2x2 =4
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The definite value of f(x) when x approaching to 3 is 14

What is limit of function ?

In mathematics, limits are the values that a function (or sequence) approaches when an input (or index) approaches a particular value. Limits are essential for calculus and mathematical analysis, and are used to define continuity, derivatives, and integrals.

Here, the function given as :

f(x) = x^2+2x-1

and it is to find the value of f(x) when x approaching to 3 that is :

[tex]\lim_{x \to 3}[/tex] f(x) = [tex]\lim_{x \to 3}[/tex] x^2+2x-1

Now, substitute x equals to 3 in f(x) to get a definite value of f(x) :

[tex]\lim_{x \to 3}[/tex] f(x) = 3^2+2 x 3 -1

[tex]\lim_{x \to 3}[/tex] f(x)  = 9 + 6 -1

[tex]\lim_{x \to 3}[/tex] f(x) = 14

Therefore, the definite value of f(x) when x approaching to 3 is 14 .

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The first five terns of the sequence are - 1,4,1,4,1

A sequence is an enumerated group of items in mathematics where repetitions are permitted and order is important. It has members, just like a set does. The length of the sequence is determined by the number of items.

an = 5 - a n-1

a1 = 1

a2 = 5 - (1) = 4

a3 = 5 - (4) = 1

a4 = 5 - (1) = 4

a5 = 5 - (4) = 1

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The value of pi in the given equation is [tex]\frac{V}{r^2 h}[/tex].

The volume of a cylinder is the capacity of the cylinder, which determines how much material it can hold. In geometry, a specific volume of a cylinder formula is used to calculate how much of any quantity, liquid or solid, can be immersed in it uniformly. A cylinder is a three-dimensional shape with two identical congruent and parallel bases.

The given equation gives us the formula to calculate the volume (V) of the any given cylinder with the help of it's height(h) and base radius (r).

Given, [tex]$\quad V=\pi r^2 h$[/tex]

Divide both sides by h.

[tex]\frac{V}{h}[/tex] = [tex]\frac{\pi r^2 h}{h}[/tex]

V/h = π/[tex]$r^2$[/tex]

Divide both sides by [tex]$r^2$[/tex].

[tex]\frac{V}{r^2 h}[/tex] = [tex]\frac{\pi r^2}{r^2}[/tex]

π = [tex]\frac{V}{r^2 h}[/tex]

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The radio station awarded all three prizes to the 300th caller.

To estimate the one caller to receive the all three prices, find the LCM of 15, 25 and 100.

LCM of 15, 25 and 100 is as follows;

3     15, 25, 100

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

4      5, 25, 100

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

5      5, 25, 25

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

5       1, 5, 5

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

         1, 1, 1

LCM = 3×4×5×5

LCM = 300

Therefore, the radio station will first award all three prizes to the 300th caller.

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The value of x is 3 and the measure of each side of isosceles ΔJKL is:

JK = 11

KL = 11

LJ = 5

We know that, in an isosceles triangle, any two sides of the triangle are equal and the angle opposite to these sides are equal in measure.

In this question, we have been given an isosceles ΔJKL with JK ≅ KL .

Also we have been given,

JK = 4x - 1, KL= 2x + 5 , and LJ = 2x - 1

As JK = KL

⇒ 4x - 1 = 2x + 5

⇒ 4x - 2x - 1 = 2x + 5 -2x

⇒ 2x = 5 + 1

⇒ 2x = 6

⇒ x = 3

So, the value of x is 3.

Now we find the measure of each side of triangle JKL

JK = 4x-1

JK = 4(3) - 1

JK = 12 - 1

JK = 11

Now the side KL

KL = 2x + 5

KL = 2(3) + 5

KL = 11

And LJ = 2x-1

LJ = 2(3) - 1

LJ = 5

Therefore, the value of x is 3 and the measure of each side of isosceles ΔJKL is:

JK = 11

KL = 11

LJ = 5

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Answer:

$2,834.31

Step-by-step explanation:

11225 × 25.25/100

11225 x 0.2525

$2,834.31

The equation of the circle x^2 + y^2 - 6x + 14y = 8 has a radius of √66 and a center located at (3 , -7).

The standard form of the equation of  circle is given by

(x - h)^2 + (y - k)^2 = r^2

where (h , k) is the location of the center and r is the radius of the circle.

On the other hand, the general form of the equation of  circle is given by

x^2 + y^2 + Dx + Ey + F = 0

where D = -2h, E = -2k, and F = h^2 + k^2 -r^2.

