1) In the given figure, name (a) the vertex opposite A to side AB (b) the angle opposite to side AC (c) the angle made by the sides CB and CA.​

cancel by 3

Answer:

[tex]\sf \dfrac{8}{21}[/tex]

Step-by-step explanation:

Given expression:

[tex]\sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x}[/tex]

When multiplying fractions, simply multiply the numerators and multiply the denominators:

[tex]\implies \sf \dfrac{6x}{-7} \cdot \dfrac{4}{-9x} = \dfrac{6x \cdot 4}{-7 \cdot -9x} =\dfrac{24x}{63x}[/tex]

Cancel the common factor x:

[tex]\implies \sf \dfrac{24 \diagup\!\!\!\!x}{63 \diagup\!\!\!\!x}=\dfrac{24}{63}[/tex]

Rewrite 24 as 3 · 8 and rewrite 63 as 3 · 21:

[tex]\implies \sf \dfrac{24}{63}=\dfrac{3 \cdot 8}{3 \cdot 21}[/tex]

Cancel the common factor 3:

[tex]\implies \sf \dfrac{\diagup\!\!\!\!\!3 \cdot 8}{\diagup\!\!\!\!\!3 \cdot 21}=\dfrac{8}{21}[/tex]

Using proportions, it is found that the length of AC is of 15 units.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The ratios in this problem are given as follows:

The entire length is of 18 units, AB is half of that, hence:

AB = 0.5 x 18 = 9 units.

BC is two thirds of the length from 6 to 15, hence:

BC = 2/3 x (15 - 6) = 6

Thus, the length of AC is:

AC = 9 + 6 = 15 units.

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El valor del número A es 692.31.

The percentage is the given definition for a fraction whose denominator is equal to 100. It is represented by %. See the following example:

[tex]\frac{50}{100} =0.5*100=50%[/tex]

The percentage is considered a math tool with several applications and areas, for example: medicine, engineering, investments, supermarkets, drugstores,banks  etc.

The exercise asks you the value of A and it gives you the value (900) that represents 130%A. Thus, you should write an equality between the division the percentage and the variable A by 100 with the value 900.

You should follow the steps below.

[tex]\frac{130*A}{100}=900\\ \\ 130A=90000\\ \\ A=\frac{90000}{130} =692.31[/tex]

You can check the result : [tex]\frac{692.31*130}{100} =\frac{90000.3}{100} =900.003=900[/tex]

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Step-by-step explanation:

Find the slope between the two points given. Then, use the slope and point ONE to write the

equation of the

The value of n in the permutation equation P(n, 5) = 2520 is 7

The expression is given as:

P(n, 5) = 2520

The above expression is a permutation expression.

The permutation expression is different from the combination expression, and the permutation expression is calculated using the following permutation formula

P(n,r) = n!/(n - r)!

Substitute 5 for r in the above equation

P(n,5) = n!/(n - 5)!

Substitute the given values in the above equation

n!/(n - 5)! = 2520

Expand the above equation

n(n-1)(n - 2)(n - 3)(n - 4)(n - 5)!/(n - 5)! = 2520

Evaluate the quotient in the above equation

n(n-1)(n - 2)(n - 3)(n - 4) = 2520

Express 2520 as 7 * 6 * 5 * 4 * 3

n(n-1)(n - 2)(n - 3)(n - 4) = 7 * 6 * 5 * 4 * 3

By comparing the equation, we have

n = 7

Hence, the value of n in the permutation equation P(n, 5) = 2520 is 7

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Answer: 80 1/4 is 5% of 1605

Step-by-step explanation:

5 percent of some number = 80.25

let x = some number

[tex]\frac{5}{100} *x = 80.25[/tex]

[tex]=\frac{100}{5} *\frac{5}{100} *x=80.25*\frac{100}{5}[/tex]

[tex]=x=80.25*20[/tex]

[tex]=x=1605[/tex]

Considering that the sine is negative and that the cosine is positive, the angle is on the fourth quadrant, hence option C is correct.

Hence, since the sine is negative and that the cosine is positive, the angle is on the fourth quadrant, hence option C is correct.

