The graph shows g(x) = x2 − 9x + 20. graph of parabola falling from the left, passing through 3 comma 2 to about 4 and one half comma negative one fourth, and rising to the right, passing through 6 comma 2 What are the x-intercepts of g(x)? (4.5, 0) and (5, 0) (0, 4.5) and (0, 5) (0, 5) and (0, 4) (5, 0) and (4, 0)

Answer:

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

Okay, just think of dilations as scaling the object bigger or smaller. You are just multiplying all points on the shape by a common scalar.

The only other thing is a negative dilation reflects the shape over the origin (which is quite intuitive cause you negate all the coordinates).

Now for question 1 your just trying to find the scale factor given an original point and a dilated point. Since all points are multiplied by the same factor,

(-3,6)x = (-4,8)

x=4/3

For the second question, just check points to see if all follow the same dilation scale factor. For our purposes it suffices to just check the each vertex.

(1,1) -> (2,2) so the scale factor must be 2

(1,4) -> (2,8) good

(5,1) -> (10,2) good

(5,4) -> (10,8) good

So, this transformation describes a dilation. The scale factor is 2.

Answer:

(gof)(x) = 14x + 1

Step-by-step explanation:

We can think of (gof)(x) as g(f(x)).  Writing it in this form shows that we must start with the inner function and work our way to the outer function.

Essentially, the input of the inner function yields an output and the output becomes the input of the outer function.

f(x) means that the input is x and since we're given no value for x (e.g. x = so and so), the output is the original function or 2x - 1

Now, this output becomes the input for g(x):

g(2x-1) = 7(2x - 1) + 8

14x -7 + 8

(gof)(x) = 14x + 1

Try going to the store and they should be surprisingly cheap.

Answer: here it is.

Step-by-step explanation:

Answer:

[tex]5 \frac{5}{9} \: {ft}^{2} [/tex]

Step-by-step explanation:

[tex]a \: (length) = 3 \frac{1}{3} \: ft[/tex]

[tex]b \: (width) = 1 \frac{2}{3} \: ft[/tex]

[tex]a \: (rectangle) = a \times b[/tex]

[tex]a = 3 \frac{1}{3} \times 1 \frac{2}{3} = \frac{10}{3} \times \frac{5}{3} = \frac{50}{9} = 5 \frac{5}{9} {ft}^{2} [/tex]

Answer:

1 solution

Step-by-step explanation:

Y = 4

Y = 4x - 1

Substitute value of Y here,

4 = 4x - 1

4 + 1 = 4x

5 = 4x

5/4 = x

1.25 = x

•°• The given equation can have only 1 solution, i.e, a linear equation with 1 variable gives only 1 solution.

______

hope this helps!

Answer:

Let's denote the length of the equal sides of the isosceles triangle by "x". Then the perimeter of the triangle can be expressed as:

Perimeter = 2x + 9

But we also know that the perimeter of the triangle is 25cm, so we can set these two expressions equal to each other and solve for x:

2x + 9 = 25

2x = 16

x = 8

Therefore, the length of each of the equal sides is 8cm. Now, we can use the formula for the area of a triangle:

Area = (base × height) / 2

Since the triangle is isosceles, we know that the height is also the perpendicular bisector of the base, dividing it into two equal parts of length 4.5cm each. Now we can find the height of the triangle using the Pythagorean theorem:

h² + 4.5² = 8²

h² + 20.25 = 64

h² = 43.75

h ≈ 6.61

Substituting these values into the formula for the area of the triangle, we get:

Area = (9 × 6.61) / 2

Area ≈ 29.76 cm²

Therefore, the area of the isosceles triangle is approximately 29.76 cm².

Answer:

Unfortunately, I cannot see the graph you are referring to since we are communicating through text. However, based on the information given, we can make some general observations.

We know that Natasha received a raise in her hourly rate of pay at some point during the year. Before the raise, she earned some initial hourly rate of pay. Let's call this initial rate of pay "x". Let's also assume that she worked for "h" hours before receiving the raise, and "k" hours after receiving the raise.

We can write an equation to represent the total amount of money she made this year:

Total amount of money = (initial hourly rate of pay x number of hours worked at the initial rate) + (new hourly rate of pay x number of hours worked at the new rate)

Using the variables we defined earlier, we can write:

Total amount of money = (x × h) + ((x + y) × k)

where y is the increase in her hourly rate of pay after the raise.

We also know that she earned a certain amount of money before the raise. Let's call this amount "M". This means that:

M = x × h

Solving for x, we get:

x = M/h

Substituting this expression for x into the first equation, we get:

Total amount of money = (M + yh) + ((M/h + y) × k)

We don't know the values of M, y, h, or k, so we cannot determine the initial hourly rate of pay x or the total amount of money Natasha made this year. However, we have set up an equation that can be used to solve for these values if we have more information.

If you know the coordinates for points between A and B, that you can use this method to determine the dimensions of the spot that is located (0, 1/3) between A and B.

A set of integers called coordinates are used to locate a spot or a shape in a two-dimensional plane. The x-coordinate as well as the y-coordinate are two integers that describe a point's location on a  [tex]2D[/tex] plane.

To find the coordinates of the point that is [tex]1/3[/tex] of the way from point A to point B. we can use the midpoint formula, which states that the coordinates of the midpoint of the line segment joining two points [tex](x1, y1)[/tex]and  [tex](x2, y2)[/tex] are:

[tex]((x1 + x2)/2, (y1 + y2)/2)[/tex]

In this case, let's assume that point A has coordinates (x1, y1) and point B has coordinates (x2, y2). Then the point that is 1/3 of the way from A to B has coordinates:

[tex]((2/3) × x1 + (1/3) × x2, (2/3) × y1 + (1/3) × y2)[/tex]

Therefore, So if you have the coordinates of points A and B, you can plug them into this formula to find the coordinates of the point 1/3 of the way from A to B.

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Answer:

2/3

Step-by-step explanation:

A six sided number cube :

Sample space = 1,2,3,4,5,6

Non composite numbers on a six sided number cube = 1,2,3,5

Probability of an event = required outcome / Total possible outcomes

Required outcome = number of non composite number = 4

Total possible outcomes = sample space = 6

P(not composite)= 4/6 = 2/3

Answer:

|x-5|=0

Step-by-step explanation:

That was easy.

The amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is calculated to be approximately 6.58 gallons.

What is unit rate?

A unit rate is the cost for only one of anything. This is expressed as a ratio with a denominator of 1. For instance, if you covered 70 yards in 10 seconds, you did so at an average speed of 7 yards per second. Although both of the ratios—70 yards in 10 seconds and 7 yards in one second—are rates, only the latter is a unit rate.

Assuming the unit rate of 1 gallon per 18.25 minutes, we can convert 2 hours to minutes by multiplying it by 60, which gives us 120 minutes.

So, in 120 minutes, the amount of liquid that can be processed at a unit rate of 1 gallon per 18.25 minutes would be:

(120 minutes) / (18.25 minutes/gallon) = 6.58 gallons

Therefore, the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes is found out to be  approximately 6.58 gallons.

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The complete question is :

What is the amount of liquid that can be processed in 2 hours at a unit rate of 1 gallon per 18.25 minutes?

The exponential equation represents a growth, and the rate of increase is 9%.

The general exponential equation is written as:

y = A*(1 + r)^x

Where A is the intial value, and r is the rate of growth or decay, depending of the sign of it (positive is growth, negative is decay).

Here we have:

y = 38*(1.09)^x

We can rewrite this as:

y = 38*(1 + 0.09)^x

So we can see that r is positive, thus, we have a growth, and the percentage rate of increase is 100% times r, or:

100%*0.09 = 9%

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Answer:

To calculate the surface area of an object, we need to know its shape. Please provide more information on the object's shape or context of the problem to calculate its surface area.

As a result, the line would not contain the point (5, 19). The right response is A. (5, 19).

A graph is characterized by a mathematical construct that connects a collection of points to express a specific function. It establishes a pairwise connection between the objects. The graph was made up of nodes (vertices) connected by edges (lines).

We can see that for any two points on a line, the difference between their y- and x-coordinates is always the same. Let's determine this difference for the ordered pairs provided:

(1, 7) - (0, 4) = (1 - 0, 7 - 4) = (1, 3)

(2, 10) - (1, 7) = (2 - 1, 10 - 7) = (1, 3)

As we can see, the difference between the x-coordinates and y-coordinates of any two consecutive points is the same, i.e. 3. Therefore, we can check which of the points given in the options has a difference of 3 between its x-coordinate and y-coordinate.

A. (5, 19): Difference = 19 - 5 = 14

B. (-1, 1): Difference = 1 - (-1) = 2

C. (-3, -5): Difference = -5 - (-3) = -2

D. (-7, -19): Difference = -19 - (-7) = -12

So, we see that option A has a difference of 14 between its x-coordinate and y-coordinate, which is not equal to 3. Therefore, the point (5, 19) would NOT be found on the line. The correct answer is A. (5, 19).

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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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Answer:

7/8 - 2/3 = 5/8 pint of water left in the bottle.

The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

What is a piecewise function ?

A piecewise function is a function that is defined by different equations on different parts of its domain. The graph of a piecewise function consists of several distinct parts, each corresponding to a different equation.

The graph shown is an example of a piecewise function. The function is defined using different equations on different intervals of the domain.

On the interval from negative infinity to negative 2, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

On the interval from negative 2 to 2, the function is defined by the equation y = -x. This means that the value of the function is equal to the negative of x on this interval.

On the interval from 2 to positive infinity, the function is defined by the equation y = 2. This means that the value of the function is always 2 on this interval, regardless of the value of x.

At the point x = -2, the function experiences a discontinuity, because the two equations that define it have different values at this point. The function is not differentiable at this point, because it does not have a well-defined tangent line.

The domain of the function is the set of all real numbers, because there are no restrictions on the values of x that are allowed.

Therefore, The range of the function is the set of all real numbers greater than or equal to -2, because the lowest possible value of the function is -2, which occurs at x = 2.

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The value of x does not exist.

What is Quadratic equation?

A quadratic equation is a second-degree polynomial equation in a single variable of the form ax^{2} + bx + c = 0, where a, b, and c are constants and x is the variable. The highest exponent of the variable in a quadratic equation is 2, and the equation can be written in standard form, where the coefficient of the squared term (a) is not equal to zero.

The given expression is:

5x² - √3x + 2

This is a quadratic expression in the variable x, which means that it can be written in the form of ax² + bx + c, where a, b, and c are constants. In this case, we have:

a = 5

b = -√3

c = 2

We can use the quadratic formula to find the roots of this expression:

x = [-b ± √(b² - 4ac)] / 2a

Now, putting the values of a, b, and c, we get:

x = [-(-√3) ± √((-√3)² - 4(5)(2))] / 2(5)

Now, Simplifying the expression under the square root, we get:

x = [√3 ± √(-71)] / 10

Since the expression under the square root is negative, there are no real roots to this equation. Therefore, the expression 5x² - √3x + 2 has no real solutions.

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Answer:

We can use the formula for continuous compound interest to find the balance in Joseph and Deb's savings account after 1 year:

A = Pe^(rt)

where A is the balance, P is the principal (initial deposit), e is the mathematical constant approximately equal to 2.71828, r is the annual interest rate as a decimal, and t is the time in years.

Substituting the given values, we get:

A = $600.00e^(0.05*1)

Using a calculator, we get:

A ≈ $632.57

Therefore, Joseph and Deb will have approximately $632.57 in their savings account after 1 year. They can spend up to this amount on their trip. Rounded to the nearest cent, the answer is $632.57.

Answer:

85 degrees.

Step-by-step explanation:

These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.

Answer:

I got 28

Step-by-step explanation:

use the formula k=y/x. 6/8=0.75

21/0.75=

Answer:

To find the domain of the function f(x) = (x-7)(x-1)/(x+3)(x-1), we need to consider the values of x that make the denominator zero since division by zero is undefined.

In this case, the denominator (x+3)(x-1) is zero when x = -3 and x = 1. Therefore, we need to exclude these values from the domain.

So, the domain of f(x) is all real numbers except x = -3 and x = 1.

In interval notation, we can write the domain as (-∞, -3) U (-3, 1) U (1, ∞).

The linear function can be written as:

f(x) = -x/3 + 17/3

A general linear function can be written as:

f(x) = ax + b

Where a is the slope, and b is the y-intercept.

If we know two points on the line (x₁, y₁) and (x₂, y₂), then the slope of the linear function is:

a= (y₂ - y₁)/(x₂ - x₁)

Here we know the pairs:

f(-4) = 7

f(5) = 4

So we have the points (-4, 7) and (5, 4), then the slope is:

a = (4 - 7)/(5 + 4) = -3/9 = -1/3

Then we can write:

f(x) = -x/3 + b

now we can use one of the given points, like f(5) = 4, replacing that there we will get:

4 = -5/3 + b

4 + 5/3 = b

12/3 + 5/3 = b

17/3 = b

So the function is:

f(x) = -x/3 + 17/3

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Answer:forgot the explanation

Step-by-step explanation: give me a equation to solve

The statements that are true regarding the diagram given are:

Angle sum property of triangle states that the sum of interior angles of a triangle is 180°.

We have in the diagram that in the diagram given, the statements that are all true are:

m∠3 + m∠4 = 180° (angles on a straight line)

m∠4 = m∠1 + m∠2 (external angle theorem)

m∠1 + m∠2 + m∠3 = 180° (triangle sum theorem).

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Answer:b

Step-by-step explanation:

trust it’s b

Answer:

130

Step-by-step explanation:

Answer: y=130  x=130

Step-by-step explanation:

Slope is zero and the y-intercept is (0,-5)

What is slope ?

In mathematics, slope is a measure of the steepness of a line. It is defined as the ratio of the vertical change (rise) between two points on the line to the horizontal change (run) between the same two points.

In other words, the slope of a line is the change in the y-coordinate divided by the change in the x-coordinate between any two points on the line. It can also be thought of as the rate at which the line rises or falls as it moves horizontally.

The formula for calculating slope is:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are two points on the line.

According to the question:
The equation Y = -5 is already in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.

Comparing the equation Y = -5 to y = mx + b, we can see that:

The slope, m, is 0, since there is no x-term in the equation.

The y-intercept, b, is -5, since that is the constant value in the equation.

Therefore, the correct answer is:

B. Slope is zero and the y-intercept is (0,-5)


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