Answer:
slope: 4
y-intercept: 2
Step-by-step explanation:
We are given an equation, y = 4x + 2, and we are asked to find the slope and y-intercept of the line. Looking carefully, we can see that the equation is given to us in slope-intercept form.
Slope-intercept form is:
y = mx + b
where m is the slope and b is the by-intercept.
Knowing this, we can find that 4 is the slope of the line and 2 is the y-intercept.
I hope you find my answer and explanation to be helpful. Happy studying.
Subtract X
2y=-x+6
Then divide by 2
Y=-1/2x+3
Perhaps the easiest way to find the midpoint between two given points is to average their coordinates: add them up and divide by 2.
A) The midpoint C' of AB is
.. (A +B)/2 = ((0, 0) +(m, n))/2 = ((0 +m)/2, (0 +n)/2) = (m/2, n/2) = C'
The midpoint B' is
.. (A +C)/2 = ((0, 0) +(p, 0))/2 = (p/2, 0) = B'
The midpoint A' is
.. (B +C)/2 = ((m, n) +(p, 0))/2 = ((m+p)/2, n/2) = A'
B) The slope of the line between (x1, y1) and (x2, y2) is given by
.. slope = (y2 -y1)/(x2 -x1)
Using the values for A and A', we have
.. slope = (n/2 -0)/((m+p)/2 -0) = n/(m+p)
C) We know the line goes through A = (0, 0), so we can write the point-slope form of the equation for AA' as
.. y -0 = (n/(m+p))*(x -0)
.. y = n*x/(m+p)
D) To show the point lies on the line, we can substitute its coordinates for x and y and see if we get something that looks true.
.. (x, y) = ((m+p)/3, n/3)
Putting these into our equation, we have
.. n/3 = n*((m+p)/3)/(m+p)
The expression on the right has factors of (m+p) that cancel*, so we end up with
.. n/3 = n/3 . . . . . . . true for any n
_____
* The only constraint is that (m+p) ≠ 0. Since m and p are both in the first quadrant, their sum must be non-zero and this constraint is satisfied.
The purpose of the exercise is to show that all three medians of a triangle intersect in a single point.
Answer:
4cm
Step-by-step explanation:
Given data
L=(2x+3)
W=(x-1)
P=28cm
A= L*W
A= (2x+3)*(x-1)
open bracket
A= 2x^2-2x+3x-3
collect like terms
A= 2x^2+x-3
P= 2L+2W
P= 2*(2x+3)+2(x-1)
P= 4x+6+2x-2
collect like terms
P= 6x-4
but p= 28
28= 6x-4
28-4= 6x
24= 6x
x= 24/6
x= 4cm
Hence x= 4cm
Answer:
hcf=(1,605; 600) = 3 × 5
Step-by-step explanation:
Prime Factorization of a number: finding the prime numbers that multiply together to make that number.
1,605 = 3 × 5 × 107;
1,605 is not a prime, is a composite number;
600 = 23 × 3 × 52;
600 is not a prime, is a composite number;
* Positive integers that are only dividing by themselves and 1 are called prime numbers. A prime number has only two factors: 1 and itself.
* A composite number is a positive integer that has at least one factor (divisor) other than 1 and itself.
Multiply all the common prime factors, by the lowest exponents (if any).
gcf, hcf, gcd (1,605; 600) = 3 × 5
gcf, hcf, gcd (1,605; 600) = 3 × 5 = 15;
The numbers have common prime factors.
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