What ordered pairs are the solutions of the system of equations shown in the graph below?

Explanation:

When solving a function, you plug in the given [tex]x[/tex]-value (what's inside the parentheses next to the [tex]g[/tex] or [tex]f[/tex]) into the corresponding equation (what [tex]f(x)[/tex] and [tex]g(x)[/tex] are set equal to).

Before starting the worksheet, take a simpler example:

Given the function [tex]h(x) = x + 2[/tex],

the following work solves for [tex]h(3)[/tex].

[tex]h(3) = 3 + 2[/tex]

[tex]h(3) = 5[/tex]

Essentially, to solve for the value of a function for a given [tex]x[/tex]-value, simply plug in that value in for [tex]x[/tex] and simplify the resulting expression.

Onto problem 14 from the given worksheet:

We are given [tex]f(x) = 3x + 2[/tex] and are asked to solve for [tex]f(4)[/tex].

Hence, all we have to do is plug [tex]4[/tex] in for [tex]x[/tex]:

[tex]f(4) = 3(4) + 2[/tex]

[tex]f(4) = 12 + 2[/tex]

[tex]f(4) = 14[/tex]

You can apply this concept to the rest of the problems.

Answer:

Y-intercept: 15

Slope: 1.3

Equation: y = 1.3x + 15

Step-by-step explanation:

Base on the table:

# of haircuts = x

Cost ($) = y

Knowing that;

y-intercept = The starting point (y)

Thus, based on the table the y-intercept is 15.

Y-intercept: 15.

To find the slope.

We first have to pick two points on the line & determine their coordinates.

Then subtract y-coordinates of these two points and also subtract x-coordinates for these two points.

After that divide the y by the x.

Shown below:

I'm going to use;

(0,15) and (1,20.5)

0 = x₁

15 = x₂

1 = y₁

20.5 = y₂

Now we do;

20.5 - 1 = 19.5

15 - 0 = 15

19.5 / 15 = 1.3

Hence, Slope = 1.3

Slope: 1.3

The equation - y = mx + b

Knowing that;

b = y-intercept

m = Slope

Substitute it in we have;

y = 1.3x + 15

Equation: y = 1.3x + 15

RevyBreeze

Answer:

this is the answer (-3,-6)

The reason to choose problem B over A is simple -  it is more relatable to them.

Problem A involves dinosaurs, which may be more interesting to students than the abstract concept of creating an area with rope. Additionally, the use of feet as a unit of measurement in Problem A may be more familiar to students than inches.

Finding a number that represents the quantity of anything is called measurement. An accepted quantity that is used to represent a physical quantity is called a measurement unit. Let's learn about some of the standard units used to measure physical quantities.

The inch, foot, yard, and mile are the fundamental units of length and distance measurement in the English system. The rod, furlong, and chain are additional length units.

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Answer:

[tex]w^{2}[/tex]

Step-by-step explanation:

Answer:

4.42857142857

Rounded:

4.4

The flowchart to find the biggest of 3 numbers is mentioned below:

A flowchart is a type of diagram that represents an algorithm, process, or workflow. It is a visual representation of the steps and decisions involved in a problem-solving or decision-making process. Flowcharts use a variety of symbols and shapes to represent different types of steps and decisions, such as inputs, outputs, process steps, and decision points. They are used to communicate the logic of a program or process to different stakeholders, such as developers, managers, and users.

An algorithm is a set of instructions or a step-by-step procedure for solving a problem or completing a task. It is a well-defined sequence of operations or actions that are taken in order to achieve a specific goal or outcome. Algorithms can be expressed using natural language, pseudocode, or programming languages. The steps in an algorithm must be unambiguous and have a clear stopping point.

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The required perimeter of the new rectangle is 66 inches.

A quadrilateral with all of its angles equal, or right angles, is a rectangle.

In addition to having all equal angles, a square also has all equal sides.

Therefore, a particular case of a square is a rectangle.

To put it another way, a rectangle can also be a square (when all sides to are equal).

Because every square is a quadrilateral with all four angles at right angles, every square is also a rectangle.

To be a square, a rectangle's sides must all be the same length, hence not all rectangles are squares.

So, a perimeter equals 2(l+b).

50 is the circumference and 17 is the length here.

Suppose the breadth is x.

50 = 2(17+x)

50 = (2*17)+(2*x)

50 = 34 + 2x

50 - 34 = 2x

16 = 2x

16/2 = x

8 = x

The first triangle's width is eight inches.

We know that the length of the other rectangle is 17.

And that the width is two times that of the first triangle.

Length = 17, width = 2*8 = 16, etc.

For the border:

p = 2(l+b)

p =  2(17+16)

p =  (2*17)+(2*16)

p =   34+32

p  =   66

Therefore, the required perimeter of the new rectangle is 66 inches.

