Answer:
y=-1/4x+8
Step-by-step explanation:
To find the equation of a line that is perpendicular to a line, you would take the opposite reciprocal of the slope.
Before that, we need to change the equation into slope-intercept form.
-4x+y=10
y=4x+10
The opposite reciprocal of the slope is -1/4.
Now, let's use the point-slope formula to find our equation of the line that passes through (-4,9).
y-y1=m(x-x1)
y-9=-1/4(x-(-4))
y-9=-1/4x-1
y=-1/4x+8
Answer: population; independently
Step-by-step explanation:
A random sample selected from an infinite population is a sample selected such that each element selected comes from the same *population* and each element is selected *independently*.
Answer:
Step-by-step explanation:
By the diagram FG = MN.
3y + 3 = 5y - 25 Add 25 to both sides
3y + 3 + 25 = 5y Subtract 3y from both sides
28 = 5y - 3y Combine
28 = 2y Divide by 2
28/2 = 2y/2
y = 15
15 is not your answer. It is just the value of y.
3y + 3 = 3*15 + 3 = 45 + 3 = 48
Answer: One POSSIBLE answer is (0,9)
Step-by-step explanation: This may look hard but it's actually super easy. All you have to do is substitute a value for x and see what you get as the y value. The first thing I would do is rearrange the equation so that the equation is in the format y = something. So the first thing you should do is subtract 6x from both sides of the equation and you should get -y=-6x+9. Right now, the y is being multiplied by -1, and to undo multiplication, you have to divide. So divide both sides of the equation by -1 (remember, what you do on one side of the equation, YOU HAVE TO DO THE SAME THING ON THE OTHER SIDE). So your new equation would be y=6x-9. Then, all you have to do is substitute a value for x and see what you get for y (x is basically the input and whatever you get for y is the output). S for example, let's say that x=0. So substitute a 0 in the equation wherever you see an x. So in this case, you would get y=(6x0)+9. Then you just simplify. So 6x0 is 0 and 0+9=9 So y=9
TO RECAP: Rearrange the equation so that the equation is in the format y = something. Then, input any number for x, and whatever you get for y is what you put in the brackets as your y value for your final answer.
Hope this helps!
Answer:
Step-by-step explanation:
Given the following complex numbers, we are to expressed them in the form of a+bi where a is the real part and b is the imaginary part of the complex number.
1) (2-6i)+(4+2i)
open the parenthesis
= 2-6i+4+2i
collect like terms
= 2+4-6i+2i
= 6-4i
2) (6+5i)(9-2i)
= 6(9)-6(2i)+9(5i)-5i(2i)
= 54-12i+45i-10i²
= 54+33i-10i²
In complex number i² = -1
= 54+33i-10(-1)
= 54+33i+10
= 54+10+33i
= 64+33i
3) For the complex number 2/(3-9i), we will rationalize by multiplying by the conjugate of the denominator i.e 3+9i
= 2/3-9i*3+9i/3+9i
=2(3+9i)/(3-9i)(3+9i)
= 6+18i/9-27i+27i-81i²
= 6+18i/9-81(-1)
= 6+18i/9+81
= 6+18i/90
= 6/90 + 18i/90
= 1/15+1/5 i
4) For (3 − 5i)(7 − 2i)
open the parenthesis
= 3(7)-3(2i)-7(5i)-5i(-2i)
= 21-6i-35i+10i²
= 21-6i-35i+10(-1)
= 21-41i-10
= 11-41i