Tickets to the baseball game are on sale for $1.50 off the regular price. Dea buys 6 tickets. If her total cost is $51, what is the regular price of each ticket? Write and solve an equation of the form p(x±q)=r. Then write a sentence to explain your answer.

Answer: A

Step-by-step explanation:

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The possible rational zeros of f(x) = [tex]2x^{3} - 15x^{2} +9x-22[/tex] are ±1, ±2, ±11, ±22, ±1/2, ±11/2.

What is mean of rational zero ?

A rational zero is a rational number, which is a number that can be written as a fraction of two integers. An irrational zero is a number that is not rational, so it has an infinitely non-repeating decimal.

By Rational Zero Theorem,

If P(x) is a polynomial with integer coefficients and if is a zero of P(x) (P( ) = 0),

then p is a factor of the constant term of P(x)

q is a factor of the leading coefficient of P(x)

Possible value of rational zero is p/q

Given, f(x) = [tex]2x^{3} - 15x^{2} +9x-22[/tex]

Here, constant term, p = +22

Leading coefficient, q = +2

The factors of the constant term +22 are ±1, ±2, ±11, ±22.

Therefore , The possible rational zeros of f(x) = [tex]2x^{3} - 15x^{2} +9x-22[/tex] are ±1, ±2, ±11, ±22, ±1/2, ±11/2.

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The required median of the first ten natural numbers is 5.5.

Natural numbers are a part of the number system, including all the positive numbers from 1 to infinity. Natural numbers are also called counting numbers because they do not include zero or negative numbers.

The median is the number in the middle of a list of numbers in ascending order, from lowest to highest.

The median is the middlemost element if the total number of elements in the list is odd, and the median is the average of the middlemost two values if the total number of elements in the list is even.

The list of the first 10 natural numbers is: 1,2,3,4,5,6,7,8,9,10

Here is the total number of elements in the list is even.

And the two middlemost elements are 5 and 6.

The required median is: 5+6 /2 = 11/2 = 5.5

Hence, the required median of the first ten natural numbers is 5.5.

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The list of the first 10 natural numbers is: 1,2,3,4,5,6,7,8,9,10

the total number of elements in the list is even.

the two middlemost elements are 5 and 6.

The required median is: 5+6 /2 = 11/2 = 5.5

the required median of the first ten natural numbers is 5.5.

Answer:

The given statement is true. Reason: Area of a square = side × side Therefore, two squares that have the same area will have sides of the same lengths.

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Step-by-step explanation:

The domain of the function y = 3x+1 is the set of all real values

From the question, we have the following parameters that can be used in our computation:

Function: y = 3x + 1

The above function is a linear function

A linear function can take any real number as its input

This means that the domain of the function contains all real values

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A system of inequalities can be solved by subtracting, adding, multiplying, or dividing both sides of the inequalities until a single variable is left on its own.

In Mathematics, an inequality can be defined as a mathematical relation that is typically used for comparing two (2) or more numerical data and variables in an algebraic equation based on any of the following inequality symbols:

For instance, the following inequality can be solved as follows;

0.75 < -1.5n

0.75 + 1.5n < 0

1.5n < -0.75

Next, we would divide both sides of the inequality by 1.5 as follows:

n < -0.75/1.5

n < -0.5

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The method to use when proving triangle congruence depends on the information given about the triangles.

Triangle congruence is a doctrine of mathematics which states that two triangles are congruent when all the corresponding sides and angles of both triangles have the same measure. This means that the two triangles are of the same size and shape, and each of their sides and angles correspond to each other in terms of size and measure. Triangle congruence is an important theorem in geometry, and is often used for solving various problems in mathematics.

If two triangles have three pairs of corresponding congruent sides, then the Side-Side-Side (SSS) method can be used. If two triangles have two pairs of corresponding congruent angles and a pair of corresponding congruent sides, then the Angle-Side-Angle (ASA) method can be used. If two triangles have two pairs of corresponding congruent sides and a pair of corresponding congruent angles, then the Side-Angle-Side (SAS) method can be used. If two triangles have three pairs of corresponding congruent angles, then the Angle-Angle-Side (AAS) method can be used.

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The value of x is 2 and y is -7/2 in the equations 2y = x + 9 and 2y − 11 = 2x.

The elimination approach involves taking one variable out of the system of linear equations by utilizing addition or subtraction together with multiplication or division of the variable coefficients. Because it allows us to remove one of the variables and solve a more straightforward equation. The elimination approach may also be referred to as the addition method or the linear combination method in some texts. This is due to the fact that we'll be adding two equations together.

