Answer:
y = 2x + 11
Step-by-step explanation:
The first thing we need to do
is to find the slope of the line that passes through the points (-4,-3) and (4,1)
Mathematically, that would be;
m = y2-y1/(x2-x1)
where (x1,y1) = (-4,-3) and (x2,y2) = (4,1)
substituting these. values we have;
m = (1-(-3))/(4-(-4)) = 4/8 = 1/2 or 0.5
Now we are told this line is perpendicular to another line that passes through another point.
We can find the slope of this other line
Since both lines are perpendicular, the product of their slope is -1.
Thus , -0.5 * m = -1
m = -1/-0.5 = 2
So the slope of the other line is 2
Using the point-slope form;
y-y1= m(x-x1)
The point for the other line is (-4,3)
So the equation will be
y-3 = 2(x+4)
y-3 = 2x + 8
y = 2x + 11
Answer:
The values of x and y are x = 6 and y = 9
Step-by-step explanation:
MNOP is a parallelogram its diagonal MO and PN intersected at point A
In any parallelogram diagonals:
- Bisect each other
- Meet each other at their mid-point
In parallelogram MNOP
∵ MO and NP are its diagonal
∵ MO intersect NP at point A
- Point A is the mid-point pf them
∴ MO and NP bisect each other
∴ MA = AO
∴ PA = AN
∵ MA = x + 5
∵ AO = y + 2
- Equate them
∴ x + 5 = y + 2 ⇒ (1)
∵ PA = 3x
∵ AN = 2y
- Equate them
∴ 2y = 3x
- Divide both sides by 2
∴ y = 1.5x ⇒ (2)
Now we have a system of equations to solve it
Substitute y in equation (1) by equation (2)
∴ x + 5 = 1.5x + 2
- Subtract 1.5x from both sides
∴ - 0.5x + 5 = 2
- Subtract 5 from both sides
∴ - 0.5x = -3
- Divide both sides by - 0.5
∴ x = 6
- Substitute the value of x in equation (2) to find y
∵ y = 1.5(6)
∴ y = 9
The values of x and y are x = 6 and y = 9
Answer:
see explanation
Step-by-step explanation:
The diagonals of a parallelogram bisect each other , then
CO = OA = b
DO = OB = a
(a)
CA = CO + OA = b + b = 2b
(b)
DC = DO + OC = a - b
(c)
CB = CO + OB = b + a = a + b
Cost = fix cost + hourly cost - discount
Cost = 4* [5 + 4x - 4x(20/100)] = 4*[5 + 4x - 0.8x] = 4*[5 + 3.2x] = 20 + 12.8x
Answer: option B) 12.8x + 20
