Prove algebraically that the straight line with equation x=2y+5 is a tangent to the circle.

The equation of the line which passing through the point and parallel to the line which has undefined slope is y=0(x)-6

Given that,

The point is (1/2,-6)

We have to find the equation of the line which passing through the point and parallel to the line which has undefined slope.

We know that,

The equation of the line has a formula that is y=mx+b

m is the slope of the line

b is the intercept

m is slope that is undefined means

m is 0.

Now, b is

y=0(x)+b

y=b

Here y is from the point -6

b is -6

So, we get equation has

y=0(x)-6

Therefore, The equation of the line which passing through the point and parallel to the line which has undefined slope is y=0(x)-6

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Answer:

4 x^3 + 24 x^2 = 4 (x^3 + 6 x^2) = 4 x^2 (x + 6)

4 x^2 (x + 6)        seems to be the lowest factor

A table of values and an equation for C, in terms of t, representing the total cost of using a computer for t minutes at the internet cafe are as follows:

C                         t

$10.60                1

$11.20                 2

$11.80                 3

C = 0.60t + 10.

In order to write an equation for the total cost, we would assign variables to the amount of time used and the total cost of using a computer, and then translate the word problem into algebraic equation as follows:

Since the cafe has an initial charge of $10 to use a computer and an additional charge of $0.60 for every minute of use, an equation for the total cost is given by:

C = 0.60t + 10

When t = 1, we have:

Total cost, C = 0.60(1) + 10

Total cost, C = $10.60.

When t = 2, we have:

Total cost, C = 0.60(2) + 10

Total cost, C = $11.20.

When t = 3, we have:

Total cost, C = 0.60(3) + 10

Total cost, C = $11.80.

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a) Probability that Meteor will release between 1 and 4 megatons of energy: 0.304

b) Probability that Meteor will release between 9 and 10.5 megatons of energy: 0.029

c) Probability that Meteor will release at least 6 megatons of energy: 0.613

What is histogram?

The spread and size of the data are measured using histograms. We can virtually analyse the data based on the histogram.

From the Histogram we get:

a) Probability that Meteor will release between 1 and 4 megatons of energy= P [X=1 to X=4]

           = [0.156+0.088+0.060]

            =0.304

b) Probability that Meteor will release between 9 and 10.5 megatons of energy= P [X=9 to X=10.5]

           = [0.020+0.009]

           =0.029

c) Probability that Meteor will release at least 6 megatons of energy         = 1- P[X≤5]

= 1-P [X=1 to X=5]

= 1- [0.156+0.088+0.060+ 0.046+0.037]

= 0.613

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When one independent variable affects the result differently based on the values of another independent variable, this is known as an interaction.

What does the statistical term "interaction" mean?

When two or more variables interact to impact a third variable in a non-additive way, this is known as an interaction in statistics.

                   To put it another way, the two variables interact to produce a result that is greater than the sum of their parts.

Give a definition of interaction and an example?

a time when two or more items or people interact or communicate with one another - There isn't enough interaction between the management and the employees.

                                Language games typically aim to promote student interaction.

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The test statistic for the given test is t = 2.59.

What is a standard deviation?

The standard deviation in statistics is a measure of the amount of variation or dispersion in a set of values. A low standard deviation indicates that the values are close to the set's mean, whereas a high standard deviation indicates that the values are spread out over a larger range.

Given data:

                    [tex]\bar D[/tex] = 4.1, Sd = 5, n = 10, μd = 0

Now the test statistic can be computed as

                [tex]t=\frac{\bar D-\mu_d}{S_d/\sqrt{n} }[/tex]

                [tex]t=\frac{4.10-0}{5/\sqrt{10}} \\\\t=2.59[/tex]

Hence, the test statistic for the given test would be t = 2.59.

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The total revenue function if the revenue from 115 devices $2116 is 200 when R'(x)=4x(x²+25000[tex])^{2/3}[/tex].

Given that,

The following function calculates the marginal revenue (in thousands of dollars) from the sale of a portable gaming system.

R'(x)=4x(x²+25000[tex])^{2/3}[/tex]

We have to find the total revenue function if the revenue from 115 devices $2116.

