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Brut [27]
3 years ago
7

Can you conclude from the figure that ABC is similar to DEF? Explain.​

Mathematics
1 answer:
pishuonlain [190]3 years ago
8 0

Answer:

Yes, we can conclude that Triangle ABC is similar to triangle DEF because the measures of the 3 angles of both triangles are congruent.

Step-by-step explanation:

We have the measure of 2 angles from both triangles, and we know that triangles have 180°, so we can solve for the measure of the third angle for both triangles.

Triangle ABC:

Measure of angle A= 60°

Measure of angle C= 40°

Measure of angle B = 180°- (measure of angle A + measure of angle C) = 180° - (60° + 40°) = 80°

Triangle DEF

Measure of angle E= 80°

Measure of angle F= 40°

Measure of angle D= 180° - (measure of angle E + measure of angle F) = 180° - (80° + 40°) = 60°

The measures of the angles in Triangle ABC are: 60°, 40°, and 80°.

The measures of the angles in Triangle DEF are: 60°, 40°, and 80°.

Since the measure of 3 angles of the two triangles are the same, we know that the two triangles are similar.

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A regression equation that predicts the price of homes in thousands of dollars is t = 24.6 + 0.055x1 - 3.6x2, where x2 is a dumm
AveGali [126]

Answer:

a) On average, homes that are on busy streets are worth $3600 less than homes that are not on busy streets.

Step-by-step explanation:

For the same home (x1 is the same), x2 = 1 if it is on a busy street and x2 = 0 if it is not on a busy street. If x2 = 1, the value of 't' decreases by 3.6 when compared to the value of 't' for x2=0. Since 't' is given in thousands of dollars, when a home is on a busy street, its value decreases by 3.6 thousand dollars.

t(x1, 0)= 24.6 + 0.055x1\\t(x1, 1) = 24.6 + 0.055x1 - 3.6\\t(x1, 1) = t(x1, 0) - 3.6

Therefore, the answer is a) On average, homes that are on busy streets are worth $3600 less than homes that are not on busy streets.

8 0
3 years ago
Complete the following statements. In general, % of the values in a data set lie at or below the median. % of the values in a da
ELEN [110]

Answer:

Complete the following statements. In general, 50% of the values in a data set lie at or below the median. 75% of the values in a data set lie at or below the third quartile (Q3). If a sample consists of 500 test scores, of them 0.5*500 = 250 would be at or below the median. If a sample consists of 500 test scores, of them 0.75*500 = 375 would be at or above the first quartile (Q1).

Step-by-step explanation:

The median separates the upper half from the lower half of a set. So 50% of the values in a data set lie at or below the median, and 50% lie at or above the median.

The first quartile(Q1) separates the lower 25% from the upper 75% of a set. So 25% of the values in a data set lie at or below the first quartile, and 75% of the values in a data set lie at or above the first quartile.

The third quartile(Q3) separates the lower 75% from the upper 25% of a set. So 75% of the values in a data set lie at or below the third quartile, and 25% of the values in a data set lie at or the third quartile.

The answer is:

Complete the following statements. In general, 50% of the values in a data set lie at or below the median. 75% of the values in a data set lie at or below the third quartile (Q3). If a sample consists of 500 test scores, of them 0.5*500 = 250 would be at or below the median. If a sample consists of 500 test scores, of them 0.75*500 = 375 would be at or above the first quartile (Q1).

5 0
3 years ago
Humans can hear sounds with frequencies up to 20,000 Hz, while dolphins can hear sounds as high as 150,000 Hz. Write these numbe
Goshia [24]
20,000 Hz = 2 × 10^4 Hz

150,000 Hz = 1.5 × 10^5 Hz
4 0
3 years ago
In the diagram, lines JK and LM at N, M MNK = 2x + 30.<br> What is the value of x?
likoan [24]

Answer:

the valu of x is 15 .....

5 0
3 years ago
Miguel borrowed $825 for a new couch. He will make 9 monthly payments of $95 to repay the loan. How much will he pay in interest
Leona [35]

Answer:

$30 is paid in interest.

Step-by-step explanation:

The couch costs $825 and Miguel will pay 9 * $95 = $855.  So the amount of interest paid is how much in total was paid $855 minuse the cost of the couch $825, or $855-$825 = $30 in interest

3 0
3 years ago
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