The bisectors BO and CO of the angles at B and C of ABC meet at O. Prove that BOC = 90° + A/2.​

Here is the five-number summary:

Minimum: 9

Lower quartile:   11

Median: 24

Upper quartile:  34

Maximum: 45

Interquartile range: 23

The minimum number is the smallest number in the dataset. The  minimum number is 9. The maximum number is the largest number in the dataset. The maximum number is 45.

The first quartile, third quartile and the interquartile range are used to measure dispersion.

The first quartile : 1/4(n + 1)

1/4 x (12) = 3rd term = 11

The third quartile : 3/4 x (n + 1)

3/4 x (12) = 9th term = 34

Interquartile range = third quartile - first quartile

34 - 11 = 23

Median can be described as the number that occurs in the middle of a set of numbers that are arranged either in ascending or descending order

Median = 25

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Step-by-step explanation:

There is 31 days in May so the probability is

[tex]p(bday \: in \: may) = \frac{2}{31} [/tex]

The length is 25 feet and the width is 135 feet

What are consecutive odd integers?

Consecutive odd integers differ by 2. If x is an odd integer, then x + 2, x + 4 and x + 6 are consecutive odd integers.

How to find the perimeter of the rectangle?

⇒Perimeter of rectangle = 2(l+w)

The perimeter of a rectangle is 320 feet

let the length of a rectangle is x

The next consecutive odd integer is x+2

width = 5(x+2)

=5x+10

2(length + width) = 320

l+w=160

x+5x+10=160

6x=150

x=25

length = 25 feet

width = 5(25+2)=135 feet

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In quadrant IV, [tex]\cos(A)[/tex] is positive. So

[tex]\sin^2(A) + \cos^2(A) = 1 \implies \cos(A) = \sqrt{1-\sin^2(A)} \approx 0.6258[/tex]

Then by the definition of tangent,

[tex]\tan(A) = \dfrac{\sin(A)}{\cos(A)} \approx \dfrac{-0.78}{0.6258} \approx \boxed{-1.2465}[/tex]

Answer:

1 boy to 15 girls.

Step-by-step explanation:

Since there is only two boys, I divided each number by two and got 1 to 15. Have an amazing day!

The ratio of boys to all children in the group is 1:16.

Given that in a group there are 2 boys and 30 girls.

We need to find the ratio of boys to all children.

To find the ratio of boys to all children in the group, we need to add the number of boys and girls together to get the total number of children.

Then, we can express the number of boys as a fraction of the total number of children.

Number of boys = 2

Number of girls = 30

Total number of children = Number of boys + Number of girls

Total number of children = 2 + 30 = 32

Now, we can express the number of boys as a fraction of the total number of children:

Ratio of boys to all children = Number of boys / Total number of children

Ratio of boys to all children = 2 / 32

To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor, which is 2:

Ratio of boys to all children = 1 / 16

So, the ratio of boys to all children in the group is 1:16.

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[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies \begin{array}{llll} y+4=4(x-3)\implies y-(\stackrel{y_1}{-4})=\stackrel{m}{4}(x-\stackrel{x_1}{3})\\\\ ~\hfill (\stackrel{x_1}{3}~~,~~\stackrel{y_1}{-4}) \end{array}[/tex]

Answer:

[tex]\sf \dfrac{4}{9}x^8[/tex]

Step-by-step explanation:

       [tex]\sf (a*b)^m = a^m *b^m\\\\(a^m)^n =a^{m*n}[/tex]

  16 = 4 *4 = 4²

 81  = 9 *9 = 9²

[tex]\sf\left (\dfrac{16}{81}x^{16}\right)^{\frac{1}{2}}= \left(\dfrac{4^2}{9^2}x^{16}\right)^{\frac{1}{2}}[/tex]

                [tex]\sf =\dfrac{4^{2*\frac{1}{2}}}{9^{2*\frac{1}{2}}}*x^{16*\frac{1}{2}}\\\\=\dfrac{4}{9}x^8[/tex]

Answer:

Identity property of addition 8 + 0 = 8

Identity property of multiplication 8 x 1 = 8

Step-by-step explanation:

He mixed up his properties.  8 + 1  does not equal 8.  I want to know what I can add to 8 and that I would still get 8, the answer is zero.