Given,

Equations,

2y = x + 9

2y − 11 = 2x

Rearranging variables and constant

Using elimination method,

x - 2y = 9

2x - 2y = 11

-----------------

x = 2

Equating x = 2 in equation 1

x - 2y = 9

-2y = 9 - 2

-2y = 7

y = -7/2

The value of x is 2 and y is -7/2 in the equations 2y = x + 9 and 2y − 11 = 2x.

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The negative infinity, which is smaller than any real number, is the idea of infinity. For the representation of negative infinity, use the sign "-∞".

Given that,

We have to find what is negative infinity.

We know that,

The negative infinity, which is smaller than any real number, is the idea of infinity. For the representation of negative infinity, use the sign "-∞".

Look closely at this representation of infinity: opposite-pointing zip lines that travel along positive and negative infinity. To get closer to negative infinity on the zip line, they must turn left. On a number line, numbers move closer to positive infinity as they advance to the left and negative infinity as they move to the right. Positive infinity is always larger than any number, while negative infinity is always smaller.

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The first Quartile of the given set of data is 13.5.

The value that splits a list of integers into quarters can be calculated with the help of the quartile formula. The information is separated into quartiles after being initially organized in ascending order. While quartiles divide data into four equal halves, the median divides it into two equal portions.

A set of observations can be divided into four equal halves using the quartile formula. Between the first term and the median is where the first quartile is located.

The quartiles are shown when the set of observations is organized in ascending order.

First Quartile (Q1) = ((n + 1)/4)thTerm

Given observations are

15, 18, 10, 20, 23, 28, 12,16

To find the First Quartile/Lower Quartile.

Arrange the given numbers in ascending order.

10, 12, 15, 16, 18, 20, 23, 28                                                        

Here there are 8 numbers

median is the = 4th term+5th term / 2 = 16+18/2 = 17

the median of the numbers below the median of the whole data set, 17. These numbers are 10,12,15,16. Since there are also an even number of numbers in this data set, the median is the average of its two middle numbers (12+15)÷2 = 27÷2 or 13.5.

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(1) 6/36

(2) 30/36

There are six possible outcomes. The probability of obtaining any side/number is 1/6,

Then for 2 dies it’s 2/36

Total possible outcomes=total numbers of the first die (6)× total numbers of the second die(6)= 36

The outcomes of rolling two dice are below:

 1 2 3 4 5 6

1 (1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

2 (2, 1) (2, 2)(2, 3)(2, 4)(2, 5)(2, 6)

3 (3, 1) (3, 2)(3, 3)(3, 4)(3, 5)(3, 6)

4 (4, 1) (4, 2)(4, 3)(4, 4)(4, 5)(4, 6)

5 (5, 1) (5, 2)(5, 3)(5, 4)(5, 5)(5, 6)

6 (6, 1) (6, 2)(6, 3)(6, 4)(6, 5)(6, 6)

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If the length of segment ef is 8 units and the length of segment ed is 10 units. The length of segment fa is 6 units.

Using Pythagoreans theorem formula to find the length of segment

c² = √a² + b²

Where:

c = Length

a = 10 units

b = 8 units

Let plug in the formula

c² = √10² - 8²

c² = √100 - 64

c² =  √36

c = 6 units

Therefore we can conclude that the length is 6 units.

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Answer:

-14

Step-by-step explanation:

(a) The probability of obtaining two rods of the desired length is (100/200) * (99/199) = 0.495.

This can be found by using the formula for independent events:

P(A and B) = P(A) * P(B)

Since the two draws are of rods without replacement,

the probability of the first-rod being of the desired length = 100/200 (there are 100 desired-length rods out of a total of 200).

The probability of the second-rod being of the desired length = 99/199 (since one of the desired length rods has already been drawn). Multiplying these two probabilities gives us the answer.

(b)The probability of obtaining exactly one rod of the desired length

=(100/200) * (100/199) + (100/200) * (100/199)

= 0.990.

This can be found by using the formula for the union of two events: P(A or B) = P(A) + P(B).

Since the two draws are rods without replacement, the first draw has a probability of 100/200 of being of the desired length (there are 100 desired-length rods out of a total of 200).

The probability of the second draw being of the desired length is 100/199 (since one of the desired length rods has already been drawn). Adding these two probabilities gives us the answer.

(c) The probability of obtaining none of the desired length is (50/200) * (50/199) = 0.015.

This can be found by using the formula for independent events

: P(A and B) = P(A) * P(B).

Since the two draws are of rods without replacement, the probability of the first-rod being of the undersized length is 50/200 (there are 50 undersized rods out of a total of 200).

The probability of the second-rod being of the undersized length is 50/199 (since one of the undersized rods has already been drawn). Multiplying these two probabilities gives us the answer.