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The computation of the equations is illustrated below.

a. x - y = 1 .... i

x + y = -9 ..... ii

Subtract the equations

-2y = 10

y = 10/-2 = -5

Since x - y = 1

x - (-5) = 1

x + 5 = 1

x = 1 - 5 = -4

b. 3x + 2y = -9

x - y = -13

Multiply equation i by 1

Multiply equation ii by 3

3x + 2y = -9

- 3x - 3y = -39

5y = 30

y = 6

Since x - y = 13

x - 6 = 13

x = 13 + 6 = 19

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The negative solution is -2.21 and positive solution is 12.21

Given the quadratic equation expressed as:

x^2-10x-27 = 0

Find the solution using the general formula

x^2-10x-27 = 0

x = 10±√(10)²-4(1)(-27)/2

x =  10±√100+108/2

x =  10±√208/2

x = 10±14.422/2

Simplify

x = 10+14.422/2 and x = 10-14.422/2

x = 24.422/2 and -4.422/2

x = 12.21 and -2.21

Hence the negative solution is -2.21 and positive solution is 12.21

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The x and y intercepts of the given equation of the line are 8 and 6 respectively for the given line 3x+4y=24. They are shown in the graph at X and Y respectively.

The standard equation of a line is ax + by + c = 0.

Then, its x-intercept is calculated by -c/a, and the y-intercept is calculated by -c/b.

In the graph, the x-intercept is obtained at y=0 and the y-intercept is obtained at x=0.

It is given that,

The equation of the given line is 3x + 4y = 24

Rewriting the given equation into the general form,

3x + 4y - 24 =0

On comparing with ax + by + c = 0,

a = 3, b = 4 and c = -24

So,

The x-intercept of the line (-c/a) = -(-24)/3 = 8 and

The y-intercept of the line (-c/b) = -(-24)/4 = 6

Therefore, the required x and y intercepts are 8 and 6 respectively.

(The graph showing the intercepts of the given line is shown below)

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[tex]f(x) = \sqrt{1 - 4{ x}^{2} } [/tex]

[tex]1 - 4x {}^{2} \geqslant 0[/tex]

[tex] - \infty \: \: \: \: \: \: \: \: - 0.5 \: \: \: \: \: \: \: \: \: 0.5 \: \: \: \: \: \: \: \: \infty \\ - \: \: \: \: \: \: \: \: \: \: \: \: \: \:0 \: \: \: \: \: + \: \: \: \:0 \: \: \: \: \: - [/tex]

[tex]domain \\ [ \: -0.5 \: , \: 0.5 \: ][/tex]

[tex]g(x) = 1 - 4x {}^{2} \\ g'(x) = - 8x \\ g'(x) = 0 \\ x = 0 \\ g(0) = 1 - 4(0) = 1 \\ maximum \: = 1[/tex]

[tex]range \\ [ \: 0 \: , \: 1 \: ][/tex]

Answer:

[tex]\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right][/tex]

[tex]\textsf{Range}: \quad [0, 1][/tex]

Step-by-step explanation:

Domain: set of all possible input values (x-values)

Range: set of all possible output values (y-values)

Given function:

[tex]f(x)=\sqrt{1-4x^2}[/tex]

As negative numbers don't have real square roots:

[tex]\implies 1-4x^2\geq 0[/tex]

Therefore, to find the domain, solve the inequality.

Subtract 1 from both sides:

[tex]\implies -4x^2\geq -1[/tex]

Divide both sides by -1 (reverse the inequality):

[tex]\implies 4x^2 \leq 1[/tex]

Divide both sides by 4:

[tex]\implies x^2\leq \dfrac{1}{4}[/tex]

[tex]\textsf{For }\:a^n \leq b,\:\:\textsf{if }n\textsf{ is even then }-\sqrt[n]{b} \leq a \leq \sqrt[n]{b}:[/tex]

[tex]\implies -\sqrt[2]{\dfrac{1}{4}} \leq x \leq \sqrt[2]{\dfrac{1}{4}}[/tex]

[tex]\implies -\sqrt{\dfrac{1}{4}} \leq x \leq \sqrt{\dfrac{1}{4}}[/tex]

[tex]\implies -\dfrac{1}{2} \leq x \leq \dfrac{1}{2}[/tex]

Therefore:

[tex]\textsf{Domain}: \quad \left[-\dfrac{1}{2}, \dfrac{1}{2}\right][/tex]

To find the range, input the endpoints of the domain into the function:

[tex]\implies f\left(-\dfrac{1}{2}\right)=\sqrt{1-4\left(-\dfrac{1}{2}\right)^2}=0[/tex]

[tex]\implies f\left(\dfrac{1}{2}\right)=\sqrt{1-4\left(\dfrac{1}{2}\right)^2}=0[/tex]

To find the limit of the range, find the extreme point(s) of the function by differentiating the function and setting it to zero.

