Answer:
Smaller number: 12
Greater number: 31
Step-by-step explanation:
Hi there!
Let x equal to the smaller number.
Let y be equal to the greater number.
<u>1) Translate the information into equations</u>
"One is 7 more than twice the other"
⇒ 
"The sum of the numbers is 43"
⇒ 
<u>2) Use substitution to solve for the smaller number</u>
Plug the equation into the above equation
Subtract both sides by 7
Divide both sides by 3 to isolate x
Therefore, the smaller number equates to 12.
<u>3) Use substitution to solve for the greater number</u>
Plug in x as 12
Subtract both sides by 12 to isolate y
Therefore, the greater number equates to 31.
I hope this helps!
Given
P(1,-3); P'(-3,1)
Q(3,-2);Q'(-2,3)
R(3,-3);R'(-3,3)
S(2,-4);S'(-4,2)
By observing the relationship between P and P', Q and Q',.... we note that
(x,y)->(y,x) which corresponds to a single reflection about the line y=x.
Alternatively, the same result may be obtained by first reflecting about the x-axis, then a positive (clockwise) rotation of 90 degrees, as follows:
Sx(x,y)->(x,-y) [ reflection about x-axis ]
R90(x,y)->(-y,x) [ positive rotation of 90 degrees ]
combined or composite transformation
R90. Sx (x,y)-> R90(x,-y) -> (y,x)
Similarly similar composite transformation may be obtained by a reflection about the y-axis, followed by a rotation of -90 (or 270) degrees, as follows:
Sy(x,y)->(-x,y)
R270(x,y)->(y,-x)
=>
R270.Sy(x,y)->R270(-x,y)->(y,x)
So in summary, three ways have been presented to make the required transformation, two of which are composite transformations (sequence).
Answer:
r/c
Step-by-step explanation:
96/48
or
24/12
Answer:
64 : 27
Step-by-step explanation:
When using scale factors
Length = scale factor
Area = scale factor squared
Volume = scale factor cubed
The ratio is 4:3
The ratio of the volume is 4^3 : 3^3
64 : 27
Answer:
Probability, P(X=3)=0.05371
Step-by-step explanation:
The experiment consists of 12 Bernoulli trials,n=12
Where sucess is defined with difference between the speakers and failure is defined with no difference between the speakers
Since people are guessing,the Probability P of sucess= 1/2
Therefore P(X=3) = b(3; 12, 0.5) = (12/3) (0.5)^3× (0.5)^9
P( X=3) = 0.0537
