state what additional information is required in order to know that the triangles are congruent for the reason given. NO LINKS!!!!​

Answer:

See Below.

Step-by-step explanation:

We want to verify the identity:

[tex]\displaystyle \frac{\sin x}{1 - \cos x} - \cot x = \csc x[/tex]

We can multiply the fraction by 1 + cos(x):

[tex]\displaystyle \frac{\sin x(1+\cos x)}{(1 - \cos x)(1+\cos x)} - \cot x = \csc x[/tex]

Difference of Two Squares:

[tex]\displaystyle \frac{\sin x(1+\cos x)}{1-\cos^2 x} - \cot x = \csc x[/tex]

From the Pythagorean Theorem, we know that sin²(x) + cos²(x) = 1. Rearranging, we acquire that sin²(x) = 1 - cos²(x). Substitute:

[tex]\displaystyle \frac{\sin x(1+\cos x)}{\sin^2 x} - \cot x = \csc x[/tex]

Cancel:

[tex]\displaystyle \frac{ 1 + \cos x}{\sin x}-\cot x = \csc x[/tex]

Let cot(x) = cos(x) / sin(x):

[tex]\displaystyle \frac{ 1 + \cos x}{\sin x}-\frac{\cos x}{\sin x} = \csc x[/tex]

Combine Fractions:

[tex]\displaystyle \frac{ 1 + \cos x - \cos x}{\sin x}= \csc x[/tex]

Thus:

[tex]\displaystyle \frac{1}{\sin x}=\csc x = \csc x[/tex]

Hence proven.

Step-by-step explanation:

Since we know that the function of the graph is continuous, then (-2, -1) is the most likely turning point because at this point the function stops increasing and starts decreasing.

Answer:

No evidence .because the configurations factors and failure mode are independent

Step-by-step explanation:

Determine if there is sufficient evidence to conclude that configuration affects the type of failure

Number of configurations = 3

Number of failures = 4

assuming Pij represents proportion of items in pop i of the category j

H0 : Pij = Pi * Pj,  I = 1,2,-- I,  j = 1,2,---J

Hence the expected frequencies will be

16.10 , 43.58 , 18, 12.31

7.5,  19.37, 8 , 5.47

10.73, 29.05, 12, 8.21

x^2 = 13.25

test statistic = 14.44. Hence the significance level where Null hypothesis will be acceptable will be = 2.5%

Answer:

3

Step-by-step explanation:

25 divided by 5 is 5

therefor 15 divided by 5  is 3

15/25 = 3/5

Answer:

3

Step-by-step explanation:

[tex]\frac{15}{25} =\frac{?\\}{5}[/tex]      25 divided by ? = 5? The number 5 so divide 15 as well

15 ÷ 5 = 3

[tex]\frac{15}{25} =\frac{3}{5}[/tex]

Hence, 3 is the answer

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Answer:

=$21075

Step-by-step explanation:

Given data

Earnings =$415 per hour

Commission =5%

Sales =$89500

Time =40 hours

Let us find the commission

5/100*89500

0.05*89500

=4475

Let us find the amount earned in 40 hours

40*415

=16600

Total

=16600+4475

=21075

Answer:

4

Step-by-step explanation:

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Answer:

Diameter(line going across the circle that you've given) = 6 in

Radius(half of diameter) = 3 in

Circumference(the perimeter of the circle) = 18.85 in

Area = 28.27^2

Step-by-step explanation:

In order to find the circumference, you will need to first find the radius(which is always half the size of the diameter which in this case is 3 in). You will then need to do this formula: 2 x 3.14 x 3 which equals to 18.85.

Answer:

The circumference of a circle is about 18.85 inches.

Step-by-step explanation:

The radius is always half of the diameter, and the diameter is 6 inches.

6 divided by 2 is 3, so the radius of this circle is 3 inches.

The formula for circumference of a circle is :

C = 2πr = 2 · π · 3 ≈ 18.84956

The circumference of a circle is about 18.85 inches.