We know that,

R'(x)=4x(x²+25000[tex])^{2/3}[/tex]

Integrating on both sides

R(x)= [tex]\int {4x(x^{2} +25000)^{2/3} } \, dx[/tex]

Let x²+25000=t

=> 2xdx=dt

=> 4xdx=2dt

We get,

R(x)= [tex]\int {2t^{-2/3} } \, dt[/tex]

R(x)= [tex]6t^{1/3}[/tex]+C

By Substitution then

R(x)= 6(x²+25000[tex])^{1/3}[/tex]+C

We get

Given R(115)=$2,116 or 2.116 (in thousands of dollars) and x=115 units

Then total revenue function(in thousands of dollars)

2.116= 6(115²+25000[tex])^{1/3}[/tex]+C

C=200

Therefore, The total revenue function if the revenue from 115 devices $2116 is 200.

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The inequality given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.

What is inequality?

Inequalities are mathematical expressions where neither side is equal. In inequality, as opposed to equations, we compare two values. Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign in between. Sometimes it can be about a "not equal to" relationship, where one thing is more than the other or less than. In mathematics, an inequality is a relationship that results in a non-equal comparison between two numbers or other mathematical expressions.

Let the number of gigabytes consumed be x,

The total cost per month will be 69.50 + 5x

accoding to the question the bill would not exceed $90.

So the inequality,

69.50 + 5x ≤ 90

Simplification for the maximum gigabyte he can buy,

5x ≤ 90 - 59.90

5x ≤ 20.5

x ≤ 4.1

Hence, the required inequality is given by 69.50 + 5x ≤ 90 and the maximum gigabyte he can buy is 4.1.

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2.5(cos 5π/6  + i sin 5π/6) is the polar form  of the complex number

Complex numbers are numbers that are expressed in the form of a+ib, where a and b are real numbers and 'i' is an imaginary number called “iota”. The value of i = (√-1)

Given: the complex number (5√3)/4 - 5/4 i

In polar form:

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

θ  = tan⁻¹( (-5/4) / (5√3 /4) )

θ = -30°

θ = -30+180 = 150°

θ = 5π/6

r = √( (5√3)/4)² +(- 5/4)²) = 2.5

Thus,

(5√3)/4 - 5/4 i = r(cosθ + isinθ)

r(cosθ + isinθ) = 2.5(cos 5π/6  + i sin 5π/6 )

Therefore, the polar form  of the complex number is 2.5(cos 5π/6  + i sin 5π/6)

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Answer:(2x+1)(3x-4)

Step-by-step explanation:Factor the expression out first by getting 6x^2+3x-8x-4. From there, factor again to 3x(2x+1)-4(2x+1) to get the answer (2x+1)(3x-4)

Answer:

(3x - 4)(2x - 1)

Step-by-step explanation:

6x^2 - 5x - 4

When factoring, we want to first find the GCF. In this case, the GCF is one so we leave it as that. Next, we want to try and find the sum and the product. Additionally, we have a leading coefficient. We will multiply the leading coefficient by the last term, which is -4. (You will need to remember this to continue on later.)

x^2 - 5x - 24

Now, we can find the sum and the product. To do this, we need to list the factors of 24. (Remember negatives as well!)

24: 1 and 24, 2 and 12, 3 and 8, 4 and 6.

As -24 is also a negative, that means it will have one positive and one negative factor. This must also add up to -5.

One pair that does this is -8 and 3. They multiply together to -24 and add up to -5.

Now, since we multiplied the leading coefficient in the beginning, we must bring it back down into the parenthesis.

(6x - 8)(6x - 3)

We must divide out and try to simplify this as much as we can to match the leading coefficient. The divisors must multiply up to 6.

(6x - 8)/2 and (6x - 3)/3.   3*2 = 6

(3x - 4)(2x - 1)

Answer:

Step-by-step explanation:

A line that is perpendicular to another will have the opposite slope.

y = [tex]-\frac{1}{3}[/tex]a + b

To find b, substitute y and a with the given values

6 =  [tex]-\frac{1}{3}[/tex](-6) + b

6 = 2 + b

-2  -2

4 = b

thus

y = [tex]-\frac{1}{3}[/tex]a + 4

A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations.

A null hypothesis is a particular kind of statistical hypothesis that asserts that no statistical significance can be found in a given set of observations. The use of sample data in hypothesis testing allows one to judge a hypothesis' veracity.

