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

For this question u have to assume value of either x or y

For example

to find the value of x

side calculation (7000/35 = 200)

let x = 200

then 35(200) +60y = 7000

7000 + 60y = 7000

60y = 7000-7000

so y = 0

so value of x should be greater than or equal to 200

x >(or equal to) 200

to find the value of y

side calculation ( 7000/60 = 116.67)

let y = 116.67

then 35x + 60(116.67) = 7000

35x + 7000 = 7000

35x = 7000-7000

35x=0

so x = 0

so the value of y should be greater than or equal to 116.67

y >( or equal to 116.67)

Answer:

74,779,038,221

Step-by-step explanation:

Answer:

Step-by-step explanation:

Given

[tex]5^3*7^5+9^8+0+0+0+0+0+0+9^7*5^6[/tex]

We can eliminate all the zeroes.

[tex]5^3*7^5+9^8+9^7*5^6[/tex]

Evaluate each term.

Raise 5 to the power of 3.

[tex]125*7^5+9^8+9^7*5^6[/tex]

Raise 7 to the power of 5.

[tex]125*16807+9^8+9^7*5^6[/tex]

Raise 9 to the power of 8.

[tex]125*16807+43046721+9^7*5^6[/tex]

Raise 9 to the power of 7.

[tex]125*16807+43046721+4782969*5^6[/tex]

Raise 5 to the power of 6.

[tex]125*16807+43046721+4782969*15625[/tex]

Multiply 125 by 16807.

[tex]2100875+43046721+4782969*15625[/tex]

Multiply 4782969 by 15625.

[tex]2100875+43046721+74733890625[/tex]

Add 2100875 and 43046721.

[tex]45147596+74733890625[/tex]

Add 45147596 and 74733890625.

[tex]74779038221[/tex]

A calculator would help but here you go.

The area of rectangle with side whole number = ab sq. units,

and area of rectangle with fraction side = ac/bd sq. units.

A quadrilateral with four right angles is a rectangle. It can alternatively be described as a parallelogram with a right angle or an equiangular quadrilateral, where equiangular denotes that all of its angles are equal (360°/4 = 90°). A square is a rectangle with four equally long sides.

Given  to find the area of rectangle,

Area of rectangle is given by product of length and width.

A = l x b

Let the dimensions of a rectangle are all whole numbers, a by b

Area = a x b

A = ab sq. units

another rectangle with dimensions all fractions say, a/b by c/d .

Area = a/b x c/d

A = ac/bd sq. units

In all situations, the area of the rectangle must be calculated by multiplying its length and breadth.

Hence the area of rectangle is product of length to width in both cases.

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Answer:

  It isn't.

  The correct relation is 4r·Area = abc.

Step-by-step explanation:

You want to show the relation between the product of triangle side lengths and the product of the triangle area and the radius of the circumcircle.

The area of the triangle in the attached diagram can be found by ...

  Area = 1/2(bc)sin(α)

The inscribed angle theorem tells you the measure of the arc subtended by an inscribed angle is twice the measure of the inscribed angle. That means the opposite chord will be twice the length of the product of the radius and the inscribed angle value:

  a = 2r·sin(α)

The product of the circumradius and the area of the triangle is ...

  r·Area = r·(1/2)(bc)sin(α) = 1/4(bc)(2r·sin(α)) = 1/4abc

Without the fractions, the relation is ...

  4r·Area = abc

__

Additional comment

As a simple example, consider a 3-4-5 right triangle. The area of the triangle is ...

  A = 1/2(3)(4) = 6

The circumradius is half the length of the hypotenuse, r = 5/2.

The relation of interest is ...

  4r·Area = abc

  4(5/2)(6) = 3·4·5

  60 = 60 . . . . . . . . . . as expected

This could be a very simple way to find the circumradius of a triangle.

Salesman C have a larger paycheck than both of the other salesmen in

None of the weeks.

In mathematics, multiplication is a method of finding the product of two or more numbers. It is one of the basic arithmetic operations, that we use in everyday life.

Here, we have,

Salesman A works  earns $65 per sale, with a maximum weekly commission of $1,300

Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale.

Salesman C does not earn any commission. His weekly salary is $900.  Now we have that, A is getting $1300 commission,

and, salary of C is $900, he has no commission.

i.e. C can't earn more than A

Hence, Salesman C have a larger paycheck than both of the other salesmen in None of the weeks.

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The solution is Option D.

