MATHEMATICS COLLEGE

Tell whether the following set is an empty set or not. A = {A quadrilateral having 3 obtuse angles}

Answers

Answer 1

Answer:

Answer:

It is not an empty set

Step-by-step explanation:

Obtuse angles are angles greater than 90 and less than 180.

There are quadrilaterals having 3 obtuse angles and they are possible.

If we imagine 3 obtuse angles of 91 degrees (obtuse angle), the 4th angle will be

360-91-91-91

=> 87 degrees

So, This quadrilateral can be constructed!

And also with 92, 93, 94 and so on!

So, Set A is not an empty set!

Answer 2

Answer:

Answer:

It is not an empty set

Step-by-step explanation:

A quadrilateral with 3 obtuse angles is possible.

A obtuse angle has a measure of more than 90 degrees and less than 180 degrees.

Let’s say three angles are measuring 91 degrees in a quadrilateral.

91 + 91 + 91 + x = 360

x = 87

The measure of the fourth angle is 87 degrees which is less than 360 degrees and is a positive integer, so it is possible.

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The planet Mars has two moons – Phobos and Deimos. Phobos has a mass of 10.8 × 1015 kilograms, and Deimos has a mass of 2.0 × 1015 kilograms. How much greater is the mass of Phobos than the mass of Deimos?
He takes a random sample of 49 recent charterholders and computes a mean salary of $172,000 with a standard deviation of $35,000. Use this sample information to determine the 90% confidence interval for the average salary of a CFA charterholder.
Suppose Mike has a dresser with 3 tan pants, 5 jeans, 2 black pants, and 3 gray pants. He also has 2 brown shoes, 3 black shoes, and 2 blue shoes. If he randomly chooses a pair of pants and shoes, what is the probability that both are black? Give your answer as an exact fraction and reduce the fraction as much as possible.
Two equivalents of 7/4

The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is:

Answers

The answer is 5.87x10^14 this is because when you multiply 5870000000000 times 100 you get 5.87x10^14

3. Dan's credit card was lost on a vacation. He immediately reported it missing. The person who found it days later used it, and charged $x worth of merchandise on the card, where x > $200. How much of the $x is Dan responsible for paying?

Answers

The question is an illustration of the Truth in Lending Act, and Dan is responsible for paying $0

Truth in Lending Act

The Truth in Lending Act is simply an act that protects people from unfair charges on their credit cards, especially in case of theft and card misplacement.

The scenarios

From the question, we have the following scenarios

His card got lost
He reported
Someone else saw the card and purchased goods worth over $200

Because Dan reported when his card got lost, he is protected by the Truth in Lending Act (TILA).

Hence, Dan is responsible for paying $0

Read more about the Truth in Lending Act at

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Final answer:

Dan is not responsible for any of the unauthorized charges made on his lost credit card, as he reported it as lost immediately. The maximum amount he could legally be held liable for, per the Fair Credit Billing Act, is $50.

Explanation:

In a scenario where Dan's credit card is lost and reported missing, the responsibility for charged dollars rests on the card issuer, not on Dan. According to the Fair Credit Billing Act (FCBA), the legal limit he's responsible for is $50. However, given that Dan reported the card as lost immediately, he should not be held responsible for any unauthorized charges made.

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#SPJ11

Create an equation to solve for x then solve for x.

Answers

Answer:

Step-by-step explanation:

In parallelogram adjacent angles are supplementary

∠U +∠V = 180

9x + 15 + 6x + 15 = 180

Combine like terms

9x + 6x + 15 + 15 = 180

15x + 30 = 180

Subtract 30 from both sides

15x = 180 - 30

15x = 150

Divide both sides by 15

x = 150/15

x = 10

∠U = 9x + 15

= 9*10 + 15

= 90 + 15

∠U = 105

∠V = 6x + 15

= 6*10 + 15

= 60 + 15

∠V = 75

Answer:

Equation: $2(9x + 15 + 6x + 15) = 360$

x = 10°

∠U = 105°

∠V = 75°

Step-by-step explanation:

Hello!

The sum of angles in a parallelogram is 360°. The oppositeangles of a parallelogram are congruent.

Part A

Equation: $2(9x + 15 + 6x + 15) = 360$

Solve

$2(9x + 15 + 6x + 15) = 360$
$9x + 15 + 6x + 15 = 180$
$15x + 30 = 180$
$15x = 150$
$x = 10$

The value of x is 10°.

