2. The Venn diagram shows the sets U, X and Y.UXY.34 246..9.512:31List the elements of the following sets:(a) X(b) Y(c) U(d) XUY(e) XnY(g) X\Y(h) Y\X(f) X'(1) (XY)2:31

Answer:

Rate of the faster group = 3.38 miles per hour

Rate of the slower group = 1.88 miles per hour

Explanation:

Let x = rate of the slower group

Therefore the rate of the faster group will be x + 1 1/2 = x + 3/2 = x + 1.5

From the question, we're told that the two groups traveled for a total hiking time of 200 hours.

We know that distance = rate x time

So the distance of the slower group will be = 200x

And the distance of the faster group will be = 200(x + 1.5)

So if the distance between each town is 1050, we can then solve of x as shown below;

Therefore the rate of the faster group = 1.88 + 1.5 = 3.38 mph.

Third row:

The balance stays the same as the previous row ($337.52).

We have 12 days between 9/7 and 9/18, so we can calculate the product/sum as:

NOTE: the product/sum will be used to calculate the average balance for the month.

Fifth row:

The balance stays the same as the previous row ($399.78).

We have 11 days between 9/20 and 9/30.

Then, the product/sum is:

Total:

The total product/sum is:

Average daily balance:

We can take the total product/sum and divide by the total amount of days.

Finance charge:

New balance:

The new balance is $404.41.

Answer

Options A and C are correct.

The triangle is a Scalen triangle and it is also an Acute triangle.

Explanation

To answer this question, we first explain what these type of triangles are

According to side lengths,

- Scalene triangle has none of its three sides having the same length as another. All the three sides have different lengths. To use angle to know this, all the three angles of a Scalene triangle have different values.

- Isoscelles triangle has two of its sides with the same lengths. In terms of angles, an Isoscelles triangle has two of its angles equal to each other.

- Equilateral triangle has all of its sides equal to one another. In terms of angles, all of the angles of an Equilateral triangle are equal to one another. Each of the angle is equal to 60°.

According to the angles,

- Acute triangle has all of the angles in the triangle being less than 90 degrees.

- Right angle triangle has one of the angles in the triangles being equal to 90 degrees.

- Obtuse triangle has one of the angles in the triangle being greater than 90 degrees but obviously less than 180 degrees.

For this triangle,

We can see that all of its sides have different lengths. Hence, the triangle is a Scalene triangle.

Also, each of the angles of the triangle is less than 90 degrees. Hence, the triangle is an Acute triangle.

Hope this Helps!!!

We will have that $2200 represent the 100%, then how much money does 12% represent.

In order to solve for the ammount of money we multiply the invested ammount ($2200) times the percentage we want to know (12%) and divide it by 100%, that is:

Here we can see, he earned $264 in those 2 years.

65 adult's ticket and 85 children's ticket was sold

Let the number of tickets for children = x

Let the number of adults ticket = y

Total tickets = 150

x + y = 150 ....equation 1

The cost of tickets per child = $4.75

The cost of tickets per adult = $7.50

Total revenue from tickets = $891.25

Total revenue from tickets = The cost of tickets per child × number of children ticket +

The cost of tickets per adult * number of adults ticket

891.75 = 4.75(x) + 7.5(y)

891.75 = 4.75x + 7.5y ...equation 2

x + y = 150 ....equation 1

891.75 = 4.75x + 7.5y ...equation 2

Using substitution method by making x the subject of formula in equation 1:

x = 150 - y

Substitute for x in equation 2:

891.25 = 4.75(150 - y) + 7.5y

891.25 = 712.5 - 4.75y + 7.5y

891.25 = 712.5 + 2.75y

891.25 - 712.5 = 2.75y

178.75 = 2.75y

y = 178.75/2.75

y = 65

Substitute for x in equation 1:

x + 65 = 150

x = 150 - 65

x = 85

Hence, 65 adult's ticket and 85 children's ticket was sold

A line can be written as an equation in the slope-intercept form:

Where m is the slope and b is the y-intercept.

We know the slope:

The y-intercept is the y value of the graph where it intercepts the y-axis, which happens when x = 0.

We know that the point x = 0 and y = 3 is on the line and, since the value of x is 0. the y value is the y-interceot, so:

Thus, we have the equation:

To calculate the other points, we just need to substitute their x values and get their y values:

x = 1:

So, when x = 1, y = 6

x = 2:

So, when x = 2, y = 9.

x = 3:

So, when x = 3, y = 12;

So, the complete table is:

x | 0 | 1 | 2 | 3

y | 3 | 6 | 9 | 12

We are given the following equation of a line.

