The sum of the first six prime numbers is ?​

Answer:

(1, 7.5)

(2, 9)

(3, 10.5)

Step-by-step explanation:

-6x+4y=24

first we want to put the equation in slope intercept form which is y=mx+b

-6x+4y=24

first we add 6x to both sides

4y=24+6x

now we divide everything by 4

y=6+6/4x

simplified

y=3/2x+6

now we input our x values to find the y values (x,y)

y=3/2(1)+6

y=15/2 or 7.5

y=3(2)+6

y=9

y=3/2(3)+6

y=21/2 or 10.5

with this information, our points to plot on the graph are

(1, 7.5)

(2, 9)

(3, 10.5)

i hope this helped! if you have any questions just ask!

Using the Factor Theorem, we have that:

a) The zeros of the function are x = 3i, x = -3i, x = 4.5.

b) The factored function is: F(x) = (x² + 9)(x - 4.5).

c) From the graph of the function given at the end of the answer, the only x-intercept is x = 4.5, which is the only real zero of the equation.

The Factor Theorem states that a polynomial function with roots(also called zeros) [tex]x_1, x_2, \codts, x_n[/tex] is given by the following rule.

[tex]f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)[/tex]

In which a is the leading coefficient of the polynomial, determining if it is positive(a positive) or negative(a negative).

For this problem, the function is defined by the following rule:

F(x) = 2x³ - 9x² + 18x - 81.

Using a calculator, the zeros of the function are given as follows:

x = 3i, x = -3i, x = 4.5.

In factored form, the function is given by:

F(x) = (x - 3i)(x + 3i)(x - 4.5)

Considering that i² = -1, we have that:

The factored function is: F(x) = (x² + 9)(x - 4.5).

From the graph of the function given at the end of the answer, the only x-intercept is x = 4.5, which is the only real zero of the equation.

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The amount Charlie and Kathy would pay interest on the loan of $20,000 is $6,344.80.

An ordinary annuity is payment of level cash flows for a defined period of time, in this case, a fixed monthly payment would be made for 10 years, hence, using the present value formula of an ordinary annuity we can determine the monthly payment:

[tex]PV=PMT*(1-(1+r)^{-N/r}[/tex]

Where:

[tex]PMT*(1+1+0.00479166666666667)^-120/0.00479166666666667\\PMT=$219.54[/tex]

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Answer:

1) 34

2) 282.4

3) $183.70

4) 0.324

Answer: 1. (21/10 or 2.1). 2. (3/2 or 1.5)

Step-by-step explanation:

1. Let's take the first equation as an example (5 1/4 ÷ 2 1/2)

2. First, make both fractions improper (21/4, and 5/2)

3. Next, multiply the first fraction by the reciprocal (numerator and denominator swapped) of the second fraction. This is because, to keep the equation mathematically the same, we need to turn the division question into a multiplication question. In this case, it is 21/4 x 2/5 which answers 21/10, or 2.1.

4. Using the same method, we get 7/2 x 3/7, which is 3/2 (simplified), or 1.5.

I didn't want to give the answers for all the equations, but I hope this method is clear and concise for figuring out the answer for the rest of the equations.

x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex] = 2

We have to find the value of x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex]

First take squares on both sides, then,

⇒ x² = 2 + [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex]

As the terms inside the square roots are non terminating, we can substitute x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex] into the above equation.

i.e.,  x² = 2 + x

⇒ x² - x -2 = 0

This is a quadratic equation which can be solved using factorization.

⇒  x²+(-2+1)x +(-2.1) = 0

⇒ (x-2)(x+1) = 0

So x = 2 or -1

But here the value of √2 is positive and square root of sum of positive numbers will always be positive.

So we can conclude that

x = [tex]\sqrt{2+\sqrt{2+\sqrt{2+...} } }[/tex] = 2

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The value of x is 13.

Any pair of angles each of which is on the same side of one of two lines cut by a transversal and on the same side of the transversal.

We have,

Two lines m and n are parallel.

Two angles (7x -1)° and (8x - 14)° are corresponding angles.

We know that corresponding angles are equal.

We can write as:

7x - 1 = 8x - 14

We will find the value of x.

We will keep the like terms on one side.

14 - 1 = 8x - 7x

13 = x

x = 13

Therefore the value of x is 13.

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Yes , the toll company is correct to give the teacher a ticket.

Mean Value Theorem for a function f(x): [a,b]→ R such that f(x) is continuous and differentiable over the interval.

(i) f(x) is continuous on [a,b].

(ii) f(x) is differentiable on (a,b).

(iii) There exist a point c in (a,b) such that f'(c)=f(b)-f(a)/(b-a).