Answer:

1/4

Step-by-step explanation:

4 divide in half so should be 1/4

Answer:

D

5 sq.rt. 3

Step-by-step explanation:

use the pythagorean theorem: a^2 + b^2 =c^2

5^2 + x^2 = 10^2

25+ x^2 =100

x^2 = 100 - 25

x^2 =75

x = [tex]\sqrt{75}[/tex]

x = 5 [tex]\sqrt{3}[/tex]

Answer:

94 degrees

Step-by-step explanation:

Answer:

[tex](x+1)^2 + (y + 1)^2 = 13[/tex]

Step-by-step explanation:

To find the centre of the circle, find the mid - point of PQ :

[tex]Centre =( \frac{x_1+x_2}{2} \ , \ \frac{y_1 + y_2}{2}) = (\frac{-2}{2} \ , \ \frac{-2}{2}) = (-1, -1)[/tex]

Diameter = 2 x Radius , To Find the diameter, find distance between P and Q:

[tex]Distance , PQ = \sqrt{(2 - (-4))^2 + (1 -(-3))^2}[/tex]

                   [tex]= \sqrt{6^2 + 4^2} = \sqrt{36+ 16} = \sqrt{52} = \sqrt{4 \times 13} = 2 \times \sqrt{13}[/tex]

PQ is the diameter , therefore radius :

                                                [tex]r = \frac{1}{2} \times 2 \sqrt{13} = \sqrt{13}[/tex]

Equation of a circle :

                              [tex](x + 1)^2 + (y + 1)^2 = 13[/tex]

Answer:

(x - 1)2 + (y - 1)2 = 13

Step-by-step explanation:

This is the answer for Acellus users

Answer:

$4800

Step-by-step explanation:

SI=PRT DIVIDED BY 100..

So it is going to be 400×2×6 divided by 100 which will be 4800

Answer:

C. The mean of the data set is 8.

Step-by-step explanation:

From the dot plot we can make a frequency table as follows:

Number of books read                      Frequency

       6                                                       2  

       7                                                       2

       8                                                       2

       9                                                       2

       10                                                      2

Since, the number of dots are  10 or then sum of the frequencies is 10.

           Hence, the number of observations are 10.

Also, the median of the set is: 8

Now, the mean is calculated as:

                  Hence, Mean of the data set is: 8

Now, the range of the data set is the difference between the minimum and the maximum value.

                  Hence, range=10-6=4

           The range of the data set is 4.

Answer:

c

Step-by-step explanation:

Step-by-step explanation:

[tex]y' + y = y^2[/tex]

We can rewrite the differential equation above as

[tex]\dfrac{dy}{dx} + y = y^2[/tex]

[tex]dy = (y^2 - y)dx[/tex]

or

[tex]\dfrac{dy}{y^2 -y} = dx[/tex]

We can rewrite the left side of the equation above as

[tex]\dfrac{dy}{y^2-y}=\dfrac{dy}{y(y-1)}= \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy[/tex]

We can the easily integrate this as

[tex]\displaystyle \int \left(\dfrac{1}{y-1} - \dfrac{1}{y} \right)dy = \int dx[/tex]

or

[tex]\displaystyle \int \dfrac{dy}{y-1} - \int \dfrac{dy}{y} = \int dx[/tex]

This will then give us

[tex]\ln |y-1| - \ln |y| + \ln |k| = x[/tex]

where k is the constant of integration. Combining the terms on the left hand side, we get

[tex]\ln \left|\dfrac{k(y-1)}{y} \right| = x[/tex]

or

[tex]\dfrac{y-1}{y} = \frac{1}{k}e^x[/tex]

Solving for y, we get

[tex]y= \dfrac{1}{1- \frac{1}{k} e^x}=\dfrac{k}{k-e^x}[/tex]

We know that [tex]y(0)= \frac{1}{3}[/tex], so when we substitute [tex]x=0[/tex], we find that [tex]k = -\frac{1}{2}[/tex].

