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1 year ago

How are rigid transformations used to justify the SAS congruence theorem?

2 answers:

6 0

Rigid transformations preserve segment lengths and angle measures. If you can find a rigid transformation, or a combination of rigid transformations, to map one triangle onto the other, then the triangles are congruent. To prove SAS, we started with two distinct triangles that had a pair of congruent corresponding sides and a congruent corresponding included angle. Then we performed a translation, followed by a rotation, followed by a reflection, to map one triangle onto the other, proving the SAS congruence theorem.

skelet666 [1.2K]1 year ago

3 0

Rigid transformations (translations, reflections and rotations) are transformations that maintain the measure of line segments and angles. Being able to map a pre-image to an image using rigid transformations means that the sides are the same length, as is the angle between the two.

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A craft vendor must sell at least $300 worth of merchandise to make a profit. Scarves sell for $10 each and hats sell for $20 ea

valina [46]

There is a missing graph in the problem given. However, we can simply solve the equation using the given data.

Items to be sold: scarves and hats. Minimum of 20 items sold in all.
Scarves sell for 10 each and hats sell for 20 each. Must sell at least 300 worth of merchandise to make profit.

Let s represent scarves and h represent hats.

10s + 20h > 300
s + h > 20

We use inequality because the problem states "at least".

s + h = 20
10s + 20h = 300

s = 20 - h
10(20-h) + 20h = 300
200 - 10h + 20h = 300
10h = 300 - 200
10h = 100
h = 100/10
h = 10

s = 20 - h
s = 20 - 10
s = 10

s + h > 20
10 + 10 > 20

10s + 20h > 300
10(10) + 20(10) > 300
100 + 200 > 300

7 0

1 year ago

Read 2 more answers

Johann fits a linear model to a set of data. The line of best fit has the equation y=0.331986x+5.33286. The scatter plot with th

Rasek [7]

Answer:

6.33

Step-by-step explanation:

Here, we are asked to give a residual value at x = 3

This mean we are to predict the value of y at the point x= 3

To do this, what we need to do is to input the value x = 3 into the line of best fit equation.

The line of best fit equation according to the question is;

y=0.331986x+5.33286

Substituting x here, we have

y = 0.331986(3) + 5.33286

y = 0.995958 + 5.33286 = 6.328818

Question asks to give answer to the nearest hundredth and that is 6.33

5 0

1 year ago

You offer senior citizens a 20% discount on their tune-ups at your gas station. Assuming that an average of 50 senior citizens g

andreyandreev [35.5K]

Percentage of discount given to senior citizens for tune-ups at the gas station = 20%
Average number of senior citizens visiting the gas station per month = 50
Average price of tune-up before discount = $49.95
Total amount that would
have been collected before discount = 49.95 * 50
= 2497.50 dollars
Total amount of discount given = (20/100) * 2497.50
= 499.50 dollars
I hope that the procedure is clear enough for you to understand.

6 0

1 year ago

What are the possible values of x if (4x – 5)2 = 49? check all that apply. -4/5 -1/2 3 5 7

dexar [7]

4 x - 5 = - 7
4 x = - 2
x = - $\frac{1}{2}$
or
4 x - 5 = 7
4 x = 12
x = 3
Answer B) and C)

9 0

2 years ago

Read 2 more answers

Two types of flares are tested and their burning times are recorded. The summary statistics are given below: n = 35 n = 40 = 19.

marusya05 [52]

Answer:

C. 3.8 min < ?X - ?Y < 4.8 min

Step-by-step explanation:

Let both flares be X and Y

For X

n1 = 35

Bar x1 =19.4

D1 = 1.4

For Y

n2 = 40

Bar X2= 15.1

S2 = 0.8

√(x1²/n1) + (x2²/n2)

=√ (1.4²/35)+(0.8²+40)

= 0.2683

Critical value, t = 2.032

We now have to calculate margin of error

0.2683x2.032

= 0.545 this is approximately equal to 0.5

Bar x1 - bar X2

= 19.4 - 15.1

= 4.3

At 95% confidence level

4.3+-0.5

4.3+0.5= 4.8

4.3-0.5 = 3.8

Therefore the answer is 3.8min<X-Y<4.8min

5 0

1 year ago