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The solutions of the cubic equation x³ + 6x² + 11x + 6 = 0 will be -1, -2, and -3.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

The equation is given below.

x³ + 6x² + 11x + 6 = 0

Factorize the equation, then we have

x³ + 6x² + 11x + 6 = 0

x³ + x² + 5x² + 5x + 6x + 6 = 0

x²(x + 1) + 5x(x + 1) + 6(x + 1) = 0

(x + 1)(x² + 5x + 6) = 0

(x + 1)[x² + 3x + 2x + 6] = 0

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

x = -1, -2, -3

The solutions of the cubic equation x³ + 6x² + 11x + 6 = 0 will be -1, -2, and -3.

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The vertex of the graph of f(x) = |x + 8| - 3 is (-8, -3). It lies in the third quadrant.

Therefore the answer is (-8, -3).

Simplifying the given graph to the form f(x) = a|x - h| + k

f(x) = |x + 8| - 3

f(x) = 1 × |x + 8| - 3

where a = 1, h = -8, k = -3

So f(x) = |x + 8| - 3 is symmetrical about the line x = -8. At x = -8, y = -3.

Therefore, the vertex of the graph is (-8, -3).

--The question is incomplete, answering to the question --

"What is the vertex of the graph of f(x) = |x + 8| - 3?"

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The median of the set of numbers 18, 16, 12, and 14 is 15. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.

The median of a set of numbers is the value that is exactly in the middle of the set when it is ordered from least to greatest. In this case, the set of numbers is 18, 16, 12, and 14. When we order this set from least to greatest, we get 12, 14, 16, and 18. There are four numbers in this set, so the median is the average of the two middle numbers. The two middle numbers in this set are 14 and 16, so the median is (14 + 16) / 2 = 15.

To find the median, we first need to arrange the numbers in order from least to greatest. If there is an odd number of numbers in the set, the median is the middle number. If there is an even number of numbers in the set, the median is the average of the two middle numbers. In this case, there are four numbers in the set, so the median is the average of the two middle numbers.

In summary, the median of the set of numbers 18, 16, 12, and 14 is 15. This is the average of the two middle numbers in the ordered set, and it is not affected by extreme values or outliers.

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If a new doughnut shop lost $624 during its first 13 days of business. If it lost the same amount of money each day, the loss each day is: A. (−624)÷13=−48; The doughnut shop lost $48 each day.

Given data:

Amount lost = $624

Days of business = 13 days

Now let determine the amount that the doughnut shop lost per day

Loss per day = Amount lost / Days of business

Loss per day  = - $624/13 days

Loss per day  = -$48

Therefore we can conclude that the correct option is A

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Answer:

x=-³√4-1

Step-by-step explanation:

x³+3x²+3x+5=0

(x+1)³+4=0

(x-1)³=-4

x+1=-³√4

x=-³√4-1

The mean absolute deviation (MAD) is a measure of forecast accuracy that is used to detect random factors in a data set. It is calculated by taking the mean of the absolute differences between the actual values and the forecast values.

The MAD can be used to eliminate forecast errors by identifying and removing random factors that are causing the errors. It is not typically used to estimate the trend line or measure forecast accuracy. Mean absolute deviation (MAD) is a measure of the variability or dispersion of a data set. It is calculated by taking the mean of the absolute differences between the individual values in the data set and the mean of the data set.

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The definite integral for this function is given as follows:

[tex]\int_{0}^{6} f(x) dx = 18[/tex]

The definite integral represents the area of the function in the interval composed by the bounds of the definite integral.

This means that the definite integral in this problem can be found merely obtaining the area of the function.

The function is composed as follows:

Hence the area of the figure is given as follows:

A = 2 x 2² + 2 x 5 = 8 + 10 = 18 units.

Which is the result of the definite integral.

The figure is given by the image shown at the end of the answer.

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Two months would pass before they received the same sum of money.

In mathematics, equivalence is a relationship that states that two quantities have the same value or that two mathematical expressions reflect the same mathematical object. A = B is the symbol for the equality of A and B, and it is also pronounced as A = B.

Total amount saved = amount started with + (amount deposited per month x number of months)

Amount saved by Tonya = $60 + $20m

Amount saved by Jull = $20 + $40m

The two aforementioned equations would be equivalent if they both saved the same amount of money:

60 + 20m = 20 + 40m

Take the below actions to find the value of m:

60 - 20 = 40m - 20m

40 = 20m

m = 40 / 20

m = 2

In the calculation that shows how much money Tonya has overall saved, replace m with:

$60 + $20(2)

$60 + $40 = $100

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When a transversal cuts two parallel lines, 8 angles are created.