The week 1 is when Salesman C have a larger paycheck than both of the other salesmen and is given by the equation C = $ 900

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the number of sales be represented as x

Let the maximum weekly salary of Salesman C be = $ 900

Now , the weekly salary of Salesman A = $ 65x

where x is the number of sales

And , the weekly salary of Salesman B = $ 300 + $ 40x

Now , on week 1,

Salesman A made 11 sales

Substitute the value of x = 11 in the equation , we get

So , the salary of Salesman A on week 1 = 65 ( 11 )

On simplifying the equation , we get

The salary of Salesman A on week 1 = $ 715

And , Salesman B made 14 sales

Substitute the value of x = 14 in the equation , we get

The salary of Salesman B on week 1 = 300 + 40 ( 14 )

On simplifying the equation , we get

The salary of Salesman B on week 1 = 300 + 560

The salary of Salesman B on week 1 = $ 860

So , Salary of Salesman C on week 1 > salary of Salesman B on week 1 > salary of Salesman A on week 1

And , $ 900 > $ 860 > $ 715

Hence , the solution to the equation is week 1

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The second row's third box AC = AC ( common side ) ( common side ) box last. Therefore, by applying the ABCD ASA congruence axiom.

Three sides, three angles, and three vertices make up the closed, two-dimensional shape of a triangle. Polygons include triangles. Triangle ABC is depicted in the above figure. Triangular polygons in geometry are those with three sides and three vertices. There are three straight sides to this two-dimensional figure. Three-sided polygons include triangles. A triangle's three angles add up to a full 180 degrees. A single plane contains the triangle. Triangulus, which means "three-cornered" or "having three angles," is a Latin word with roots in tri-, "three," and angulus, "angle or corner."

given

AB||DC , BC||AD

To show that

ΔABC≅ ΔCDA

First box

AB || DC (given )

below box to the first box

∠BAC = ∠DCA ( parallel lies cut by the transverse form congruent alternate interior angles )

Second box

BC||AD ( given )

Below box to the second box

∠DAC = ∠BCA ( parallel lies cut by the transversal form congruent alternate interior angles )

Third box in the second row

AC = AC ( common side )

Last box

So by using ASA congruence axiom

ΔABC ≅ΔCDA

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Answer:

912 cm²

Step-by-step explanation:

Formula for area of triangle: 1/2bh

So you'll first multiply the base by the height of the triangle

48 x 38 = 1,824

Then you'll multiply 1,824 by 1/2(which is the same as dividing it by 2)

1,824 ÷ 2 = 912

He needs to make 1 and a half trips to the well to fill the barrel which has a height of 15 inches and  radius 10 inches.

A cuboid is a three-dimensional geometric shape that has six rectangular faces, three of which meet at each corner. A cuboid has three dimensions: length, width, and height. It is also commonly referred to as a rectangular prism. The formula for the volume of cuboid is [tex]V = l *w * h[/tex], where l is the length, w is the width, and h is the height. The formula for the surface area of a cuboid is [tex]2lw + 2lh + 2wh[/tex]. Cuboids are used in everyday life such as building blocks and package boxes.

The cylindrical barrel has a volume of [tex]\pi * r^2 * h = \pi * 10^2 * 15 = 1500\pi[/tex] cubic inches.

The hemisphere has a volume of [tex](2/3) * \pi * r^3 = (2/3) * \pi * 10^3 = (2000/3)\pi[/tex] cubic inches.

So, to fill the barrel, Brad must make [tex]1500\pi / (2000/3)\pi = 3/2 = 1.5[/tex] trips to the well.

In other words, he needs to make 1 and a half trips to the well to fill the barrel.

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Answer:

Step-by-step explanation:

The GCF of the given expressions is 4x⁷⁶

The greatest common factor, abbreviated as GCF, of two numbers is the largest number that is a factor of, or divides evenly into, both of the numbers. When two numbers are relatively small, we have a quick and simple way to calculate their greatest common factor. We do this by listing all of the factors of each number, and then identifying the largest number that is in both lists.

Given here, The expressions 20x⁷⁶ and 8x⁹² and GCF(20,8)=4

and x⁷⁶ is a factor of  8x⁹²

∴ GCF(20x⁷⁶ , 8x⁹²) =4x⁷⁶

Hence, The GCF of the given expressions is 4x⁷⁶

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Answer:

x = 11

Step-by-step explanation:

The two angles are consecutive interior angles so they add up to 180

13x -26 + 5x + 8 = 180

13x + 5x -26 + 8 = 180

18x - 18 = 180
18x = 180 + 18

18x = 198

x = 11

Answer:

17.3 miles / gallon

Step-by-step explanation:

Rates can be represented in different forms, such as speed (meters per second) or water flow rate (liters per minute or second)

Given information from the question,

2 gallons = 34.6 miles

1 gallon = 34.6 ÷ 2 = 17.3 miles / gallon

Answer:

y = -x - 6

Step-by-step explanation:

The equation is y = mx + b

m = the slope

b = y-intercept

The slope = rise / run or (y2 - y1) / (x2 - x1)

Let's pick 2 points ( -6, 0) (-5, -1)

We see the y decrease by 1 and the x increase by 1, so the slope is

m = -1

The y-intercept is located at (0,-6)

So, our equation is

y = -x - 6

Rotation is the process of turning a figure a specific amount around a point. When we dilate a figure, we increase or decrease its size.

The circular movement of an item about a primary axis is referred to as rotation or spin. A revolving object in two dimensions only has one conceivable central axis and can revolve either clockwise or counterclockwise. There are many conceivable central axes and rotating orientations for a three-dimensional object.

Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.

On a coordinate plane, forms can be rotated and dilated in addition to translated and reflected. When a shape is rotated, the new shape is consistent with the old. When you dilate a shape, the resulting shape is similar to the original.

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x² + 6x + 9, this is a perfect square trinomial, which is expressed as

(x + 3)².

Trinomials are algebraic formulas that include three dissimilar terms, therefore the name "trinomial."

An algebraic expression called a trinomial contains three terms that are non-zero. Trinomial expression illustrations: The trinomial x + y + z has three variables: x, y, and z.

A trinomial is formed when three monomials are added together or subtracted from one another. A quadratic trinomial has the following form: ax² + bx + c, where a, b, and c are real, non-zero values.

Given that,

x² + 6x + 9

= (x)² + 2(3x) + 9

= (x)² + 2(x)(3) + 3²

This is similar to a² + 2ab + b² = (a + b)²

so, we can write:

= (x + 3)²

= (x +3) (x + 3)

so, this is a perfect square trinomial.

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Answer:

All real numbers for both Range and Domain

R

or

(−∞,∞)

Answer:

43%

Step-by-step explanation:

calculate percentage as

( number of students in athletics team ÷ total students ) × 100%

= ( 86 ÷ 200) × 100%

= 0.43 × 100%

= 43%

Answer:

yes, it uses the Associative Property

Step-by-step explanation:

The two expressions (8 + 27) + 52 and 8 + (27 + 52) are equivalent because they both equal 87. This is an example of the Associative Property of Addition which states that the order of the terms within an expression can be changed without changing the result.

Therefore , the solution of the given problem of triangle comes out to be

OAC angle arc is = 55 degrees.

Triangular polygons in geometry are those with right side and three vertices. There are three straight sides to this two-dimensional shape. Three-sided polygons include triangles. A triangle's three angles add up to a whole 180 degrees. A single plane contains the triangle.

Here,

Half of the arc AB is the measure of angle OAC, hence the measure of angle OAC is:

OAC = 0.5 times 220 degrees.

110 degrees is OAC.

If the angle OAC is measured as a quarter of an arc AB, then the angle OAC is measured as follows:

OAC equals 0.25 x 220 degrees

OAC = 55 degrees

Therefore , the solution of the given problem of triangle comes out to be

OAC angle arc is = 55 degrees.

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The common difference is 0.42. The comparison of each ratio's successive values over time for a single firm.

Now, According to the question:

What is meant by ratio?

Therefore, simplifying the equation then we get,

if you take the ranges (y) and subtract one from the other you get 0.42.

(22.84 - 22.42)/(2 - 1) = 0.42/1 = 0.42

(23.26 - 22.84)/(3 - 2) = 0.42

(23.68 - 23.26)/(4 - 3) = 0.42

Hence, The common difference is 0.42

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The number of people who bought fewer than 30 items exists 204.

The frequency distribution of a few data points for one variable is represented graphically by a histogram. Heterogeneous "bins" or "range groups" are frequently used in histograms in order to categorize data and count the number of data points that are part of each bin.

Among graphing tools, the histogram is widely used. It is utilized to encapsulate discrete or continuous data that is measured on an interval scale. It is frequently employed as a convenient way to highlight the key characteristics of the data distribution.

As opposed to bar charts, which show categorical variables, histograms visualize quantitative or numerical data. Typically, a histogram's numerical data will be continuous (having infinite values).