The null hypothesis states that the estimate is only based on chance. If the observed data (in the sample) do not differ from what would be predicted solely by chance, then the null hypothesis is true. The alternative hypothesis is what the null hypothesis has as its counterpart.

Two population parameters, such as an independent variable and a dependent variable, are said to be unrelated under the null hypothesis. It's possible that an experimental or sampling error caused the result if the hypothesis indicates a relationship between the two parameters.

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hybrids research When she does, the camden depositor is actually higher than the reported percentage. Here, we have the report 126 percent, the winners on the portion computer. It indicates that the proportion of the underling hypothesis at noon will be equal to 26.

The abon 26 point notte will be greater than the b of the means 10. In this question, which is the right-hand exam, we will provide the sembiante 340, which will be equal to 31 percent, and we must contend with the statistical test. The test is therefore equal to the z moving forward. It will be calculated using the following formula: hat: minus b over square root, times: 1 minus p over the hot equal to 131 p equal to 261 square 261 minus 26. If we compare it to my 340 point, we get 126 times 74 divided by 340, then we take the square root of that number. The 131 minus 7.26 is then divided by the industry standard.I respond with a number equal to 2.10, rounding up to two decimal places before moving on to the step's following inquiry. 3. This is the 110 test since the test pair is on 1 here and then the next 1 in his right hand. The choice must be made hypotheses, though. Rule and we need to identify the critical value, and since that will be the right hand, we must make sure that the critical value is both equal to and far beyond that. 05. It will check the z table to see if the value equals 1.645, and if it does, we'll use the decision rule to reject the null hypothesis. If so, the test result will exceed the cutoff of 1.645 points, and we will observe Because the test we determined to be equivalent to 2.10 is higher than the 1.645 point, we can observe that. We will thus rule out the known hypothesis and come to the conclusion that there is sufficient evidence to back up the prediction that the proportion will be higher than 26%.

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Answer: Side of an empty cubicle carton = 9 cm.

Now as we know that volume of the cube is the cube of its side.

So the volume of an empty cubicle carton having side 9 cm, V = (9)3=729 cm3.

Now we have to find out can 1000 cubes of side 1cm fit in it.

So the volume of the cube of side 1 cm is, V’ = (1)3=1 cm3

So the volume of the 1000 such cubes = 1000 (1) = 1000 cubic centimeters.

Now if the ratio of the volume of the empty cubicle carton to the volume of 1000 cubes of 1 cm is greater than 1 then we can will 1000 cubes of side 1 cm into an empty cubicle carton otherwise not.

So the ratio of the volume of the empty cubicle carton to the volume of the 1000 cubes is,

⇒VV′=7291000=0.729 < 1

So as we see that the ratio is less than one so we cannot fit 1000 cubes of side 1 cm into an empty cubicle carton of side 9 cm.

Step-by-step explanation:

I really hope this works!

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An equation in slope-intercept form that represents the situation is y = 3x - 208.

Mathematically, the slope of a straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

From the information provided, we have the following points:

Points on x-axis = (103, 105).

Points on y-axis = (101, 107).

Substituting the given points into the formula, we have;

Slope, m = (107 - 101)/(105 - 103)

Slope, m = 6/2

Slope, m = 3

Mathematically, the slope-intercept form of a straight line is given by;

y = mx + c

Where:

At point (103, 101), an equation in slope-intercept form is given by:

y - y₁ = m(x - x₁)

y - 101 = 3(x - 103)

y - 101 = 3x - 309

y = 3x - 309 + 101

y = 3x - 208.

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If the three sides of the triangle is (x + 5), (2x - 3), (21 - x), then the perimeter of the triangle is 23 + 2x

The perimeter of the triangle is the summation of all three sides of the triangle

Perimeter = a + b + c

= (x + 5) + (2x - 3) + (21 - x)

= 2x + 23

= 23 + 2x

Therefore, if the three sides of the triangle is (x + 5), (2x - 3), (21 - x) then the perimeter of the triangle  23 + 2x.

Any two-dimensional figure's perimeter is determined by the space surrounding it. By adding the lengths of the sides, we can determine the perimeter of any closed shape.

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If the car's speed is 65 kilometres per hour, then the bus' speed may be 75 kilometres per hour.

How to find the distance travelled by an object?

