3 units then y increases by 1 units i.e.(3,1) and similarly another points becomes
(7,2) and so on.
In above lines, the value of x is exactly equal to that of y in line B.
therefore, line B has constant proportionality between x and y.
Answer:
y +2 = 2(x +3)
Step-by-step explanation:
The equation in point-slope form for a line with slope m through point (h, k) is ...
y -k = m(x -h)
The slope of your given line is the coefficient of x, -1/2. The slope of a perpendicular line will be the negative reciprocal of that: -1/(-1/2) = 2. So, you have m = 2, (h, k) = (-3, -2), and your desired equation is ...
y -(-2) = 2(x -(-3)) . . . . . . which can be simplified to ...
y +2 = 2(x +3)