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Complete question:

Najib cuts out a rectangle that has a perimeter of 50 inches and a length of 17 inches. He cuts out another rectangle that is the same length and twice as wide. What is the perimeter of the new rectangle?

Answer:

8 + 56d

Step-by-step explanation:

We will open the parentheses, multiplying the stuff outside by the stuff inside. So, we get:

8*1 + 8*7d

Then, we can simplify by giving us:

8 + 56d

Hope this helped!

Check the picture below.

[tex]\stackrel{\textit{\LARGE Areas}}{\stackrel{rectangle}{(4)(20)}~~ + ~~\stackrel{triangle}{\cfrac{1}{2}(\underset{b}{5})(\underset{h}{20})}}\implies 80+50\implies \text{\LARGE 130}~m^2[/tex]

The number of children that swam in the public pool that day is 194

and the number of adult that swam in the public pool that day is 117

Let x represent the number of children that swam in the public pool that day.

Let y represent the number of adult that swam in the public pool that day.

On a certain hot summer day, 311 people used the public swimming pool. This means that

x + y = 311

The daily prices are 1.50 for children and 2.00 for adults. The receipts for admission totaled to $525. This means that

$1.50x + $2.00y = $525 - - - - - - - -1

Substituting x = 311 - y into equation 1, it becomes

1.50(311 - y) + 2.00y = 525

466.5 - 1.50y + 2.00y = 525

0.5 y = 58.5

y = 117

Substituting y = 117 into x = 311 - y, it becomes

x = 311 - 117

x = 194

Hence , the number of children that swam in the public pool that day is 194 and the number of adult that swam in the public pool that day is 117.

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So on solving the provided question, here  we can say that by is a simultaneous equations the value of x = - 3/5 and y = 9/10

Multiple algebraic equations that have the same unknowna as the give in the  variables and the same answer are referred to as simultaneous equations. This suggests that there is a single solution to the simultaneous equations. Examples of simultaneous equations include: 2x - 4y = 4, 5x + 8y = 3, and others. This implies that the simultaneous equations have a single solution. The simultaneous equations 2x - 4y = 4, 5x + 8y = 3, and others are examples.

y = -x + 1.5

y = 1.5x + 2.5

x = -3/5

y = 9/10

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The longest side of a triangle is opposite the largest interior angle, and the shortest side is opposite the smallest angle.

Triangle

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle. The sum of all three angles of the triangle is equal to 180 degrees.

Angle

A figure which is formed by two rays or lines that shares a common endpoint is called an angle. The word “angle” is derived from the Latin word “angulus”, which means “corner”. The two rays are called the sides of an angle, and the common endpoint is called the vertex.

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C) The whole hundredths of 2347 is 234700 hundredths.  Zero-tenths are in 2,347. The whole tenth of 2347 is 2470tenth.

D) The tenth in 234. 7 are 7. The whole tenth of 234. 7 is 2347.

What is the tenth?

The tenth place is represented by the first digit following the decimal. The hundredth place is represented by the digit that follows the decimal.

Given number is 2347.

To find the whole hundredth, multiply the number by 100.

The whole hundredth in 2347 is 2347 × 100 = 234700.

The given number can be written as 2347.0.

Thus tenth of 2347 is 0.

To find the whole tenth, multiply the number by 10.

The whole tenth in 2347 is 2347 × 10 = 23470.

Thousand     Hundred       Ten      decimal point     Tenth

     2                      3              4                   .                    7

The tenth of in 234. 7 is 7.

The whole tenth in 234. 7 is 234.7 × 10 = 2347.

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The quantities which are proportional to 12/4 are 36/12 and 3/1 .

What is proportional ?

If the corresponding elements of two sequences of numbers, frequently experimental data, have a constant ratio, known as the coefficient of proportionality or proportionality constant, then the two sequences of numbers are proportional or directly proportional.

In mathematics, proportionality denotes a linear relationship between two quantities or variables. Both quantities increase in size when one doubles, and both decrease in size when one drops to a tenth of its original value.

The relationship between two quantities is constant for all values when they are proportional, which indicates that as one quantity rises, the other rises as well. An illustration would be the ratio of a circle's circumference to its diameter, which is equal to pi.

12/4 ⇒ 3/1

          = 24/9

          = 8/3

The quantity 12/4 is not proportional to 48/18

        = 18/6

        = 3/1

The quantity 12/4 is proportional to 36/12

       = 7/3

The quantity 12/4 is not proportional to 35/15

       = 12/8

       = 6/4

       = 3/2

The quantity 12/4 is not proportional to 24/16

The quantity 12/4 is proportional to 3/1

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Answer:

Any value

Step-by-step explanation:

X is a variable, meaning it can be any number, and they are just using our variable, x, as a little mask to hide the exact value. In math, we will usually need to find x by solving different equations.