The distance travelled by an object in a specified direction is velocity×time.

if the car's speed is 65 kilometres per hour then in 2 hours it will travel a distance of 65×2 kilometres.

65×2=130 kilometres

if the bus' speed is 75 kilometres per hour then in 2 hours it will travel a distance of 75×2 kilometres.

75×2=150 kilometres

So, after 2 hours the distance between the two vehicles will be 130+150= 280 kilometres

which is less than 350 kilometres.

Hence, it is possible that if the car's speed is 65 kilometres per hour then the bus' speed is 75 kilometres per hour.

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Answer:

Is that all

_______

_______

Answer:

16.(a)  24

16.(b)  See attachment.

Step-by-step explanation:

Cumulative frequency means ‘running total’. A cumulative frequency diagram plots this running total so you can estimate the median and the quartiles easily.

According to the given cumulative frequency graph, the number of necklaces that have a mass 21 g or less is 16.

Therefore, an estimate of the number of necklaces with a mass of 21 g or greater is:

[tex]\implies 40-16=24[/tex]

To draw a box plot to represent the data, estimate the median and quartiles from the graph.  

Calculate the position of the median and quartiles, then go to the position on the vertical scale of the graph and read off the value from the horizontal axis.  (See attached annotated graph).

[tex]\sf Median \; position=\dfrac{40}{2}=20[/tex]

So the median = 22

[tex]\sf Q_1 \; position = \dfrac{1}{4} \times 40=10[/tex]

So Q₁ = 18

[tex]\sf Q_3 \; position = \dfrac{3}{4} \times 40=30[/tex]

So Q₃ = 24

Draw the box plot with the calculated median and quartiles, and the given lowest and highest values.  (See second attachment).

the total force exerted on the new dam to that on the original dam f new is given by F = 624010000 lb.

What is Pascal's Principle.?

Consider a flat surface that is immersed vertically in a fluid whose weight density is p, according to Pascal's Principle.

A flat surface experiences fluid force (F) which is

F = ∫ph(x)w(x) dx

where h(x) is the height of the point x in the x-axis' vertical direction and w(x) is the surface's width.

to determine fluid force applied

Assume that x is equal to the height of the water. At height x on the dam, width of the dam is w(x) = 200 ft (given), and height is h(x) = x ft.

F = ∫ph(x)w(x) dx

F =0→100 ∫62.4 x  200 dx

F = 12480*  0 →100∫ x dx

F = 12480*  0 →100(x²/2)

F =

F = 6240((100)²- (0)²)

F= 6240(10000)

F = 624010000 lb

Hence the total force exerted on the new dam to that on the original dam f newf is given by F = 624010000 lb.

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Answer:

The 8th term of the AP= 113/5 or 22.6

Answer:

22.6

Step-by-step explanation:

Given:

Find the value of a₆:

[tex]\implies a+a_6=20[/tex]

[tex]\implies a_6=20-a[/tex]

[tex]\implies a_6=20-3[/tex]

[tex]\implies a_6=17[/tex]

Therefore:

General form of an arithmetic sequence:

[tex]\boxed{a_n=a+(n-1)d}[/tex]

Where:

Substitute a = 3 and a₆ = 17 into the formula and solve for d:

[tex]\begin{aligned}\implies a_6=3+(6-1)d&=17\\3+5d&=17\\5d&=14\\d&=2.8\end{aligned}[/tex]

Therefore, the equation for the nth term is:

[tex]\implies a_n=3+(n-1)2.8[/tex]

[tex]\implies a_n=3+2.8n-2.8[/tex]

[tex]\implies a_n=2.8n+0.2[/tex]

To find the 8th term, substitute n = 8 into the equation for the nth term:

[tex]\implies a_8=2.8(8)+0.2=22.6[/tex]

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

760% can be written in fraction form as 38/5.

760% can be written in mixed form as 7(3/5).

The percentage is calculated by dividing the required value by the total value and multiplying by 100.

Example:

Required percentage value = a

total value = b

Percentage = a/b x 100

Example:

50% = 50/100 = 1/2

25% = 25/100 = 1/4

20% = 20/100 = 1/5

10% = 10/100 = 1/10

We have,

760%

This can be written as a fraction.

760/100

= 76/10

= 38/5

or

= 7(3/5)

Thus,

760% can be written in fraction form as 38/5.

