Answer:
<h2>A rotation -90° around point I.</h2><h2>A translation upwards 2 units.</h2><h2>
Step-by-step explanation:</h2>
The given figures are attached.
We have to find two transformations that help to show that both polygon are congruent.
First transformation would be a rotation -90° around point I.
Second transformation would be a translation upwards 2 units.
Applying these transformation, we would have both polygons at the same position, that will show the congruence between them.
Answer:
See joint picture.
Step-by-step explanation:
The study lasts 6 days. Since the amount of plant food decreased an equal amount each day, and since the whole 72 millimeters were used, it means that plants consumed 72/6 = 12 millimeters daily.
All the results given come from this justification.
The shape of the graph is similar to the letter W; however, the region of interest will lie on the right of the origin, which means only the right half of the W(a negative number of cans cannot be produced). The profit produced will be maximized if the number of cans produced is greater than 3. The company will be at a loss if the number of cans produced is near 2.5. The break even situations are present if the company produces 2 or 3 cans.
We know that the angles of a triangle sum to 180°. For ΔABC, this means we have:
(4x-10)+(5x+10)+(7x+20)=180
Combining like terms,
16x+20=180
Subtracting 20 from both sides:
16x=160
Dividing both sides by 16:
x=10
This means ∠A=4*10-10=40-10=30°; ∠B=5*10+10=50+10=60°; and ∠C=7*10+20=70+20=90.
For ΔA'B'C', we have
(2x+10)+(8x-20)+(10x-10)=180
Combining like terms,
20x-20=180
Adding 20 to both sides:
20x=200
Dividing both sides by 20:
x=10
This gives us ∠A'=2*10+10=20+10=30°; ∠B'=8*10-20=80-20=60°; and ∠C'=10*10-10=100-10=90°.
Since the angle are all congruent, ΔABC~ΔA'B'C' by AAA.
Answer with explanation:
Given : Sample mean =
Standard deviation : 
Sample size : n = 36
Claim : 
∴ 
Since the alternative hypothesis is two tail , then the test is two tail test.
By using a z statistic and a 0.05 level of significance. Reject 
if z < -1.960 or is z> 1.960.
Then , the test static for population mean is given by :-
We reject since 
. We have statistically significant evidence at 
to show that the mean amount of garbage per bin is not different from 50.
