Can you please help me with this question

Answer:

check the attached file

Step-by-step explanation:

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

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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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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The answer would be (5,0)

The value of c is 0 guaranteed by the Mean Value Theorem for Integrals for the function 2x+1 on the interval [3,6].

Mean value theorem states, roughly, that for a given planar arc between two endpoints, there is at least one point at which the tangent to the arc is parallel to the secant through its endpoints.

Given.

Function is 2x+1 on the interval [3,6]

f(x)=2x+1

f(x) continuous on [3, 6] and differentiable on (3, 6) so the MVT applies here.

f(3)=7

f(6)=13

Average rate of change of f on [3,6]

= (13-7) / (6-3) = 6/3=2

To find the c-value guaranteed by the MVT, such that the instantaneous rate of change when x = c is 2, we differentiate, set f'(x) = 2, and solve:

f'(x) = 2 and x = 1.

c = 0 is the only c-value in the interval at which the instantaneous rate of change = the average rate of change.

Hence, the value of c is 0 guaranteed by the Mean Value Theorem for Integrals for the function 2x+1 on the interval [3,6].

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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.

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Midpoint of the line segment from (1,-3) to(-5,2) is (-2,-1/2).

A straight line is just a line with no curves. So, a line that extends to both sides to infinity and has no curves is called a straight line.

The midpoint of a line segment is a point that lies exactly halfway between two points

The formula for midpoint (x,y)=(x₁+x₂/2,y₁+y₂/2)

We need to find midpoint of the line segment from (1,-3) to(-5,2)

Midpoint=(1-5/2,-3+2/2)

=(-4/2, -1/2)

=(-2,-1/2)

Hence, midpoint of the line segment from (1,-3) to(-5,2) is (-2,-1/2).

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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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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

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:

[tex]\textsf{Vertex form}: \quad f(x)=(x-4)^2+2[/tex]

[tex]\textsf{Standard form}: \quad f(x)=x^2-8x+18[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{5.6 cm}\underline{Vertex form of a quadratic equation}\\\\$y=a(x-h)^2+k$\\\\where:\\ \phantom{ww}$\bullet$ $(h,k)$ is the vertex. \\ \phantom{ww}$\bullet$ $a$ is some constant.\\\end{minipage}}[/tex]

From inspection of the given graph:

Substitute the vertex and point (0, 18) into the vertex formula and solve for a:

[tex]\begin{aligned}y&=a(x-h)^2+k\\\implies 18&=a(0-4)^2+2\\18&=a(-4)^2+2\\18&=16a+2\\16a&=16\\a&=1\end{aligned}[/tex]

Substitute the found value of a and the vertex into the formula:

[tex]\implies y=1(x-4)^2+2[/tex]

[tex]\implies f(x)=(x-4)^2+2[/tex]

To write the equation in standard form, expand the brackets:

[tex]\implies f(x)=(x-4)^2+2[/tex]

[tex]\implies f(x)=(x-4)(x-4)+2[/tex]

[tex]\implies f(x)=x^2-8x+16+2[/tex]

[tex]\implies f(x)=x^2-8x+18[/tex]

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:

$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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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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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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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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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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No solution is the answer

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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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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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:

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

Answer:

slope = 4

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

Step-by-step explanation:

line going through quadrants 1 and 3. Straight line.

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.

it is Abe and afe

hope this helps

Answer: 80

Step-by-step explanation:

⇒  −(8 − 12) + 60 + (−4)²

⇒ -(-4) + 60 + 16

⇒ 4 + 60 + 16

⇒ 80

Answer:

h(2)=-1

h(2)=-1

Step-by-step explanation:

Use the given functions to set up and simplify

h

(

2

)