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1 year ago

Which of the following statements must be true about this diagram? Check all that apply.

Mathematics

1 answer:

pishuonlain [190]1 year ago

8 0

Answer:

Options (D), (E) and (F) are the correct options.

Step-by-step explanation:

From the figure attached,

1). Angle 4 is the exterior angle of the given triangle having interior angles 1, 2 and 3.

Therefore, by the property of exterior angle,

∠4 = ∠1 + ∠2

2). Since ∠4 = ∠1 + ∠2,

Therefore, ∠4 will be greater than ∠1

Similarly, ∠4 will be greater than ∠2

Therefore, Options (D), (E) and (F) are the correct options.

You might be interested in

The sum of two numbers is 90. The larger number is 14 more than 3 times the smaller number. Find the numbers

e-lub [12.9K]

Answer:

The numbers are 19 and 71.

Step-by-step explanation:

Let x and y represent the two numbers. Then x + y = 90.

Also, if we assume that the larger number is y, then y = 3x + 14.

We must solve this system of linear equations. Since we already have the result of solution for y (y = 3x + 14), let's use the substitution method to find the solution:

x + y = 90 becomes x + 3x + 14 = 90, or:

4x = 76. Thus, x = 76/4, or 19. If x = 19, then y = 3(19) + 14, or y = 71.

The numbers are 19 and 71.

Note that these add up to 90, as they must, and that 71 is 14 more than 3 times 19.

7 0

1 year ago

Rachel measured the lengths of a random sample of 100 screws. The mean length was 2.9 inches, and the population standard deviat

MaRussiya [10]

Answer:

z = 10

Step-by-step explanation:

The value of the z-statistic is given by:

$z = \frac{X - \mu}{s}$

In which:

X is the measured value.

$\mu$ is the expected value.

$s = \frac{\sigma}{\sqrt{n}}$ is the standard deviation of the sample. $\sigma$ is the standard deviation of the population.

In this question:

The mean length was 2.9 inches, and the population standard deviation is 0.1 inch.

This means that $\mu = 2.9, \sigma = 0.1$

Random sample of 100 screws.

This means that n = 100.

To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?

3 inches, so $X = 3$

$s = \frac{0.1}{\sqrt{100}} = 0.01$

$z = \frac{X - \mu}{s}$

$z = \frac{3 - 2.9}{0.01}$

$z = 10$

8 0

1 year ago

What is the slope of a line perpendicular to the line whose equation is 3x-12y=2163x−12y=216.

Keith_Richards [23]

Answer:

Deleted account

Step-by-step explanation:

Here 3x-12y-216=0

Reducing into slope intercept form

-12y= -3x + 216

12y = 3x - 216

Which is in the form of, y = mx + c

Slope (m) = 3

Step-by-step explanation:

5 0

2 years ago

Read 2 more answers

· Josh Duchene worked at three jobs in three weeks. In the first week, he earned $360. In the next week, he

Mademuasel [1]

$345.00?????????????????????

7 0

2 years ago

Read 2 more answers

4C. Quintin is using the three different shaped

Sauron [17]

The smallest number of tiles Quintin will need in order to tile his floor is 20

The given parameters;

number of different shapes of tiles available = 3

number of each shape = 5

area of each square shape tiles, A = 2000 cm²

length of the floor, L = 10 m = 1000 cm

width of the floor, W = 6 m = 600 cm

To find:

the smallest number of tiles Quintin will need in order to tile his floor

Among the three different shapes available, total area of one is calculated as;

$A_{one \ square \ type} = 5 \times 2000 \ cm^2 = 10,000 \ cm^2$

Area of the floor is calculated as;

$A_{floor} = 1000 \ cm \times 600 \ cm = 600,000 \ cm^2$

The maximum number tiles needed (this will be possible if only one shape type is used)

$maximum \ number= \frac{Area \ of \ floor}{total \ area \ of \ one \ shape \ type} \\\\maximum \ number= \frac{600,000 \ cm^2}{10,000 \ cm^2} \\\\maximum \ number= 60$

When all the three different shape types are used we can get the smallest number of tiles needed.

The minimum or smallest number of tiles needed (this will be possible if all the 3 different shapes are used)

$3 \times \ smallest \ number = 60\\\\smallest \ number = \frac{60}{3} \\\\smallest \ number = 20$

Thus, the smallest number of tiles Quintin will need in order to tile his floor is 20

Learn more here: brainly.com/question/13877427

3 0

1 year ago