Write your answer in standard form with integer coefficients.
2x + 3y = 30 ; (2,-5)

A B) hexagon is the shape with 6 sides.

A hexagon is a polygon with six straight sides and six angles. In geometry, hexagons are commonly used in various designs and structures due to their symmetry and stability.

Regular polygon refers to a polygon with equal sides and equal angles, such as a hexagon. Hexagons have the property of being equilateral and equiangular, making them regular polygons.

Six Electron Groups form an octahedron, which is a polyhedron made up of identical equilateral triangles and has six identical vertices, showcasing the connection between the number six and geometric shapes.

Therefore, option B is correct.

Answer:

The correct option is C.

Step-by-step explanation:

The given table represent the number of contestants in each round of the competition.

The average rate of change of f(x) from x = 3 to x = 5.

[tex]m=\frac{f(x_2)-f(x_1)}{x_2-x_1}[/tex]

[tex]m=\frac{f(5)-f(3)}{5-3}[/tex]

[tex]m=\frac{4-16}{2}[/tex]

[tex]m=\frac{-12}{2}[/tex]

[tex]m=-6[/tex]

The average rate of change of f(x) from x = 3 to x = 5 is -6, it represents the average rate at which the number of contestants decreased from the third round to the fifth round.

Therefore option C is correct.

Cuharra studied for 52.5 minutes on Monday and 67.5 minutes on Tuesday.

To find out how long Cuharra studied on Monday and Tuesday, we can set up an equation. Let's say C represents the amount of time she studied on Monday. According to the information given, on Tuesday she spent an extra 15 minutes studying, which means she studied for C + 15 minutes. The total time she studied was 120 minutes. So, we can write the equation as C + (C + 15) = 120.

Now, we can solve this equation to find the values of C and C + 15. Combining like terms, we get 2C + 15 = 120. Subtracting 15 from both sides, we get 2C = 105. Divide both sides by 2, and we get C = 52.5.

Therefore, she studied for 52.5 minutes on Monday and 52.5 + 15 = 67.5 minutes on Tuesday.

Final answer:

Cuharra studied for 52.5 minutes on Monday and 67.5 minutes on Tuesday to make a total of 120 minutes of study time over the two days.

Explanation:

The question involves solving for the number of minutes cuharra studied on Monday and Tuesday. Since the total study time for both days is 120 minutes and she studied 15 minutes extra on Tuesday, we can set up two variables to represent the study times on each day. Let x be the number of minutes studied on Monday, then x + 15 will be the number of minutes studied on Tuesday.

To solve for x, we set up the equation x + (x + 15) = 120. Simplifying, we get 2x + 15 = 120. Subtracting 15 from both sides gives us 2x = 105. Dividing both sides by 2, we find that x = 52.5. Therefore, cuharra studied for 52.5 minutes on Monday and 52.5 + 15 = 67.5 minutes on Tuesday.

The distance travel Rachelle in 1 hour (60 minutes) will be 3.75 miles.

The distance covered by the particle or the body in an hour is called speed. It is a scalar quantity. It is the ratio of distance to time.

We know that the speed formula

Speed = Distance/Time

Rachelle can walk 2.5 miles in 40 minutes.

Then the speed will be

Speed = 2.5 / 40

Speed = 0.0625 miles per minute

At this rate, distance travel Rachelle in 1 hour (60 minutes) will be

0.0625 = d / 60

d = 3.75 miles

The distance travel Rachelle in 1 hour (60 minutes) will be 3.75 miles.

More about the speed link is given below.

https://brainly.com/question/7359669

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1. The measure of angle A is [tex]\(22^\circ\).[/tex]

2. The measure of angle B is[tex]\(68^\circ\).[/tex]

To find the measures of angles A and B, we can use the fact that they are complementary, meaning their measures add up to[tex]\(90^\circ\).[/tex]Let's set up an equation using the given information:

[m_A + m_B = 90]

Given that[tex]\(m_A = 3x - 8\)[/tex]and (m_B = 5x + 10), substitute these expressions into the equation:

3x - 8 + 5x + 10 = 9

Combine like terms:

8x + 2 = 90

Subtract 2 from both sides:

8x = 88

Divide by 8:

x = 11

Now that we know the value of (x), we can find the measures of angles A and B:

[tex]\[m_A = 3x - 8 = 3(11) - 8 = 33 - 8 = 25\][/tex]

[tex]\[m_B = 5x + 10 = 5(11) + 10 = 55 + 10 = 65\][/tex]

Therefore, the measure of angle A is \(25^\circ\) and the measure of angle B is [tex]\(65^\circ\).[/tex] To check, we can verify that these angles are indeed complementary:

25 + 65 = 90

So, angles A and B satisfy the condition of being complementary.

By factoring and simplifying the given polynomials, we found that the expressions simplify to r + 2. Therefore, the correct answer is option A. This process involves cancelling out common factors from the numerator and the denominator.

