Answer:
R'(3,-4)
Step-by-step explanation:
we know that
When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places
so
The rule of the reflection across the line y=x is equal to
(x,y) ------> (y,x)
we have
R(-4,3) ------> R'(3,-4)
Short AnswerThere are two numbers
x1 = -0.25 + 0.9682i <<<<
answer 1x2 = - 0.25 - 0.9582i <<<<
answer 2 I take it there are two such numbers.
Let one number = x
Let one number = y
x + y = -0.5
y = - 0.5 - x (1)
xy = 1 (2)
Put equation 1 into equation 2
xy = 1
x(-0.5 - x) = 1
-0.5x - x^2 = 1 Subtract 1 from both sides.
-0.5x - x^2 - 1 = 0 Order these by powers
-x^2 - 0.5x -1 = 0 Multiply though by - 1
x^2 + 0.5x + 1 = 0 Use the quadratic formula to solve this.

a = 1
b = 0.5
c = 1

x = [-0.5 +/- sqrt(0.25 - 4)] / 2
x = [-0.5 +/- sqrt(-3.75)] / 2
x = [-0.25 +/- 0.9682i
x1 = -0.25 + 0.9682 i
x2 = -0.25 - 0.9682 i
These two are conjugates. They will add as x1 + x2 = -0.25 - 0.25 = - 0.50.
The complex parts cancel out. Getting them to multiply to 1 will be a little more difficult. I'll do that under the check.
Check(-0.25 - 0.9682i)(-0.25 + 0.9682i)
Use FOIL
F:-0.25 * -0.25 = 0.0625
O: -0.25*0.9682i
I: +0.25*0.9682i
L: -0.9682i*0.9682i = - 0.9375 i^2 = 0.9375
NoticeThe two middle terms (labled "O" and "I" ) cancel out. They are of opposite signs.
The final result is 0.9375 and 0.0625 add up to 1
Answer:
The slope is 4
Step-by-step explanation:
The answer is 4
Answer:
Step-by-step explanation:
Hello!
The variable of interest, X: height of women at a college, has an approximately normal distribution with mean μ= 65 inches and standard deviation σ= 1.5 inches.
You need to look for the value of height that marks the bottom 20% of the distribution, i.e. the height at the 20th percentile of the normal curve, symbolically:
P(X≤x₀)= 0.20
To know what value of height belongs to the 20% of the distribution, you have to work using the standard normal distribution and then reverse the standardization with the population mean and standard deviation to reach the value of X. So the first step is to look for the Z-value that accumulates 20% of the distribution:
P(Z≤z₀)=0.20
z₀= -0.842
z₀= (x₀-μ)/σ
z₀*σ= (x₀-μ)
x₀= (z₀*σ)+μ
x₀= (-0.842*1.5)+65
x₀= 63.737 inches
I hope it helps!