Which set of ordered pairs is made up of points on the graph of the function below?

y=-2x+8

A. (10,-1), (8,0), (1,6), (2,4)
B. (-1,10), (0,8), (1,6), (2,4)
C. (10,-1), (8,0), (6,1), (4,2)
D. (-1,10), (8,0), (1,6), (4,2)

1. ƒ is one-to-one and f(0) = 7, then f⁻¹(7) = 0 and (f(0))⁻¹ = 1/7. 2. A domain on which ƒ is one-to-one and non-decreasing is (4, ∞).

In mathematics, a function is a relation between two sets of elements, called the domain and the range, where each element in the domain is paired with a unique element in the range. The domain is the set of input values for the function, while the range is the set of output values.

A function is usually denoted by a symbol such as f, and is defined by a rule that assigns to each element in the domain a unique element in the range. This rule can be given in various forms, such as an algebraic expression, a graph, or a table of values.

For example, the function f(x) = 2x assigns to each input value x a unique output value that is twice the value of x. If we plug in x = 3, we get f(3) = 2(3) = 6, which means that 3 is mapped to 6 by the function f.

Question 1:

If ƒ is one-to-one and f(0) = 7, then f⁻¹(7) = 0 and (f(0))⁻¹ = 1/7.

Since ƒ is one-to-one, every element in the domain is mapped to a unique element in the range. This means that if f(0) = 7, then f⁻¹(7) = 0, which is the unique element in the domain that maps to 7.

Also, (f(0))⁻¹ = (7)⁻¹ = 1/7.

Therefore, f⁻¹(7) = 0 and (f(0))⁻¹ = 1/7.

Question 2:

Let f(x) = (x - 4)².

For f to be one-to-one and non-decreasing, the function must be strictly increasing or decreasing on its domain.

To find a domain on which ƒ is one-to-one and non-decreasing, we can take the derivative of ƒ and look at its sign:

f'(x) = 2(x - 4)

f'(x) is positive for x > 4, which means that ƒ is increasing on the interval (4, ∞).

Therefore, a domain on which ƒ is one-to-one and non-decreasing is (4, ∞).

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(x+2), (x+1), and (x-2) are factors of f(x) because they correspond to the roots of the polynomial.

What is Polynomial function ?

A polynomial function is a type of mathematical function that consists of a sum of terms, where each term is a product of a constant coefficient and one or more variables raised to non-negative integer powers. In other words, a polynomial function is an algebraic expression that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

Thank you for providing the graph of the polynomial f(x). Based on the graph, we can see that the polynomial has roots at x = -2, x = -1, x = 2, and x = 7. Therefore, (x+2), (x+1), and (x-2) are factors of f(x) because they correspond to the roots of the polynomial.

However, since there is no point on the graph where f(x) is equal to zero when x = -7, we can conclude that (-x+7) is NOT a factor of f(x).

Therefore, (x+2), (x+1), and (x-2) are factors of f(x) because they correspond to the roots of the polynomial.

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Answer:

Step-by-step explanation:

To calculate the company's debt ratio, we need to know its total liabilities and total assets. We can use the total assets turnover ratio to calculate the company's total assets:

Total assets turnover = Sales / Total Assets

1.04 = R6,500,000 / Total Assets

Total Assets = R6,500,000 / 1.04 = R6,250,000

Since the company is financed entirely with debt and common equity, its total liabilities are equal to its total debt. We can use the return on equity (ROE) formula to calculate the company's total equity:

ROE = Net Income / Total Equity

0.14 = R217,000 / Total Equity

Total Equity = R217,000 / 0.14 = R1,550,000

Now, we can calculate the company's debt ratio:

Debt Ratio = Total Debt / Total Assets

Debt Ratio = (Total Assets - Total Equity) / Total Assets

Debt Ratio = (R6,250,000 - R1,550,000) / R6,250,000

Debt Ratio = R4,700,000 / R6,250,000

Debt Ratio = 0.752 or 75.2%

Therefore, the company's debt ratio is 75.2%.

The average rate of change representing the state whose temperature is decreasing slower is given as follows:

-1.5ºF/day.

The average rate of change of a function is given by the change in the output of the function divided by the change in the input of the function. Hence we must identify the change in the output, the change in the input, and then divide then to obtain the average rate of change.

For Maine, in 9 days, the temperature fell by 13.5ºF, hence the rate is given as follows:

-13.5/9 = -1.5ºF/day.

For Connecticut, in 2.5 days, the temperature fell by 6.25ºF, hence the rate is given as follows:

-6.25/2.5 = -2.25 ºF/day.