If the equation of the circle in general form is x^2 + y^2 - 6x + 14y = 8, then the coefficients are:

D = -6

E = 14

F = -8

If D = -2h and D = -6, then

-6 = -2h

h = 3

If E = -2k and E = 14, then

14 = -2k

k = -7

If F = h^2 + k^2 -r^2 and F = -8, then

-8 = 3^2 + (-7)^2 - r^2

r^2 = 9 + 49 + 8

r^2 = 66

r = √66

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The equation that could be used to determine c, the cost of labor per hour is $603.75= x × 5.25 and cost of labour per hour is $115

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

The total amount paid by Andres is the sum of the total cost of labour and the cost of the parts.

The Total amount paid = total cost of labour + cost of parts

$719.75= total cost of labour + $116

The total cost of labour = $719.75- $116

= $603.75

The total cost of labour = cost of labour per hour x total time worked

$603.75= x × 5.25

xx = $603.75/ 5.25

xx = $115

Hence, The cost of labour per hour is $115

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By elimination, the solution of the system of equations, 2a + 3b = 12 and 5a - b = 13, is (a , b) = (3 , 2).

A system of equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy all the equations.

There are three methods that can be used to solve system of equations.

1. Elimination

2. Substitution

3. Graphing

Using the elimination method, given two equations in a and b, a variable should be eliminated by adding/subtracting the two equations.

Multiply first equation 2 by 3.

5a - b = 13     (equation 2)

15a - 3b = 39

Adding the two equations will eliminate the variable b.

2a + 3b = 12     (equation 1)

15a - 3b = 39     (equation 2)

17a        = 51

a = 3

Substitute the value of a to any of the two equations and solve for b.

2a + 3b = 12     (equation 1)

2(3) + 3b = 12

3b = 12 - 6

3b = 6

b = 2

Hence, the solution of the system of equations is (a , b) = (3 , 2).

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Answer:

23

Step-by-step explanation:

8+3(4+6)/2

8+3(10)/2

8+30/2

8+15

=23

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The screen size of the HDTV is approximately 36.65 inches.

Here,

The screen aspect ratio of a high-definition television is 16:9, which means the width is 16 units and the height is 9 units.

We are given that the width of the HDTV is 41 inches.

To find the screen size, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the diagonal distance across the screen) is equal to the sum of the squares of the other two sides (width and height).

Let's assume the height is h inches.

Using the Pythagorean theorem, we have:

[tex](41^2) = (16^2) + (9^2) + (h^2)[/tex]

Simplifying this equation, we get:

[tex]1681 = 256 + 81 + h^2\\1681 = 337 + h^2\\h^2 = 1681 - 337\\h^2 = 1344\\[/tex]

Taking the square root of both sides, we find:

h ≈ 36.65 inches

Therefore, the screen size of the HDTV is approximately 36.65 inches.

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Simply divide by the decimal points to make it a fraction and then divide to make it a mixed fraction. The answer is

a) 7/10

b) 4/100

c) 40 45/10

d) 20 19/10

Represent the number as fraction or mixed number

Fractions are defined as the parts of a whole. The whole can be an object or a group of objects. In real life, when we cut a piece of cake from the whole of it, then the portion is the fraction of the cake.

Mixed Number is the combination of a whole number and a fraction. The numerator and denominator are part of the proper fraction that makes the mixed number. It is two-part in a fraction that helps to make the mixed number. Mixed fraction can only be made when the numerator is greater than denominator.

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The volume of the larger ball the company sells is 220,893.2 cubic centimeters.

If the diameter of the smaller ball is 55 centimeters, and the ratio of the diameters of two different sizes of exercise balls is 15 : 11, then

diameter of larger ball / diameter of smaller ball = 15 : 11

diameter of larger ball = 15 (55 cm) / 11

diameter of larger ball = 75 cm

If the diameter of the larger ball is 75cm, and half of the diameter is the radius, then:

r = D/2

r = 75cm/2

r = 37.5 cm

Solving for the volume of the larger exercise ball using the formula for the volume of the sphere given by:

V = 4/3πr^3

V = 4/3π(37.5 cm)^3

V = 220,893.2335 cubic centimeters

Rounding off to the nearest tenth.

V = 220,893.2 cubic centimeters

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According to the question, the triangles ABC and DFE are mapped with each other.

Triangle DFE is right-angled triangle with ABC. And triangle ABC uses acute-angled theorem to mapped onto triangles DFE. Finally, the triangles are scalene triangles.

What is triangle?

The triangle can be defined as a polygon shape with three sides as well as three vertex. Depending upon the sides as well as angles, the triangles can be differentiated.

When all the sides are different, they comes under scalene triangles. When two sides are equal in a triangle then they are isosceles triangle. And finally, when all the sides are equal they are called as equilateral triangle.

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Answer: Triangle DFE is a rotation and reflection of triangle ABC. Since triangle ABC uses only rigid transformations to map onto triangle DFE, the triangles are congruent.

Step-by-step explanation:

See attached image below for proof

The probability of the event P(A is on [tex]\bar{DE}[/tex]) is 9/26.

Probability:

Probability defines the possibility of the event.

And it can be calculated as,

Probability = favorable event / total event

Given,

Point A is chosen at random on [tex]\bar{BE}[/tex].

Here we need to find the the probability of the following event.

P(A is on [tex]\bar{DE}[/tex]).

Let us consider the following image, in order to solve this.

Based on the image we have identified that the probability of the event  P(A is on [tex]\bar{DE}[/tex]) is calculated by dividing the length of DE by the length of BE.

So, the probability of the event P(A is on [tex]\bar{DE}[/tex]) is,

P(A is on [tex]\bar{DE}[/tex]) =  (length of DE) / (length of BE)

Apply the values then we get,

P(A is on [tex]\bar{DE}[/tex]) = 9 / ( 5 + 12 + 9)

P(A is on [tex]\bar{CD}[/tex]) = 9 / 26

Therefore, the probability of the event P(A is on [tex]\bar{DE}[/tex]) is 9/26.

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The mean number of packages is 19.

It should be noted that mean also means the average of a set of numbers given.

In this case, there are four packages.

The total cards will be:

= 17 + 21 + 22 + 16

= 76

Therefore, the average will be:

= Total cards / Number of package

= 76/4

= 19

Therefore, the mean number of packages is 19.

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The first package has 17 cards second package has 21 thrid has 22 fourth has 16. What is the mean?

Answer:

angle 7 has a measure of 135 degrees because it's a vertical angle with the given angle

40320 ways can they line up to purchase their tickets.

What in mathematics is a permutation?

given that n = 8 people

1st person have 8 choices to take ticket &

2nd person have 7 choices & 3rd  person have 6 like that 8 people can purchase their tickets in = 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1  ways

                                         = 8 !

                                         = 40320

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9r - 177 > - r + 233

9r + r > 233 + 177

10r > 410

^^^Divide both sides

Answer:

r > 41

Alternative form:

r ∈ ( 41, + ∞ ), { r | r > 41 }

It's correct! :)

Answer:

Hello im sorry but I am unable to answer this.

Step-by-step explanation:

There is no parallelogram shown to answer.

The estimated speed of light travel meter per second is 300 m/s

Light: 300,    000,     000 ;    8;      3;        8;

Sound: 300;    2;         3;        2.       3*10^8 > 3 * 10^2

According to the question, the greatest place value 299,792,458

sound travel at 332 m/s.

299,792,458 ≈ 300,000,000

322≈300 (estimation)

First of all, you refer to physics. Physicists detest miles per second estimate units. They would use meters per second (SI units),centimeters per second (CGS or less desirable SI units), or the value 1 (so-called natural units) be dependent on the type of work they are doing experimental.

Second, suppose you are mention to the condition of a vacuum. Light slows down when passing through the other a vacuum.

Third, even if physicists use miles per second as units, the values you gave are quite discrepant. The value 299 792 458 m/s is one of the  values of the international system of units (SI). The speed of light is not explained to be this value, but it is a fixed value regarded as exact to be used in explain what is a meter . If in any case, it is not a calculate value and it has no uncertainty. If we do an exact conversion of this exactly value to miles per second, which is 186282 (39937/100584) m/s .

We see that, the meter per second value you stated is require, the mile per second value is only a rounded approximation and is off by about 0.15 %.

The 299 792 458 m/s value is what physicists use when they are doing calculations as part of their research, because they require the exactness. they will round off to one significant digit (actually the value is correct to three significant digits but it looks like just one) and use 300 000 000 m/s = 3 × 10⁸ m/s, which is almost trivial to multiply or divide by mentally (unlike the 186 000 mi/s) and is only 0.07 % off.

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Answer:

The volume of a solid hemisphere is 19404 cm3. Its total surface area is. 4158 cm.

Step-by-step explanation:

I hope this will be helpful for you and please like my answer.

The [tex](x +2 )^2+(y-1)^2=113[/tex]

The equation of a circle with centre (h,k) and radius r may be written:[tex](x -h )^2+(y-k)^2=r^2[/tex]

We are given (h,k)=(-2,1), so the only unknown is [tex]r^2[/tex].

So,

[tex](x +2 )^2+(y-1)^2=r^2[/tex]

Since the circle passes through (6,−6), the values

x=6, y =−6 will satisfy the equation and we find:

[tex]r^2 = (6-(-2))^2 + (-6-1)^2\\r^2 = (8)^2+(-7)^2\\r^2 = 64 + 49\\r^2 = 113[/tex]

So,

[tex](x +2 )^2+(y-1)^2=113[/tex]

Therefore the equation of the circle that has center (-2, 1) and passes through (6, -6) is [tex](x +2 )^2+(y-1)^2=113[/tex].