The identity property of multiplication is showing that any number multiplied by 1 is itself.

Answer:

[tex]\huge\boxed{\sf a_{400}=1276}[/tex]

Step-by-step explanation:

79, 82, 85, 88, ....

[tex]a_n=a_1+(n-1)d[/tex]

Where,

Put the givens in the above formula

[tex]a_{400}=79 +(400-1)3\\\\a_{400}=79 + 399\times3\\\\a_{400}=79+ 1197\\\\a_{400}=1276\\\\\rule[225]{225}{2}[/tex]

Answer:

6x^4-5x^3-8x^2+3x

Step-by-step explanation:

-factor it using FOIL (first outside inside last)

The required percentage increase is 36%. So, a number increased by 36% is the same as the number multiplied by 1.36.

The formula for calculating the percentage increase of a number is

%increase = 100 × (Final - initial)/initial

Consider the number as 'x'

The result when the number is multiplied by 1.36 is 1.36x

So, the percentage increase is calculated as follows:

%increase = 100 × (Final - initial)/initial

Where Initial = x and Final - 1.36x

⇒ %increase = 100 × (1.36x - x)/x

⇒ %increase = 100 × x(1.36 - 1)/x

⇒ %increase = 100 × 0.36

⇒ %increase = 100 × 36/100

∴ %increase = 36

Thus, when a number is multiplied by 1.36, the result obtained is equal to the 36% increase in the number.

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The test That holds true for this inequality is given as 1/4 and 1

3/2 y - 2x > 1

The goal is to make y the subject

then

3/2 y > 2x + 1

We have to divide through the equation by 3/2

Such that  y  > 4/3 x + 2/3

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The probability that the machine produces fewer than 5 defective widgets in a production run of 100 items is 0.10

A probability refers to the ratio of favorable events to the n number of total events.

Also, it means the chance that a particular event (s) will occur expressed on a linear scale from 0 to 1 which can also be expressed as a percentage between 0 and 100%.

Given data

An industrial machine produces 5 widgets.

It has a 0.07 defective rate.

Defective rate fewer than 5

Total Probability = P of 4 defective + P for 3 defective + P for 2 defective + P for  1 defective.

Total Probability = 4/100 + 3/99 + 2/98 + 1/97

Total Probability ≈ 0.10

Therefore, the required probability for fewer than 5 defective rate is 0.10

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First symmetrically cut the octagon to get 8 pieces. (So that you will get the idea that this polygon is divided into 8 triangles)

Then find the area of one of the triangles:

Area of Triangle = [tex]\frac{1}{2} * b* h[/tex]

A = [tex]\frac{1}{2}[/tex] × 12 × 19

A = 114 cm²

To find the area of the whole octagon shape:

A = 114 × 8 = 912 cm²

Hope it helps!

Answer:

Step-by-step explanation:

You cannot do this unless you are certain that P is the center of the octagon. I don't know if that's solvable from the information given. So I will make the assumption that P is the center.

Determine the midpoint of BC. Call it E.  Draw a line from P to E. By symmetry EP = AP. BE = 1/2 * BC = 19/2 = 9.5 by construction

You have a trapezoid witch is 1/4 the area of the octagon. Three more trapezoids can fit into the octagon.

Formula

Area = (AP + BE)*PE / 2

Givens

AP = 12

BE = 9.5

PE = 12

Solution

Put the givens and constructions into the formula

Area = (12 + 9.5)*12/2

Area = 21.5 * 12/2

Area = 21.5 * 6

Area = 129

That's the area of one of the trapezoids. Multiply the area here by 4.

You get 516.

Answer:

$0.17425/Km

Step-by-step explanation:

8.5L/100Km*$2.05/L

= $0.17425/Km

The values of the three trigonometric ratios for angle L, in simplest form, are:

Given -

The triangle LMN is given in the question.