Examples:

x + 4 = 7

Know, x in this case is 3 because we just know 3 + 4 = 7, but x can be any value, and sometimes it gets more complicated than this. For example, we can have something like:

2x + 8 = 16

In this case, we need to have multiple steps to solve for x. First, we minus 8 from both sides:

2x = 8

Then we divide by 2:

x = 4

So, we know x = 4. In conclusion, x is a variable that is hiding a value, and you will need to either solve or substitute x. Meaning x can be any value.

Hope this Helped!

On solving the provided question, we can say that coordinates of the point in the unit circle  S = ( cos [tex]3\pi /2[/tex] , sin [tex]3\pi /2[/tex] ) => S= ( 0 , -1 )

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. At every angle, it is also rotationally symmetric about the center. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

S = (0, -1 )

coordinates of the point in the unit circle

S = ( cos [tex]3\pi /2[/tex] , sin [tex]3\pi /2[/tex] )

S= ( 0 , -1 )

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The density of the wood is between 0.35 g/cm^3

The density of a substance can be calculated using the formula:

density = mass / volume

To calculate the volume of the cuboid, we can use the formula:

volume = length x width x height

So, using the measurements provided:

volume = 13.2 cm x 16.0 cm x 21.7 cm = 5541.44 cm^3

To calculate the density of the wood, we divide the mass by the volume:

density = 1970 g / 5541.44 cm^3

We can convert cm^3 to g/cm^3 by converting the volume to g

1cm^3 = 1g/cm^3

density = 1970 g / 5541.44 g/cm^3

density = 0.3555 g/cm^3

However, as the measurements provided have a degree of uncertainty, we should consider bounds to find the range of possible densities.

The lower bound for the length is 13.2 cm - 0.1 cm = 13.1 cm

The upper bound for the length is 13.2 cm + 0.1 cm = 13.3 cm

The lower bound for the width is 16.0 cm - 0.1 cm = 15.9 cm

The upper bound for the width is 16.0 cm + 0.1 cm = 16.1 cm

The lower bound for the height is 21.7 cm - 0.1 cm = 21.6 cm

The upper bound for the height is 21.7 cm + 0.1 cm = 21.8 cm

The lower bound for the mass is 1970 g - 5 g = 1965 g

The upper bound for the mass is 1970 g + 5 g = 1975 g

We can now use these bounds to calculate the range of possible densities:

Density lower bound = 1965 g / (13.3 cm x 16.1 cm x 21.8 cm) = 0.350 g/cm^3

Density upper bound = 1975 g / (13.1 cm x 15.9 cm x 21.6 cm) = 0.360 g/cm^3

So the density of the wood is between 0.35 and 0.36 g/cm^3 to one decimal place.

So the density is 0.35 g/cm^3 with an uncertainty of 0.01 g/cm^3

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On solving the provided question, we can say that by fraction they will have the same amount of fish in 5 months.

Any number of equal portions, or fractions, can be used to represent a whole. Fractions in standard English indicate how many units of a certain size there are. 8, 3/4. A whole includes fractions. The ratio of the numerator to the denominator is how numbers are expressed in mathematics. Each of these is an integer in simple fractions. In the numerator or denominator of a complex fraction is a fraction. True fractions have numerators that are less than their denominators. A fraction is a sum that constitutes a portion of a total. By breaking the entire up into smaller bits, you can evaluate it. Half of a full number or item, for instance, is represented as 12.

Month / Brent / Gretel

0/4/ 128

1/ 16 / 256

2 / 64 / 512

3 / 256 / 1024

4 / 1024 / 2048

5 / 4096 / 4096

They will have the same amount of fish in 5 months.

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Answer:

Step-by-step explanation:

4/56\8

Answer:

  ∠LOP = 96°

Step-by-step explanation:

Given an inscribed angle of 48°, you want to know the measure of the central angle that subtends the same arc.

The measure of an inscribed angle is half the measure of the arc it subtends.

  ∠LMP = 1/2(arc LP)

  48° = 1/2(arc LP) . . . . . . use the given value

  96° = arc LP . . . . . . . . . multiply by 2

The measure of an arc of a circle is the same as the measure of the central angle it subtends: the arc measure and its central angle measure are identical.

  arc LP = ∠LOP

  96° = ∠LOP

__

Additional comment

That's a long way of saying the central angle is twice the inscribed angle that subtends the same arc. ∠LOP = 2×∠LMP.

The polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.

What is polynomial?

