Answer:
B. rotation 90° counterclockwise about the origin.
Step-by-step explanation:
Transformation is the process by which the size or orientation of a given figure is altered without any effect on its shape. Examples are; rotation, reflection, translation and dilation.
Rotation is the process of turning a figure about a reference point called the origin. While reflection is turning a figure about a line to produce its image.
In the given question, ∆ABC is mapped onto ∆A'B'C' by rotating it at 90° counterclockwise about the origin.
-x-y=-9
-3x-2y=-28
eliminate the x first
multiply the first system of equations by 3
(3)(-x)=-3x
(3)(-y)=-3y
(3)(-9)=-27
-3x-3y=-27
-3x-2y=-28
eliminate the systems of equations by subtracting
-3x--3x-3y--2y=-27--28
-3x+3x-3y+2y=-27+28
-y=1
multiply -1 for -y=-1 to get positive y
(-y)(-1)=(1)(-1)
y=-1
substitution method by using y=-1 into one of the system of equations
-x-y=-9
-x--1=-9
-x+1=-9
move +1 to the other side
sign changes from +1 to -1
-x+1-1=-9-1
-x=-10
multiply by -1 for -x=-10 to get positive x
(-x)(-1)=(-10)(-1)
x=10
answer:
x=10, y=-1
banana: 5*$0.8=$4
apple: 5*$1.4 = $7
4+7=11
so Janice's mother gave $1 less than needed
Answer:
435,307
Step-by-step explanation:
Given that :
p = 0.18
Zcritical = 99%
Error (E) = 1.5% = 1.5/100 = 0.0015
Sample size (n) can be obtained using the relation :
n = (Zcrit / E)^2 * (p * q)
q = 1 - p ; q = 1 - 0.18 = 0.82
Zcrit at 99% equals 2.576
n = (2.576 / 0.0015)^2 * (0.18 * 0.82)
n = (1717.3333)^2 * (0.1476)
n = 2949233.66328889 * 0.1476
n = 435306.888701440164
n = 435,307 samples
Answer:
$462.5
Step-by-step explanation:
Given the cost function expressed as;
C = 37000/100−p
To get C(20), we will substitute p = 20 into the expression and get C as shown;
C(20) = 37000/100-20
C(20) = 37000/80
C(20) = 462.5
Hence the cost needed to clean 20% of the stream is $462.5