Let us first solve the above equation for x.

Divide both sides of the equation by -2

So, the solution is x = 0

This means that the two ordered pairs must contain the x-coordinate 0 and the y-coordinate can be any value you like.

For example:

(0, -5) and (0, 5)

Here the x-coordinate is 0 and the y-coordinate is -5 and 5.

Let us plot these ordered pairs and the line on the given graph.

Choose the scenarios that demonstrate a proportional relationship for each person's income.

Millie works at a car wash and earns $17.00 per car she washes.

Bryce has a cleaning service and charges $25.00 plus $12.50 per hour.

Carla makes sandwiches at her job and earns $7.85 per hour.

Tino is a waiter and makes $3.98 per hour plus tips.

Given the parent function

From the graph,

The range of the function is best modelled by the interval

Comparing the function with general equation of the cosine function,

The formula for the period is,

There

Solve the given equation for x as shown below

Solution:

Given:

The circumference (C) of a circle is given by;

Hence,

Thus,

Therefore, the circumference of the circle is 100.48m

Answer:

c. you can't be feeling alive with wearing,weakness of body and mind.

The amount of money that Abdul is going to donate to the City Youth Fund is denoted by x, and the amount of money that Abdul is going to donate to the Educational Growth Foundation is denoted by y.

Since Abdul will donate up to $500, the sum of those amounts must be less or equal to 500.

It is not possible to donate less than zero, therefore, we also have the following constrains

Abdul wants the amount of money donated to the Educational Growth Foundation to be at least 4 times the amount of money donated to the City Youth Fund, therefore, we have our final constrain

Combining those four regions, the solution is their interception, which is

Sharon lives [tex]4\frac{7}{20}[/tex] miles away from Lisa .

In the question ,

it is given that

distance between Sharon and Library is [tex]1\frac{3}{5}[/tex] miles .

distance between Library to Lisa's house is [tex]2\frac{3}{4}[/tex] miles .

So according to the question

distance between Sharon's house and Lisa's house = (distance between Sharon and Library) + (distance between Library to Lisa's house) .

On substituting the values from above ,

we get ,

distance between Sharon's house and Lisa's house = [tex]1\frac{3}{5}[/tex] + [tex]2\frac{3}{4}[/tex]

= (5+3)/5 + (8+3)/4

= 8/5 + 11/4

taking LCM as 20 and solving further we get

= 32/20 + 55/20
= 87/20

= [tex]4\frac{7}{20}[/tex]

Therefore , Sharon lives [tex]4\frac{7}{20}[/tex] miles away from Lisa .

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Answer: By inspecting the triangle we can come up with the following relationships, using the proportionality:

Solving the three equations, (1) (2) and (3) gives the answer for x,y,z which are the three sides of the smaller triangle, the steps are as follows:

Therefore the perimeter is as follows:

Problem

Which of the following equations represents a line that passes through the

points (6,-5) and (-6, -7)?

Solution

For this case the equation for a line is given by:

y= mx +b

And we can find the slope m with this formula:

And replacing we got:

Then we can find the intercept with this formula:

-5 = 1/6 (6)+b

And solving for b we got:

b= -5-1 =-6

And our equation would be:

y= 1/6 x -6

And the best option would be:

I.

To solve the exercise, it is helpful first to draw the situation that the statement describes:

The total area of ​​the figure will be

Then, we can calculate the area of ​​the square using the following formula:

So, we have:

Now, we can calculate the area of the triangle using the following formula:

So, we have:

Finally, we calculate the total area of ​​the figure

Therefore, the total area of the figure is 112.5 square inches, and the correct answer is option C.

Question:

Solution:

Step 1: Find the equation of a line:

Notice that the line passes through the point (x2,y2)= (4,-2) and (x1,y1)=(0,3). Then, the slope of this line would be:

now, notice that the y-intercept of this line is b=3. Then, the equation for this line is:

Step 2:

note that the shaded region is all points on the line and those above it. So, the shaded region can be represented by the following inequality:

and it is shown graphically like this:

So that, we can conclude that the correct answer is:

We have the next system of equations

2x+3y=0 ...(1)

6x+9y=0 ...(2)

I order to solve this system by elimination we will multiply the first equation by -3