A polynomial is an expression in mathematics that only uses the operations of addition, subtraction, multiplication, and powers of positive-integer variables. It consists of indeterminates and coefficients. The polynomial x^2 4x + 7 is an illustration of one with a single indeterminate x.

We have to find the polynomial in intercept form so that P(x)=0 has the roots 2 and √3.

Let 2 and √3 are the roots of the polynomial so,

x = 2,  x = √3

⇒ x - 2 = 0,  x - √3 = 0

⇒ (x - 2)(x - √3) = 0

x^2 - √3x - 2x + 2√3 = 0

Hence, the polynomial in intercept form so that P(x)=0 has the given roots is, x^2 - √3x - 2x + 2√3 = 0.

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On solving the provided question we can say that - the prime factors of 32 are 2 × 2 x 2 x 2 x 2 and of 64 are - 2 x 2 × 2 x 2 x 2 x 2

Any natural number other than 1 with just itself and the number 1 as its divisors is considered a prime factor. Actually, 2, 3, 5, 7, 11, and so on are some of the first prime numbers. an amount that has been multiplied to produce another amount. By dividing 15 by 3 and 5, for instance, we get 3 5 = 15. main elements: Prime factors include all factors that are prime but are not composite. A few prime factors of 30 are 2, 3, and 5. Only 2 and 3 are prime factors of 12, so listing 2 twice as 2 2 3 (or 22 3) is necessary to factorize 12. The sum of 2 + 3 is not 12.

the prime factors of

32 are 2 × 2 x 2 x 2 x 2

64 are - 2 x 2 × 2 x 2 x 2 x 2

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The combined gas law for a gas is discussed below.

Given is the combined gas law.

The ideal combined gas law is given by →

PV = nRT

Where -

{P} = pressure     {T} = temperature     {V} = volume    

{n} = number of moles   {R} = gas constant

Non ideal gases are often modelled by the Van der Waals equation as →

(p + n²a/V²)(V - nb) = nRT

Where -

{a} and {b} = constants for a particular gas

{p} = pressure       {v} = volume    

{n} = number of moles       {t} = temperature  

{R} = gas constant

Therefore, the combined gas law for a gas is discussed above.

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The number of times the diameter of Uranus is larger than the diameter of Mars is 7.5 times

From the question, we have the following parameters that can be used in our computation:

The diameters of Uranus and Mars

These diameters are given as

Diameter of Uranus: 5.11×10^4 kilometers

Diameter of Mars: 6.79×10^3 kilometers

Express the diameters properly

So, we have the following representation

Diameter of Uranus: 5.11 × 10⁴ kilometers

Diameter of Mars: 6.79 × 10³ kilometers

This means that

Number of times larger = Diameter of Uranus/Diameter of Mars

Substitute the known values in the above equation, so, we have the following representation

Number of times larger = 5.11 × 10⁴ kilometers/6.79 × 10³ kilometers

Evaluate the quotient

So, we have the following representation

Number of times larger = 7.5

Hence, the number of times is 7.5

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The rate of recycling 200 pounds of cans based on the mentioned information is $110.

Firstly calculating the cost of cans per pounds. Then we will proceed to actual calculation about rate of recycling 200 pounds.

Cost of recycling one pound of can = total cost ÷ number of recycled cans

Keep the values in formula

Cost of recycling one pound of can = 23.65/43

Performing division

Cost of recycling one pound of can = 0.55

Cost of recycling 200 pounds of cans = 0.55 × 200

Performing multiplication

Cost of recycling 200 pounds of cans = 110

Therefore, the required rate is $110.

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As a result, using the values provided, we can turn these data into a bar graph.

A graph is a type of non-linear data structure that consists of nodes, also called vertices, and edges. Any two edges can connect the nodes, which are also known as vertices in a graph. This graph's vertices are 1, 2, 3, and 5, while its edges are 1, 2, 1, 3, 2, 5, and 4, 50.

Here,

The gene contributes to the development of pigment.

Yes, factors such as temperature, light cycle, and the presence of mutagens can affect the color of the fur.

In the evolution chart, Mcl provided has ullets that it runs. In mature solutions, the dominating truit moderate is thus always present.

Therefore, using the supplied numbers, we may convert these data into a bar graph.

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Answer:

To enclose the rectangular garden, Owen will need to put fencing along the length of the garden, which is 25 feet, and along the width of the garden. He wants to use less than 8 feet of fencing, so the width of the garden must be less than 8 feet.

The total amount of fencing needed will be equal to the length of the garden plus the width of the garden, multiplied by 2 (since there are two sides to the garden for each of the length and width).

For example, if the width of the garden is 5 feet, the total amount of fencing needed will be 25 + 5 + 25 + 5 = 60 feet, which is less than 8 feet.

So, the width of the garden can be any value less than 8 feet.

Step-by-step explanation: