Graph the image of the figure on the right under the given translation.T(3, -1) (x,y)

Taking into account the definition of a system of linear equations, the number of adult tickets sold was 50.

A system of linear equations is a set of linear equations in which two or more variables are related.

In the systems of equations, the values of the unknowns must be found, with which when replacing, they must give the solution proposed in the  equations.

In this case, a system of linear equations must be proposed taking into account that:

You know:

The system of equations to be solved is

3c + 5a= 340

c + a= 80

From the several methods to solve a system of equations, it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.

In this case, isolating the variable "c" from the second equation:

c= 80- a

Replacing this expression in the first equation:

3×(80- a) + 5a= 340

Solving:

3×80- 3a + 5a= 340

3×80- 3a + 5a= 340

240- 3a + 5a= 340

- 3a + 5a= 340- 240

2a= 100

a=100÷ 2

a= 50

Finally, 50 adult tickets were sold.

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The range is the difference between the largest and the smallest and the range is 5.2

This is a graph that is divided into two vertical axes such that one axes represent the stem and the other axis represents the leaf

From the question, we have the following parameters:

Stems = 12, 13, 14, 15, 16, and 17

Each of these stem elements have their own leaves

So, the complete stem and leaf plot is as follows

12     |  3, 3, 6, 7, 9, 9.

13     |  1, 1, 4, 5, 5.

14     |  0, 0, 2, 3, 3, 8, 8, 9.

15     |  2, 2, 2, 2, 2, 3, 5, 5, 7.

16     | 4, 5, 5, 9, 9.

17      | 3 5.

Key

12 | 3 means 12.3.

To determine the range, we simply take the smallest number and the largest number represented by the plot and calculate the difference

In (a), we have

The range is calculated from the smallest number and the largest number represented by the plot

So, we have

Smallest = 12.3

Largest = 17.5

So, the range is

Range = 17.5 - 12.3

Evaluate

Range = 5.2

Hence, the range is 5.2

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The individual that has a greater rate of reading is Rhoni.

Rate measures how fast a person is reading a book. Rate is the total pages read per time. Rate is determined by dividing total pages read by the total time spent reading.

Division is the operation used in mathematics that is used to determine the quotient of two or more numbers. It entails grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

Rie's rate = pages read / time

195 / 3 = 65 pages per hour

325 / 5 = 65 pages per hour

Rie's rate is 65 pages per hour. While Rhoni's rate is 75 pages per hour. This means that Rhoni reads faster than Rie.

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Answer: its associative property Hope I helped

Step-by-step explanation:

Answer: slope is -3

Step-by-step explanation: (-5,6) and (-9,-6)

Take your Y values and subtract them -6-6=-12

Take your X values and subtract them -9-(-5) or -9+5= -4

Then your -12 will be your numerator and your -4 will be your denominator

Then Divide

-12/-4= -3

I hope this helps!  

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. The equation 9 x 5 = 45 consists of the two equations are separated by the 'equal' sign.

Assume that a team has N players.

Each squad may have anywhere from 3 to 5 players, so

3 ≤ 5 ...(i)

Let P represent a player's total points in a single game round.

Each round of the game allows for a maximum of 10 points for each player, so

0 ≤ p ≤ 10 ....( i)

(1) Elena assembled a team of five people.

As a result, 5 players' points in 1 round equal 5P.

Equation (ii) yields the range of

0 ≤ 5p ≤ 50.

As a result, Elena's team's points total ranges from 0 to 50.

(2) If each shot is off by one point, then

One player's points in one round are equal to 10-1=9.

So, 9 x 5 = 45 points were collected by 5 players in 1 round.

(3) Assume that R represents the number of teams as an integer.

the game involves at least three teams, therefore

R ≥ 3 ...( iii)

Given that N players make up one team,

R team has NR players, where R is 3, 4, or more.

Next, using equation (i)

3R ≤ 5R

Therefore, the number of players ranges from 3R to 5R if there are at least 3 teams.

The game can have anywhere from 3x3=9 to 5x3=15 players when R=3.

Answer:

(I) Between 0 and 50.

(ii) Between 3 and 5.

(iii) Between 3R and 5R, where R = 3,4,5,...

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The state income tax owed on a $90,000 per year salary is $5,175.

Tax is a compulsory amount that is levied by the government on the income of individuals or on certain goods and services. Progressive tax is when the amount of tax paid by individuals increases as the amount of income earned increases. The amount paid as tax can be determined by multiplying the appropriate tax rate by the total income.

Tax paid = income x tax rate

$90,000 x 5.75%

$90,000 x 0.0575 = $5,175

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The state income tax owed on an $90,000 per year salary is  $5,175.

Taxes are mandatory contributions levied on individuals or corporations by a government entity

Given,

A certain state uses the following progressive tax rate for calculating individual income tax: Income Progressive Range ($) Tax Rate 0 - 3000 2% 3001 - 5000 3% 5001 - 17,000 5% 17,001 and up 5.75%

We need to find the state income tax owed on an $90,000 per year salary.

Tax paid = income x tax rate

$90,000 x 5.75%

5.75% should be converted to decimal by dividing with 100.

5.75/100=0.0575

So $90,000 x 0.0575 = $5,175

Hence the state income tax owed on an $90,000 per year salary is  $5,175.

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The conservationist expects to be in the lake would be; 142 trouts.

An equation is an expression that shows the relationship between two or more numbers and variables.

Given, that determine the number of trout in a lake, a conservationist catches 200 trout, tags them, and throws them back into the lake.  

We have to find conservationists who expect to be in the lake.

Now, initially, trout count = 200

Then, again 56 trouts caught then, trout count = 200 + 56

But 14 of them are tagged that means; they are part of 200 trouts so we should not count again in 56 trouts.

So, trout count = 200 + 56 – 14  = 142.

Hence, the conservationist expects would be; 142 trouts.

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These are the solutions of all the questions

The volume of a cylinder is given by the following formula:

Where r is the radius and h is the height of the cylinder.

By replacing 8 for r and 6 for h into the above formula, we get:

Then, the volume of the cylinder equals 1205.76 units³

ANSWER

(-4, 2)

(Option D)

EXPLANATION

The triangle in the picture is dilated with scale factor 2.

This simply means that the size of the triangle was increased by 2.

To do this, first, let us write out the cordinates of the vertices of the original triangle:

M(-2, 1)

P(2, -2)

A(3, 5)

To dilate this, we will multiply the cordinates by 2, they become:

M' (-4, 2)

P' (4, -4)

A' (6, 10)

Therefore, the vertex M on the image after the dilation is (-4, 2).

(Option D)

Answer:

A, 61.

Step-by-step explanation:

(2x+24). If we sub in 61 for x, we get (2(61)+24). Follow order of operations.

2 times 61= 122. Add 24 and you get 146. We can know this is correct because we are given the other angle and it's degrees, whch is also 146 degrees. Therefore, the answer is A, 61.

Answer:

In this photo.

Put a heart and 5 mark for the answer.

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When two lines and a transversal form comparable angles that are congruent, the lines are parallel, which is the converse of the corresponding angles theorem's flow proof. Which means that line c ║ to line d.

The two different lines that meet at an angle of 90 degrees are called perpendicular lines. Do your walls' connecting corners—or the letter "L"—share any similarities? They are the straight lines, referred to as perpendicular lines, that intersect at the proper angle. An angle of 90 degrees between two straight lines is known as a perpendicular. The illustration depicts a little square in between two perpendicular lines to indicate the 90° angle, which is also known as a right angle. Here, a right angle between the two lines Two lines that cross each other at a 90° angle are referred to as perpendicular lines in mathematics. I

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The coordinate of the midpoint AB is (1/2, 1/2)

From the question, the coordinates of the points are given as

A = (-2, 2)

B = (3, -1)

The midpoint of a line or points is then calculated using the following midpoint formula

Midpoint = 1/2 * (x₂ + x₁, y₂ + y₁)

Where x and y are the coordinates of A and B

Substitute the known values in the above equation

So, we have the following equation

AB = 1/2 * (-2 + 3, 2 - 1)

Evaluate the sum

AB = 1/2 * (1, 1)

Evaluate the products

AB = (1/2, 1/2)

Hence, the midpoint is (1/2, 1/2)

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The radius of the snowball decreasing by -2.

What is rate?

A rate is the ratio of two related values expressed in various units. [1] If one of these numbers is used as the ratio's denominator and it is assumed that this quantity can be altered in a predictable way (i.e., is an independent variable), then the numerator of the ratio represents the rate of change in the other (dependent) variable.

Let r(t) be a function of the radius of the sphere over time.

The volume of the sphere over time is then [tex]v(t) = \frac{4}{3} \pi r(t)^3[/tex]

The rate of change of the volume is then  [tex]v'(t) = 4\pi r(t)^2r'(t)[/tex]

Comparing is to the surface area of the sphere [tex]s(t) = 4\pi r(t)^2[/tex],  it seems perfectly possible for the volume to decrease at a rate equal to  2s(t).

That just means that

[tex]v'(t) = -2s(t)\\4\pi r(t)^2r'(t) = -8\pi r(t)^2\\r'(t) = -2[/tex]

Therefore, the radius must shrink by two units of distance every unit of time, it is now obvious.

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After solving the equation x^2-2x-7=0, values of x are -1 + 2√2 and

-1 - 2√2.

A quadratic equation has a leading coefficient of the second degree.

What is a quadratic equation?

A quadratic equation is an equation whose leading coefficient is of second degree also the equation has only one unknown while it has 3 unknown numbers.

It is written in the form of ax²+bx+c.  

