Complete the equation describing how x and y are related.

X | Y
0 | -1
1 | -1.5
2 | -2
3 | -2.5
4 | -3
5 | -3.5

Y= [?]x + [?]

The parabola g(x) is reasonable because it can be derived of parabola f(x) by rigid transformations.

Parabolas are represented by second order polynomials in vertex form, whose definition is shown below:

y - k = C · (h - k)²

Where:

In this problem we must create the expression for the image of the parabola by means of rigid transformations, that is, transformations that change the parabola without changing Euclidean distances. Most common rigid transformations are listed below:

The procedure is summarized below:

Now we proceed to apply the rigid transformations in that order:

Step 1

y = f(x) → y = f(x - 3)

y = x² → y = (x - 3)²

Step 2

y = f(x - 3) → y - 2 = f(x - 3)

y = (x - 3)² → y - 2 = (x - 3)²

Step 3

y - 2 = f(x - 3) → y - 2 = - f(x - 3)

y - 2 = (x - 3)² → y - 2 = - (x - 3)²

Step 4

y - 2 = - f(x - 3) → y - 2 = - f[0.5 · (x - 3)]

y - 2 = - [0.5 · (x - 3)]²

Finally, we proceed to plot both parabolae by help of a graphing tool.

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Answer: When solving a system of equations, the following are possible outcomes:

Consistent and dependent: The system has infinitely many solutions, and the equations are dependent. This occurs when the equations represent the same line.

Consistent and independent: The system has a unique solution, and the equations are independent. This occurs when the equations represent two distinct lines that intersect at one point.

Inconsistent: The system has no solutions, and the equations do not have a point of intersection. This occurs when the equations represent parallel lines or lines that do not intersect.

Option A,B,C are possible outcomes.

A: Consistent and dependent: The system has infinitely many solutions, and the equations are dependent. This occurs when the equations represent the same line.

B: Consistent and independent: The system has a unique solution, and the equations are independent. This occurs when the equations represent two distinct lines that intersect at one point.

C: Inconsistent: The system has no solutions, and the equations do not have a point of intersection. This occurs when the equations represent parallel lines or lines that do not intersect.

Step-by-step explanation:

Answer:

Opposite Sides are perpendicular (only correct answer)

Step-by-step explanation:

Not every parallelogram has diagonals that are perp to each other (form right angles.

The polynomial 2q⁹ is monomial.A polynomial can have one or more terms, whereas a monomial, binomial, trinomial, and a trinomial all have one term each.

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Answer:

3f = 9

Step-by-step explanation:

[tex]3f + 1 = 10 \\ 3f = 10 - 1 \\ 3f = 9 \\ f = \frac{9}{3} \\ f = 3[/tex]

Answer:

[tex] \sf \: f = 3[/tex]

Step-by-step explanation:

Given equation,

→ 3f + 1 = 10

Now the value of f will be,

→ 3f + 1 = 10

→ 3f = 10 - 1

→ 3f = 9

→ f = 9 ÷ 3

→ [ f = 3 ]

Hence, the value of f is 3.

21 days it will take before both bloggers have the same number of followers

Two or more expressions with an Equal sign is called as Equation.

Given a blogger has 460 followers on his social media accounts, but is losing followers at a rate of 6 people per day based on his comments.

y=460-6d

Where d represents the number of days

Another blogger has 128 followers on her social media accounts and gains an average of 10 new followers per day.

y=128+10d

We need to find equation to find the number of days it will take before both bloggers have the same number of followers

460-6d=128+10d

Add 6d on both sides

460=128+16d

Subtract 128 on both sides

460-128=16d

332=16d

d=20.75=21

Hence, 21 days  it will take before both bloggers have the same number of followers

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Answer:

A, B, and D

Step-by-step explanation:

Substitute all the coordinates into the equation. (x, y)

3(-2) - (-7) = 1

-6 - (-7) = 1

1 = 1

3(-1) - (-4) =1

-3 - (-4) = 1

1 = 1

3(0) - (1) = 1

0 - (1) = 1

-1 does not equal 1

3(3) - (8) = 1

9 - (8) = 1

1 = 1

The unknown angle in the triangle is as follows:

A triangle is a polygon with three sides. The sum of angles in a triangle is 180 degrees.

An equilateral triangle is a triangle that has all it sides and angles equal to each other. Each angle of an equilateral triangle is 60 degrees.

An Isosceles triangle is a triangle that has two of it sides and angles equal to each other. The base angles of an isosceles triangle are equal and the two legs are equal.