Number of people who bought fewer than 30 items

= (0.14 + 0.12 + 0.24)400

= 0.51 x 400 = 204

Therefore, the correct answer is option B) 204.

The complete question is:

The histogram shows the number of items that customers bought during a trip to the grocery store one day. Four hundred customers took a trip to the grocery store that day. Which is the best estimate for the number who bought fewer than 30 items during their trip?

A) 278

B) 204

C) 148

D) 106

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[tex]\textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=13.33 \end{cases}\implies V=\pi (3)^2(13.33)\implies V\approx 376.90[/tex]

The y-intercept of (0,4) is 4.

A y-intercept, also known as a vertical intercept, is the location where the graph of a function or relation intersects the coordinate system's y-axis. This is done in analytic geometry using the common convention that the horizontal axis represents the variable x and the vertical axis the variable y. These points satisfy x = 0 because of this.

The y-coordinate of the y-intercept is determined by computing  f(0) if the curve in question is supplied as y=f(x), y=f(x), etc. There is no y-intercept for functions that have an  value at x = 0.

The constant term a is the y-coordinate of the y-intercept if the function is linear and is written in slope-intercept form as  f(x)=a+bx"

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Answer:

90

Step-by-step explanation:

If we know that for every cup, we can take 3 of 1/3-ounce cups, we can use an equation that looks like this:

number of cups × 3 = total 1/3-ounce cups

If there are 30 cups, then we can simply insert 30 into the equation.

30 × 3 = 90

Therefore, you can make 90 1/3-ounce cups from the cereal box.

Most likely one of these unrelated factors that could possibly have an impact on how long it takes to finish the race is the environment

Therefore the correct option is a) Number of people the stadium can hold

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Answer:

4

Step-by-step explanation:

-28 = ±2^2 x ±7
60 = ±2^2 x ±3 x±5
72 = ±2^3 x ±3^2
=> Gcf of -28, 60, 72: 2^2 = 4

Answer: 12

Step-by-step explanation:

Therefore, the highest common factor of 60 and 72 is 12.

:) I know somebody already answered but like..im answering some stuff today, hope this helped by the way!

The fourth point is (-6.5, -14)

Vertices of a parallelogram?

The three vertices you've provided are (-7,-6), (6,3), and (4,-4). To find the fourth vertex of a parallelogram, we can use the fact that opposite sides of a parallelogram are parallel and congruent, meaning they have the same length and the same slope.

The three vertices you've provided are (-7,-6), (6,3), and (4,-4). To find the fourth vertex of a parallelogram, we can use the fact that opposite sides of a parallelogram are parallel and congruent, meaning they have the same length and the same slope.

One way to find the fourth vertex is to use the vector that connects one vertex to another. The vector from (-7,-6) to (6,3) is (13,9), and from (6,3) to (4,-4) is (-2,-7)

If we use the vector which is opposite of (-2,-7) that is (2,7) and add it to the third point (4,-4) , we will get the fourth point.

(2,7) + (4,-4) = (6,3)

so the fourth point is (6,3)

Another way is to find the midpoint of the diagonal of the parallelogram which are (-7,-6) and (4,-4) and then add the vector which is opposite of (6,3) to (4,-4) that is (-6,-9) which is also the vector from (6,3) to (4,-4)

Midpoint of (-7,-6) and (4,-4) = (-0.5,-5)

(-0.5,-5) + (-6,-9) = (-6.5, -14)

Hence, the fourth point is (-6.5, -14)

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Answer:

55

Step-by-step explanation: i think

Answer:

Step-by-step explanation:

it would be 55 because he does 11 each minute.

The population of the city grew from 2010 to 2020 by 13.37%.

A percentage is a number that tells us how much out of 100 and can also be written as a decimal or a fraction.

We have to given that;

In 2010, the population of a city was 237,000.

And, From 2010 to 2015, the population grew by 7.6%. From 2015 to 2020, it fell by 4.7%.

We know that;

Where, A = P (1+r)ⁿ

A = final population.

P = Initial population.

r = rate

n = time

Hence, The population in 2015 is, =

A = 237,000(1 + 0.076)⁵

A = 341829.629

And, The population in 2020 =

A = P (1 - r)ⁿ

A = 341829.629 (1 - 0.047)⁵

A = 268704.047

So, Percent grow = (268704.047 - 237,000) / 237,000 × 100

                           = 31704.047 / 237,000 × 100

                            = 13.37 %

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