As the trigonometric properties of a triangle state that the value of sin, cos, and tan for the respective angle can be written as:

Using the above trigonometric properties, the value of sin(L):

Similarly, the value of cos(L):

And, the value of tan(L) is:

Therefore, the values of the three trigonometric ratios for angle L, in simplest form, are:

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The question you are looking for is given below:

What are the values of the three trigonometric ratios for angle L, in simplest form?

The complete question is:

Create a matrix for this linear system:

what is the solution of the system?

[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]

The solution straight from the matrix as

[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]

[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex]

and z = r

A solution to a system of equations exists a set of values for the variable that satisfy all the equations simultaneously.

Given:

[tex]$\left[\begin{array}{rrr}1 & -1 & -2 \\ 2 & 3 & -1\end{array}\right] c=\left[\begin{array}{r}1 \\ -2\end{array}\right]$[/tex]

By applying two more row operations, we get

[tex]$&{\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\2 & 3 & -1 & -2\end{array}\right] R_{2}+(-2) R_{1} \rightarrow R_{2}} \\[/tex]

[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 5 & 3 & -4\end{array}\right] \frac{1}{5} R_{2} \rightarrow R_{2} \\[/tex]

simplifying the above matrix, we get

[tex]&\equiv\left[\begin{array}{rrr|r}1 & -1 & -2 & 1 \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right] R_{1}+R_{2} \rightarrow R_{1} \\[/tex]

[tex]$&\equiv\left[\begin{array}{rrr|r}1 & 0 & -\frac{7}{5} & \frac{1}{5} \\0 & 1 & \frac{3}{5} & -\frac{4}{5}\end{array}\right]$$[/tex]

The solution straight from the matrix as

[tex]$&x=\frac{1}{5}+\frac{7}{5} r \\[/tex]

[tex]$&y=-\frac{4}{5}-\frac{3}{5} r \\[/tex] and

z = r

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Answer:

1.78 feet.

Step-by-step explanation:

If they cost $20 each and its $2 per square foot, the area of the spheres

is 20 / 2 = 10 ft^2.

Area of sphere = 4 π r^2 = 10   (where r = the radius)

---> r^2 = 10 / 4π

            =   0.796

---> r = 0.892 ft

So the diameter = 2 * r  

                           =  1.78 feet to nearest hundredth.    

Answer:

2/6

Step-by-step explanation:

Count up and over going from one point to the next and you get slope intercept. This one is up 2 over 6

Answer:

y = 1/3x - 3

Step-by-step explanation:

Slope-intercept form follows the format y = mx + b, where m is the slope of the line, and b is the y-intercept.

First let's find the slope. The slope is the amount the graph rises/runs. From point (0,-3), it rises by 1, and runs to the right by 3 where it meets the next point on the graph, meaning that the slope is 1/3.

Now, let's find the y-intercept. The y-intercept is the point on the graph where the line touches the y-axis. In this line, we can clearly see that the line touches (0,-3), therefore, the y-intercept is -3.

Using this information, we can construct the equation y = 1/3x - 3

Answer:

21

Step-by-step explanation:

In the diagram, the three tangents (segment touching a circle at one point) have equal length.

6y - 3 = 29 - 2y

8y = 32

y = 4

Since the lengths of segments AM and AN are equivalent, we can substitute the value of y into the expression, 6y - 3, to find AN.

6y - 3 = 6*4 - 3 = 24 - 3 = 21

The distance the bird has flown by the time Alice and Bob meet is 40 feet.

Given that the distance between Alice and Bob is 1000 feet and their running speed is 10 feet per second and the speed of bird is 20 feet per second.

Distance equals speed multiplied by time.

Distance between Alice and Bob=1000 feet.

Distance between the bird and Bob=1000 feet.

Speed of Alice and Bob=10 feet per second.

The combined speed of Alice and Bob=20 feet per second.

Since the two are running directly toward each other the distance each will cover at the meeting point is 50 feet (1000/20)

The time covered at the meeting point=20 second (1000/50)

Speed of the bird=20 feet per second.

The distance covered by the bird towards Bob at their meeting point is 40 feet(20 feet*20 seconds).