Therefore, let's use these principle to find the ∠ABC.

∠DBC = 60 degrees

∠ABD = 180 - 64 - 64 = 180 - 128 = 52 degrees

Hence,

∠ABC = 52 + 60 = 112 degrees.

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The inequality that represents the greatest number of rides that Daniel can go is 1.50x + 10 ≤ 40

From the question we would have the inequality that would be written as

1.50x + 10 ≤ 40

admission is 10 dollars

cost of rides is 1.50 dollars

So, the equation would be -

1.50x + 10 ≤ 40

we are to solve for the value of x. Such that we would have

1.5x ≤ 40 - 10

1.5x ≤ 30

divide through by 1.5

x = 30 / 1.5

x = 20

Proof

Hence we would have

1.5 * 20 = 30 + 10 = 40

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The value of the expression as a fraction in its simplest form is 2/7.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

1 ÷ ( 5/2 x (2 x (1(3/5) - 2/5) - 1) )

Step 1:

Removing the parenthesis.

We will solve (1(3/5) - 2/5) first.

8/5 - 2/5 = 6/5

1 ÷ ( 5/2 x (2 x 6/5 - 1) )

Step 2:

Solve this (2 x 6/5 - 1)

12/5 - 1 = 7/5

1 ÷ ( 5/2 x 7/5)

Step 3:

Solve (5/2 x 7/5)

5/2 x 7/5 = 7/2

1 ÷ 7/2

Step 4:

1 ÷ 7/2

= 1 x 2/7

= 2/7

Thus,

The value of the expression is 2/7.

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After 11 months, Derek would have $89 in his account

Derek has $82 in his account

The bank charges a service fee of $5.50 each month

For 6 months Derek deposits $11.25 in his account

Therefore the amount of money in his account after 11 months can be calculated as follows

82 + 11.25(6)

82 + 67.5

= 149.5

The service charge for the entire 11 months is

= 5.50(11)
= 60.5

The money in the account is

149.5-60.5

= 89

Hence Derek has $89 in his account after 11 months

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Katherine need to invest $432.4 for the value of the account to reach $960 in 16 years.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Katherine is going to invest in an account paying an interest rate of 5.8% compounded monthly.

We know that;

⇒ [tex]A = P e^r^t\\[/tex]

Let the invest amount = x

Here, The amount = $960

And, The time = 16 years

And, Rate = 5.8% = 0.058

So, We can formulate;

⇒ [tex]A = P e^r^t\\[/tex]

⇒ [tex]960 = P * e^{0.058 * 16} \\[/tex]

⇒ 960 = P × 2.22

⇒ P = 960 / 2.22

⇒ P = $432.43

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An unfair comparison between two numbers or other mathematical expressions is referred to as an inequality. It is most frequently used when comparing the sizes of two numbers on a number line. The attachment contains the graph for each inequality or equation.

A graph is a graphical representation of statistical data or the functional relationship of variables. Graphs can highlight broad trends in the quantitative behaviour of data, which is useful for forecasting. They can, however, be inaccurate and occasionally deceptive as mere approximations.

Most graphs have two axes: one for independent variables and one for dependent variables. A broken-line graph is the most common type of graph, with time serving as the independent variable.

16. 2y – 4x < 8

=  2y < 4x + 8

= y < 2x + 4

17. -4y > -x + 12

= y > x/4 + -3

18. | x + 3 |= y

y = | x + 3 |

19.  |2x – 6| + 2 = y

y = |2x – 6| + 2

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Answer:

The hourly charge is $4 per hour for the first 3 hours.

The rate then drops to $2 per hour until the end of the 6th hour.  

The hourly rate drops further to $1 per hour between the 6th and 10th  hours.

The maximum price of the bike rental is $30.

Step-by-step explanation:

The slope of the graph corresponds to the hourly rate for the bike rental.

During the first three hours of the bike rental, the price increases by $4 each hour.

Between the 3rd  and 6 th hours, the slope of the graph is 2, which means the hourly rate of the bike rental is $2 per hour.

Between the 6th and 10th hours, the rate is $1 per hour.

After the 10th  hour, the price, P, stops increasing. The maximum price of the bike rental is $30.

Answer: one hundred + fourteen point six hundred + seventy four

Step-by-step explanation:

Answer:

One hundred and fourteen point six seven four

Since , solution of percentage problem is Kayden has a collection of 120 coins, the number of coins that represent the 5% of his collection is 6.

