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Graph the equations y=-1/2x+3 and y=2x-2 in the applet below.

1) After you graph the two lines, be sure to take a screenshot of your work and include it in your answer below.

2) What is the solution to the system of equations?

3) Prove that the answer you provided in part 2 is correct, by substituting the solution into the original equations. Be sure to show all your work.

If a,b,c are positive real numbers, the inequality [tex]\frac{(a+b)^{2} }{c} +\frac{c^{2} }a[/tex] [tex]\geq 4b[/tex] is not correct because it gives the value a³+2a²b+ab²≥4abc

How to find the solution set of an inequality?

Inequality is a mathematical statement showing that two quantities are not equal.

The given inequality is [tex]\frac{(a+b)^{2} }{c}[/tex] +[tex]\frac{c^{2} }{a}[/tex][tex]\geq[/tex]4abc

Simplifying the inequality we have [tex]\frac{(a+b)(a+b)}{c}[/tex] +[tex]\frac{c^{2} }{a }[/tex] [tex]\geq[/tex]4b

This implies that: [tex]\frac{a^{2}+ab+ab+b^{2} }{c}[/tex] +[tex]\frac{c^{2} }{a}[/tex] [tex]\geq[/tex] 4b

Taking the LCM,

[tex]\frac{a^{2}+2ab+b^{2} }{c}[/tex] +[tex]\frac{c^{2} }{a}[/tex] [tex]\geq[/tex]4b

Simplifying further

[tex]\frac{a^{3}+2a^{2}b+ab^{2}+c^{3} }{ac}[/tex] [tex]\geq[/tex]4b

The expression gives that: a³+2a²b+ab²≥4abc

Comparing the values of a,b,c on both sides of the inequality,  the inequality is wrong.

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Answer:

796.2 million

(796,200,000)

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{9 cm}\underline{General form of an Exponential Function with base $e$}\\\\$y=ae^{kx}$\\\\where:\\\phantom{ww}$\bullet$ $a$ is the initial value ($y$-intercept). \\ \phantom{ww}$\bullet$ $e$ is Euler's number. \\ \phantom{ww}$\bullet$ $k$ is some constant.\\\end{minipage}}[/tex]

Given exponential function:

[tex]A=796.2e^{0.006t}[/tex]

where:

The initial value is 796.2, which means the population of the country in 2003 was 796.2 million.

The answer would be (5,0)

Answer:

slope = 4

points on graph = (0,0), (1,4)

Step-by-step explanation:

line going through quadrants 1 and 3. Straight line.

Answer: These rates are not equivalent.

Step-by-step explanation:

2/22 = 1/11

4/40 = 1/10

Hence, 1/11 and 1/10 are not equivalent because they do not have the same denominator.

78383884848484848383838

For the two sets F = {v | v < 4} and H = {v | v ≥ 7}, F∩H = Ф and

F∪H = {v | v ∈ R} - {4, 5, 6}.

A set is a collection of well-defined objects.

A subset contains all the elements or a few elements of the given set.

The improper subset is when it contains all the elements of the given set and the proper subset is when it doesn't contain all the elements of the given set.

Given, Are two sets F = {v | v < 4} and H = {v | v ≥ 7}.

Now, F∩H are those elements of the sets that are common to both here none of the elements are coom so F∩H is Ф.

F∪H are those elements that are either in F or in H or in both.

∴ F∪H = {v | v < 4 or v ≥ 7} Or  F∪H = {v | v ∈ R} - {4, 5, 6}

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Hence, the fractuon of the animals at the zoo are elephants is [tex]\frac{7}{12}[/tex].

What is the fraction?

A fraction defined as the part of the whole thing.

Fractions help to distribute and judge the numbers easily and make the calculation faster.

Here given that,

At the zoo [tex]\frac{1}{3}[/tex] of the animals are mammals [tex]\frac{1}4}[/tex] of the mammals are elephants.

So, the fraction of the animals at the zoo are elephants is

[tex]\frac{1}3}+\frac{1}{4}=\frac{4+3}{12}\\\\=\frac{7}{12}[/tex]

Hence, the fractuon of the animals at the zoo are elephants is [tex]\frac{7}{12}[/tex].

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Answer: The numbers are 25 and 68.

Step-by-step explanation:

Answer:

x = 68

y = 25

Step-by-step explanation:

Let the larger number be x and smaller number be y.

x = 18 + 2y ----------------(1)

x + y = 93 -----------------(2)

Put Eq. (1) in Eq. (2)

18 + 2y + y = 93

18 + 3y = 93

Subtract 18 to both sides

3y = 93 - 18

3y = 75

Divide 3 to both sides

y = 72/3

Put y = 24 in Eq. (1)

x = 18 + 2(25)

x = 18 + 50

[tex]\rule[225]{225}{2}[/tex]

Answer:

$19,760 per year

$1,520 per month

Step-by-step explanation:

There are 4 weeks in 1 month, so multiply $380 by 4:

380 x 4 = $1,520 per month.

