Find the distance between the pair of parallel lines with the given equations. (Lesson 3-6)
y=-4x-6 y=-4x+11

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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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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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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Answer:

Step-by-step explanation:

A. The common factor of the expression is 5[tex]x^{3}[/tex]y

B. In order to find a common factor, you find the prime factor. In this case, the biggest number that goes evenly into 40 and 25 is 5.

C. Divide the original problem by the common factor  5[tex]x^{3}[/tex]y

that gives you  5[tex]x^{3}[/tex]y(8x[tex]y^{2}[/tex]-5)

Hope this helps!

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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The line that passes through the points (6,-4) and (6,-1) is:

x = 6

We want to find the equation of the line that passes through the points (6, -4) and (6, -1)

Now, this is really trivial, as you can see that both points have the same x-value (the x-value is the first value of each coordinate pair), which means that our line is x = constant = 6

Then we have a vertical line:

x = 6

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Answer:

6?

Step-by-step explanation:

24=10x-6x

24=4x

6=x

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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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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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).

The correct option is (C) 18.84 in. The circumference of the circle with a diameter 6 in is 18.84 in.

A circle's perimeter is known as its circumference. It is the circumference of the circle as a whole. A circle's circumference is calculated by multiplying its diameter by the constant. This measurement of a circle's diameter is necessary for someone crossing a circular park or for enclosing a circle. The units for the circumference, which is a linear variable, are the same as those for length.

Given, the diameter of the circle = 6 in.

The radius of a circle is calculated as

r = d / 2

r = 6 / 2

r = 3 in

The circumference of a circle is calculated as

C = 2πr

Substitute r = 3 in the circumference formula

=2 × 3.14 × 3

= 6 × 3.14

= 18.84 in

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The circumference of the given circle with a diameter of 6in is 18.84in.

So, the diameter is 6in.

Then, the radius is:

The formula for the circumference of the circle: 2πr

Now, substitute 'r = 3' in the formula of circumference as follows:

Therefore, (C) 18.84 is the circumference of the given circle.

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Using translation concepts, it is found that the transformation is a reflection over the y-axis.

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

For this problem, we have that A is mapped to C and vice-versa. Since they are equidistant to the y-axis, we have that the rule is given by:

(x,y) -> (-x,y).

Meaning that the transformation is a reflection over the y-axis.

For O and B, the rules are given as follows:

Showing that points O and B are invariant, keeping the same coordinates and confirming that the transformation is a reflection over the y-axis.

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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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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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The simplified form of the given expression is 1/9. Therefore, option B is the correct answer.

The given expression is [tex](\frac{(\frac{1}{3})^{7}}{(\frac{1}{3})^{6} } )^{2}[/tex].

We need to evaluate the given expression.

Laws of exponents:

Now, [tex](\frac{(\frac{1}{3})^{7}}{(\frac{1}{3})^{6} } )^{2}=((\frac{1}{3})^{7-6})^{2}[/tex]   (Because [tex]\frac{a^{m} }{a^{n} } =a^{m-n}[/tex])

[tex]=(\frac{1}{3})^{2}[/tex]

=1/9

The simplified form of the given expression is 1/9. Therefore, option B is the correct answer.

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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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According to the given statement the slop of the given points are: -(1/2).

The slope of the line is the mathematical ratio of overall rise to the run, or rise divided by the run. It expresses the slope of a line in the coordinate plane. Calculating the slope of a line is comparable to finding the slope between two separate places.

The procedure for calculating the slope from such an equation will vary based on the form of the equation presented to you. If the equation is written as y=mx+c, the slope (or gradient) is simply m. If the formula does not exist in this form, try rearrangement.

The slope of a line is easily calculated by hand using small, whole number coordinates.

so,

X1 = 7

X2 = 3

Y1 = 2

Y2 = 4

Applying the formula for slope:

slope = (y₂ - y₁) / (x₂ - x₁)

         = (4 - 2) / (3 - 7)

         = 2/(-4)

         = - (1/2)

The slop of the given points are: -(1/2)

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In the given sequence, the next term is obtained by multiplying the next term by (-1), hence it is a geometric sequence with r = 1. The next two terms are 3, -3.

Arithmetic sequence.

In a arithmetic sequence, the next term = the previous term + common difference. Or mathematically:

a(n) = a(n-1) + d

or d = a(n) - a(n-1) for all n

Where d = common difference.

Geometric sequence.

In a geometric sequence,  the next term = the previous term x common ratio. Or mathematically:

a(n) = a(n-1) . r

or r = a(n)/a(n-1) for all n

Where r = common ratio

The sequence given:

           3,-3,3,-3, . . . . .

In this sequence:

a(1) = 3

a(2) = -3

a(3) = 3

a(4) = -3

The next two terms means a(5) and a(6). We already have a(4) = -3. Hence,

a(5) = a(4) . r = -3. (-1) = 3

a(6) = a(5) . r = 3. (-1) = -3

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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 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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The number of lines located on plane A using the given diagram are 4.

As given in the question,

Number of lines located on plane A are as follow:

Point outside the plane A are T, W, S

Points located on plane A are as follow:

V, M, N, P

Lines formed by located points V, M, N, P on plane A

VM, VN, VP and MP

Therefore, number of lines located on plane A using the given diagram are 4.

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Answer:

Yes, they are similar as the difference between the smaller rectangle and the larger one is a scale factor of 2.

answer:

yes

explanation:

you can tell if figures are similar (proportional side lengths with points of the same orientation), if you can divide the respective side lengths of the image and preimage together.

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

The simplification by combining like terms  of 3a + b + a is 4a + b.

According to the given question.

We have an expression 3a + b + a.

As we know that, like terms are terms whose variables (and their exponents such as the 2 in x2) are the same.  when we combine like terms, such as 2x and 3x, we add or subtract their coefficients.

Since, we have to combine the like terms of the given expression  3a + b + a.

Here 3a and a both are the like terms.

So, we add coeffcients of a to simplify the given expression.

Therefore, the simplification of 3a + b + a is given by

3a + b + a

= 3a + a + b

= 4a + b

Hence, the simplification by combining like terms  of 3a + b + a is 4a + b.

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