A percentage is a way to express a number as a fraction of 100.To calculate percentage increase, subtract the original value from the new value and divide by the original value. To calculate percentage decrease, subtract the new value from the original value and divide by the original value.

Here,

As given by the question , the total number ko coins Kayden has in his collection is , 120 coins.

To know how many of his coins represent 5%, we can calculate ,

5% of 120 coins

=  5/100 * 12

= 6 coins

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Take the reciprocal of the second fraction, and Multiply it by the first fraction. later reduce the resultant fraction to its lowest terms.

The quotient of a fraction is the whole number that is obtained when we simplify the fraction. If the simplification of a fraction is not a whole number, the quotient is the decimal form of the fraction.

The quotient can also be the solution to a division problem involving two fractions. That division is a method of sharing equally and putting into equal groups. We divide a whole number by the divisor to get the quotient.

The reciprocal of a fraction is a simple way of interchanging the fraction's numerator and denominator.

Consider an example:

2 3/7=3 *2/7 =3 + 2/7

3 is the quotient

2 is the remainder

7 is the divisor

23 is the dividend

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The outcome or result of adding two or more integers is known as the SUM.

The outcome of adding numbers or quantities mathematically is a summation, often known as a sum. A summation always has an even number of terms in it. There may be just two terms, or there may be 100, 1000, or even a million. Some summations include an infinite number of terms.

the sum of two or more numbers, magnitudes, quantities, or specifics as determined by or as though decided by the addition process in mathematics.

The outcome of adding two or more numbers, objects, or things is referred to in mathematics as the sum.

The result or solution we obtain from adding two or more integers is known as the SUM. Addends are the figures that are combined.

[tex]Simplify $\frac{x}{x+3}+\frac{3}{x+3}+\frac{2}{x+3}: \frac{x+5}{x+3}$Steps$$\frac{x}{x+3}+\frac{3}{x+3}+\frac{2}{x+3}$$Apply the fraction rule: $\frac{a}{c}+\frac{b}{c}=\frac{a+b}{c}$$$=\frac{x+3+2}{x+3}$$Add the numbers: $3+2=5$$$=\frac{x+5}{x+3}$$[/tex]

Therefore, the correct answer is option b) [tex]$=\frac{x+5}{x+3}$[/tex]

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474 is the Annual percentage rate (APR).

What is APR in plain English?

If you have a balance on your credit card, you will pay an annual percentage rate (APR) of interest. The cost of borrowing money is what you pay in interest on a credit card. The interest rates on credit cards are often expressed as an annual rate. The yearly percentage rate is used to describe this (APR).

                     Certain credit cards feature variable APRs, which means that your rate may increase or decrease over time.

$331.16 * 24 + 775 - 7775 = 947.84

She over paid $ 947.84

24 months equals two years.

  947.84/2 = 473.92 ≈ 474

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The sum of the polynomials (4x^2+3x-1) + (x^2-5x-6) is 5x^2-2x-7

we will add the coefficients of the same degree terms.

(4x^2+3x-1) + (x^2-5x-6) = (4x^2+x^2) + (3x-5x) + (-1-6) = 5x^2-2x-7

Therefore, the sum of the polynomials (4x^2+3x-1) + (x^2-5x-6)  is 5x^2-2x-7

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Answer:

For 10% interest, you can multiply the original number by 1.1.

$50 x 1.1 = $55 after one year

$55 x 1.1 = $60.50 after two years

$60.50 - $50 = $10.50

In 2 years, Eva will earn $10.50 in interest.

As an example, consider 3x + 5 = 3x - 5. This equation has no solution. There is no value that will ever satisfy this type of equation.

What is  infinite solution?

Both sides of an infinite solution are equal. As an illustration, 6x + 2y - 8 = 12x + 4y - 16 Using a formula or method for infinite solutions, you can simplify the equation and make both sides to equal one another, making it an infinite solution. The concept of infinite connotes boundlessness or infinity. Typically, it is denoted by the symbol "".

What is an infinite number?

There are an unlimited number of numbers in a series. a collection of infinitely many natural integers, as an illustration. The initial value 0, and the initial value infinite, are represented by the logarithms and +, respectively.

                   The original values 0 and infinity are similarly treated when we consider both of the conceivable values and + as a single infinity.

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There are 22 event at an indoor track and field meet. The ratio of track event to field event is 8:3. Therefore, there are 16 track events.