[tex]\implies f(x)=(1-4x^2)^{\frac{1}{2}}[/tex]

[tex]\implies f'(x)=\dfrac{1}{2}(1-4x^2)^{-\frac{1}{2}} \cdot -8x[/tex]

[tex]\implies f'(x)=-\dfrac{4x}{\sqrt{1-4x^2}}[/tex]

Setting it to zero and solving for x:

[tex]\implies -\dfrac{4x}{\sqrt{1-4x^2}}=0[/tex]

[tex]\implies -4x=0[/tex]

[tex]\implies x=0[/tex]

Substitute x = 0 into the function:

[tex]\implies f(0)=\sqrt{1-4(0)^2}=1[/tex]

Therefore, the range is [0, 1]

1a.The mean is 8.

b. The median is 8.

c. The mode is 8.

2. The shape of the data is: perfectly symmetrical distribution.

To find the mean of the data set given for the difference in weight, 4, 8, 9, 5, 12, 7, 6, 15, 10, 4, 8, 8, 1, add all the values and divide by the number of values given, which is, n = 12.

Mean = (4 + 8 + 9 + 5 + 12 + 7 + 6 + 15 + 10 + 4 + 8 + 8)/12

Mean = (96)/12

Mean = 8

The median is the center of the data when it is ordered.

Ordered data: 4, 4, 5, 6, 7, 8, 8, 8, 9, 10, 12, 15

The center (median) is the average of the two center values = (8 + 8)/2 = 16/2

Median = 8

The mode of the data is 8, because 8 appeared most in the data set.

The mean is 8.

The median is 8.

The mode is 8.

Thus, when the mean, median, and mode of a data set are the same, then it means the data is non-skewed or perfectly symmetrical.

Therefore the shape of the data is: perfectly symmetrical distribution.

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The main difference between the two nets is the top face.

The net of a box with a closed top is a 3-dimensional figure that is made up of 6 faces. The faces are all rectangles, and they are connected to each other by flaps. The flaps are the parts of the net that fold over to create the closed top.

The net of a box with an open top is a 3-dimensional figure that is made up of 5 faces. The faces are all rectangles, and they are connected to each other by flaps. However, the top face of the net is not a rectangle. Instead, it is a trapezoid. The trapezoid is created by the flaps that fold over to create the open top.

As you can see, the main difference between the two nets is the top face. The top face of the net of a box with a closed top is a rectangle, while the top face of the net of a box with an open top is a trapezoid.

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Answer:

2.5

Step-by-step explanation:

2.5 is the only positive number amongst the options, so it must be the greatest.

The correct statement regarding the probabilities is given as follows:

P(Male or Type B) > P(Male | Type B)

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem, there is a total of 200 people, of which 103 are males and 12 are Type B females, hence:

P(Male or Type B) = 115/200 = 0.575

Of the 103 males, 38 are Type B, hence:

P(Male|Type B) = 38/103 = 0.3683.

Hence:

P(Male or Type B) > P(Male | Type B).

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Answer:

The balance in Bank B will be greater.

Step-by-step explanation:

Because simple interest is just interest on the principle only which is 50 every year doesn't change but with compound interest you will get 2% Interest every year.  principle+interest

Answer:

True

Number of people is dependent

Answer:

true because it's hots and people cool of by getting by getting the water

Answer:

27.53

Step-by-step explanation:

The apothem of the pentagon is 2.7528 ft, area of pentagon is 25.528 ft² and perimeter of pentagon is 20ft.

Polygon can be defined as a flat or plane, two-dimensional closed shape bounded with straight sides

Given,

A hot tub is in the shape of a regular pentagon.

The side of polygon is 4ft.

We need to find the apothem of the pentagon, area and perimeter.

In the middle we will have 360 degrees.

If we divide the polygon to five triangles, then one of the verte will have 36 degree measure.

h=2/tan 36=2.7528

Perimeter of polygon=5 a

a is side of polygon

Perimeter=5×4=20 ft.

Area=1/2 perimeter ×apothem

=1/2×20×2.7528

=27.528 ft²

Hence the apothem of the pentagon is 2.7528 ft, area of pentagon is 25.528 ft² and perimeter of pentagon is 20ft.

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Answer:

116

Step-by-step explanation:

zinc : copper

4      :     11

11 = 319

zinc = 4 / 11 * 319

Zinc = 116

The net that can be folded to form a pyramid is A net has a square at the center. 2 triangles are on 1 side, and 2 triangles are on another side.

A net is a two-dimensional representation of a three dimensional solid object showing its faces.

Examples of material which can have nets are

Now, for a pyramid, we know that a pyramid is a three dimensional solid object that has one square base and four triangular sides.

So, when a pyramid is split into its net, it will have one square at the center and four triangles on the sides of the squares.

So, the net that can be folded to form a pyramid is A net has a square at the center. 2 triangles are on 1 side, and 2 triangles are on another side.

