What is the answer to the following questions: 2 x 5

Add or subtract.Simplify where possible.

[tex]\frac{4}{x^{2}-36} +\frac{x}{x-6}[/tex] =  [tex]\frac{4+x^{2}+6x}{(x+6)(x-6)}[/tex]

How the given expression is simplified?

[tex]\frac{4}{x^{2}-36} +\frac{x}{x-6} \\\\\text{On taking LCM of the denominator}\\\\\frac{4}{x^{2}-36} +\frac{x^{2}+6x }{x^{2}-36}\\\\\frac{4+x^{2}+6x}{x^{2}-36}\\\\\frac{4+x^{2}+6x}{(x+6)(x-6)}[/tex]

What is simplification?

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This sequence follows the rules of Arithmetic Progression

Arithmetic Progression is an example of mathematical sequences. In this sequence, the next term is generated by adding the previous term to a fixed number which is called 'Common Difference'. This is generally represented by 'd'. It is calculated by subtracting any two consecutive terms in the sequence.

We can generally find out any term of the given statement. The  [tex]n^{th}[/tex] term of a sequence is calculated by adding the previous term to the common difference. The formula to calculate the [tex]n^{th}[/tex] term of an Arithmetic Progression is :

                     =>  [tex]a_{n} = a_{n-1} + d[/tex]

Here, n = No. of term, [tex]a_{n-1}[/tex] = previous term, and d = common difference

In the given sequence, 5,22,39,56......

Each term is separated by a common difference 'd'

Calculating d = a2-a1   => d = 22-5 => d = 17

Every term has a common difference of 17 so this is an Arithmetic Sequence

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If Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. The number of  seconds  it will take for the frisbee to hit the ground is: 6.2 seconds.

Given:

0.145t² + 0.019t + 5.5 = 0

Using almighty formula or quadratic formula

t=-b±√b²-4ac/2a

Where:

b²=19²

a=145

c=5500

Let plug in the formula

t=-19±√19²- 4(-145) (5500)/2(-145)

t=-19±√361+(3,190,000)/-290

t=-19±√3,190,361/-290

t=-19±1,786.158/-290

Hence,

-19-1,786.158/-290; -19+1,786.158/-290

t=6.2; 6.09

Therefore If Kira is a lovable dog who is full of energy. Her owner thought it would be fun to train her by throwing a frisbee for her to catch. The number of  seconds  it will take for the frisbee to hit the ground is: 6.2 seconds.

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The geometric mean between pair of numbers 4√3 and 10√3 is 10.95

We know that for a sequence of numbers x1, x2, . . . , xn

The formula of geometric mean is,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have been given two numbers 4√3 and 10√3

We need to find the geometric mean between pair of numbers, 4√3 and 10√3.

Using the formula for the geometric mean,

[tex]\Pi=\sqrt[n]{x_1.x_2.x_3...x_n}[/tex]

In this question, we have two numbers.

So, the value of n is 2.

[tex]\Pi=\sqrt{4\sqrt{3}\times 10\sqrt{3} } \\\\\Pi=\sqrt{4\times 10 \times \sqrt{3}\times \sqrt{3} } \\\\\Pi=\sqrt{40 \times 3 } \\\\\Pi=\sqrt{120}\\\\ \Pi=2\sqrt{30}\\\\\Pi=10.95[/tex]

Therefore, the geometric mean between pair of numbers 4√3 and 10√3 is 10.95

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Step-by-step explanation:

Given that

To find

So, according to the question

we have,

         (0,40) and (15,70)

We have to find the equation of line

So, we know that

               y = mx + c, ---------------(1)

From graph,

           c = 40 and

           m = slope (we have to find it)

We kwon the slope of any two point

      m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Where,

        x₁ = 0 , and y₁ = 40

        x₂ = 0 , and y₂ = 40        

So,

      m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

      m = [tex]\frac{70-40}{15-0}[/tex]

      m = [tex]\frac{30}{15}[/tex]

      m = 2

Now putting the all values in equation (1)

We will get,

               y = mx + c, ---------------(1)

               y = 2x + 40

Answer:

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The value of x so that the equation based on a and b has a solution is x = -7/5

  An equation is about two expressions, either arithmetic or algebraic, that are related with a "=" sign that indicates equality of expressions.

  Equations can be graphed, they are used to model many problems and theories.

     As we can see, we have the following equation:

(a + 2)b + 13 = 5x

  and we have the values of the coefficients a and b, and these are:

   We substitute these values in the equation:

(a + 2)b + 13 = 5x

(18 + 2)-1 + 13 = 5x We solve the equation

(20)-1 +13 = 5x

-20 + 13 = 5x

5x = -7

x = -7/5

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If the tire says P235/65R17, the diameter of your wheel will be 17 inches.