1 year = 52 weeks:

380 x 52 = $19,760 per year.

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The maximum number of hours that he can hire the cleaning service is 5.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us consider the number of hours for which the total cost would be the same be x

The first equation would be

$15x > $75

Now equate these equations

$15x - $75 = 0

15x = 75

x = 5

Hence, the maximum number of hours that he can hire the cleaning service is 5.

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The required property justifies the step is an addition property of equality.

What is mathematical property?

The rules governing how numbers relate to and interact with one another are known as mathematical properties. There are four fundamental properties. i.e. distributive, addition, commutative and subtraction.

Given, 2x +3 = -5x -1

Applying addition property of equality,

Adding 5x to both sides, we get

7x + 3 = -1

Hence, the required property justifies the step is an addition property of equality.

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Answer: 80

Step-by-step explanation:

⇒  −(8 − 12) + 60 + (−4)²

⇒ -(-4) + 60 + 16

⇒ 4 + 60 + 16

⇒ 80

The rational function f(x) = (x - 3) / (x + 2) have a domain corresponding to any real number except x = - 2.

In this problem we find a defined rational functions whose numerator and denominator are both linear equation. The domain of a function is the set of all values of x such that f(x) exists.

By function theory, the domain of all linear equations is the set of all real numbers and the domain of rational equations is the domain of the numerator except the values of x such that the denominator becomes zero.

Then, we need to determine the values of x such that:

x + 2 = 0

x = - 2

The domain of the rational function f(x) = (x - 3) / (x + 2) is all the real numbers except x = - 2.

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it is Abe and afe

hope this helps

Answer:

f = -7

Step-by-step explanation:

1 + 8f = -6 + 7f

Add 6 on both sides

7 + 8f = 7f

Subtract 8f on both sides

7 = -1f

Divide by -1 to make f positive

f = -7

Answer:

h(2)=-1

h(2)=-1

Step-by-step explanation:

Use the given functions to set up and simplify

h

(

2

)

Using the formula of simple interest, the total interest paid on a $20000 loan at rate of 2% over 4 years is $1600

Simple interest is calculated with the following formula: S.I. = P × R × T, where P = Principal, R = Rate of Interest in % per annum, and T = Time, usually calculated as the number of years. The rate of interest is in percentage r% and is to be written as r/100.

The formula is given S.I = P(1 + RT)

Data;

S.I = 20000(1 + 0.02 * 4)

S.I = 21600

The total interest paid is 21600 - 20000 = 1600

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The Range and Domain for the apples as per the given information is (1, 20) and (1, 20).

The difference between the greatest and lowest values of a set of integers is defined as its range. To find it, subtract the distribution's lowest number from its highest.

Because the term "range" can have multiple meanings, it is recommended that it be defined the first time it is used in a textbook or article. When older books use the term "range," they usually indicate what is currently known as the codomain. More recent works, if they use the phrase "range," usually use it to refer to what is now known as the picture. A number of current books avoid using the word "range" entirely to avoid confusion.

Given,

We need to spend $20 for each apple

And also given that,

The cost of each apple is $1

Here the independent variables are apples

Range=(1, 20)

Domain=(1, 20)

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No solution is the answer

For the given equation, [tex](x-7)2=36[/tex] the value for [tex]x=25[/tex].

Calculating the value of the unknown variable while keeping the equation balanced on both sides is the process of solving equations.

A condition on a variable is an equation when it ensures that two expressions in the variable have the same value. The equation's solution is the amount of the variable for which the condition is met.

Initially, the equation [tex](x-7)2=36[/tex] must be made simplified to find [tex]x[/tex].

[tex](x-7)2=36[/tex]

By using distributive law,

⇒ [tex](x-7)2=36[/tex]

⇒ [tex]2x-14=36[/tex]

Now add 14 on both sides,

⇒ [tex]2x-14+14 =36+14[/tex]

⇒ [tex]2x =36+14[/tex]

⇒ [tex]2x =50[/tex]

As the next step, divide both sides by 2,

⇒ [tex]\frac{2x }{2} =\frac{50}{2}[/tex]

⇒ [tex]x=25[/tex]

Therefore, after solving the equation step-by-step, [tex]x=25[/tex].

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Answer:

Step-by-step explanation:

t says that's 4 units distant from the another vertex. So, if a square is formed by 4 equal sides and 4 right angles, then you just have to add 4 units on x or y.

-> (2, 1) -> + 4 units on X

-> = (6, 1)

or

-> (2, 1) -> +4 units on Y

-> = (2, 5)

(2, 5) isn't an answer so the unique possible answer is (6, 1)

Answer: (6, 1)

Answer: No solution

Step-by-step explanation:

Since both equations are equal to y you can set them equal to each other

5x+4=5x-2

0=-6

zero does not equal -6 which is that there is no solution.

