Answer:
1. y = 4x - 27
2. y = -4x - 15
Step-by-step explanation:
If two lines are parallel, then they have the same slope. So, the slope of the line we are looking for needs to be 4. We can start by writing a point-slope equation:
y - y1 = m(x - x1)
We can substitute the values we have, the point we are using is (8, 5) because it needs to be on the line:
y - 5 = 4(x - 8)
We can distribute:
y - 5 = 4x - 32
y = 4x - 27
We are not given the slope-intercept form, so we must divide both sides by two to get it:
y = 1/4 x + 8
A perpendicular line has the slope that is the negative reciprocal of the one that is given. So, the slope of the line would be - 4. We can start by writing a point-slope equation:
y - y1 = m(x - x1)
We can substitute the values we have, the point we are using is (-5, 5) because it needs to be on the line:
y - 5 = -4(x + 5)
We can distribute:
y - 5 = -4x - 20
y = -4x - 15
1)
LHS = cot(a/2) - tan(a/2)
= (1 - tan^2(a/2))/tan(a/2)
= (2-sec^2(a/2))/tan(a/2)
= 2cot(a/2) - cosec(a/2)sec(a/2)
= 2(1+cos(a))/sin(a) - 1/(cos(a/2)sin(a/2))
= 2 (1+cos(a))/sin(a) - 2/sin(a)) (product to sums)
= 2[(1+cos(a) -1)/sin(a)]
=2cot a
= RHS
2.
LHS = cot(b/2) + tan(b/2)
= [1 + tan^2(b/2)]/tan(b/2)
= sec^2(b/2)/tan(b/2)
= 1/sin(b/2)cos(b/2)
using product to sums
= 2/sin(b)
= 2cosec(b)
= RHS
The main idea here is to "translate" the words into maths.
First we need to identify the unknowns and label these.
We need to know the number if dimes and the number of quarters. So lets say
x: number of dimes
y: number of quarters
Now lets write equations from the written problem.
We know that there are 36 coind total, thus:
x + y = 36
We also know that the coins total 5.85 dollars, but it is better to count in cents, that is 585 cents.
x are the number of dimes, their value is x*10
y are quarters with value of y*25
thus:
10x+25y=585
We have two equations and two unknowns now, that needs to be solved to get the answer.
x + y = 36
10x+25y=585
Answer:
y = 140, x = 159
Step-by-step explanation:
Angle y:
we can find this angle by subtracting 40 from 180, 180-40 = 140 = y
Angle x:
Some measure of an angle plus angle b is equal to 180 degrees: 180-61 = 119
We can now find the measure of the third angle of the triangle: 180-(119+40) = 21
The third angle plus angle x is equal to 180: 180-21 = 159 = x
The answer is $3.57 because you must multiply 2.55 by 140 then divide that by 100 to find your answer hope this helps.
