All categories

2 years ago

AB and DC are parallel.

Mathematics

1 answer:

bekas [8.4K]2 years ago

6 0

Answer:

583 cm²

Step-by-step explanation:

To find the area of triangle BCD, we need to know the length of segment BD. That can be found from the law of sines:

BD/sin(A) = BA/sin(D)

BD = (sin(A)/sin(D))BA = sin(70°)/sin(74°)·(39 cm) ≈ 38.1249 cm

Then the area of BCD is ...

A = 1/2(DB)(DC)sin(BDC)

Angle BDC, together with the marked angles, makes a total of 180°.

∠BDC = 180° -74° -70° = 36°

A = 1/2)(38.1249 cm)(52 cm)sin(36°) ≈ 582.64 cm² ≈ 583 cm²

_____

<em>Additional comment</em>

The angle relation we used comes from the fact that consecutive interior angles where a transversal crosses parallel lines are supplementary. That means angle DAB and ADC are supplementary. Angle ADC is the sum of angles ADB and BDC, so we have ...

∠DAB +∠ADB +∠BDC = 180°

∠BDC = 180° -∠DAB -∠ADB

You might be interested in

What is 2/4 as a decimal and percent

galben [10]

.5 as a decimal and 50% as a percent

3 0

3 years ago

Read 2 more answers

Model the unknown number situation by writing an algebraic expression.

vampirchik [111]

Answer:

number 1 or A i got it

Step-by-step explanation:

6 0

3 years ago

Single-sample t test and paid days off: The number of paid days off (e.g., vacation, sick leave) taken by eight employees at a s

SVEN [57.7K]

Answer:

A. µ is the population average number of paid days off taken by employees that the company.

Null Hypothesis: µ=15 days

Alternate Hypothesis: µ≠15 days

B. one-sample t-test

C. We are unsure if it meets the conditions for a one-sample t-test

D. t=-0.79178; df=7

Step-by-step explanation:

For the null and alternate hypotheses, you want to first define what µ represents. Next, you state them, the null hypothesis being equal to the previously known average, and the alternate hypothesis being greater than, less than, or not equal to the previous average, selecting one depends on the context in the problem.

A one-mean t-test would be used as we are looking to compare the mean of a data set, as well as the fact that we do not know the population standard deviation.

When conducting these tests, we need to ensure that three conditions are being met. The first is random, which means that the data set is randomly gathered, or not, the data here does not seem to be random, which may be concerning. Next is independence, this is done when we survey less than 10% of the overall population, in this case it is a small company, so we do not know if it is less than 10% of the population. Last is normality, the data set is not sufficiently large (greater than 30 people surveyed) so we cannot use the central limit theorem to justify that the data is normal. We can use a normality plot, but when the data is placed on a normality plot most of the data appears to be linear, but the 27 day data point does not seem to be normal, so we cannot fully ensure that it is normal. Based on the data not following these conditions, we have concerns about proceeding with the test, we will therefore have to proceed with caution.

For the last part, use that T-test function on a calculator with statistics functions. Remember to include the degrees of freedom in the answer. (The degrees of freedom is one less than the sample size).

6 0

3 years ago

Please find y intercept with work

Goryan [66]

Answer:

Step-by-step explanation:

When x is 0, y is 1 and the y intercept is the y value when x is 0.

7 0

2 years ago

Read 2 more answers

PLEASE SHOW ALL THE STEPS THAT YOU USE TO SOLVE THIS PROBLEM

Mademuasel [1]

Answer:

{x = 1 , y=1, z=0

Step-by-step explanation:

Solve the following system:

{-2 x + 2 y + 3 z = 0 | (equation 1)

{-2 x - y + z = -3 | (equation 2)

{2 x + 3 y + 3 z = 5 | (equation 3)

Subtract equation 1 from equation 2: