Graph f(x) = 2x - 3 on a coordinate plane.
Can you explain what you are going to do in order to graph this equation?
What do you expect the graph to look like?

Answer:

Step-by-step explanation:

integer and rational

The 2nd term exists 12 and 7th term exceeds the 4th by 15 exists AP : 7,12,17,....

Given : The second term exists 12th and the 7th term exceeds the 4th term by 15

The formula of the nth term :

[tex]$a_{n}=a+(n-1) d[/tex]

Where d exists a common difference

n be the number of terms

a be the first term

Substitute the value of n = 2

[tex]$a_{2}=a+(2-1) d=a+d[/tex]

Let, the second term exists 12

So, a + d = 12 ..........(1)

Substitute the value of n = 7

[tex]$a_{7}=a+(7-1) d=a+6 d[/tex]

Substitute n = 4

[tex]$a_{4}=a+(4-1) d=a+3 d[/tex]

We are given that the 7th term exceeds the 4th term by 15

So, a+6d-a-3d = 15

3d = 15

d = 5

Substitute the value of d in (1)

So, a+5 = 12

a = 12-5

a = 7

AP : a,a+d,a+2d,.... = 5, 7+5, 7+2(5),....=7,12,17,....

Therefore, AP : 7,12,17,....

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A vertically opposite angle is a pair of angles formed due to the intersection of two lines, and are said to be equal. Thus the angle that is the same as <BPD is <APC.

ii. The value of x is [tex]47^{o}[/tex].

The intersection of two or more lines at a point will always produce a set of angles. Some of these angles when compared may have similar measures or properties.

Two angles can be equal with respect to their measure if they are vertically opposite. Vertically opposite angles are angles formed when two lines intersect, such that a pair of opposite angles about the point of intersection are equal.

Thus from the given question, the angle that is the same as <PBD is <APC.

i.e <BPD ≅ <APC (vertically opposite property)

Also,

x + 133 = 180 (sum of angles on a straight line)

x = 180 - 133

  = 47

x = [tex]47^{o}[/tex]

Therefore the value of x is [tex]47^{o}[/tex].

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We have enough data to reject our null hypothesis if the value of our test statistics falls below critical values of z at a 1.25% level of significance (critical values are -1.645 and 1.645). This is because the test statistic value will not fall within this region.

Given that the population mean is 650, we do a two-tail hypothesis test with a level of significance of 0.025.

Let, μ = population mean

Thus, Null hypothesis, [tex]H_{0}[/tex]:μ= 650.

Alternate Hypothesis, [tex]H_{A}[/tex]:μ≠650

In this case, the population mean is equal to 650, according to the null hypothesis.

The alternative hypothesis, on the other hand, contends that the population mean is not 650.

First things first: the level of significance to be accepted for the two-tailed test is ([tex]\frac{\alpha }{2}[/tex]= [tex]\frac{0.025}{2}[/tex]) = 0.0125 or 1.25%.

Therefore, the following is the decision rule for rejecting a null hypothesis:

We have enough data to reject our null hypothesis if the value of our test statistics falls in the rejection region and is less than the critical values of z at a 1.25% level of significance (critical values are -1.645 and 1.645). This is because the test statistic value will not fall within this region.

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According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.

Herein we have a series in rational form, whose convergence can be proved by the ratio criterion, whose defintion is shown below:

x = lim (n → ∞) |aₙ/aₙ₊₁|   (1)

The series converges if x < 0 and diverges when x > 1. If x = 1, the criterion cannot be used and another criterion must be used instead. Now we proceed to apply it on the expression behind the series:

|aₙ/aₙ₊₁| = [(2 · n + 1) · (2 · n + 2)] / [5 · (n + 1)²]

|aₙ/aₙ₊₁| = [4 · n² + 5 · n + 2] / [5 · n² + 10 · n + 5]

Then, by applying the limit property for rational equations we find that limit of the expression within the series is:

L = 4 / 5

According to the ratio criterion, the rational series presented in the picture converges as x < 1. The limit L was 4 /5.

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By the ratio test, the series diverges.

[tex]\displaystyle \lim_{k\to\infty} \left| \frac{5^{k+1} ((k+1)!)^2}{(2(k+1))!} \cdot \frac{(2k)!}{(5^k (k!)^2}\right| = 5 \lim_{k\to\infty} \frac{(k+1)^2}{(2k+2)(2k+1)} = \frac54 > 1[/tex]

Answer:

8 Hours

Step-by-step explanation:

We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.

[tex]\frac{220}{5}x=352[/tex]

Multiply both sides by 5

[tex]220x=1760[/tex]

Divide both sides by 220

[tex]x=8[/tex]

Therefore it would take 8 hours.

8 Hours long would it take to travel 352 miles,

The distance that an object travels in relation to the amount of time it takes to do so can be used to define speed. In other words, it is a measurement of an object's motion's speed without direction Velocities are what we get when speed and direction are combined. The SI unit system is most frequently used to express speed units. In that system, since distance is measured in metres and time is measured in seconds, speed is expressed in metres per second, or m/s. Three components make up the speed formula: distance, time, and speed.

We know she travels 220 miles in 5 hours, so lets create an equation with a ratio which finds the miles she drives in a single hour, multiply that by x, and then set it equal to 352.

Multiply both sides by 5

Divide both sides by 220

Hence, it would take 8 hours.

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Answer: D

Step-by-step explanation: The line of best fit is a straight line that passes through as many points as possible and has around the same number of points above and below it. D meets those requirements the best.

Answer:

Line D

Step-by-step explanation:

Line D is most fit because it intercepts more of the dots on the graph, if not, comes close to touching the majority of them.

The correct option is B.

The enrollment capacity be 3 years from now is 2410

A series of integers in which the difference between succeeding words is always the same is referred to as an arithmetic sequence or arithmetic progression. For instance, the difference in the arithmetic series 1, 5, 9, 13, 17,... is always 4. The common difference is what we refer to as.

The formula for determining the nth term is used to locate a specific term in an arithmetic sequence. Step 1: An = a + (n - 1)d determines the nth term of an arithmetic series. Add the variables a = 2 and d = 3 to the formula in order to find the nth term.

At = a1 + (n - 1) x d is an equation that can be used to express the number of applications each year.

N equals 4 based on the information provided above. This corresponds to the term, which begins in three years.

At = 2200 + (4 - 1) x 70 = 2410

Thus, 2410 students could enroll at one time.

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Answer:

- (2x^2 - 13x + 6)

The above expression is in brackets and a negative sign is outside of the brackets. This means that when expanding the expression, we have to multiply each number with the negative sign (each number would switch their signs to the opposite one). Therefore, 2x^2 becomes -2x^2, -13x becomes 13x and 6 becomes -6.

Answer:

5) 26

6) 18

Step-by-step explanation:

Substitute the value of the variables in the expression and evaluate.

x = 2 ; y = -3 and z = 1

Absolute value:  Absolute value of a real number is the non negative a value of x without regard its sign.

Example: I-3I = 3

               I 3I = 3

5) 24 + Ix - 4I =24 + I 2 - 4I

                      = 24 + I-2I

                      = 24 + 2

                      = 26

6) 13 + I 8 +y I = 13 + I 8 + (-3)I

                       = 13 + I 5 I

                       = 13 + 5

                       = 18

The direction does the parabola open is right. Option C

It is important to note that the general equation of a parabola is: y = a(x-h)² + k or x = a(y-k)² +h

where

⇒ (h , k) denotes the vertex.

Also, the standard equation of a regular parabola is y² = 4ax.

From the equation given , we have

We know that when the vertex of the parabola is (0, 0) and the directrix is x = - a, the parabola will have the form;

y² = 4ax

It is important to note that ;

From this, we can see that the parabola would open in the right direction

Thus, the direction does the parabola open is right. Option C

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Answer:

1/12 mile

Step-by-step explanation:

He walks 7/12 mile in 7 minutes.