A slower decline is in Maine, as it has a lower rate of change.

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Answer:

Step-by-step explanation: 1. is Yes 2 is no 3. is all 4 is Y and 50 5 is yes and -1

A triangle must have a third side that is bigger than the sum of any two of its sides. There cannot be a triangle with these side lengths because in this instance, 5 + 15 = 20 is not greater than 250.

To check whether the given lengths can form the sides of a right triangle, we need to check if they satisfy the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

Let's label the sides of the triangle as a, b, and c, where c is the hypotenuse. Then, the Pythagorean theorem can be written as:

a^2 + b^2 = c^2

Plugging in the given values, we get:

5^2 + 15^2 = (√250)^2

Simplifying the left-hand side, we get:

25 + 225 = 250

This is not true, since 25 + 225 = 250 does not hold. Therefore, the given lengths cannot form the sides of a right triangle.

In fact, we can see that the given lengths violate the triangle inequality, which states that the sum of any two sides of a triangle must be greater than the third side. In this case, 5 + 15 = 20 is not greater than √250, so a triangle with these side lengths cannot exist.

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The area of the shaded region under normal distribution is: 3.51

The standard normal distribution is defined as the normal distribution with a mean of 0 and a standard deviation of 1.

The z-table or the  standard normal table is one that provides the area under the standard normal curve to the left of a specified value, or "z-value". The value for the area is also the probability that the variable is less than the specified z-value.

To the right of -2.25 and to the left of -0.35

From standard normal table, we have the p-values as:

Area to the left of -0.35 = 0.3632

Area to the left of -2.25 = 0.0122

Area of the shaded region = 0.3632 - 0.0122 = 0.351

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Answer: To find the points where the two skaters might collide, we need to find the values of x and y that satisfy both equations:

y = -3x + 8

y = -2x^2 + 7x

We can set the two equations equal to each other and solve for x:

-3x + 8 = -2x^2 + 7x

This simplifies to:

2x^2 - 10x + 8 = 0

Dividing both sides by 2, we get:

x^2 - 5x + 4 = 0

Factoring the left side, we get:

(x - 1)(x - 4) = 0

So the solutions for x are x = 1 and x = 4.

To find the corresponding values of y, we can substitute these values of x into either equation. Let's use y = -3x + 8:

When x = 1, y = -3(1) + 8 = 5

When x = 4, y = -3(4) + 8 = -4

Therefore, the two skaters might collide at the points (1, 5) and (4, -4).

Step-by-step explanation:

Answer:

Step-by-step explanation:

The total mass of the alloy is the sum of the masses of the two metals:

mass = density x volume = (8800 kg/m³ x 15 m³) + 850 kg = 132,000 kg + 850 kg = 132,850 kg

The total volume of the alloy is the sum of the volumes of the two metals:

volume = 15 m³ + 6.2 m³ = 21.2 m³

Therefore, the density of the alloy is:

density = mass / volume = 132,850 kg / 21.2 m³ ≈ 6266 kg/m³

Rounding to the nearest integer, the density of the alloy is 6266 kg/m³.

Answer:

4906 that is the answer. also your welcome and sorry if I misunderstood the question

The Correct answer is  D) Most students read more often than they draw.as the median of the "read" plot is lower than the median of the "draw" plot.

Based on the box plots, we can see that:

The median for the "read" data is around 8 days per month, and the interquartile range (IQR) is between 4 and 12 days.

The median for the "draw" data is around 12 days per month, and the IQR is between 8 and 16 days.

So, we can conclude that:

A) Most students read less than 12 days a month. This is true, since the median for the "read" data is below 12 days per month, and the box plot shows that most of the data is concentrated in the lower half of the range.

B) Most students draw at least 12 days a month. This is not true, since the median for the "draw" data is around 12 days per month, and the box plot shows that there is a considerable amount of data below that median.

C) Most students draw more often than they read. This is not true, since the median for the "read" data is lower than the median for the "draw" data.

D) Most students read more often than they draw. This is true, since the median for the "read" data is lower than the median for the "draw" data, and the box plot shows that most of the "read" data is concentrated in the lower half of the range, while most of the "draw" data is concentrated in the upper half of the range.

The box plots below show data from a survey of students under 14 years old. They were asked on how many days in a month they read and draw. Based on the box plots, which is a true statement about students? pg780337 A Most students read less than 12 days a month. B Most students draw at least 12 days a month. C Most students draw more often than they read. D Most students read more often than they draw.

