The equation of the line that is parallel and passes through the point (2,3) is; x +2y =8.
<h3>What is the equation of the line that passes through (2,3)?</h3>
If follows from the task content that the slope of the first line is; (-4-0)/(4-(-4)) = -1/2.
Hence, since the lines are parallel, they have the same slope and the equation of the second line is;
-1/2 = (y-3)/(x-2)
-x+2 = 2y -6
x +2y =8.
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The length of side x in simplest radical form with a rational denominator is 8√3
<h3>How to find the length of side x in simplest radical form with a rational denominator?</h3>
The given parameters are:
Triangle type = Equilateral triangle
Height (h) = 12
Missing side length = x
The missing side length, x is calculated using the following sine ratio
sin(60) = Height/Missing side length
This gives
sin(60) = 12/x
Make x the subject of the formula
So, we have
x = 12/sin(60)
Evaluate the quotient
So, we have
x = 12/(√3/2)
This gives
x = 24/√3
Rationalize
x = 24/√3 * √3/√3
Evaluate
x = 8√3
Hence, the length of side x in simplest radical form with a rational denominator is 8√3
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The factorization if the given expression 128 + 2d³ is 2(64 + d³).
<h3>Factorization</h3>
128 + 2d³
There are two parameters in the expression;
The common factors between 128 and 2d³ is 2
So,
128 + 2d³
= 2(64 + d³)
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Area of sector
so the area = 37.71 square metre
Answer:
She went on the slide 8 times and on the roller coaster 4 times
Step-by-step explanation:
We convert each statements to a mathematical equation.
Firstly, let's represent the number of times she went on the coaster with R and the number of times on the slide with S. We know quite well she went on 12 rides. Hence the summation of both number of times yield 12.
Mathematically, R + S = 12. ........(i)
Now we also know her total wait time was 3hours. Since an hour equals 60 minutes, her total wait time would equal 180 minutes.
To get a mathematical representation for the wait time, we multiply the number of roller coaster rides by 25 and that of the slides by 10.
Mathematically, 25R + 10S = 180 .......(ii)
Here we now have two equations that we can solve simultaneously.
From equation 1 we can say R = 12 - S. We can then substitute this into equation 2 to yield the following:
25(12 - s) + 10s = 180
300 - 25s + 10s = 180
300 - 25s + 10s = 180
300 - 15s = 180
15s = 300 - 180
15s = 120
S = 120/15
S = 8
S = 8 , and R = 12 - S = 12 - 8 = 4
