Use the graph of the function to find the domain and range of f (Enter your answers using interval notation)

[tex]\huge\text{Hey there!}}[/tex]

[tex]\mathsf{x^2 - 4x = 0}[/tex]

[tex]\text{Factor the LEFT side of your given equation to make it easier to solve}[/tex]

[tex]\mathsf{x(x - 4) = 0}[/tex]

[tex]\text{Set the factors to equal to the number 0}[/tex]

[tex]\mathsf{x - 4 = 0\ \& \ x = 0}[/tex]

[tex]\text{Simplify find and you should be able to have your answer to the given equation}[/tex]

[tex]\mathsf{x = 4 \ \& \ x = 0}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = 4\ or \ x = 0}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

[tex]y=0[/tex]

Step-by-step explanation:

[tex]y+25=25 \\ \\ y=25-25 \\ \\ y=0[/tex]

Answer:

[tex] \sf \: y = 0[/tex]

Step-by-step explanation:

Given equation,

→ y + 25 = 625 ÷ 25

Now the value of y will be,

→ y + 25 = 625 ÷ 25

→ y + 25 = 25

→ y = 25 - 25

→ [ y = 0 ]

Hence, the value of y is 0.

Use synthetic division to divide (3x2 + 7x - 18) by (x - 3).The result of the division is (3x + 5)/(x - 3).

The first step is to write out the dividend and the divisor, and put a 0 in the box below the dividend.

3x2  +7x  -18

x - 3   0

The next step is to divide the divisor into the first term of the dividend.

3x2  +7x  -18

x - 3   0

3  -9

Next, we multiply the divisor by the result from the previous step and subtract it from the second term of the dividend.

3x2  +7x  -18

x - 3   0

3  -9  5

Next, we multiply the divisor by the result from the previous step and subtract it from the third term of the dividend.

3x2  +7x  -18

x - 3   0

3  -9  5  -15

Finally, we divide the last result by the divisor.

3x2  +7x  -18

x - 3   0

3  -9  5  -15  3

The result of the division by synthetic division is (3x + 5)/(x - 3).

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A semi-circular protractor with a diameter of 15 cm has the perimeter of 38.5 cm.

What is the perimeter?

The complete length of a shape's boundary is referred to as the perimeter in geometry. A shape's perimeter is calculated by adding the lengths of all of its sides and edges. Its dimensions are expressed in linear units like centimetres, metres, inches, and feet.

The formula for perimeter of a semi-circle is -

πr+2r

Where r is the radius of the semi-circle.

The diameter d of semi-circle is 15 cm.

The radius of the semi-circle is -

r=d/2

r=15/2

r=7.5 cm

Plugging the values in the equation -

=πr+2r

=(3.14)(7.5)+2(7.5)

=23.5+15

=38.5 cm

Therefore, the value for perimeter is obtained as 38.5 cm.

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Answer:e5

Step-by-step explanation:

Here you go

Answer: 110% of 120 minutes is equal to 132 minutes.

Step-by-step explanation:

To calculate percentiles:

f(n) = 56 + 3(n − 1) is the correct option represents the formula for the sequence.

In arithmetic sequences, each term is made larger by the addition or removal of a constant called k. Unlike a geometric sequence, where each term increases by being multiplied by or divided by a fixed constant k,

If there is a consistent difference between the words in a sequence of numbers, the sequence is referred to as an arithmetic progression. Think about the mathematical progression where the numbers 5, 7, 9, 11, 13, and so on all have a common difference of 2.

An is defined as a1 + d(n - 1), where d is the average difference between terms in the series, and a1 is the first term.

Given data :

This is the formula of an arithmetic sequence.

f(n) =   a1 + d(n - 1)

An arithmetic sequence begins with 56, 59, 62, 65, 68,

=   = 56.

d = 59 - 56 = 3

so the formula is f(n) = 56 + 3(n − 1)

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Answer: 14 pieces.

Step-by-step explanation: 1 foot = 12 inches

12 feet of rope = 144 inches of rope

144 / 20 = 7.2 = 7 sections can be cut from each package.