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The ship that can last forever for the given parallelogram is REHIFSDPI.

A unique variety of quadrilateral made up of parallel lines is called a parallelogram. A parallelogram can have any angle between its neighbouring sides, but it must have opposing sides that are parallel for it to be a parallelogram. If the opposing sides of a quadrilateral are parallel and congruent, it will be a parallelogram. Hence, a quadrilateral in which both sets of opposite sides are parallel and equal is referred to as a parallelogram.

The letter corresponding to each answer is:

1. congruent - R

2. parallelogram - E

3. pair - N

4. Bisect - H

5. sometimes - I

6. Sum of angles of parallelogram is 360, also opposite angles are equal, thus,

72 + 72 + 2x = 360

x = 108 - F

7. Sum of angles of parallelogram is 360, also opposite angles are equal, thus,

89 + 89 + x + x = 360

178 + 2x = 360

x= 91 - S

8. Diagonals of parallelogram bisect each other CO = 16. - D

9. Opposite sides of parallelogram are congruent thus,

4x + 2 = 5x - 3

x = 5 - P

10. Opposite sides are equal,

2x + 1 = x + 8

x = 7 - I

Hence, the ship that can last forever for the given parallelogram is REHIFSDPI.

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Answer:

To find the interest rate, we can use the formula for simple interest:

I = Prt

Where:

I = Interest earned

P = Principal (initial investment)

r = Interest rate

t = Time

We are given that P = $100, t = 3 years, and I = $15. Substituting these values, we get:

15 = 100 * r * 3

Solving for r, we get:

r = 15 / (100 * 3) = 0.05

Therefore, the interest rate on the savings account is 5%.

Fabric cost ($15 per yard) and curtain making and hanging ($250). x represents the total cost of the fabric and Mrs. Andretti can use the formula 15x to calculate the fabric cost and add the $250 fixed charge to get the total cost of the curtain. 

Cost computation helps in deciding on pricing, manufacturing output, and sales. It also helps in figuring out the costs of the products and services the company sells.

X does not represent the cost of fabric. X represents the number of yards of fabric used.

15x + 250

Could be read as ($15 × # of yards) + $250

She must therefore pay $15 per yard of cloth in addition to the $250 base cost of having them produced and hung.

She may indicate the price of fabric with an additional variable.

Example: Y

Y= 15x

Cost of fabric is equal to $15 per yard × # of yards.

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Answer:

Step-by-step explanation: To find (f+g)(x), we simply add the two functions:

(f+g)(x) = f(x) + g(x)

= (3x - 5) + (7x - 3)

= 10x - 8

Therefore, (f+g)(x) = 10x - 8.

To find (f-g)(x), we subtract g(x) from f(x):

(f-g)(x) = f(x) - g(x)

= (3x - 5) - (7x - 3)

= -4x - 8

Therefore, (f-g)(x) = -4x - 8.

Answer:

Step-by-step explanation:

An example of an expression with 4 terms where 3 of them are like terms is:

$5x^2 + 7x - 2x^2 + 3x$

To rewrite this expression by combining like terms, we add the coefficients of the terms with the same variables raised to the same power. In this case, the two terms with $x^2$ are like terms, so we can add their coefficients:

$5x^2 - 2x^2 + 7x + 3x = 3x^2 + 10x$

The resulting expression has 2 terms.

Answer:

Step-by-step explanation: it is -2x + 430298= -9n79000.

Answer:

The Gordon's should buy TV2

Step-by-step explanation:

To determine which TV the Gordons should buy, we need to compare the total cost of each TV over the 8-year period. Let's define some variables:

- Let x be the number of years the TV is used.

- Let y1 be the total cost of TV 1 over x years.

- Let y2 be the total cost of TV 2 over x years.

- Let P1 be the purchase price of TV 1.

- Let P2 be the purchase price of TV 2.

- Let O1 be the annual operating cost of TV 1.

- Let O2 be the annual operating cost of TV 2.

Using these variables, we can write the following equations:

y1 = P1 + x * O1

y2 = P2 + x * O2

To compare the total cost of each TV over 8 years, we need to find y1 and y2 when x = 8. Plugging in the given values, we get:

y1 = 330 + 8 * 14 = 462

y2 = 369 + 8 * 9 = 441

Therefore, the total cost of TV 1 over 8 years is $462, and the total cost of TV 2 over 8 years is $441. Since TV 2 has the lower total cost, the Gordons should buy TV 2.

From a mathematical standpoint, we can also use rational functions to analyze this problem. The total cost of each TV is a linear function of x, so we can write:

y1(x) = P1 + x * O1

y2(x) = P2 + x * O2

The ratio of these functions is:

y1(x) / y2(x) = (P1 + x * O1) / (P2 + x * O2)

To determine which TV is cheaper over 8 years, we need to compare the ratios when x = 8:

y1(8) / y2(8) = (330 + 8 * 14) / (369 + 8 * 9) ≈ 1.051

Since this ratio is greater than 1, TV 1 is more expensive than TV 2 over 8 years. Therefore, the Gordons should buy TV 2.

All four ratios are equal to 1/3, the scale factor of the dilation is 1/3

In mathematics, a scale factor is a ratio that describes how much larger or smaller an object or shape is in comparison to its original size. In particular, a scale factor is often used to describe the effect of dilation on an object.

Dilation is a transformation in which an object is enlarged or reduced uniformly in all directions from a fixed point known as the center of dilation. The scale factor for dilation is the ratio of the length of the image to the length of the pre-image.

For example, if a square has a side length of 4 units and is dilated by a factor of 2, the resulting image will have a side length of 8 units. In this case, the scale factor for dilation is 2.

More generally, if an object is dilated by a factor of k, then the length of any given segment in the image will be k times the length of the corresponding segment in the pre-image. Thus, the scale factor for dilation is simply k.

To find the scale factor of the dilation, we need to find the ratio of the corresponding side lengths of the trapezoid A'B'C'D' to the side lengths of trapezoid ABCD.

We can start by finding the length of each side of trapezoid ABCD:

AB = √[(9-(-3))² + (3-0)²] = √(144+9) = √153

BC = √[(9-9)² + (9-3)²] = 6

CD = √[(-3-9)² + (3-9)²] = √(144+36) = √180

DA = √[(-3-(-3))² + (3-0)²] = 3

Next, we can find the length of each corresponding side of trapezoid A'B'C'D':

A'B' = √[(3-(-1))² + (1-0)²] = √(16+1) = √17

B'C' = √[(3-3)² + (3-1)²] = 2

C'D' = √[(-1-3)² + (1-3)²] = √(16+4) = √20

D'A' = √[(-1-(-3))² + (1-0)²] = √4 = 2

Finally, we can find the ratio of the corresponding side lengths of the trapezoid A'B'C'D' to the side lengths of trapezoid ABCD by dividing the lengths of the corresponding sides:

[tex]\frac{A'B'}{AB} =\frac{\sqrt{17} }{153} \\\frac{B'C'}{BC} =\frac{2}{6}=\frac{1}{3} \\\frac{C'D'}{CD} =\frac{\sqrt{20} }{80} =\frac{\sqrt{45} }{445} =\frac{\sqrt{5} }{3\sqrt{5} } =\frac{1}{3} \sqrt{5} \\\frac{D'A'}{DA} =\frac{2}{3}[/tex]

Since all four ratios are equal to 1/3, the scale factor of the dilation is 1/3.

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The fraction in simplest form of 52.5% is 21/40.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator.

Decimals are the numbers, which consist of two parts namely, a whole number part and a fractional part separated by a decimal point.`

Steps to convert Decimal to Fraction:

52.5%

=> 525/10%

=> 525/10*100

=> 525/1000

=> 21/40

Therefore, The fraction in simplest form of 52.5% is 21/40.

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We may conclude after answering the presented question that None of the given quotient equations are true.

What is an equation?

A formula is a statement that two expressions are equal. An equation consists of two sides separated by an algebraic equation (=).  

For example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the number "9."

The purpose of equation solving is to determine the value or values of the variable(s) that will allow the equation to be true. Equations can be simple or complicated, regular or nonlinear, and include one or more elements.

[tex]x^2 + 2x - 3 = 0.[/tex] Lines are utilized in many different areas of mathematics, such as algebra, calculus, and geometry.

None of the given quotients are true.

A. 1/2 ÷ 2 = 1/4, not 4.

B. 1/3 ÷ 4 = 1/12, not 4/3.

C. 1/2 ÷ 6 = 1/12, not 1/6.

D. 1/5 ÷ 2 = 1/10, not 10.

E. 1/8 ÷ 3 = 1/24, not 1/3.

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Answer:

(-0.5, -0.5)

Step-by-step explanation:

d = √ (a - ax)2 + (b - bx)2

plug in

Answer:

%......

............….

Since the function is already in standard form (ax^2 + bx + c form) you don't have to change anything and simply rewrite it.

