Which equation has infinitely many solutions?
A. 6(3x - 5) = 10 - 2x
B. -3(4x - 8) = 6x + 12
C. -7(-8x + 3) = -21 + 56x
D. 9(3x - 4) = 27x + 36

The number of sodas sold was three times the number of hot dogs sold, so if we set up an equation, it would be 3x + x = 220, where x is the number of hot dogs sold. To solve this equation, we can subtract x from both sides, leaving us with 2x = 220. Then, we can divide both sides by 2, leaving us with x = 110. This means that 110 hot dogs were sold and 3x = 330 sodas were sold.

The horizontal line test is used to determine if a given function is one-to-one, which means that for every unique x-value, there is a unique y-value.

A function that is one-to-one can be inverted, meaning that it has an inverse function. Inverse functions are important in many areas of mathematics, such as solving equations, finding derivatives, and studying geometric transformations.

The horizontal line test is used because it provides a simple and easy way to determine if a function is one-to-one without having to solve for the inverse function. By drawing a horizontal line through the graph of a function and seeing if the line intersects the graph at most once, it is possible to determine if the function is one-to-one without the need for complex calculations or algebraic manipulations.

Another reason is that the horizontal line test can be applied to functions that are defined on a closed interval or on all real numbers and it is a visual way to understand if a function is one-to-one.

In conclusion, the horizontal line test is used to determine if a given function is one-to-one, which is important because one-to-one functions can be inverted.

The test is simple and easy to apply, and it provides a visual way to understand if a function is one-to-one without the need for complex calculations or algebraic manipulations. It can be applied to functions that are defined on a closed interval or on all real numbers.

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Therefore, the appropriate response for function problem  is Option B) This cat weighs 4 kilos at 7 months of age.

A science called mathematics studies numbers, its variations, arithmetic and the local tissue, shapes, and both their existing and projected places. The relationship between a group of inputs, which each have a corresponding output, is described by a function. A function is a collection of inputs that together produce a single variable, recognizable output with each input. A city, municipality, or scope—often referred to as a realm—is assigned to each function. Usually, the letter f is used to represent functions (x).

Here,

When the cat is m months old, w provides the cat's weight in kg.

the meaning of w(7) = 4 must be determined.

We already know that w represents weight in kilos.

When we enter the age in years, it returns the weight, which is what we consider to be the input.

W(7) stands for the weight of the cat at 7 months old.

where w(7) = 4 denotes the cat's weight at 7 months old, which is 4 kilograms.

Therefore, the appropriate response is Option B) This cat weighs 4 kilos at 7 months of age.

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A homogeneous mixture with two or more substances is called a solution. Household remedies frequently take the form of substances that have been dissolved in water, like juice concentrate.

Solutions are any mixtures of substances that have been dissolved.

A solution can be diluted by adding more solvent or by removing solutes. You can concentrate it by removing solvent or adding more solutes.

The following are some illustrations of simple fixes:.

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Answer:

(-4,-2)

Step-by-step explanation:

To solve this system of equations, we can substitute the expression for y in the second equation:

5x + 2(x+2) = -24

We can then simplify and solve for x:

5x + 2x + 4 = -24

7x = -28

x = -4

We can then substitute this value of x back into the first equation to find the value of y:

y = -4 + 2

y = -2

So the solution of the system of equations is (x, y) = (-4, -2)

Answer:

4

Step-by-step explanation:

Step 1:

Substitute:

0.5(17)-1.5(3)

Step 2:

Multiply:

8.5-4.5

Step 3:

Subtract:

4

Each angle is 53 degrees, 32 degrees, and 95 degrees.

A triangle is a three-sided polygon that is sometimes (but not always) referred to as the trigon. Every triangle has three sides and three angles, which may or may not be the same. Triangles are three-sided polygons with three vertices. The angles of the triangle are formed by connecting the three sides end to end at a point. The total of the triangle's three angles equals 180 degrees. A triangle is a three-sided polygon with three vertices. The angle produced within the triangle is 180 degrees. It signifies that the total of a triangle's internal angles equals 180°.