The primary purposes of a car's tires are to carry the weight of the car, transmit traction and braking forces to the road surface, insulate against shocks from the road, and change and maintain the direction of motion.

It offers traction for braking and acceleration and reduces the number of road vibrations that reach the car's body.

It should be noted that the numbers that are written on the tire are vital in knowing the diameter that's illustrated.

In this case, when the tire says P235/65R17, the diameter of your wheel will be 17 inches.

In conclusion, it is 17 inches.

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Angle 213.7°  the bearing of D from towns  A, B, C and D .

What is an angle in math?

The bearing of B from D is angle ADB, which is

∠ADB = arctan(30/45) ≈ 33.7°

The bearing of D from B is that angle plus 180°, so is

180° +33.7° = 213.7°

We use angle ADB because the reference direction for bearings is North.

The tangent of an angle (ADB) is the ratio of its opposite side (AB) to its adjacent side (AD).

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Answer:

I would say y=3x+6

Step-by-step explanation:

To find the discontinuities, we need to factor the polynomial below. Once we have the two binomials, we set each to 0. This way, you can find the value that produces 0 in the denominator.

Let's factor x2−5x+6

x2−5x+6

The middle number is -5, and the last number is 6.

Factoring means we want something like

(x+_) (x+_)

Which numbers go in the blanks?

We need two numbers that...

Add together to get -5

Multiply together to get 6

Can you think of the two numbers?

Try -2 and -3:

-2+-3 = -5

-2*-3 = 6

Fill in the blanks in

(x+_) (x+_)

with -2 and -3 to get...

(x-2) (x-3)

Since you cannot divide by 0, the discontinuities at these points exist as a vertical asymptote. Therefore, the vertical asymptote exists at x= two and x= 3.

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Answer:

last one is the correct one

Mark please

The line's equation is y=3x-4.

What is Equation of line?

Whenever the equation of a line is written in the form y = mx + b, it is called the slope-intercept form of the equation where the slope of line is m and b is the y- intercept. The slope is defined as

m = (y-y1)/(x-x1)

Given:

For two lines to be perpendicular to each other, they must have slopes that are negative reciprocals of each other (i.e. the negative reciprocal of n is -1/n). The slope of the given line is –1/3 which means the slope of a line perpendicular to it would be 3.

From the given slope equation of the line

y=3x+b,

where b is the y-intercept. Since we know the line passes through the point (2,2).

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

y-2 = 3*(x-2)

y=3x-6+2

y=3x-4

The value of b = -4

Therefore, the equation of the second line is y=3x-4.

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The point slope form finds the equation of a straight line that passes through a given point and is inclined to the x-axis. Each point on a line must satisfy the line's equation. Two-variable linear equations symbolize lines. The point slope formula is utilized when we know the line's slope and a point. The next section explains the point slope form and how to calculate its formula.

The equation of a straight line that is inclined at a particular angle to the x-axis and passes at a given point may be found by using the point slope form. This form is used to get the equation of the line. An equation may be said to be the equation of a line if it can be shown to be fulfilled by every point along the line. This indicates that a line is represented by a linear equation that has two variables. Whereas the Point slope formula is only used in situations in which both the slope of the line and a point on the line are known. In the next part, let's get more in-depth knowledge about the point slope form as well as how to derive the formula that is used to express the point slope form.

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Answer:

C,D, and E

Step-by-step explanation:

-29/4 is an improper fraction version of -7 1/4

-7- 1/4 = -7 1/4

-(7 + 1/4) is -29/4

Just make -29/4 into a mixed number, which is -7 1/4

Answer:

Step-by-step explanation: the answer is the last 3 ones because if you add them together, you get -7 1/4.  Remember that -(number) = -1(number). So, -(1) = -1(1).

Answer:

a₁ = 15

Step-by-step explanation:

the sum to n terms of an arithmetic sequence is

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

given S₁₄ = - 63 , then

[tex]\frac{14}{2}[/tex] [ 2a₁ + 13d ] = - 63

7(2a₁ + 13d) = - 63 ( divide both sides by 7 )

2a₁ + 13d = - 9 → (1)

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

given a₁₄ = - 24 , then

a₁ + 13d = - 24 → (2)

subtract (2) from (1) term by term to eliminate d

a₁ + 0 = - 9 - (- 24)

a₁ = - 9 + 24 = 15

The number of milliliters of blood the volunteers donated will be given by expression 470(32 - n).

When the relevant factors and natural laws of a mathematical model are given values, the outcome of the calculation it describes is the expression's outcome.

There were 32 volunteers to donate blood. Unfortunately, n of the volunteers did not meet the health requirements, so they couldn't donate. The rest of the volunteers donated 470 milliliters each.

Then the expression will be given as

⇒ 470(32 - n)

The number of milliliters of blood the volunteers donated will be given by expression 470(32 - n).

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The inequality that can be used to determine the maximum number of outfit she can purchase is 55.17oo  ≤ 117.47.

The first step is to determine which inequality sign would be used.

The following are inequality signs and what they mean:

> means greater than

< means less than

≥ means greater than or equal to

≤ less than or equal to

The sign that would be used is the less than or equal to sign- ≤  . This is because Audrey cannot spend more than her budget.

The next step is to determine the total cost of items bought:

Total cost = $295.33 + (17.86 x 3) + 33.62 = $382.53

Now determine the amount of money she has left : $500 -  $382.53 = $117.47

(Total amount spent on outfit) amount left

(oo x $55.17)  ≤ 117.47

55.17oo  ≤ 117.47

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Answer:

$6.95

Step-by-step explanation:

Kole: $ 6.50

His sister : $6.50+$0.40

= $6.90

Half of his sister: $6.90/2 =$3.45

$10-($6.50 +$3.45)

=$10-$3.05

=$6.95

Answer: 1 ) other angle = 32.0°

2 ) A = ( -2, -2 )

B = ( 2, 5 )

C = ( 4, 2 )

Step-by-step explanation for first picture:

When the sum of two angles is equal to 90 degrees, they are called complementary angles.

x + 58° = 90°

x = 90° - 58°

x = 32.0°

Step-by-step explanation for second picture:

( number on x line, number on y line )

A = ( 2, -2 )

B = ( -2, 5 )

C = ( -4, 2 )

reflection

A = ( -2, -2 )

B = ( 2, 5 )

C = ( 4, 2 )

Answer : second option

When measuring height, it is necessary to represent both the vertical position and the separation between the minimum and maximum place or location. The height of Kara's building is 186.6 ft.

In math, height can be defined as the vertical distance from the top to the base of the object. Height is the distance between an object's highest and lowest points.

The measurement of an object's height from the base to the top is known as the height. It is sometimes referred to as altitude in geometry. The vertical distance between the lowest and highest point is measured. In coordinate geometry, it is often the measurement along the y-axis of an object.

Mount Everest's summit serves as an illustration of height.

Ignoring the height of Kara,

h = 50 tan 75°

substituting the value of tan 75°, we get

= 50 × 3.7321

Height of building = 186.6 ft.

Therefore, the approximate height of Kara's building is 186.6 ft.

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Main Answer:

The required value of PB is 21.

An equation is a mathematical statement with an equal symbol between two expressions that have equal values.

Given: If A-P-B and if AP=2x-9, AB=32, and PB=1.5x+6.

To find: Find PB.

According to the question,

AP + PB = AB

On putting the given values, we get,

(2x-9)+(1.5x+6) = 32

2x - 9 +1.5x + 6 = 32

3.5x - 3 = 32

3.5x = 32+3

3.5x= 35

x=10

Now, we will substitute the value of x=10 in the equation, we get,

PB= 1.5x+6

PB= 1.5 × 10 + 6

PB=15 + 6

PB=21

Final Answer:

The simplified value of PB = 1.5x + 6 is 21.

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45 because it's 45 and I'm smart with a PhD in maths

Answer:

6?

Step-by-step explanation:

24=10x-6x

24=4x

6=x

The number 6 comma 107 comma 200 can be expressed using scientific notation as [tex]6.1072*10^{6}[/tex].

Scientific notation is used to represent a very large number or a very small number in Simple way.

Steps to find scientific Notation of a number

Step (i) Move the decimal point until a number between 1 and 10 is created.

Step (ii) Count the number of times the decimal is moved .

Step (iii) If the decimal is moved n times then multiply the term by n times of 10.

In the given question

the number 6107200.

Step (i) We will move the decimal 6 place towards left.

number becomes 6.107200

Step (ii) The decimal is moved 6 place towards left.

Step (iii) we will multiply by [tex]10^{6}[/tex].

[tex]=6.1072*1000000[/tex]

So , the number becomes [tex]6.1072*10^{6}[/tex]

Therefore , the number 6107200 can be expressed using scientific notation as [tex]6.1072*10^{6}[/tex]

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