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Answer:

B

Step-by-step explanation:

You need to use the net that only have 1 square because a pyramid only has 1 square, it also has all the triangle sides needed which is 4. You can use a model to make a pyramid out of this net

The solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1

The equation is given as:

[tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex]

Split the equation as follows:

[tex]y\ =\ \left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}[/tex]

[tex]y = 1 + x^2[/tex]

Next, we plot the graph of both equations (see attachment)

From the attached graph, the intersection point is (1, 2)

Remove the y value

x = 1

Hence, the solution to [tex]\left(2+\sqrt{2}\right)^{\log_2\left(x\right)}+x\left(2+\sqrt{2}\right)^{\log_2\left(x\right)} = 1 + x^2[/tex] is x = 1

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Answer:

Step-by-step explanation:

let x be the price of ticket,then

120-x=3(80-x)

120-x=240-3x

3x-x=240-120

2x=120

x=120/2=60

Price of ticket=$60

Mr.Chandra has 80-60=20 $ after buying the ticket.

Answer:

There is only 1 solution, and it is ½

Step-by-step explanation:

-46x - 23 = 46x + 23

46x + 46x = 23 + 23

92x = 46

x = 46 / 92

x = ½

Answer: B

Step-by-step explanation:

The vertical asymptotes are at x=-4 and x=1, so the denominator needs to have factors of (x+4) and (x-1).

This eliminates everything except for B.

a. The equation of the tangent at (1,3) is y = -x/3 + 10/3

b. The equation of the normal at (1,3) is y = 3x

c. Find the graph in the attachment

Since x² + y² = 10, we differentiate the equation with respect to x to find dy/dx which the the equation of the tangent.

So, x² + y² = 10

d(x² + y²)/dx = d10/dx

dx²/dx + dy²/dx = 0

2x + 2ydy/dx = 0

2ydy/dx = -2x

dy/dx = -2x/2y

dy/dx = -x/y

At (1,3), dy/dx = -1/3

Using the equation of a straight line in slope-point form, we have

m = (y - y₁)/(x - x₁) where

So, m = (y - y₁)/(x - x₁)

-1/3 = (y - 3)/(x - 1)

-(x - 1) = 3(y - 3)

-x + 1 = 3y - 9

3y = -x + 1 + 9

3y = -x + 10

3y + x = 10

y = -x/3 + 10/3

So, the equation of the tangent at (1,3) is y = -x/3 + 10/3

Since the tangent and normal line are perpendicular at the point, for two perpendicular line,

mm' = -1 where

So, m' = -1/m

= -1/(-1/3)

= 3

Using the equation of a straight line in slope-point form, we have

m' = (y - y₁)/(x - x₁) where

So, m = (y - y₁)/(x - x₁)

3 = (y - 3)/(x - 1)

3(x - 1) = (y - 3)

3x - 3 = y - 3

y = 3x - 3 + 3

y = 3x + 0

y = 3x

So, the equation of the normal at (1,3) is y = 3x

c. Find the graph in the attachment

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The graph of changing length of shadow of a stick from 12pm to 5pm shows that length of shadow increases.

When an object (like the stick in the cartoon) blocks some of the Sun's light, it casts a shadow. The shadow always points away from the Sun. How long the shadow is depends on how low or high the Sun is in the sky. If the Sun is low, we see a longer shadow. Is the Sun is high, we see a shorter shadow.

Length of shadow due to the Sun's light is smallest when the Sun is vertically above. This happens at 12 noon.

Thus the graph of changing length of shadow of a stick from 12pm to 5pm shows that length of shadow increases.

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i think this is the answer

Answer:

C

Step-by-step explanation:

Equation 1:

[tex]1+\frac{\cos^{2} \theta}{\cot^{2} \theta(1-\sin^{2} \theta)}\\ \\ 1+\frac{\sin^{2} \theta}{\cos^{2} \theta} \\ \\ 1+\tan^{2} \theta \\ \\ \sec^{2} \theta[/tex]

Equation 2:

[tex]15\cos \theta \left(\frac{1}{\cos \theta}-\frac{\cot \theta}{\csc \theta} \right) \\ \\ 15\cos \theta \left(\frac{1}{\cos \theta}-\frac{\cos \theta / \sin \theta}{1/\sin \theta} \right) \\ \\ 15\cos \theta \left(\frac{1}{\cos \theta}-\cos \theta \right) \\ \\ 15\cos \theta \left(\frac{1-\cos^{2} \theta}{\cos \theta} \right) \\ \\ 15(1-\cos^{2} \theta) \\ \\ 15\sin^{2} \theta[/tex]