For the vertex, if you have a quadratic function in standard form -b/2a is the x value of the vertex.

-b/2a = -4/(2(2)) = -1

Since we now know the x-value of the vertex we can plug it into the function to find the corresponding y-value.

h(-1) = 2(-1)^2 + 4(-1) - 10 = -12

So, the vertex is at (-1,-12)

The values represents the linear function are:

x y

0 1

1 5

2 9

3 13

4 17

What is linear function ?

A linear function is a mathematical function that can be represented by a straight line on a graph. It has the form of:

y = mx + b

where m is the slope of the line, which determines how steeply the line rises or falls, and b is the y-intercept, which is the point where the line crosses the y-axis.

According to the question:
The table of values that represents the linear function y=4x+1 is:
x y

0 1

1 5

2 9

3 13

4 17
To generate these values, we can substitute different values of x into the equation y=4x+1 and solve for y.

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Q) which table of values represents the linear function y=4x+1 ?

One solution: (6,2)

Systems of equations are a set of equations that share variables.

Number of Solutions

There are multiple ways to find the number of solutions to a system of equations. Firstly, if 2 lines are parallel, then there will never be a point that satisfies both equations. This means that there will be no solutions. If 2 equations create the same line, then there will be infinitely solutions. Lastly, if there are 2 linear lines that are not parallel or the same, then they will have exactly one solution.

Solving Systems of Equation

The solution to a system of equations is the point that makes both equations true. When looking at a graph, the solution to a system of equations will be where the lines intersect. In this question, the lines intersect at (6,2). This means the solution to the system of equations is (6,2).

Answer:

7/36

Step-by-step explanation:

It is given that we have two dice numbered from 1 to 6 . The maximum sum that can be obtained by rolling two dice is 6+6 = 12 and the minimum sum that can be obtained by rolling is 1+1 = 2 .

Now between 2 and 12 , the numbers which are perfect square are 4 and 9 .

Getting a sum of 4 :-

We can get a sum of four from two dice as ,

Getting a sum of 9 :-

So there are a total of 7 possibilities by which we can can get a perfect square number by rolling two dices .

Now total number of possible outcomes = 6*6 = 36 .

Henceforth the required probability would be ,

[tex]\rm\implies P( getting \ a \ square\ number) =\dfrac{Total \ number\ of \ favourable\ outcomes}{Total \ number \ of \ possible \ outcomes} [/tex]

[tex]\rm\implies \underline{\underline{\red{ P( getting \ a \ square\ number)=\dfrac{7}{36}}}}[/tex]

Hence the required probability is 7/36 .

The probability of getting a square number as the sum is therefore 7/36.

WHAT IS PROBABILITY ?

Probability is a branch of mathematics that deals with the study of random events or phenomena. It involves analyzing the likelihood of an event occurring, given the conditions or circumstances that surround it. Probability is expressed as a number between 0 and 1, where 0 represents an impossible event and 1 represents a certain event. The probability of an event is determined by dividing the number of favorable outcomes by the total number of possible outcomes. Probability is widely used in many fields, including statistics, physics, finance, engineering, and social sciences, to name a few.

There are 36 possible outcomes when two dice are thrown since each die has 6 possible outcomes.

Let's find the possible outcomes where the sum of the numbers on the dice is a square number. The only possible sums that are squares are 4, 9 and 16.

To get a sum of 4, the dice must land on 1 and 3 or 3 and 1. There are two possible ways of doing this, so there are 2 outcomes.

To get a sum of 9, the dice must land on 3 and 6, 4 and 5, 5 and 4, or 6 and 3. There are four possible ways of doing this, so there are 4 outcomes.

To get a sum of 16, the dice must both land on 6. There is only one possible way of doing this, so there is 1 outcome.

Therefore, there are 2 + 4 + 1 = 7 outcomes where the sum of the numbers on the dice is a square number.

The probability of getting a square number as the sum is therefore 7/36.

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Answer:

1. is 10

2. is 4

3. is 2

?= is 2

Answer:

We can use the formula for the present value of an annuity:

PV = PMT x [(1 - (1 + r)^(-n)) / r]

where PV is the present value, PMT is the monthly payment, r is the monthly interest rate, and n is the number of payments.

Substituting the given values, we have:

PV = $31.48 x [(1 - (1 + 0.152/12)^(-18)) / (0.152/12)]

PV = $31.48 x [(1 - 0.5159) / 0.0127]

PV = $1,007.97

Therefore, the equivalent cash price of the iPod is $1,007.97.