Here,

The sum of angles of triangle is 180 degrees.

4x+5+7x+11+2x+8=180

13x+24=180

13x=156

x=12

T=4x+5

=4*12+5

=53 degree

U=2x+8

=2*12+8

=32 degree

V=7x+11

=7*12+11

=95 degree

The measure of each angle is 53 degree, 32 degree and 95 degree.

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Answer: 3 : 8

Step-by-step explanation:

red to blue is 3 : 5

blue to yellow is 3 : 8

red to yellow is 3 : 8

Answer:

78 that he added

Step-by-step explanation: not needed

The school's population in the year 2017 is given by the equation A = 1620

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 school's population in 2017 be represented as A

Now , the equation will be

The school's population in 2016 = 1500 students

The percentage of increase in population = 8 %

So , school's population in 2017 A = school's population in 2016 + ( 8/100 ) x school's population in 2016

Substituting the values in the equation , we get

The school's population in 2017 A = 1500 + ( 0.08 x 1500 )

On simplifying the equation , we get

The school's population in 2017 A = 1500 + 120

The school's population in 2017 A = 1620 students

Hence , the population is 1620 students

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The graph of the image of the rectangle DEFG after 270° rotation counterclockwise is created using Microsoft Word and included here in the exercise

A pair of numbers called coordinates can be used to determine the position of a point or shape in a two-dimensional plane. A point's position on a 2D plane is described using the phrases "x-coordinate" and "y-coordinate."

A specific point on a grid, also known as a coordinate plane, is identified by coordinates, a pair of numbers (also known as Cartesian coordinates), or sporadically a letter and a number. The two axes of a coordinate plane, which has four quadrants, are the x (horizontal) and y (vertical) axes (vertical).

To find a point's coordinates in a coordinate system, perform the opposite.

Starting at the point, slide up or down a vertical line until you reach the x-axis. It's where your x-coordinate is.

Repeat the preceding procedures while adhering to a horizontal line to obtain the y-coordinate. The x and y coordinates can be used to find a location on the coordinate axes. The x and y coordinates of two points can be used to determine their separation. Using the x and y coordinates for two points simplifies the process of determining a line's slope.

The coordinates of the vertices of the rectangle DEFG are;

D(7, 8), E(10, 8), F(10, 9), G(7, 9)

A rotation of 270° counterclockwise about the origin gives;

Point of preimage = (x, y), point of image after the rotation = (y, -x)

The preimage point D(7, 8) has the image point as D'(8, -7) after the 270° CCW rotation

Similarly, after the 270°CCW rotation, we have;

The preimage point E(10, 8) has an image at E'(8, -10)

The preimage point F(10, 9) has an image at F'(9, -10)

The preimage point G(7, 9) has an image at G'(9, -7)

The graph of the image of the rectangle DEFG after 270° rotation counterclockwise is created using Microsoft Word and included here in the exercise

The complete question is,

Graph the image of rectangle DEFG after a rotation 270° counterclockwise around the origin

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The polynomial with the given zeros can be written as:

p(x) = x^3 + 4x^2 + x - 6

If a polynomial has a leading coefficient a and the N zeros {x₁, x₂, ...} then we can write the polynomial as:

p(x) = a*(x - x₁)*(x - x₂)*...

Here we know that the leading coefficient is 1, and the zeros are:

{-3, -2, 1}

Then the polynomial is:

p(x) = (x + 3)*(x + 2)*(x - 1)

p(x) = (x^2 + 5x + 6)*(x - 1)

p(x) = x^3 - x^2 + 5x^2 - 5x + 6x - 6

p(x) = x^3 + 4x^2 + x - 6

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[tex](7j+8)-(4j+6)[/tex]

Distribute negative sign:

[tex]7j+8+-1(4j)+(-1)(6)[/tex]

[tex]7j+8-4j-6[/tex]

Combine Like terms:

[tex](7j-4j)+(8-6)[/tex]

[tex]\fbox{3j + 2}[/tex]

Answer:

The Answer would be 0.6666 repeated

Step-by-step explanation:

I don't think that I have to explain the process. it would be too long to read!

The greatest number of rolls that Melissa received if she spent less than $63 is 206.

Linear inequalities are defined as those expressions which are connected by inequality signs like >, <, ≤, ≥ and ≠ and the value of the exponent of the variable is 1.

Cost for a large sandwich roll = $0.25

Cost for a small sandwich roll = $0.15

Let x be the number of small rolls that Melissa ordered.

Then number of large rolls she ordered = x + 130

Total cost for the rolls = 0.25(x + 130) + 0.15x

Melissa spent less than $63.

0.25(x + 130) + 0.15x < 63

(0.25x) + (0.25 × 130) + 0.15x < 63

0.4x + 32.5 < 63

0.4x < 30.5

x < 76.25 ≈ 76

Number of small rolls she ordered maximum is 76.

Number of large rolls she ordered is 76 + 130 = 206

Hence Melissa ordered 206 large rolls at maximum.

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The fraction number 35 / 80 equivalent to the fraction numbers will be 7 / 16 and 21 / 48. Then the correct options are C and E.

The equivalent is the expression that is in different forms but is equal to the same value.

The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.

The fraction number is given below.

⇒ 35 / 80

⇒ 7 / 16

⇒ 21 / 48

The fraction number 35 / 80 equivalent to the fraction numbers will be 7 / 16 and 21 / 48. Then the correct options are C and E.

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Answer:

$6.36

Step-by-step explanation:

6 x 1.06 = 6.36

Answer:

  176 cm

Step-by-step explanation:

You want the circumference of a wheel with a radius of 28 cm.

The circumference of a circle is given by ...

  C = 2πr

For r = 28 cm, this is ...

  C = 2π(28 cm) = 56π cm ≈ 176 cm

The circumference of the wheel is 56π cm, about 176 cm.

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The solution of the quadratic inequality x² - 3x + 2 < 0 is 1 < x < 2

Standard form of a quadratic equation is:

ax² + bx + c = 0

If we change the equal sign '=' to inequality signs <, >, ≤ , ≥ , then it becomes a quadratic inequality.

To solve a quadratic inequality,  first find its roots or the solution of its corresponding quadratic equation. Then, evaluate the signs around the roots.

The given quadratic inequality is:

x² - 3x + 2 < 0

First we find the roots by solving the corresponding quadratic equation:

x² - 3x + 2 = 0

(x - 1) (x - 2) = 0

x = 1 or x = 2

Now, since the coefficient of x² is positive, it means the graph of f(x) = x² - 3x + 2 opens upward. The function intercepts x-axis at x = 1 and x = 2, it means that f(x) < 0 at the interval 1 < x < 2.

Hence, the solution is 1 < x < 2

Your question is incomplete, but most likely your question was:

What are the solutions of quadratic inequality x² - 3x + 2 < 0 ?

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The fraction of the marble in the bag are blue is 4/15

The term fraction can be found by dividing part of a whole by the whole. Here the example if 2 students out of a total of 4 are picked, then the part is 2 and the whole is 4 while the fraction is 2 by 4.

Here we have given that a bag has 16 blue, 20 red, and 24 green marbles.

And we need to find the fraction of the marbles in the bag are blue

While looking into the given question, we have identified that the number of blue marbles is 16.

And the total number of marbles is calculated by adding the number of each marbles, then we get,

=> 16 + 20 + 24 = 60.

Here we know the the resulting fraction is obtained by the number of blue marbles out of the total marbles is,

Then it can be written as

=> 16/60

When we simplify this one then we get,

=> 4/15

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Therefore , the solution of the given problem of function comes out to be the cost of every month is $5 ( 5%) dollar increases every month.

The exponential distribution frequently addresses the elapsed time before a particular event. Consider the exponential distribution of the time (starting right now) before an earthquake happens. Other examples include how long long-distance business calls last (in minutes) and how long an automobile battery lasts (in months).

Here,

Given data :

f(x) = ax,

5% is greater than I growth

$100 = 100 %

After one month =

$105 = 105 %

so $5 ( 5%) dollar increases every month

Therefore , the solution of the given problem of function comes out to be the cost of every month is $5 ( 5%) dollar increases every month.

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The complete question is "An exponential function can be used to simulate the price each night at a hotel. The price per night was $100 when the hotel first opened, and it has been rising by 5% annually since then. find the value of interest."

The series of transformations that would map figure D onto figure E is a

reflection over Y = -X.

There are two ways of reflection.

Along x-axis:

(x, y) – (x, -y)

Along y-axis:

(x, y) - (-x, y)

We have,

The coordinates of Figure D are:

(4, 1), (1, 9), (5, 9), (7, 4), (6, 4).

The coordinates of Figure E are:

(-1, -4), (-9, -1), (-9, -5), (-4, -7), (-4, -6)

We see that,

The coordinates transformation:

(4, 1) → (-1, -4)

(1, 9) → (-9, -1)

(5, 9) → (-9, -5)

(7, 4) → (-4, -7)

(6, 4) → (-4, -6)

This is a reflection over Y = -X.

The reflection over Y = -X is (x, y) → (-y, -x).

Thus,

The transformations that would map figure D onto figure E are a

reflection over Y = -X.

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The two main types of coordinate systems used in mathematics and physics are Cartesian and Polar Coordinates.

A coordinate system is a system used to identify and locate a point in space. It is the basis for maps, navigation and surveying. Coordinate systems can be two-dimensional or three-dimensional, and can use a variety of units such as latitude, longitude, and feet. Coordinate systems are used in a variety of fields such as engineering, architecture, geology, and navigation. Coordinate systems help to identify and locate points in space and are essential for charting and mapping the physical world.

Cartesian Coordinates, named after the French mathematician and philosopher René Descartes, use a two-dimensional plane to represent points with an x-axis and a y-axis. These coordinates are expressed as ordered pairs (x,y) and represent points in relation to the origin (0,0). This can be used to plot graphs and equations, and is the most commonly used coordinate system.

Polar Coordinates are based on a two-dimensional plane centered on a pole. Points are expressed as ordered pairs (r,θ) where r is the distance from the pole and θ is the angle from the polar axis. This coordinate system is useful for finding distances and angles in a circle. It is used frequently in physics and astronomy.

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Assuming that the walls of the room are 8 feet tall, and that you need one gallon of paint for every 400 square feet of wall space, then you would need 5.125 gallons of paint to paint the walls of the room.

1. Calculate the square footage of the walls:

10.5ft x 7ft x 2 (sides of walls) = 147 sq. ft

2. Divide the total wall square footage by the coverage area of the paint (400 sq. ft.):

147 sq. ft. ÷ 400 sq. ft. = 0.36 gallons

3. Add 10% extra paint for wastage:

0.36 gallons x 1.1 = 0.396 gallons

4. Round up to the nearest gallon:

0.396 gallons = 0.4 gallons

5. Multiply the gallon of paint by 4 (4 walls):

0.4 gallons x 4 = 1.6 gallons

6. Round up to the nearest gallon:

1.6 gallons = 2 gallons

Hence, you would need 5.125 gallons of paint to paint the walls of the room.

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The quotient of the given expression is calculated by dividing one fraction by another fraction. The result is 0.75.

When two numbers are divided, a new number called a quotient is produced. The formula to calculate this quotient is Quotient = Dividend÷Divisor. Consider the expression 40÷4. Here, 40 is the dividend, 4 is the divisor, 10 is the quotient, and 0 is the remainder.

The given expression is (-2/3)/(-8/9). This can be solved using the formula   [tex]\frac{A}{B}\div\frac{C}{D}=\frac{A}{B}\times\frac{D}{C}[/tex]. Here, A is -2, B is 3, C is -8, and D is 9. Substituting these values, we get,

[tex]\begin{aligned}\frac{A}{B}\div\frac{C}{D}&=\frac{A}{B}\times\frac{D}{C}\\\frac{-2}{3}\div\frac{-8}{9}&=\frac{-2}{3}\times\frac{9}{-8}\\&=\frac{3}{4}\\&=0.75\end{aligned}[/tex]

The required answer is 0.75.