Part B

To find the measures of each angle, simply plug in 10° for x in each equation.

∠U

$9x + 15$
$9(10) + 15$
$90 + 15$
$105$

Angle U is 105°.

∠V

$6x + 15$
$6(10) + 15$
$60+15$
$75$

Angle V is 75°.

$√(2) ^( √(7) )$ use a calculator to find an approximation for each power. give the maximum number of decimal places that your calculator displaysround this value to ,7 decimal places,.

Answers

We are given the following expression

$\sqrt[]{2}^{\sqrt[]{7}}$

Here the base is √2 and its power (exponent) is √7

The value of this expression can easily be calculated using any scientific calculator.

The maximum number of decimal places depends upon the type of calculator you use.

$\sqrt[]{2}^{\sqrt[]{7}}=2.50164253682$

Let us round this value to 7 decimal places.

$\sqrt[]{2}^{\sqrt[]{7}}=2.5016425$

Make a conjecture. How could the distance formula and slope be used to classify triangles and quadrilaterals in the coordinate plane? Check all that apply. Use the distance formula to measure the lengths of the sides. Use the slope to determine whether opposite sides are parallel. Use the slope to check whether sides are perpendicular and form right angles. Use the distance formula to compare whether opposite sides are congruent. Use the slope to check whether the diagonals are perpendicular to each other. Use the distance formula to compare whether diagonals are congruent.

Answers

Answer:

1. Use the distance formula to measure the lengths of the sides.

3. Use the slope to check whether sides are perpendicular and form right angles.

5. Use the slope to check whether the diagonals are perpendicular to each.

Step-by-step explanation:

We know that, the distance formula given by

$d = \sqrt{ ({y_(2)-y_(1)}) ^(2)+({x_(2)-x_(1)}) ^(2)}$ ,

gives the length of the line joined by $(x_(1),y_(1))$ and $(x_(2),y_(2))$ .

Now, after using this formula, if:

1. The length of the opposite sides are equal, then the quadrilateral could be a rectangle or a parallelogram.

2. The length of all sides are equal, then the quadrilateral could be a square or a rhombus.

So, this gives us option 'Use the distance formula to measure the lengths of the sides' is correct.

Now, we use slope to find the angles i.e. If:

1. The product of two slopes is -1, then the lines are perpendicular and so, forms right angle between them.

2. The slope of two lines are equal, then the lines are parallel.

So, this gives us that the option 'Use the slope to check whether sides are perpendicular and form right angles' is correct.

Since, some quadrilaterals have the property that the diagonals are perpendicular bisector of each other.

So, the option 'Use the slope to check whether the diagonals are perpendicular to each other' is also correct.

Hence, option 1, 3 and 5 are correct.

Using a limited selection from among the options, a quadrilateral, or

triangle can be classified into one of the eleven classes.

The correct options are;

Use the distance formula to measure the lengths of the sides

Use the slope to determine whether the sides are perpendicular and form right angles

Use the slope to check whether the diagonals are perpendicular

Reasons:

The classification of triangles are;

Right triangles; Having two legs that are perpendicular

Isosceles triangles; Having two sides equal

Equilateral triangles; Having all sides equal

Scalene triangle; Have all sides of different dimensions

Classification of quadrilaterals are;

Kite, rhombus, rectangle, parallelogram, square, trapezoid, isosceles trapezoid

Use the distance formula to measure the lengths of the sides;

The above process can be used to classify parallelograms, equilateral triangles, isosceles trapezoids, kite

The process can be used to classify all triangles

Use the slope to determine whether the sides are perpendicular and form right angles;

The above process can be used to differentiate parallelogram from squares and rectangles, kite trapezoid

The process can be used to determine if the triangle is a right triangle

Use the slope to check whether the diagonals are perpendicular;

The above process can be used to differentiate squares from rectangles, kite, and rhombus

Learn more about slope, distance formula, triangles and quadrilaterals here:

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Consider the following function.Step 2 of 2 : Find two points on the line to graph the function.

Answers

The twο pοints οn the line are:

A. (0, 3)

B. (3,−2)

What exactly dοes functiοn mean?

Functiοn is wοrk expressiοn the cοnnectiοns between variοus cοmpοnents that wοrk tοgether tο prοduce the same result. A utility is made up οf a variety οf distinctive cοmpοnents that cοοperate tο create distinct results fοr each input.

Here,

$$\mathrm{r(x)=3 - \frac53 (x)}$