In 1 minute, he walks 1/7 of the distance.

1/7 of 7/12 mile = 1/12 mile

Answer:

This is the answer of this question. Hope it helps.

Answer:  2.5 meters

This value is exact without any rounding.

======================================================

Explanation:

The first task is to convert the mixed number 20⅚ into an improper fraction

I'll write 20⅚ as 20 & 5/6

The rule to use is a & b/c = (a*c + b)/c

So,

a & b/c = (a*c + b)/c

20 & 5/6 = (20*6+5)/6

20 & 5/6 = 125/6

This means the volume is exactly (125/6)pi cubic meters.

Plug this into the sphere volume formula and isolate the radius r like so

V = (4/3)*pi*r^3

(125/6)pi = (4/3)*pi*r^3

125/6 = (4/3)*r^3

(4/3)*r^3 = 125/6

4r^3 = 3*(125/6)

4r^3 = 125/2

r^3 = (125/2)*(1/4)

r^3 = 125/8

r = (125/8)^(1/3)

r = 5/2

r = 2.5

Answer:

[tex]\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]

Step-by-step explanation:

We are given the expression:

[tex]\displaystyle{\dfrac{3}{x^2-9} + \dfrac{5}{x+3}}[/tex]

First, factor the denominator [tex]\displaystyle{x^2-9}[/tex] to [tex]\displaystyle{(x+3)(x-3)}[/tex] via difference of two squares:

[tex]\displaystyle{\dfrac{3}{(x+3)(x-3)} + \dfrac{5}{x+3}}[/tex]

Next, multiply the expression 5/(x+3) by [tex]\displaystyle{x-3}[/tex] both denominator and numerator:

[tex]\displaystyle{\dfrac{3}{(x+3)(x-3)} + \dfrac{5(x-3)}{(x+3)(x-3)}}[/tex]

Add both together since they have same denominator now:

[tex]\displaystyle{\dfrac{3+5(x-3)}{(x+3)(x-3)} }[/tex]

Simplify the numerator:

[tex]\displaystyle{\dfrac{3+5x-15}{(x+3)(x-3)} }\\\\\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]

Therefore, the sum is:

[tex]\displaystyle{\dfrac{5x-12}{(x+3)(x-3)} }[/tex]

Using the linear equation, T = 20x + 31, the total number of computers at the end of 2005 is: C. 191.

A linear equation is expressed as y = mx + b, where x is a function of y, m is the rate of change and b is the y-intercept or starting value.

In the scenario stated, we are given the linear equation for total number of laptop computers at the school after 1997 as, T = 20x + 31.

Rate of change = 20

y-intercept/starting value = 31

x = 2005 - 1997 = 8

To find the total number of laptop computers at Grove High School at the end of 2005 (T), substitute x = 8 into the equation, T = 20x + 31.

T = 20(8) + 31

T = 160 + 31

T = 191 computers.

Thus, total number of computers at the end of 2005 is: C. 191.

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The mpg and hp is print(paste("The car with the best combination of mpg and hp is",rownames(myCars[myCars$combination==max(myCars$combination),])))

MPG is an abbreviation for 'miles-consistent with gallon and it is used to give you an indication of the fuel financial system of a vehicle or industrial vehicle. It helps you to work out how reasonably-priced or high-priced an automobile might be to run.

As for a new vehicle, an awesome MPG is around 50 to 60. Having this stepped forward gasoline economy facilitates minimizing going for walks fees and cheaper avenue tax due to decreased CO2 emissions. consistent with What car's featured blog, here are a number of the most gasoline-green automobiles in the marketplace nowadays.

The gas economic system of a car relates to the space traveled via an automobile and the quantity of fuel fed on. intake can be expressed in terms of the volume of gasoline to travel a distance, or the gap traveled according to the unit quantity of gasoline consumed.

The car has the “best” combination of mpg and hp, where mpg and hp must be given equal weight.