Answer:

Step-by-step explanation:

the answer is 2 1/2 miles

Answer:

a. 31/6; 33/6; 35/6

b. + 2/6

c. 37/6; 39/6; 41/6

d. 49/6

Step-by-step explanation:

First we need to find the first three terms.

To do so solve the equations in the boxes.

When dividing by a fraction you multiply by the reciprocal so the equations are now as follows:

2 * 31/12

3 * 11/6

5 * 7/6

Solve these to get

62/12 = 31/6

33/6

35/6

The term to term rule as shown above is adding 2/6 or 1/3.

To find the next three terms in the sequence add 2/6 to the term.

35/6 + 2/6 = 37/6

37/6 + 2/6 = 39/6

39/6 + 2/6 = 41/6.

To find the 10th term you need to write out the arithmetic sequence equation.

an = a1 + (n-1)d

an is the term you want to find and n is the term number in this case that is 10. D is the common difference which in this case is 2/6. Plug these into the equation. A1 is the first term in the equation which in this case is 31/6.

31/6 + (10-1) 2/6

31/6 + (9)2/6

31/6 + 18/6 = 49/6

The value of n (FUGUR) will be;

⇒ n (FUGUR) = 112

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The data of mathematics students is,

60 study French, 30 study French and German

55 study German, 25 study French and Russian

75 study Russian, 35 study German and Russian

12 students study all the three languages.

Now,

Let F, G, R denote the set of students studying French, German and Russian respectively.

And, The data of mathematics students is,

n (F) = 60, n (F ∩ G) = 30

n (G) = 55, n (F ∩ R) = 25

n (R) = 75 , n (G ∩ R) = 35

n (F ∩ G ∩ R) = 12

Since, We know that;

⇒ n (FUGUR) = n (F) + n (G) + n (R) - n (F ∩ G) - n (F ∩ R) - n (G ∩ R)

                        + n (F ∩ G ∩ R)

Substitute all the values, we get;

⇒ n (FUGUR) = n (F) + n (G) + n (R) - n (F ∩ G) - n (F ∩ R) - n (G ∩ R)

                        + n (F ∩ G ∩ R)

⇒ n (FUGUR) = 60 + 55 + 75 - 30 - 25 - 35 + 12

⇒ n (FUGUR) = 112

Thus, The value of n (FUGUR) will be;

⇒ n (FUGUR) = 112

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The value of angle RPQ in the circle is 115 degrees.

Using angles of intersecting chord theorem, If two chords intersect inside a circle, then the measure of the angle formed is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Therefore,

∠RPQ = 1  / 2 (arc angle RQ + arc angle SA)

arc angle RQ = 175 degrees

arc angle SA = 55 degrees

Hence,

∠RPQ  = 1 / 2 (175 + 55)

∠RPQ  = 1 / 2 (230)

∠RPQ  = 115 degrees.

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Answer: 115 degrees

Step-by-step explanation:∠

RPQ  = 1 / 2 (175 + 55)

∠RPQ  = 1 / 2 (230)

∠RPQ  = 115 degrees.

The linear equation of the line that goes through points (7,20) and (2,10) is y = 2x + 6.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

A linear equation or function is given as ;

y = mx + b

Now,

At x = 0 ⇒ y = b so it will be a y-intercept.

The slope associated with two points (x₁, y₁) and (x₂, y₂) is given by

Slope = (y₂ - y₁)/(x₂ - x₁)

Slope = (10 - 20)/(2 - 7) = 2

Substitute,(2,10) and m = 2

10 = 2(2) + b

b = 6

Thus, the equation will be y = 2x + 6

Hence "The linear equation of the line that goes through points (7,20) and (2,10) is y = 2x + 6".

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Answer:

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

Given system:

We see constants are same with opposite sign.

To make them same multiply both sides of the second equation by -1:

Now we have two equations with same left sides but different right sides:

This is false and hence the system has no solution.

Answer:

h = 4.5

Step-by-step explanation:

16.5 + 2.75h = 9h + 7.5 − 4.25h

Combine like terms on the right side.

16.5 + 2.75h = 4.75h + 7.5

Subtract 4.75 h from both sides.

16.5 - 2h = 7.5

Subtract 16.5 from both sides.

-2h = -9

Divide both sides by -2.

h = 4.5

Answer:

h = 1.2

Step-by-step explanation:

1.) Isolate the variable H. To isolate the variable H, you have to move numbers onto one side and variable onto another. I will show this process in the next steps:
2.) First, move the numbers onto one side. You will subtract 7.5 on both sides, ending up with 16.5 - 7.5 + 2.75h = 9h - 4.25h.

3.) Now, move the variable to one side. You will subtract 2.75h on both sides, and get 16.5 - 7.5 = 9h - 4.25h + 2.75h.

4.) Finally, Simplify. 16.5 - 7.5 = 9. 9h - 4.25h + 2.75h = 7.5h. Therefore, 7.5h = 9.
5.) If we divide both sides by 7.5, we get h = 9/7.5, which is 1.2. By this, h = 1.2