After applying the quadratic formula to it we get,

[tex]x = \frac{-b +\sqrt{b^{2} - 4ac } }{2a} \\ x = \frac{-b -\sqrt{b^{2} - 4ac } }{2a}[/tex]

where a = 1

b = 2

c = -7

After putting the values of a,b, and c, we get

x = -1 + 2√2 and,

x = -1 - 2√2 .

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Answer:

24° , 60° , 96°

Step-by-step explanation:

sum the parts of the ratio, 2 + 8 + 5 = 15 parts

divide the sum of the angles in a triangle by 15 to find the value of one part of the ratio.

180° ÷ 15 = 12° , then

2 parts = 2 × 12° = 24°

5 parts = 5 × 12° = 60°

8 parts = 8 × 12° = 96°

the 3 angles in the triangle are 24° , 60° , 96°

Answer:

Explanation:

Here, we want to get the dimensions of the rectangle

Let us represent the length by l and the width by w

From the question:

The length of the rectangle is 3 m less than double the width

Mathematically:

The product of the two represents the area

Now, let us substitute the first equation with the second:

Solving the quadratic equation, we have:

Recall:

If covariance between two variables is near 0, it implies that the variables are not linearly related.

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The width of the paper in the smaller notebook is 4 1/4 inches.

When two shapes are similar, the ratio of their corresponding sides are equal, and their corresponding angles are equal.

For two notebooks in the shape of a rectangle, the ratio of their lengths must be equal to the ratio of their widths.

If one sheet of paper in a notebook is 8 1/2 inches by 11, and the pages of the smaller similar notebook are 5 1/2 inches long, then the width of the paper in the smaller notebook is

11 inches / 5 1/2 inches = 8 1/2 inches / width of smaller notebook

width of smaller notebook = 4 1/4 inches

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The multiplication we need to make is:

To answer this question we need to use the following rules for multiplications with signs:

We can see that in our expression we have the last case: a negative number multiplied by a positive number. In this case, the negative number is -6 and the positive number is 1.

So, we know from the rule that the result will be negative.

And finally, we multiply just the numbers: 6 by 1 is 6.

In summary, the result is:

Answer: -6

Answer:

-6

Step-by-step explanation:

hope this helps

Step-by-step explanation:

I wrote it on paper. I hope this is helpful

First convert the angle measure from radians to degrees using the formula

Were θ represents the angle of interest

So for this exercise the angle is pi, so:

Now using the calculator you can determine tha tangent of negative 180º

tan(-180º)=0

So the tangent of negative pi should also be zero

Hello!

First, let's write the possible options:

Dice: 6 different results.

• 1, 2, , 4, 5, 6.

Spinner: 4 different results.

• A, B, C, D.

Knowing it, let's solve each alternative of your exercise:

In the dic, we have 6 possible results and we want a specific number. SOo, we can write it as 1/6.

In the spinner, we have 4 possible results and we want a specific one too. So, we have 1/4.

Now, remember he r"and" rule: when we consider two events happening simultaneously, we must multiply their probabilities.

Solving:

We'll solve it in a similar way.

We have three possible odd numbers (1, 3, 5) in a total of 6 options. So, 3/6 = 1/2.

For the spinner, the reasoning will be the same: 1/.

Let's calculate:

In a dice, we have four numbers less than 5: 1, 2, 3,4.

In the spinner, there are 3 consonants (B, C, D).

Let's calculate:

Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.

Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.

If we start with 180 g of the isotope, after one half-life the quantity will diminish to  180 g/2 = 90 g which exists half the original quantity.

This can be written mathematically as: [tex]$180 g\left(\frac{1}{2}\right)^1$[/tex]

After the second half life: [tex]$\frac{90 g}{2}=45 g=\frac{180 g}{4}=(180 g)\left(\frac{1}{2}\right)^2$[/tex]

After the third half life: [tex]$\frac{45 g}{2}= 22.5 g=\frac{180 g}{8}=(180 g)\left(\frac{1}{2}\right)^3$[/tex]

But now that we are dividing the amount by 2 to a power that grows as the number of half-lives, we can start to notice a pattern.

The original quantity can then be rapidly computed for six half-lives using the formula below:

[tex]$(180 g)\left(\frac{1}{2}\right)^6=(180 g)\left(\frac{1}{64}\right)=\frac{180 g}{64}=2.8 g$$[/tex]

Depending on the particular isotope, this process can take a variety of times. While for some it will take years and decades, it will just take a microsecond for individuals. Usually, the isotope will decay into a different element or isotope.

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The standard form of a hyperbola with center (h,k) is

We know the vertices are at (5,0) and (-5,0)

The vertices are at (h+a,k) and ( h-a,k)

The center must be at (0,0) and the a value is 5

The coordinates of the foci are at ( h+c,k) and ( h-c, k) and we know one of the foci is at (6,0)

c is equal to 6

We know that c^2 = a^2+b^2

6^2 = 5^2 + b^2

36 = 25+b^2

11 = b^2

We can write the equation

Answer:

a) 1.6×10∧-6

b)2×10∧7