#sum the scaled values of mpg and hp and add a new column called combination

myCars$combination<-scale(myCars$hp)+scale(myCars$mpg)

#Which car has the best combination of mpg and hp?

print(paste("The car with the best combination of mpg and hp is",rownames(myCars[myCars$combination==max(myCars$combination),])))

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The series converges to  1/(1-9x) for -1/9<x<1/9                  

Given the series is  ∑ [tex]9x^{n} x^{n}[/tex]

We have to find the values of x for which the series converges.

We know,                

∑ [tex]ar^{n-1}[/tex]    converges to  (a) / (1-r) if r < 1

Otherwise the series will diverge.

Here, ∑ [tex](9x)^{n}[/tex] is a geometric series with |r| = | 9x |

And it converges for |9x| < 1

Hence, the given series gets converge for -1/9<x<1/9

And geometric series converges to a/(1-r)

Here, a = 1 and r = 9x

Therefore, a/(1-r) = 1/(1-9x)

Hence, the given series converges to   1/1-9x  for  -1/9<x<1/9

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Debido a restricciones de extensión y la características del ejercicio, recomendamos leer la explicación de esta pregunta para mayores detalles sobre la adición de números enteros.

En este ejercicio tenemos un grupo de sumas con números enteros positivos y negativos, en las cuales se prueba la capacidad del estudiante para realizar varias operaciones en serie (adición, sustracción) y comprender las diferencias entre números positivos, negativos y neutros. Ahora procedemos a determinar el resultado de cada una de las expresiones:

20 + 50 + 30 + 7 = 107

30 + 5 + 2 = 37

- 200 - 50 - 70 - 8 = - 328

- 500 + 100 - 20 + 50 = - 370

10 - 5 = 5

20 + 50 - 25 - 10 = 35

- 100 + 20 = - 80

- 30 + 5 + 4 - 20 + 8 = - 33

- 258 + 8 = - 250

- 10 + 20 + 520 - 100 + 8 = 438

- 20 - 5 - 42 + 3 = - 64

1000 - 200 + 50 + 30 - 45 + 75 - 87 + 90 + 50 - 100 + 50 - 10 = 903

- 400 + 500 - 200 - 50 + 48 + 8 - 47 - 50 = - 191

300 + 20 - 50 + 30 - 84 + 35 - 7 + 20 - 40 + 10 - 45 + 65 + 8 - 55 = 207

800 + 50 - 69 + 8 - 35 + 85 - 54 + 40 + 85 + 74 - 32 - 8 + 65 - 27 = 982

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a) The equation represents an ellipse.

b) The equation represents a circle.

c) The equation represents a parabola.

In this problem we have general equations of the form A · x² + B · y² + C · x + D · y + E = 0, which have to be modified into standard form to infer its graphical form. This procedure can be done by algebra properties:

16 · x² + 4 · y² + 96 · x - 8 · y + 84 = 0

[(4 · x)² + 2 · 12 · (4 · x)] + [(2 · y)² - 2 · 2 · (2 · y)] = - 84

[(4 · x)² + 2 · 12 · (4 · x) + 144] + [(2 · y)² - 2 · 2 · (2 · y) + 4] = 64

(4 · x + 12)² + (2 · y + 2)² = 64

4² · (x + 3)² + 2² · (y + 2)² = 64

(x + 3)² / 4 + (y + 2)² / 16 = 1 : Ellipse

x² + y² + 8 · x - 6 · y - 15 = 0

(x² + 8 · x) + (y² - 6 · y) = 15

(x² + 2 · 4 · x + 16) + (y² - 2 · 3 · y + 9) = 40

(x + 4)² + (y - 3)² = 40 : Circle

x² + 6 · x + 4 · y + 5 = 0

x² + 6 · x + 5 = - 4 · y

y = - (1 / 4) · x² - (3 / 2) · x - (5 / 4) : Parabola

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The total cost that company ABC uses to produce x graphing calculators in a month is given by y = 1.5x + 150

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

The standard form of a linear function is:

y = mx + b

Where m is the rate of change and b is the initial value of y.

