Answer:
y = (-1/2)x + 9/2
Step-by-step explanation:
the equation of a straight line can be written as;
y = mx + c ......1
Where;
m = slope
c = intercept
For two lines to be perpendicular their slope must be opposite reciprocal of each other.
m1 × m2 = -1 .....2
Given;
The equation Contains (3, 3); and perpendicular to the line y = 2x - 1
Slope of the given equation m1 = 2
Slope of the line m2; substituting m1 to equation 2.
2 × m2 = -1
m2 = -1/2
So,
y = (-1/2)x + c
To solve for c, let's substitute the given point on the line; (3,3).
3 = (-1/2)(3) + c
3 = -3/2 + c
c = 3 + 3/2
c = 9/2
Therefore, the equation of the line that has the given properties is;
y = (-1/2)x + 9/2
For each of these problems, all you need to do is isolate the variable. I’ll do the first few to help you out :)
32) 7 = -12 + e
Add 12 to both sides to isolate e.
19 = e
35) (r + 4) + 2 = 1
Subtract 2 from both sides.
r + 4 = -1
Subtract 4 from both sides to isolate r.
r = -5
38) -2 + (1 + p) = 5
Add 2 to both sides.
1 + p = 7
Subtract 1 from both sides to isolate p.
p = 6.
So essentially, all you need to do is add and subtract from each side to isolate the variable given in each problem. :)
Extra tip: In order to get rid of a number on one side (to isolate a variable), you must perform the opposite operation. For example, -2 + x = 1. In order to isolate x, add 2 to the left side to get rid of it, as well as adding it onto the right side so that it is not erased completely to get x=3)
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Answer:
Each small candleholder holds 3 candles, and each large one holds 5 candles.
Step-by-step explanation:
This question can be solved by a system of equations.
I am going to say that:
x is the number of candles that a small candleholder holds.
y is the number of candles that a large candleholder holds.
24 small candle holders and 3 large candle holders, using a total of 87 candles.
This means that
Simplifying by 3
14 small candle holders and 7 large candle holders, for a total of 77 candles.
This means that 
Simplifying by 7
Since
Each small candleholder holds 3 candles, and each large one holds 5 candles.
Divide 49.2 by 6 to get 8.2, which is about 8
