The preimage is the solid triangle while the image is the dashed triangle. Recall that any transformation takes a preimage and maps it to an image. The "preimage" is the "before"; while the "image" is the "after"
Preimage ---> Image
Before ---> After
The "pre" is one way to help remember it means "before".
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The preimage has a horizontal segment length of 15 units (count from x=-9 to x=6 and you should count out 15 spaces). The corresponding horizontal piece on the dashed triangle is only 3 units long. Divide the image length over the preimage length
(image length)/(preimage length) = 3/15 = 1/5 = 0.2
Now if the figure wasn't reflected over the point (6,6), then the final answer would be either 1/5 or 0.2; however, this reflection does happen so we need to make the scale factor negative. So we go from 1/5 to -1/5, and we go from 0.2 to -0.2
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Final Answer as a fraction: -1/5
Final Answer in decimal form: -0.2
Answer:
C. D: -2≤x≤3 ; R: -1≤y≤4
Step-by-step explanation:
The domain is all the values on the x-axis (horizontally) and the range is all the values on the y-axis (vertically).
The x-axis values (domain) go from -2 to +3, which is -2≤x≤3.
The y-axis values (range) go from -1 to +4, which is -1≤y≤4.
St=d
s=d/t
t=d/s
so we have several things:
distance of alfredo
speed of alfredo
time of alredo
distance of louisa
speed of louisa
time of louisa
we will represen them as follows
distance of alfredo=d1
speed of alfredo=s1
time of alredo=t1=2=t2
distance of louisa=d2
speed of louisa=s2
time of louisa=t2=2=t1
d=distance
t=time
total d=15 miles
t=2 hours
they both walk towards each other
louisa's speed is 1 mile per hour more than Alfredo so s2=s1+1
so we also have
d1+d2=15
s2=s1+1
t1=t2=2
we want to solve for s1 and s2
d=st
d1=(s1)(2)
d2=(s2)(2)
subsitute s1+1 for s2
d2=(s1+1)(2)
put back ino equation
(s1)(2)+(s1+1)(2)=15
distribute
2s1+2s1+2=15
2(s1)+2(s1)+2=15
add like terms
4(s1)+2=15
subtract 2 from both sides
4(s1)=13
divide both sides by 4
s1=13/4=3 and 1/4 mph
s2=s1+1
s2=3 and 1/4
s2=4 and 1/4 mph
check
d=st
t=2
alfredo's distance=(3 and 1/4) times 2=6 and 1/2
louisa's distance=(4 and 1/4) times 2=8 and 1/2
6 and 1/2+8 and 1/2=6+1/2+8+1/2=14+1=15
Alfredo's walking speed=3 and 1/4 miles per hour
Louisa's walking speed=4 and 1/4 miles per hour
aka
Alredospeed=3.25 mph
Louisaspeed=4.25 mph
Answer:
The mistake made by Manuel was not reducing 4 as a product of its prime numbers. That is, . 4 is a composite number and a product of 2 prime numbers.
Step-by-step explanation:
The factors of a given entire numbers consists in simplifying it several times until an equivalent product of prime numbers is found. Let is show the procedure for 60:
1) Given
2) Definition of multiplication.
3) Definition of multiplication.
4) Commutative property/Result.
The mistake made by Manuel was not reducing 4 as a product of its prime numbers. That is, . 4 is a composite number and a product of 2 prime numbers.