Let y represent the total cost of producing x calculators in a month, hence:

y = 1.5x + 150

The total cost that company ABC uses to produce x graphing calculators in a month is given by y = 1.5x + 150

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A polygon is a figure that has a given number of sides.

A polygon is an n - sided figure. The number of sides in a polygon is almost infinite. Let us now match the properties with the type of polygon.

a. 12.gon - An interior angle measures 150°

The polygon that has 12 sides is called the Dodecagon.

Given that the sum of the interior angles in a dodecagon is 1800, then  each interior angle is; 1,800/12

= 150°

b. 15-gon - An exterior angle measures 24°

The polygon that contains 15 sides is called pentadecagon. Given that the sum of the exterior angles of polygon is 360 degrees and each exterior angle is  24° then;

360/ 24° = 15 sides

c. 16-gon - The sum of the interior angles is 2,520°

The polygon that contains 16 sides is called the hexadecagon. The sum of its interior angles is 2,520° hence each interior angle measures; 2,520°/16 =  157.5°

d. 18-gon - An interior angle measures 160°

A polygon that contains 18 sides is called an octadecagon .

We have;

160 = (n−2) × 180° / n

160n = 180n - 360

360 = 20n

n = 18

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Missing parts;

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Match the properties to the regular polygons they describe.

An interior angle measures 150".

An exterior angle measures 24.

The sum of the interior angles is 2520°.

An interior angle measures 160".

The sum of the exterior angles is 180º.

The sum of the interior angles is 2160°.

15-gon

16-gon

12.gon

18-gon

Answer:

Step-by-step explanation:

Answer:[tex]\Large\boxed{First~choice.~y\leq \frac{1}{2}x+2 }[/tex]

Step-by-step explanation:

Given function form

Point-Slope form : y = mx + b

Given the information from the graph

Since the graph crosses (0, 2), b = 2

Find the slope

Choose any two points from the graph

(x₁, y₁) = (0, 2)

(x₂, y₂) = (2, 3)

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (3 - 2) / (2 - 0)

Slope = 1 / 2

m = 1 / 2

Therefore, the equation form of the inequality is y = (1/2)x + 2

Since it is a solid line, the values on the line are also included. Thus, it must be either greater than or equal to, or less than or equal to.

The shaded region is below the solid line, therefore, it is ≤

Therefore, the inequality is [tex]\Large\boxed{y\leq \frac{1}{2}x+2 }[/tex]

To double-check the sign, we can substitute (0, 0) into the inequality to see whether it is true.

y ≤ (1/2) x + 2

0 ≤ (1/2) 0 + 2

0 ≤ 2              TRUE

Hope this helps!! :)

Please let me know if you have any questions

Answer:

x > 6

Step-by-step explanation:

2x - 7 > 5

2x > 5 + 7

2x > 12

x > 6

Answer:

(a)

(b) range of sample means =0.6

(c)

Based on the various costs resulting from the lease terms at the local dealership, the total cash to pay at signing is $5,480

This can be found by the formula:

= Down payment + Monthly payment + Security deposit + Acquisition fee

Solving gives:

= 4,100 + 475 + 415 + 490

= $5,480

In conclusion, option A is correct.

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Answer: B. $5005

Step-by-step explanation:

Answer:

The answer is x=2 and y=0.

Step-by-step explanation:

The given Equations are:

                    5x-2y=10      ----------------- (i)
                    4y+20=10x   ----------------- (ii)

From equation find the value of x, that is:

         5x=10+2y         (Obtained By adding 2y on both side of Equation (i))

Next divide with 5 on both side to get x:

          x=(10+2y)/5           ------------------ (iii)

Put this value of x in equation (ii):

        4y+20=10((10+2y)/5)

Simplifying the above equation:

         4y+20=2(10+2y)

         4y+20=20+4y

From the above equation the solution of y is not possible.

We can make it 0. So,
         y=0

Put this value of y in equation (iii), to get value of x:

        x=(10+2(0))/5

        x=(10+0)/5

        x=10/5

        x=2