When two lines do not cross one another, they are said to be parallel. In addition, parallel lines are two lines that cross each other at infinity.

A transversal line is one that crosses two other lines at two different locations. Line l meets a and b in the image below at two different locations, P and Q. Line l is the transversal line as a result.

Corresponding angles are those that are created when two parallel lines and a transversal intersect, also known as matching corners or corresponding corners.

∠1 and ∠6

∠4 and ∠8

∠2 and ∠5

∠3 and ∠7

When a transversal connects two coplanar lines, alternate interior angles are created.

∠4 and ∠5

∠3 and ∠6

However, each pair of alternate interior angles is equal if a transversal meets two parallel lines.

∠4 = ∠5

∠3 = ∠6

The pair of angles that are created on the outer side of two lines but on the other side of the transversal are known as alternate exterior angles.

Consecutive interior angles, related angles, and co-interior angles are other names for interior angles that are on the same side of the transversal.

∠3 and ∠5

∠4 and ∠6

When a transversal cuts two parallel lines, 8 angles are created.

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∠1 and ∠6

∠4 and ∠8

∠2 and ∠5

∠3 and ∠7

When a transversal connects two coplanar lines, alternate interior angles are created.

∠4 and ∠5

∠3 and ∠6

However, each pair of alternate interior angles is equal if a transversal meets two parallel lines.

∠4 = ∠5

∠3 = ∠6

Consecutive interior angles, related angles, and co-interior angles are other names for interior angles that are on the same side of the transversal.

∠3 and ∠5

∠4 and ∠6

The equation that can be used  to find the amount, v, Festive Features normally charges for a vest is given as follows:

12(v - 6) = 132.

The normal price is obtained applying the proportions in this problem, considering the total amount paid and the number of items purchased.

The parameters are given as follows:

Then the equation used to find the standard price is presented as follows:

12(v - 6) = 132.

The missing sentence is:

Which equation can you use to find the amount, v, Festive Features normally charges for a vest?

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Answer:

2*|x-4|-6

Type it into desmos to see what the graph will look like

Answer:

  1282 miles

Step-by-step explanation:

You have a rectangle with sides 365 and 276 miles, and you want to know the perimeter. (This is an approximation of the state of Wyoming.)

The perimeter of a rectangle is the sum of its side lengths. The formula is ...

  P = 2(L +W)

  P = 2(365 +276) = 2(641)

  P = 1282

The perimeter of Wyoming is about 1282 miles.

A Simple sentence best describes sentence 7 (They rule the earthly world of men together)

This means that it consists of only one independent clause - meaning there is only one finite verb in the sentence. In this case, the verb rules.

A compound sentence has at least two independent clauses; a compound-complex sentence has at least two independent clauses plus at least one dependent clause; a dependent clause cannot exist on its own because it is just a fragment of a larger sentence, which is obviously not the case here.

Complete question:

Read the summary of the conclusion of “The World on Turtle’s Back.” [1] When the twins grew up, they continued to fight. [2] One day they decided to hold a contest to determine who was stronger. [3] Though they tried to defeat each other in many different ways, neither one could win. [4] On the last day, they fought with weapons. [5] Using a deer antler, the right-handed twin overpowered his brother, and he threw him off the edge of the Earth. [6] Today, the right-handed twin lives in the Sky-World, and the left-handed twin lives in the dark underworld. [7] They rule the earthly world of men together. Which best describes sentence 7? It is a compound sentence. It is a compound-complex sentence. It is a simple sentence. It is a dependent sentence.

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A Simple sentence best describes sentence 7 (They rule the earthly world of men together)

It only has one independent clause, which means there is only one finite verb in the sentence, according to this definition. This time, the verb is in charge.

A dependent clause cannot exist on its own because it is just a fragment of a larger statement, which is obviously not the case in this sentence. A dependent clause cannot exist on its own because it is just a fragment of a larger sentence, which is obviously not the case in this sentence.

Read the summary of the conclusion of “The World on Turtle’s Back.” [1] When the twins grew up, they continued to fight. [2] One day they decided to hold a contest to determine who was stronger. [3] Though they tried to defeat each other in many different ways, neither one could win. [4] On the last day, they fought with weapons. [5] Using a deer antler, the right-handed twin overpowered his brother, and he threw him off the edge of the Earth. [6] Today, the right-handed twin lives in the Sky-World, and the left-handed twin lives in the dark underworld. [7] They rule the earthly world of men together. Which best describes sentence 7? It is a compound sentence. It is a compound-complex sentence. It is a simple sentence. It is a dependent sentence.