In the given question

Speed Limit = 60 mph

Time of entrance on toll road = 6:00

Time of exit from toll road = 7:00

Total time on toll road  = 1 hr

Mile marker on entry in toll road = 15 mile

Mile marker on exit from toll road = 100 mile

Total distance travelled on toll road = 100-15= 85 miles

[tex]Average.Speed=\frac{total . distance}{total.time}[/tex]

Substituting the values we get .

Avg Speed = 85/1 = 85  mph

Overspeed = Avg Speed - Speed Limit

=85-60

=25 mph

The teacher over speed by 25 mph.

Since 85 mph is the average speed , it means that for some instance he was travelling below the average speed and for some instance he was travelling above the average speed.  

By Mean value Theorem , it is clear that there have been at least one point where the teacher was travelling above 85 mph , which means he was over speeding .

Therefore , Yes , the toll company is correct to give the teacher a ticket.

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The answer is

7x-1/8x

Answer:

10 Dimes, 5 quarters, and 7 Nickels

Step-by-step explanation:

10 Dimes - 1 dollars

5 Quarters - 1.25 dollars

7 Nickels - 35 cents

1 + 1.25 = 2.25

2.25 + 35 = 2.60

To write the expression log₅4 - log₅6 in a single logarithm, we have to use division property of logarithm.

Given that expression is log₅4 - log₅6.

We have to tell the name of the property of logarithm which will help us to express the expression in a single logarithm.

The quotient rule for logarithms tells us that the logarithm of a quotient is equal to a difference of logarithms. Just as with the product rule we  use the inverse property to derive the quotient rule.

Division of logarithm says that log(m/n)=log m-log n.

The expression is  log₅4 - log₅6.

log₅4 - log₅6=[tex]log_{5}[/tex](4/6)

=[tex]log_{5}[/tex] 0.67

Hence to write the expression log₅4 - log₅6 in a single logarithm, we have to use division property of logarithm.

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The answer is cone -7 7=9÷7

The inequality that is represented by the given graph is; y ≤ (3/4)x - 2

From the given inequality graph, we see that;

Slope; m = 3/4

x-intercept = -2.5

y-intercept = -2

Now, the equation of a line in slope intercept form is;

y = mx + c

where;

m is slope

c is y-intercept

Thus, our graph is ordinarily;

y = (3/4)x + (-2)

y =  (3/4)x - 2

However, it is an inequality that is shaded at the bottom with a thick line and so the inequality becomes;

y ≤ (3/4)x - 2

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The equation that could represent a balanced hanger B, which is equivalent to hanger A, is: 6x + 3y = 3(3y + x).

Variables, which are alphabets represents unknown values and can be used in creating equations that model a scenario.

For example, in the model shown in the image, x represents the weight of each triangle while y = the weight of each square.

From the first balance, we can rearrange the squares and triangles to create hanger B.

The first equation is: 3(2x + y) = 9y + 3x

The second equation that can be created using the set of shapes would be:

6x + 3y = 3(3y + x)

Therefore, the equation that could represent a balanced hanger B, which is equivalent to hanger A, is: 6x + 3y = 3(3y + x).

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Answer: 2x+y=3y+x

Step-by-step explanation:

Answer:

11.9a − 3

Step-by-step explanation:

Answer:

-120

Step-by-step explanation:

Answer:

yes, each input (x) has only one output (y)

Step-by-step explanation:

The equation for r₁ as a function of r₂ is r₁ = ∛ 18 ₂² and the equation for r₂ as a function of r₁ is r₂ = r₁ / 3 √r₁ / 2.

We are given that:

To fill a pond whose volume is given as V₁ = 1 / 2 (4 / 3 π r₁³), we need a cylindrical tank whose volume is given by V₂ = 12 π r₂².

Also, V₁=V₂

So, we get that:

1 / 2 (4 / 3 π r₁³) = 12 π r₂².

4 / 3 π r₁³ = 24 π r₂²

r₁³ = 18 r₂²

r₂ = √ ( r₁³ / 18)

r₂ = r₁ / 3 √r₁ / 2

Now, r₁³ = 18 r₂²

r₁ = ∛ 18 ₂²

Therefore, the equation for r₁ as a function of r₂ is r₁ = ∛ 18 ₂² and the equation for r₂ as a function of r₁ is r₂ = r₁ / 3 √r₁ / 2.

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now, the assumption is that, "x" is a simple variable whilst "y" is a function in x-terms, so

[tex]e^{\frac{x}{y}}=3x-y\implies \stackrel{\textit{\LARGE chain~rule}}{e^{\frac{x}{y}}\stackrel{quotient~rule}{\left( \cfrac{1\cdot y-x\cdot \frac{dy}{dx}}{y^2} \right)}} =3-\cfrac{dy}{dx} \\\\\\ \cfrac{ e^{\frac{x}{y}}y-e^{\frac{x}{y}}x\cdot \frac{dy}{dx}}{y^2}=3-\cfrac{dy}{dx}\implies e^{\frac{x}{y}}y-e^{\frac{x}{y}}x\cdot \cfrac{dy}{dx}=3y^2-y^2\cfrac{dy}{dx}[/tex]

[tex]e^{\frac{x}{y}}y-3y^2=e^{\frac{x}{y}}x\cdot \cfrac{dy}{dx}-y^2\cfrac{dy}{dx}\implies e^{\frac{x}{y}}y-3y^2= \cfrac{dy}{dx}\left( e^{\frac{x}{y}}x-y^2 \right) \\\\[-0.35em] ~\dotfill\\\\ ~\hfill {\LARGE \begin{array}{llll} \cfrac{e^{\frac{x}{y}}y-3y^2}{e^{\frac{x}{y}}x-y^2}=\cfrac{dy}{dx} \end{array}}~\hfill[/tex]

The value for the given equation ( log₅ 1/ 125) = log₅¹ - 3

The similarity between the characteristics of exponents linear logarithms can be used to find the property for a quotient's logarithm. To create multiple numbers with the same base using exponents, add the exponents. Subtraction of exponents is used to split two numbers having the same base.

logb(xy) = logbx + logby.

logb(x/y) = logbx - logby.

logb(xn) = n logbx.

logbx = logax / logab.

log₅ 1/ 125 given

log₅ 1/ 125 applying the log property (log[tex]_a[/tex]ᵇ = log b/log a)

(log 1 - log 125)/ log 5

(log 1 - log 5³)/ log 5

(log 1 - 3log 5)/ log 5

((log1)/log 5 )) - 3

log₅¹ - 3

The value for the given equation ( log₅ 1/ 125) = log₅¹ - 3

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[tex](\stackrel{x_1}{2}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{12}~,~\stackrel{y_2}{20}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{20}-\stackrel{y1}{8}}}{\underset{run} {\underset{x_2}{12}-\underset{x_1}{2}}} \implies \cfrac{12}{10}\implies {\LARGE \begin{array}{llll} \cfrac{6}{5} \end{array}}[/tex]

Shape C is different from shape A and B.

Here, we are given 3 shapes as shown in the image below.

Let us look at each of the shapes one by one.

Shape A-

The height of shape A is 4

The width of shape A is 5

The ratio of width and height = 5/4

Shape B-

The height of shape B is 10

The width of shape B is 8

The ratio of width and height = 8/10 or 4/5

Shape C-

The height of shape C is 10

The width of shape C is 6

The ratio of width and height = 6/10 or 3/5

Thus, we can see that the ratio of width and height is equal for shape A and B. Thus, C is different.  

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Your question was incomplete. Check for the missing image below.

A. 559 meters Is the answer

Answer:

Step-by-step explanation:

To graph any point (±x, ±y) we must follow the steps as illustrated below.

The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.

These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.

Given, The points (- 4,- 4.5), (1, 2.5), and (- 2, - 0.5).

Now, To graph the point (-4, - 4.5) we should move 4 units left along the x-axis and down 4.5 units along the y-axis.

Similarly, for points (1, 2.5) and (- 2, - 0.5) we must follow the exact steps.

The graph of the points is shown in the attached image.

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The midpoint of the given numbers (1.29 and 1.3) is 1.295

From the question, we are to calculate the midpoint of the given numbers

The given numbers are 1.29 and 1.3

To determine the midpoint of two numbers on a number line, we will add the two numbers together, and then divide value of their sum by 2

Adding up the numbers

1.29 + 1.3

= 2.59

Now, divide the result by 2

Dividing

2.59/2

= 1.295

∴ On the number line, the midpoint of the given numbers is 1.295

Hence, the midpoint of the given numbers (1.29 and 1.3) is 1.295

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Based on the information given, the values are:

1. 80 rides

2. 53. 3%

3. 56. 6%

4. 30 students

Percentage can be defined as the ratio of a number to 100.

It is denoted with the symbol, '%'

How to determine the values;

1.. 24 rides = thirty percent of the total rides

Total rides = 24 rides/ 30%

Total rides = 24/ 30/ 100 = 24/ 0. 3 = 80 rides

2.  There are 14 Apple computers

16 PC computers

% of PC computers = 16/ 16 + 14 × 100/ 1

% of PC computers  = 16/ 30 × 100

% of PC computers  = 0. 53 × 100 = 53. 3

3.  3 out of 30 are not working

% of the working computers = 30- 3/ 30 × 100

% of the working computers = 17/ 30 × 100

% of the working computers = 56. 6

4.

If 12 students = 0. 4

Then x students = 1 - 0. 4 = 0. 6

cross multiply

x = 18 students

Total number of students = 40% + 60% of students = 18 + 12 = 30

Thus, the values are 80 rides, 53. 3%, 56. 6% , 30 students respectively.

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