The greatest number of pieces from 2 packages = 14 pieces

Answer

14 pieces

Step-by-step explanation:

First you need to convert the 24 feet into inches. Do this by multiplying 24 (feet) by 12 (inches) since 1 foot has 12 inches in it and you have 12 feet. This means he has 288 inches of rope. Then divide 288 by 20 since he wants to see how many 20 inch pieces he can cut. You should get 14.4 but since it asks for the greatest number of pieces you need to round it down to 14 since he wants full 20 inch pieces.

Answer:

x = -2/4 = -1/2

Step-by-step explanation:

The sum of 4 times a number and 5 is 3.

Let sum = +

times = *

is means =

a number = x

So, 4x + 5 = 3.  Then we solve it !

Subtract 5 to both sides to get 4x = - 2.

Next, we divide 4 to both sides to get x = -2/4 = -1/2

Answer:

The number is -8

Step-by-step explanation:

You can set up the question as (x/4)+5 = 3

x/4 = -2

x = -8

The expression that best represents the value of π is 37.68 / 12.

The circumference of a circle is the distance round the circle. The radius of a circle is the distance from the center of the circle to any point on the circumference.

The formula for circumference of a circle = 2πr

Where:

π = pi

r = radius

π = circumference / 2r

π = 37.68 / (2 x 6)

π = 37.68 / 12

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The value of  expression - a² - 2bc - |c| if a = -2, b = 3, and c = -3, is 11.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

Given:

- a² - 2bc - |c|, a = -2, b = 3, and c = -3,

Plug the values of a, b, and c as shown below,

- a² - 2bc - |c|  = -(-2)² - 2 × (3) × (-3) - |-3|

- a² - 2bc - |c|  = - 4 - 6 × (-3) - 3

- a² - 2bc - |c|  = -4 + 18 - 3

- a² - 2bc - |c|  = 18 - 7

- a² - 2bc - |c|  = 11

Thus, the value of the expression is 11.

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The correct answer is option A. For P= -1/2 0 1/2 1/2 0 -1/2 0 0 1 D= 0 4 0 0 0 4 -1 0 0. The matrix can be diagonalized using the eigenvectors.

To diagonalize the matrix, the eigenvectors must be found first. The eigenvectors can be found by solving the characteristic equation and finding the eigenvalues. The eigenvalues of the matrix are 2 and -1. The eigenvectors associated with each eigenvalue are determined by solving the eigenvalue equation.

The eigenvectors for the matrix are [1, -2], [1, 2], [1, 0], and [0, 1]. After the eigenvectors are found, the matrix can be diagonalized by constructing the transformation matrix P. The transformation matrix P is composed of the normalized eigenvectors. The transformation matrix P is: P=[-1/2, 0, 1/2, 1/2, 0, -1/2, 0, 0, 1], and the diagonal matrix D is composed of the eigenvalues.

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Answer:

[tex]80^{\circ}[/tex]

Step-by-Step Explanation:

The interior angles of the triangle are [tex]70^{\circ}, (14+6x)^{\circ}[/tex], and [tex](3x-3)^{\circ}[/tex].

Angles in a triangle add to [tex]180^{\circ}[/tex].

[tex]70+14+6x+3x-3=180 \\ \\ 81+9x=180 \\ \\ 9x=99 \\ \\ x=11[/tex]

So, [tex]m\angle A=14+6(11)=80^{\circ}[/tex].

The greatest possible quotient of any two distinct members of the set; { 2 / 5, 1 / 2, 5, 10 } as required to be determined is; 25.

It is evident from the task content that the set from which the two numbers whose quotient is to be maximised is; { 2 / 5, 1 / 2, 5, 10 }.

On this note, since the quotient which is to be maximised is hypothetically; x / y;

Therefore, in a bid to maximize the result of the quotient; it follows that the numerator, x must be as great as possible and the denominator, y must be as less as possible.

On this note, since the maximum number in the set is 10 and the minimum is 2 / 5; we have that;

10 / (2 / 5)

= ( 10 × 5 ) / 2

= 25.

Ultimately, it can be inferred that the greatest possible quotient as required is; 25.

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Answer:

[tex]\{x|x\in \mathbb{Z}, 7 < x < 50\}[/tex]

Step-by-step explanation:

Basically, the above answer tells us that the set of all x such that x belongs to Z, the set of integers, and x is between 7 and 50.

Answer: Maisie walked 6.4 miles.

Step-by-step explanation:

Since Maisie is walking at a constant pace of 1.6 miles per hour we can set up the following equation:

y = 1.6(x)

In this equation, Y is the number of miles Maisie walked in total and X is the number of hours she walked. All we have to do is plug in 4 hours as x and solve.

y = 1.6(4)

y = 6.4 miles.

When two figures have the same shape but differ in size, they are said to be similar figures. In other words, two figures are said to be comparable when they have many characteristics but aren't necessarily identical.

For instance, despite appearing to be the same size, the sun and moon are actually different sizes. However, because both of our figures are circular in shape, we are comparable figures. This phenomenon is seen as a resemblance property while taking shape and distance into consideration.

When two shapes, such triangles, polygons, or quadrilaterals, have the same dimension or common ratio but a different size or length, they are referred to as comparable figures in geometry.

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Answer:

The union of the intervals is (0,8]

The intersection of the intervals is [1,5]

Hope this helped!

Each child's real height falls between 1.60 and 1.28, with the tallest child's height difference at 0.32 and the smallest child's height difference at 0.04 respectively.

a) The ranges that each child's actual height falls within is ;

Here, Daisy is 1.28 meters short while Isaac is 1.56 meters tall at his tallest.

b) The largest height difference between the tallest and shortest child is 1.60-1.28 =0.32m , while the smallest height difference is 1.60-1.56 = 0.04meters.

A number's possible range of values before being rounded or truncated is known as an error interval. Inequalities are frequently used to express error intervals as a range having a lower bound and an upper bound.

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The cuboidal tank has a volume of [tex]6m^3[/tex] with dimensions of 4 m in length, 2 m in width, and 0.75 m in height.

The total amount of room or volume that a cuboidal tank can hold is known as its capacity. By multiplying the tank's length, width, and height collectively, it is determined.

The tank in this instance measures 4 metres long, 2 metres wide, and 0.75 metres high. We must multiply these three parameters collectively to determine the tank's capacity:

[tex]4m * 2m * 0.75m = 6m^3[/tex]

The tank can therefore hold [tex]6m^3[/tex] of liquid.

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Solutions refers to the answer to the problem, Real Solutions are realistic and practical whereas ideal solutions are the best cases for the solutions.

In mathematics, a solution refers to a value or set of values that satisfies a given equation, system of equations, or problem. For example, if the equation is x + 2 = 4, then the solution is x = 2, because substituting 2 for x in the equation makes it true. In the case of systems of equations or more complex problems, a solution may be a set of values that satisfies all the equations or conditions of the problem. In such case, the solution may be represented graphically or as coordinates of a point.

In mathematics, an ideal solution refers to a solution that meets all the desired criteria or requirements without any constraints. It is the "best case" scenario. A real solution, on the other hand, refers to a solution that takes into account all the limitations and constraints of a problem. It is a more practical and realistic solution.

Ideal Solutions - Best cases, Usually not possible.

Real Solutions - Practical and possible to attain.

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Natha can chew between 9 to 10 chewing gum each day so that it could last for 6 days.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, Nathan had 58 pieces of gum that he wants to make last six days.

Therefore, The number of chewing gums he can chew is the total number of chewing gums he has divided by the total number of days which is,

= (58/6).

= 9.66 chewing gums but it should be a whole number.

So, Nathan can chew between 9 to 10 chewing gums each day.

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The three sides of a triangle are referred to as the base, the height, and the hypotenuse.

The base and height of a triangle can be used to calculate the area of the triangle using the formula:

Area = (Base x Height) / 2

To calculate the hypotenuse of a triangle, the Pythagorean Theorem is used. The theorem states that the sum of the squares of the lengths of the two sides of a right triangle is equal to the square of the length of the hypotenuse.

The formula for the Pythagorean Theorem is:

a2 + b2 = c2

where a and b are the two sides of the triangle and c is the hypotenuse.

To calculate the hypotenuse of a triangle, the following steps are taken:

1. Measure the length of each side of the triangle.

2. Square the length of each side (multiply the length by itself).

3. Add the two values together.

4. Find the square root of the sum. This is the length of the hypotenuse.

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Answer:

35/20 and 36/20

Step-by-step explanation:

Answer:   The mystery number is 5.5

5.5 converts to the fraction 11/2.

=================================================

Explanation:

The phrasing "subtract 10 from the number, then square the result" leads to the expression [tex](\text{x}-10)^2[/tex]

The phrasing "Square the number, then subtract 10 from the result" means we have [tex]\text{x}^2-10[/tex]

Set those expressions equal to one another so we can solve for x like shown in the steps below.

[tex](\text{x}-10)^2 = \text{x}^2-10\\\\\text{x}^2-20\text{x}+100 = \text{x}^2-10\\\\-20\text{x}+100 = -10\\\\-20\text{x} = -10-100\\\\\text{x} = -110/(-20)\\\\\text{x}=11/2\\\\\text{x} = 5.5[/tex]

The x^2 terms cancel out in the third step (since we subtract x^2 from both sides).

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

Check:

[tex](\text{x}-10)^2 = \text{x}^2-10\\\\(5.5-10)^2 = (5.5)^2-10\\\\(-4.5)^2 = (5.5)^2-10\\\\20.25 = 30.25-10\\\\20.25 = 20.25[/tex]

The answer is confirmed.

All points in Quadrant IV have a positive x-coordinate and a negative y-coordinate.

The fourth quadrant, indicated as Quadrant IV, is in the bottom right quadrant. The x-axis in this quadrant has positive values, whereas the y-axis has negative numbers.

A two-dimensional Cartesian system's axes split the plane into four infinite areas called quadrants, each of which is limited by two half-axes. These are frequently numbered from first to fourth.

A quarter of a circle; a 90° arc. the region enclosed by an arc and two radii are drawn one to each extreme. As a mechanical component, anything is shaped like a quarter of a circle.

All Quadrant I points have two positive coordinates.

Quadrant II points all have a negative x-coordinate and a positive y-coordinate.

All Quadrant III locations have two negative coordinates.

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Marina's pension amount is calculated by multiplying 1.6% of her average salary for the last 5 years by the number of years she has worked, which is 30.

1.6% x $80,900 = $1,282.40

1.6% x $90,200 = $1,444.32

1.6% x $95,000 = $1,520.00

1.6% x $99,000 = $1,584.00

1.6% x $104,000 = $1,664.00

Total = $7,604.72

Pension amount = $7,604.72 x 30 years

= $228,141.60

Marina's pension amount is determined using a formula set by her employer, the Washington Performing Arts Center. This formula takes into account her average salary for the last five years, which is $469,100, and multiplies it by 1.6%, then by the number of years she has worked for the Center, which is 30. This results in a pension amount of $228,141.60. This amount will be paid each year until her death. This pension amount is calculated based on the salaries she has earned over the past five years, which include $80,900; $90,200; $95,000; $99,000; and $104,000.

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Answer:

3

Step-by-step explanation:

[tex]\displaystyle \frac{4}{7}*5\frac{1}{4}=\frac{4}{7}*\frac{21}{4}=\frac{21}{7}=3[/tex]

Yes, the statement is true. If a proportional relation has the point (1, r), then r is the unit rate.

Here we have the following statement:

"The point (1, r) on the graph of a proportional relationship shows the unit rate r."

First, remember that a proportional relationship between two variables x and y can be written as:

y = k*x

There k is what we call the constant of proportionality or the unit rate.

If we evaluate that equation in x = 1, we will get:

y = k*1

y = k

Then we have the point (1, k).

In this case, we know that our proportional relation has the point (1, r), comparing this with the case above, we can see that r is the unit rate of the proportional relation.

So the statement is true.

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The system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a.

To determine if the system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a, we can use the elimination method.

We want to eliminate one of the variables, so let's start by multiplying the first equation by 3 and the second equation by -1.

This gives us:

3Ax + 9y = 3a, -3x - ay = -A.

Now we add the equations together to get:

2Ax + 8y = 3a - A.

Now we can see that the equation is not solvable as there is no value of a that will make the equation true. Therefore, the system of linear equations Ax + 3y = a, 3x + ay = A has no solutions for any value of a.

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