Answer:
So ofc it's third
Step-by-step explanation:
You'll need to use the Pythagorean theorem:
a²+b²=c²
36² + 15² = c²
1296 + 225 = c²
1521 = c²
= 39
. 1−|3p+1|=−3! Thank you
1 answer:
Answer:
p = - , p = 1
Step-by-step explanation:
Given
1 - | 3p + 1 | = - 3 ( subtract 1 from both sides )
- | 3p + 1 | = - 4 ( multiply both sides by - 1 )
| 3p + 1 | = 4
The absolute value function always returns a positive value, however, the expression inside can be positive or negative, thus
3p + 1 = 4 OR - (3p + 1) = 4
Subtract 1 from both sides
3p = 3 ( divide both sides by 3 )
p = 1
OR
- (3p + 1) = 4, that is
- 3p - 1 = 4 ( add 1 to both sides )
- 3p = 5 ( divide both sides by - 3 )
p = -
As a check
Substitute these values into the left side of the equation and if equal to the right side then they are the solutions
p = 1 : 1 - | 3 + 1 | = 1 - |4| = 1 - 4 = - 3 ← true
p = - : 1 - | - 5 + 1 | = 1 - | - 4 | = 1 - 4 = - 3 ← true
Thus the solutions are p = 1, p = -
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An equation of the form y=ax+b, where a and b are constants; y and x are variable, is called a linear equation.
They are called "linear" because if we draw all the solutions of such an equation, they form a line.
This also means that it is enough to:
1. find to solutions
2. plot them on the coordinate axis
3.join those 2 points
and all the solutions of the equation y=ax+b will be on that line.
Thus, to draw line y=-3x+3
let x=0, then y=3, so one solution is (0, 3)
let y=0, then x=1 so a second solution is (1, 0)
(remark we can pick x or y to be any value, then solve for the other)
to draw the second line y=2x-7
let x=0, then y=-7
let x=3, then y=-1
plot these points and join them as shown in the picture.
The solution of the system is the point where the lines intersect, which is
(2, -3)
They are called "linear" because if we draw all the solutions of such an equation, they form a line.
This also means that it is enough to:
1. find to solutions
2. plot them on the coordinate axis
3.join those 2 points
and all the solutions of the equation y=ax+b will be on that line.
Thus, to draw line y=-3x+3
let x=0, then y=3, so one solution is (0, 3)
let y=0, then x=1 so a second solution is (1, 0)
(remark we can pick x or y to be any value, then solve for the other)
to draw the second line y=2x-7
let x=0, then y=-7
let x=3, then y=-1
plot these points and join them as shown in the picture.
The solution of the system is the point where the lines intersect, which is
(2, -3)
Answer: There are 32 pints of first type and 128 pints of second type in mixture.
Step-by-step explanation:
Since we have given that
Percentage of pure fruit juice in first type = 60%
Percentage of pure fruit juice in second type = 85%
Percentage of pure fruit juice in mixture = 80%
We will use "Mixture and Allegation" to find the ratio of first and second type in mixture:
First type Second type
60% 85%
80%
------------------------------------------------------------------------
85-80 : 80-60
5% : 20%
1 : 4
so, the ratio of first and second type is 1:4.
Total number of pints of mixture = 160
Number of pints of mixture of first type in mixture is given by
Number of pints of mixture of second type in mixture is given by
Hence, there are 32 pints of first type and 128 pints of second type in mixture.