In triangle DEF m D=43 , m E=62, m EF=22. What is DE to the nearest tenth

Answers

Answer 1

Answer:

The measure of DE of the triangle is given by law of sines and DE = 31.3

What is the law of sines?

The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

Given data ,

Let the triangle be represented as ΔDEF

Now , the measure of sides of the triangle are

The measure of EF = 22

The measure of angle ∠D = 43°

The measure of ∠E = 62°

And , the measure of ∠F = 180° - 43° - 62° = 75°

From the laws of sines , we get

a / sin A = b / sin B

On simplifying , we get

EF / sin 43° = ED / sin 62°

So , the measure of DE = ( 22 / 0.7 ) ( sin 75° )

And , the measure of DE = 31.3 units

Hence , the measure of DE of triangle is 31.3 units

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Answer 2

Answer: DE = 31.3
Detailed solution is attached

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Remy has $150 to spend on party supplies. She spends $75.50 on decorations and various other supplies. She spent the remaining money to order invitations. If she invited 20 people to her party, how much was the cost to print each invitation?

Answers

Answer:

the cost to price of each invitation is $3.725

Step-by-step explanation:

Given that

On party supplies she incurred $150

For decorations and various other supplies she incurred $75.50

The remaining amount i.e.

= $150 - $75.50

= $74.50

This amount would be incurred for the invitations

Now she invited 20 people

SO the cost to price of each invitation is

= $74.50 ÷ 20 people

= $3.725

Hence, the cost to price of each invitation is $3.725

Luke’s parents started a savings account to help him pay for college or a technology school when he turned 11 years old. Each month they put $125 into the savings account, and they continued this until he was 18 years old. The savings account did not accumulate any interest. Luke figured out that the first year of a technology school that he wanted to attend would cost him $12,480. If he had one year to save the rest of the money, how much would he need to save each month? A. 165
B.40
C.1980
D.1040

Answers

B has a savings account, into which he must deposit $40 each month.

What's the point of the example?

Interest is frequently calculated as an annual percentage of the amount borrowed. This percentage represents the loan's interest rate. For instance, a bank will pay interest if you deposit money in a high-yield savings account.

From the time he was 11 to the time he was 18, Luke's parents saved for him for 8 years, or 8 years x 12 months every year, or 96 months.

Since they were saving $125 per month throughout this time, Luke had amassed the following sum:

$125/month x 96 months = $12,000

Luke must still pay the following expenses because he needs $12,480 for his first year of technological school:

$12,480 - $12,000 = $480

If he has one year left to save this amount, he will need to save:

$480÷12months = $40per month

Therefore, the answer is B. $40.

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What is the value of the expression? 19.2+(–7+3.8)a. 16
b. 24
c. 29
d. 30

Answers

$19.2+(-7+3.8)=19.2+(3.8-7)=19.2+(-3.2)\n\n=19.2-3.2=\huge\boxed{16}\leftarrow\boxed{a}$

The first thing I would do to solve this is do the () so -7+3.8=-3.2 +19.2=16 So your answer would be A. I hope this helps. :)

Simplify the following expression: (5x2 + 3x + 4) − (2x2 + 5x − 1). If the final answer is written in the form Ax2 + Bx + C, what is the value of A? Numerical Answers Expected! Answer for Blank 1:

Answers

Taking out the parentheses of expression
(5x2 + 3x + 4) − (2x2 + 5x − 1)

= 5x2 + 3x+ 4 -2x2 - 5x + 1

Grouping together the like terms and arranging the expression:
= 5x2 - 2x2 + 3x - 5x + 4 + 1

Combining the like terms:
= 3x2 - 2x + 5

Therefore,
A = 3

Answer: 3

Step-by-step explanation:

48.7 to one significant figure

Answers

48.7 rounded to one significant figure would be 50

48.7 rounded to the closest significant figure would be 50. Hope I helped!

Clayton drove at a constant rate on the highway for a trip to the beach. He did not make any stops along the way. The distance Clayton had driven at any given time describes a linear function. At 3:00 p.m., he had driven 90 miles. At 4:30 p.m., he had driven 180 miles. Which statement about Clayton’s trip is true?1.Clayton started driving at 1:30 p.m., and he drove 60 miles per hour.

2.Clayton started driving at 3:00 p.m., and he drove 60 miles per hour.

3.Clayton started driving at 1:30 p.m., and he drove 90 miles per hour.

4.Clayton started driving at 4:30 p.m., and he drove 90 miles per hour.

Answers

The answer is the first 1 !!

Here is how we see if it is true!

If Clayton drives 60 miles per hour, that means, that after one hour has passed, they should have traveled 60 miles!

If we look at the number of hours that have passed between 1:30 and 4:30, it is 3 hours.

If someone travels 60 miles every hour that has passed, and they traveled for 3 hours. To find how far they have traveled we just need to multiply 60 miles by 3 hours!

Let's solve that!

60 × 3 = 180 miles!

Clayton started driving at 1:30 pm and went 60 miles per hour.

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I need help solving x^2+3xy-y^2=12 and x^2-y^2=-12

Data Set 1 has a mean of 120 and a MAD of 4. Data Set 2 has a mean of 132 and a MAD of 3.What can you conclude about the two distributions? Choose exactly two answers that are correct. A.The means-to-MAD ratio is 3. B.The means-to-MAD ratio is 4. C.The distributions are somewhat similar. D.The distributions are different.

a store sells small notebooks for $7 and large notebooks for $14. if a student buys 6 note books for $63, how many notebooks each did she buy