The complete question is -

What is the quotient (-2/3)/(-8/9)?

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The daily increase in Mrs. Miller's daily class is $2 more than it is in Mr. Taylor's class.

Option D is the correct answer.

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

Mr. Taylor:

The coordinates from the graph.

(1, 10), ), (2, 20), (3, 30)

The rate of change.

= (20 - 10) / (2 - 1)

= 10

This means,

Each day the amount is increased by $10.

Mrs. Miller:

From the table,

(3, 24), (5, 60)

Rate of change.

= (60 - 24) / (5 - 3)

= 36 / 2

= 12

This means,

Each day the amount is increased by $12.

Thus,

Mrs. Miller's daily increase is $12.

Mr. Taylor's daily increase is $10.

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1 . Price of car 8 years later is $4305.

The price of a car that was bought for $10,000 and has depreciated 10% yearly can be calculated by multiplying the original price of the car ($10,000) by (1 - 0.10) raised to the power of the number of years (8). It means the car will lose 10% of its value each year for 8 years. Therefore, the price of the car 8 years later would be $4304.67. This is the final amount after 8 years of deprecation on the original price of the car.

2. The yearly value of the card 25 years later is $16.93 and equation of price is given by 5 * (1 + 0.05)^t where t is time.

The formula used to calculate the future value of an item that appreciates at a certain annual rate is called compounding. In this case, the baseball card was bought for $5 and has appreciated at a rate of 5% per year. The formula used to find the value of the card 25 years later is "Price = initial value * (1 + interest rate)^number of years". Plugging in the given values, we get: "Price = 5 * (1 + 0.05)^25"

Price=5(1+0.05)^25

Price=5(1.05)^25

Price=16.93

so the final price of baseball is $16.93

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Food lion sells one can at $0.8 and Aldi sells one can at $1.

The unitary technique involves first determining the value of a single unit, followed by the value of the necessary number of units.

For example, Let's say Ram spends 36 Rs. for a dozen (12) bananas.

12 bananas will set you back 36 Rs. 1 banana costs 36 x 12 = 3 Rupees.

As a result, one banana costs three rupees. Let's say we need to calculate the price of 15 bananas.

This may be done as follows: 15 bananas cost 3 rupees each; 15 units cost 45 rupees.

Given:

Food Lion sells 5- 15 ounce cans of beans for $4.00.

Aldi sells 4- 15 ounce cans for $4.00.

So, Food lion sell one can

= 4/5

= $0.8

and, Aldi sells one can at

= 4/4

= $1

Hence, Food lion sell at $0.8 and Aldi sells for $1.

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The hourly rate of Sheila Blige if she worked for 40 regular hours and 8 overtime hours and paid a gross of $884.00 is $17

Total regular hours worked = 40

Total overtime hours worked = 8

Total gross pay = $884.00

Let

Hourly rate = x

Overtime rate = 1.5x

So,

40x + 8(1.5x) = 884

40x + 12x = 884

52x = 884

divide both sides by 52

x = 884 / 52

x = $17

Therefore,

Hourly rate = x

= $17

Overtime rate = 1.5x

= 1.5(17)

= $25.5

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The fourth graph (the right graph in the bottom row) is discovered to represent the function f using translation notions (x).

A sort of transformation called a translation involves moving each point in a figure the same distance in the same direction.

In terms of operations like multiplication or sum/subtraction in its definition, a translation is represented as a change in the function graph.

has a vertex at the origin and [tex]$f(x)=\sqrt{x}$[/tex] is the parent function.

In this issue, the translated function is [tex]$f(x)=2 \sqrt{x+1}$[/tex] It was left 1 unit relocated and vertically stretched by a factor of 2 units, resulting in a new vertex position of (0,-1).

As a result, the fourth graph, on the right side of the bottom row, represents the function f. (x).

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