Hence the distance the bird has flown by the time Alice and Bob meet is 40 feet.

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See attachment for the graph of the functions y = x + 2, y = 2x and y = -x

Equation 14

The equation is given as:

y = x + 2

When x = 0, we  have

y = 0 + 2 = 2

When x = 1, we  have

y = 1 + 2 = 3

When x = 2, we  have

y = 2 + 2 = 4

So, the complete table is

x    y

0     2

1      3

2     4

See attachment for the graph of the function y = x + 2

Equation 15

The equation is given as:

y = 2x

When x = 0, we  have

y = 2 * 0 = 0

When x = 1, we  have

y = 2 * 1 = 2

When x = 2, we  have

y = 2 * 2 = 4

When x = 3, we  have

y = 2 * 3 = 6

So, the complete table is

x    y

0    0

1     2

2    4

3    6

See attachment for the graph of the function y = 2x

Equation 16

The equation is given as:

y = -x

When x = -3, we  have

y = 3

When x = -1, we  have

y = 1

When x = 1, we  have

y = -1

When x = 3, we  have

y = -3

So, the complete table is

x    y

-3    3

-1     1

1     -1

3    -3

See attachment for the graph of the function y = -x

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Based on the number of songs in each genre that Josiah listened to, the statements about his solution that are true are:

To find the average of the number of rock songs, he should have taken the average of rock songs he listened to which were 4 and 6:

= (4 + 6) / 2

= 5

Because he has a total of 1,500 songs on his player, he should have multiplied both the numerator and denominator by a number that would lead to 1,500 which is 75 and not 30.

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Answer: b. the two triangles are similar by SAS

Step-by-step explanation:

       These two triangles (ABC and ADE) both share angle A. This means that one angle is congruent.

       Next, we will look at the sides. Triangle ADE has side lengths of 6, 9, and x. Triangle ABC has side lengths of 8+6, 12+9, y. Let us see how these side lengths compare.

[tex]\frac{8+6}{12+9} =\frac{14}{21} =0.6666[/tex]

[tex]\frac{6}{9} = 0.6666[/tex]

       THey are similar. This means the triangles can be prooven similar with SAS.

Answer:

I x² +12x I = -32

Step-by-step explanation:

Absolute value equation:

  x = -4  ; x = -8

x + 4 = 0  and     x + 8 = 0

(x +4)(x + 8) = 0

x*x + x*8 + 4*x + 4*8 = 0

     x² + 4x + 8x  + 32 = 0

         x² + 12x   + 32   = 0

Absolute value equation:

  I x² + 12x I = -32

Answer:

Future Amount ≈ 32

Step-by-step explanation:

substitute x = 8 into the given formula , that is

future amount = 16[tex](1.09)^{8}[/tex] = 16 × 1.99256.. ≈ 32 ( nearest whole number )

Using a linear function, we have that:

a) The costs are:

i. C(x) < $1.3.

ii. C(x) > $2.3.

b) The times are:

i. Less than 9 minutes.

ii. At least 16 minutes.

A linear function is modeled by:

y = mx + b

In which:

In this problem, the y-intercept is of 0.3, while the slope is of 0.2, hence the cost for a call of x minutes is:

C(x) = 0.3 + 0.2x.

For calls shorter than 5 minutes, the costs are:

C(x) < 0.3 + 0.2 x 5

C(x) < $1.3.

For calls longer than 10 minutes, the costs are:

C(x) > 0.3 + 0.2 x 10

C(x) > $2.3.

The cost is less than $2.10 for calls of less than x minutes, found as follows:

0.3 + 0.2x < 2.1

0.2x < 1.8

x < 9.

The cost is greater or equal to $3.50 for calls of at least x minutes, found as follows:

0.3 + 0.2x >= 3.5

0.2x >= 3.2

x >= 16.

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Answer:

6/10

Step-by-step explanation:

3/6 = 0.5

6/10 = 0.6

0.6>0.5

Then

6/10 is greater than 3/6

Answer: A) 23,00

Step-by-step explanation:

A=23,00

B=8,600

C=12,00

D=3,600