760% can be written in mixed form as 7(3/5).

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Answer:

y = - [tex]\frac{3}{2}[/tex] x + 4

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

given

6x + 4y = 16 ( subtract 6x from both sides )

4y = - 6x + 16 ( divide through by 4 )

y = [tex]\frac{-6}{4}[/tex] x + [tex]\frac{16}{4}[/tex] , that is

y = - [tex]\frac{3}{2}[/tex] x + 4 ← in slope- intercept form

The single trigonometric function form of the expression is 2sin(3π/8) cos(3π/8).

Trigonometric function:

In math, trigonometric functions are the periodic functions which denote the relationship between angle and sides of a right-angled triangle.

Given,

Here we need to write the given expression as a single trigonometric function. 2 sine (start fraction 3 pi over 8 end fraction) cosine (start fraction 3 pi over 8 end fraction)

Here we have the expression,

2 sine (start fraction 3 pi over 8 end fraction) cosine (start fraction 3 pi over 8 end fraction)

Now, we have to convert this into the form of trigonometric function,

For that we have to rewrite the given expression based on the arithmetic operators, then we get the resulting function as,

=> 2sin(3π/8) cos(3π/8).

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Answer:C

Step-by-step explanation:

did it on edge

The cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.

A mathematical operation is a function that converts a set of zero or more input values (also called "b" or "arguments") into a defined output value.

From the question , we are given that the laptop costs $350 more than the desktop, therefore,

let x represent the cost of the laptop thus, x-350 will be the cost of the desktop .

The total finance charge of $388 is equal to 8% of the cost of the laptop and 7.5% of the cost of the desktop, we solve as;

388 = 0.08(x) + 0.075(x - 350)

252 = 0.08x + 0.075x - 26.25

278.75 = 0.155x

x = 278.75/0.155

x = 1798

Recall that the cost of desktop = x -350

therefore:

1,798- 350 = 1448

The cost of laptop = $1798

The cost of desktop = $1448

Thus, the cost of laptop and cost of desktop are; $1,800 and $2,100 respectively.

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Since ∠7,∠2, and 5 are vertically opposite angles their value must be equal. The measure of angles 2 and 5 will be 120°

It is defined as the angles when two lines intersect each other and at the intersecting point, some pair of angles are formed which we call vertically opposite angles, as the name describes that they have vertically opposite angles.

∠7,∠2, and 5 are vertically opposite angles.

Thus, ∠7,∠2, and 5 are vertically opposite angles their value must be equal. The measure of angles 2 and 5 will be 120°

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For a student with a shoe size of 9, the student's height is equal to 65 inches.

For a student with a height of 60 inches, the student's shoe size is equal to 6.5.

From the information provided, an equation for the line of best fit that represents or models the heights x (in inches) and shoe sizes y of several student is given by this mathematical expression:

y = 0.50x - 23.5

Where:

For a student with a shoe size of 9, the student's height is given by:

y = 0.50x - 23.5

0.50x = y + 23.5

Student's height, x = (y + 23.5)/0.50

Student's height, x = (9 + 23.5)/0.50

Student's height, x = 32.5/0.5

Student's height, x = 65 inches.

For a student with a height of 60 inches, the student's shoe size is given by:

y = 0.50x - 23.5

y = 0.50(60) - 23.5

y = 30 - 23.5

y = 6.5

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The three statements about his solution that are true include the following:

1. He should have found the average of the number of rock songs by averaging 4 and 6 to get 5.

2. He did not multiply the numerator and denominator by the correct number to equal 1,500.

5. He should have multiplied the numerator and denominator by 75, not 30,  because 20 × 75 = 1,500.

Based on the information provided, a mathematical expression which models the number of songs of each genre on Josiah's MP3 player to be 300 songs:

10/20 = x/1500

Multiplying the mathematical expression by 75, we have the following:

75 × (10/20) = x/1,500

750/1500 = x/1500

1,500x = (750 × 1,500)

x = (750 × 1,500)/1,500

x = 750.

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Answer:

[tex]7\sqrt{5}[/tex]

Step-by-step explanation:

Using the geometric mean theorem, [tex]n=\sqrt{28 \cdot 7}=14[/tex].

Using the Pythagorean theorem, [tex]m=\sqrt{7^2+14^2}=7\sqrt{5}[/tex]