Ratio:

In mathematics, ratios indicate the number of times one number contains another number. For example, if you have 8 oranges and 6 lemons in your fruit bowl, the ratio of oranges to lemons is 8 to 6 (that is, a ratio of 8:6, or 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to whole fruit is 8:14 (or 4:7).

Now,

If you want to know the number of events in track events, we can calculate it in two steps:

Divide 22 in the ratio 8:3.

First,

add the numbers = 8 + 3 =11

Second,

For 08, We Multiple and divide  = 8/11 × 22

                                                     = 16

Again,

For 03, We again multiple and Divide = 3/11 × 22

                                                              = 06.

Therefore, there are 16 track events.

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Answer: -1/4

Step-by-step explanation:

Answer: the answer to your question I believe is d= -1/4 = -0.25

The radius of the circle is 12.5 cm. So the option b is correct.

In the given question, the diameter of a circle is 25 cm.

We have to find the radius of the circle.

The radius of a circle is the distance a circle's centre from any point along its perimeter. Usually, "R" or "r" is used to indicate it. In almost all calculations containing spheres, this quantity is essential. In terms of radius, a circle's area and circumference are also calculated.

The distance from any circular object's centre to its outermost border or boundary is measured in terms of radius. A radius is a property of not only circles but also spheres, semi-spheres, cones with circular bases, and cylinders with circular bases.

The given diameter = 25 cm.

Now the radius = diameter/2

Radius = 25/2

Radius = 12.5 cm

So the option b is correct.

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Answer: y = 6x + 20, or E = 6t + 20

Step-by-step explanation:

Taking two points on the graph, (10, 80) and (30, 200), you can find the slope ("E") with the equation (y2-y1)/(x2-x1), which when plugged into the formula would be (200-80)/(30-10) = 120/20 = 6. To get your "t", you would plug this back into the formula y=mx+b along with any point on the graph, which would be:

80 = 6(10) + b

80 = 60 + b

b = 20

So the final equation should be y = 6x + 20

We can write an equation of a line in slope intercept form when given a graph of a line by using the equation y = mx + c.

There are various forms in which an equation is present. Based on the given equation or graph values, we can determine the form we should use. The line with m as the slope, m and c as the y-intercept is the graph of the linear equation y = mx + c. The values of m and c are real integers in the slope-intercept form of the linear equation.

The slope, m, is a measure of how steep a line is. Sometimes, the gradient of a line is referred to as its slope. A line's y-intercept, ab, denotes the y-coordinate of the location where the line's graph crosses the y-axis.

We first see the point where the line cuts the y-axis, then we calculate the slope of the line using the formula,

Slope= Δy/Δx

Once we get these values, we can substitute them in the equation for our final answer.

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As the value of 2 is 1.414, 6root 2 is 8.484, and 5 root2 is 7.071, the value of 6root 2 - 5 root2 is 1.413.

The square root or nth root is represented by the radical sign. Square roots are a component of root expressions. There is a radical's radicand—a number or word that appears. Radicals like 7 and 2y+1 serve as examples. Additional terms that describe radicals include: Radical equations are those equations that include radicals. A "root expression" is the phrase used to describe the expression contained within the square root. To demonstrate radical representations, consider the numbers 2, 372, 2x+7, and 41p. The phrase "root expression" refers to the expression contained within the square root. Examples of radical representations are the numbers 2, 372, 2x+7, and 41p.

given

6root 2 - 5 root2

√2 value is 1.414. therefore 6×1.414

= 8.484

5 root2

√2 value is 1.414. therefore 5 * 1.414

= 7.071

so  6root 2 - 5 root2 = 8.484 -  7.071

= 1.413

As the value of 2 is 1.414, 6root 2 is 8.484, and 5 root2 is 7.071, the value of 6root 2 - 5 root2 is 1.413.

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The equation -3(4x - 8) = 6x + 12 has infinitely many solutions.

An equation has infinitely many solutions when the equation is true for all possible values of the variable. One way to identify that an equation has infinitely many solutions is to see if the equation is true when the variable is replaced by any value.

A system of equations is a set of two or more equations that involve the same variables. The goal is to find the values of the variables that satisfy all of the equations in the system. There are different methods to solve a system of equations, depending on the type of equations and the number of variables involved.

The equation that has infinitely many solutions is:

B. -3(4x - 8) = 6x + 12

To see this, we can simplify the equation to:

-12x + 24 = 6x + 12

-12x = 12

x = -1

Now, if we put x = -1 in the equation, we see that it is true. If we put x = -2, x=0, x = 1, x = 3 and so on, we can see that the equation is true for all values of x.

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