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The equation of circle that has center (-2, 1) and passes through (6, -6) is [tex](x+2)^2+(y-1)^2=113[/tex]

The equation of a circle with centre (h,k) and radius r may be written:

[tex](x-h)^2+(y-k)^2=r^2[/tex]

We are given (h,k)=(-2,1), so the only unknown is [tex]r^2[/tex].

So,

[tex](x+2)^2+(y-1)^2=r^2[/tex]

Since the circle passes through (6,−6), the values x=6, y =−6 will satisfy the equation and we find:

[tex]r^2=(6+2)^2+(-6-1)^2\\r^2=(8)^2+(-7)^2\\r^2=64+49\\r^2=113[/tex]

So,

[tex](x+2)^2+(y-1)^2=113[/tex]

Therefore the equation of the circle that has center (-2, 1) and passes through (6, -6) is [tex](x+2)^2+(y-1)^2=113[/tex]

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The translation of a coin from A to C using a translation vector is ;

Vector AC = (7, 3).

A translation in arithmetic a structure left or right and/or up or down. The translated shapes appear to be of the same size as the initial structure, indicating that the shapes are congruent.

Now, as per the given question.

See the given figure.

The coordinates if the points A and C are.

A = (-3, -1) and C = (4, 2)

The translation from A to C is estimated as;

AC = (4 + 3) ,(2 + 1)

Translation AC = (7, 3)

Thus,  the given point A shifts 7 units to its right and then 3 units up to the point C.

Therefore, the representation of the translation of A and C in the form of

translation vector is  AC = (7, 3).

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The given polynomial, 6•x² + 12•x + 6, can be factored by rearranging and looking for the common factors to give;

6•x² + 12•x + 6 = 6•(x + 1)²

The given polynomial is presented as follows;

6•x² + 12•x + 6

The coefficients in the terms and the constant have a common factor of 6, which gives;

6•x² + 12•x + 6 = 6•(x² + 2•x + 1)

x² + 2•x + 1 = x² + x + x + 1

x² + x + x + 1 = x•(x + 1) + 1•(x + 1)

x•(x + 1) + 1•(x + 1) = (x + 1)•(x + 1) = (x + 1)²

Therefore;

x² + 2•x + 1 = (x + 1)²

6•(x² + 2•x + 1) = 6•(x + 1)²

6•x² + 12•x + 6 = 6•(x² + 2•x + 1)

Therefore;

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The expression 83−7.5t represent C. the volume of water left after t hours.

From the information, each hour, 7.5 liters drain from a large water tank and thee tank initially held 83 liters of water.

Therefore, the expression 83−7.5t represent the volume of water left after t hours.

In conclusion, the correct option is C.

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The value of the given expression is 4,096/729. Therefore, option A is the correct answer.

The given expression is ((-4/3)²)³.

We need to evaluate the given expression.

A number's exponent indicates how many times the number has been multiplied by itself.

Now, ((-4/3)²)³=((-4/3)×(-4/3))³

=(16/9)³

=(16/9)×(16/9)×(16/9)

=(16×16×16)/(9×9×9)

=4,096/729

The value of the given expression is 4,096/729. Therefore, option A is the correct answer.

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The reasons for statements 2 and 3 are

Vertical opposite angles are angles formed when two lines intersect one another. When the lines intersect the angles facing each other or opposite the next is called the vertical opposite angle. The angles formed in this case are equal

Following the figure angle 3 and angle 2 are vertical opposite angles and they are equal. They are formed by intersection of the the parallel line L and the diagonal line running across. Similarly, angle 1 and angle 4 are vertical opposite angles since angle 1 and angle 4 face each other at the point of intersection.

When the sum of two angles is equal to 180 degrees, such angles are called supplementary angles. These angles usually lie on a straight line and the angle on a straight line is 180 degree

Considering the given figure angle 3 and angle 5 are supplementary angles. that is to say that their sum is 180 degrees.

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The similarity between common difference and common ratio is that both are used to find the next term, but common difference is added while common ratio is multiplied.

Common difference (d) is defined as the difference between consecutive terms in an arithmetic sequence. It is determined by subtracting the term from the preceding term. For example, in an arithmetic sequence 2, 5, 8, 11,…, the common difference is 5-2=3 or 8-5=3.

The sequence will be: a, a+d, a+2d, a+3d,… a+nd.

In the general form:

d=an -an-1, where an is the nth term and an-1 is the preceding term.

Common ratio (r) is defined as the quotient between consecutive terms in a geometric sequence. It is determined by dividing the term by the preceding term. For example, in an geometric sequence 2, 4, 8, 16,…, the common ratio is 4/2=2 or 8/4=2.

The sequence will be: a, ar, ar^2, ar^3,…ar^n.

In the general form:

r=an/an-1, where an is the nth term and an-1 is the preceding term.

Hence, both common difference and common ratio shows relationship between consecutive terms in a sequence. Common difference is added to the term to find the next term while common ratio is multiplied to the term to find the next term.

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