So we will have

-6x-9x=0

then we add the equation above with the second equation

-6x-9x=0

+6x+9y=0

As we can see we obtain 0=0 which means that we have infinity solutions

ANSWER

Infinity solutions

Answer: [tex]r(s(5))=-26[/tex]

Step-by-step explanation:

[tex]s(5)=5^2 +2=27\\\\r(s(5))=r(27)=-27+1=-26[/tex]

The formula for the area of a sector of a circle is:

Where

θ is the angle

r is the radius

Given,

θ = 100

r = 7

We substitute into the formula and figure the answer out [remembering to use 3.14159 as π]:

Rounding to the nearest thousandth [3 decimal places], we have:

Advanced tickets(x): $15

Same day tickets(y) : $30

For one more performance there are 55 tickets sold

x+ y= 55 (a)

The total amount paid for them was 1275

15x+30y= 1275 (b)

System of equations:

x+y= 55 (a)

15x+30y = 1275 (b)

Solve for x in (a)

x=55-y

Replace x on (b)

15(55-y)+30y = 1275

82

The probability that we do not dealt a card with number 2 to 9 is 5/13

What is Probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Given,
A pack of card = 52 cards

The Cards having Hearts = 13

The Cards having Spade = 13

The Cards having Diamond = 13

The Cards having Clubs = 13

According to question

The cards numbered from 2 to 9 are 8 cards, specifically 2, 3, 4, 5, 6, 7, 8, and 9.

But there are four suits:  diamonds, hearts, spades, and clubs.

Therefore you multiply 8 by 4 to get 32

The probability of getting dealt one of those cards would be:

32/52, or

8/13

But we have to find the probability of not getting such cards

Thus,

1 - 8/13 = 5/13

Hence,  the probability that you are not dealt a card with number from 2 to 9 will be 5/13

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a number that can be written as the ratio of two integers (option B)

Irrational number cannot be written in the fractional form

Rational numbers can be written in the form of fraction

Checking the options:

a) Circumference = πd

where d = diameter

π = Circumference/diameter

π is an irrational number

b) A number written as ratio of two intergers can be written in the form of fraction

Hence, it is rational

c) A number that we can use in solving an algebraic equation can be any real number.

From a real number, we have rational and irrational numbers. So, there is the likelihood we get an irrational number

d) side of a square = a

diagonal² = a² + a²

length of diagonal of a square = √(a² + a²) = √2a²

This can also yield either irrational or rational numbers.

A number that cannot be irrational means a number that is rational.

From the option, the only one without doubt that it is rational is a number that can be written as the ratio of two integers (option B)

56º,34º

1) A kite is a quadrilateral that according to the following theorem:

2) And examining that picture, we can tell that the angle labeled as 8x is congruent to its opposite counterpart.

3) In addition to this, but not less important that bigger diagonal bisects that the other pair of opposite angles. So we can sketch the following

So we can pick one triangle and write out the following according to the Triangle sum theorem:

4) Finally, let's plug into each one the quantity of x and get the measure of those angles:

Explanation

We are asked to fill in the missing blanks

Part 1

The weight of a Candy bar is in grams

So the answer will be

Amanda bought a candy bar. Its mass was about 50 grams

Part 2

A dollar bill should be about 15 centimeters

Therefore, the answer is

A dollar bill is about 15 centimeters long

Part 3

A can of soda should a capacity in mililiters

Therefore, the answer will be

The can of soda held about 350 mililiters

Given the function

The graph of the function is dhoe below

To answer this question we need the equation of a parabola that uses the distance from the focus to the vertex.

This formula is,

where,

p is the distance from the focus to the vertex, and the point (h,k) is the vertex.

Let us now substitute the data into the equation of the parabola,

Hence, the equation for the parabola is, x² = 8y.

Option C is the correct answer.

The two rational number D and point R are found as 2/7 and 4/7 respectively.

For the given question.

The number line is given with the rational number D and R to be plotted.

There are 7 units between the points 4 and 5.

D point is 2 units right of 4.

Thus, D = 2/7

R point is 4 units right of point 4.

Thus, R = 4/7

Thus, the two rational number D and R are found as 2/7 and 4/7 respectively.

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Dilation involves adjusting the size of an object or a figure, without altering its shape.

The object can be increased or decreased depending on its scale factor.

A scale factor less than 1 results in a figure of reduced dimensions whereas, a scale factor greater than 1 results in a figure or an object of enlarged dimensions.

In the ΔABC, a dilation of 4/3, which is greater than 1, will thus result into an enlargement.

The correct option is B.