Polynomial Multiplication and Simplification

To solve the problem, we need to multiply the given rational expressions and simplify the result. The expressions are:

(r^2 + 7r + 10) / 3 and (3r - 30) / (r^2 - 5r - 50)

First, let's factor the polynomials where possible:

Now, the problem can be written as:

([tex](r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]

Next, we simplify by canceling out the common factors:

[tex]=( (r + 2)(r + 5) / 3 ) * ( 3(r - 10) / (r - 10)(r + 5) )[/tex]

The (r + 5) terms and the (r - 10) terms can be canceled:

[tex]= (r + 2) / 1[/tex]

So, the simplified answer is r + 2,

The correct  option is  A. r+2

"The correct expression to show the total number of empty spaces in the bike racks is [tex]\( 4 \times 15 - 16 \).[/tex]

To arrive at this expression, we start by calculating the total capacity of all the bike racks combined. Since there are 4 bike racks and each can hold 15 bikes, the total capacity is [tex]\( 4 \times 15 \).[/tex] This gives us the maximum number of bikes that can be parked in all the racks.

Next, we subtract the number of bikes that are currently parked in the racks from the total capacity. There are 16 bikes parked. Therefore, the expression to find the number of empty spaces is:

[tex]\[ \text{Total capacity} - \text{Number of bikes parked} \][/tex]

Substituting the given numbers into the expression, we get:

[tex]\[ 4 \times 15 - 16 \][/tex]

This expression represents the total number of empty spaces in the bike racks. When evaluated, it will give us the number of spaces available for additional bikes to be parked."

Step-by-step explanation:

Let r₁ be the rate of filling of small pipe, r₂ be the rate of filling of large pipe  and V be the volume of swimming pool.

[tex]\texttt{Rate of small pipe},r_1=\frac{V}{t_1}\\\\\texttt{Rate of large pipe},r_2=\frac{V}{t_2}=\frac{V}{0.5t_1}=2r_1[/tex]

If both pipes are combined it takes 213 hours, that is

              [tex]t=\frac{V}{r_1+r_2}\\\\213=\frac{V}{r_1+2r_1}\\\\V=639r_1[/tex]

Now we need to find how much time it takes to fill the pool by large pipe,

That is

               [tex]t_2=\frac{V}{r_2}=\frac{639r_1}{2r_1}=319.5hours[/tex]

By large pipe only it will take 319.5 hours to fill the pool.          

Answer:

Step-by-step explanation:

Answer:

you would graph (0,3) and (9,0)

Step-by-step explanation:

Consider the provided equation.

The x intercepts are the points where y value is zero. Similarly the y intercepts are the points where x values is zero.

In order to find the x intercept substitute y = 0 in the provided equation.

0=-1/3x + 3

-3=-1/3(x)

-9=-x

9=x

Thus, the x intercept is (9,0)

In order to find the y intercept substitute x = 0 in the provided equation.

y=-1/3(0) + 3

y=3

Thus, the y intercept is (0,3)

Now use the x and y intercepts to draw the graph of the equation.

The required graph is shown in figure 1.

Therefore, the x- and y- intercepts is (9,0) and (0,3)

Answer:

Collinear, coplanar, and between the points

Step-by-step explanation:

Collinear means that the points are in the same line.

Coplanar means that the points are in the same plane.

Between the points is used when three points are in the same line an you want tro express that one of them is between the others.

So those three relationships can apply for the three points.

noncollinear not apply because it means that the points don't lie in a line.

1. an angle congruent to a given angle

2. x = 68, y = 75

3. corresponding angles

maximum area is a square

the side of the square would be 52/4 = 13 feet

 area = 13*13 = 169 square feet

Answer:

Width = 13 ft

Maximum Area = 169 ft²

Step-by-step explanation:

Given: A rectangular dog pen whose fencing is 52 feet.

Let length be y and width be x

Fencing = 2(l+b)

52 = 2 (x+y)

x + y = 26

y = 26 - x

Area of rectangular pen = Length x width

                                        = y . x

                  [tex]A=x(26-x)[/tex]

                  [tex]A=26x-x^2[/tex]

It is parabolic equation. Maximum/Minimum at vertex.

[tex]x=-\dfrac{b}{2a}[/tex]

where, a=-1, b=26

[tex]x=\dfrac{26}{2}=13[/tex]

Now we put x=13 into A

[tex]A=13(26-13)[/tex]

[tex]A=169[/tex]

Hence, The width is 13 feet and Maximum area is 169 ft²

We are given that:

vi, initial velocity = 24 m/s

v, final velocity = 15 m/s

t, time = 12 s

The formula for acceleration is:

a = (v – vi) / t

a = (15 – 24) / 12

a = - 0.75 m/s^2                                (deceleration)