Therefore, the final form of the solution to the differential equation above is

[tex]y = \dfrac{1}{1+2e^x}[/tex]

Answer:

Margo will pay $ 44 in interest.

Step-by-step explanation:

Given that Margo borrows $ 1600, agreeing to pay it back with 3% annual interest after 11 months, to determine how much interest will she pay, the following calculation must be performed:

3/12 x 11 = 0.25 x 11 = 2.75

1600 x 1.0275 = X

1644 = X

1644 - 1600 = 44

Therefore, Margo will pay $ 44 in interest.

Answer:

A) -8x+2

Step-by-step explanation:

-8x + 7 - 5 - 5x + 5x

-8x -5x + 5x + 7 - 5

- 8x+2

Answer:

Last month the grocery store sold 578.88 gallons of ice cream and 632.8 pounds of broccoli.

Step-by-step explanation:

Since a grocery store manager notices that this month her store sold a total of 521 gallons of ice cream, which represents a decrease of 10% from last month, and on the other hand, her store sold 791 pounds of broccoli this month, which It represents an increase of 25% from last month, to determine how much ice cream and broccoli did the store sell last month, the following calculation must be performed:

Ice cream = 100 - 10 = 90

90 = 521

100 = X

100 x 521/90 = X

52,100 / 90 = X

578.88 = X

Broccoli = 100 + 25 = 125

125 = 791

100 = X

100 x 791/125 = X

79,100 / 125 = X

632.8 = X

Therefore, last month the grocery store sold 578.88 gallons of ice cream and 632.8 pounds of broccoli.

Answer:

Step-by-step explanation:

sorry im not sure

Answer:

Hope you find it helpful

Answer:

[tex]\begin{array}{ccc}{Industry} & {Frequency} & {RF}& {Bank} & {26} & {13\%}& {Cable} & {44} &{22\%} & {Car} & {42} & {21\%} &{Cell} & {60} & {30\%} & {Collection} & {28} & {14\%} &{Total} & {200} & {100\%}\ \end{array}[/tex]

Step-by-step explanation:

Given

[tex]n =200[/tex]

[tex]Bank = 26; Cable = 44; Car = 42; Cell = 60; Collection = 28[/tex]

Required

The frequency relative frequency table

The frequency table is as follows:

[tex]\begin{array}{cc}{Industry} & {Frequency} & {Bank} & {26} & {Cable} & {44} & {Car} & {42} & {Cell} & {60} & {Collection} & {28} & {Total} & {200} \ \end{array}[/tex]

Relative frequency (RF) is calculated using:'

[tex]RF = \frac{Frequency}{Total} * 100\%[/tex]

So, we have:

[tex]Bank = \frac{26}{200} * 100\% = 13\%[/tex]

[tex]Cable = \frac{44}{200} * 100\% = 22\%[/tex]

[tex]Car = \frac{42}{200} * 100\% = 21\%[/tex]

[tex]Cell = \frac{60}{200} * 100\% = 30\%[/tex]

[tex]Collection = \frac{28}{200} * 100\% = 14\%[/tex]

So, we have:

[tex]\begin{array}{ccc}{Industry} & {Frequency} & {RF}& {Bank} & {26} & {13\%}& {Cable} & {44} &{22\%} & {Car} & {42} & {21\%} &{Cell} & {60} & {30\%} & {Collection} & {28} & {14\%} &{Total} & {200} & {100\%}\ \end{array}[/tex]

Answer:

C

Step-by-step explanation:

the probability of the outcome being greater than 63 is x≥63

Answer:

A=B=C... wouldn't both B and C be equal to A? Also I can't see the statements.

Answer:

ASA

Step-by-step explanation:

..................

To prove ABC = ADC, We use ASA triangle postulate.

We know two similar planer figures are congruent when we have sides or angles or both that are the same as the corresponding sides or angles or both.

The similarity of triangles on the other hand is when the corresponding angles are equal but the corresponding sides are not equal but they have the same common ratio.

From the given diagram a quadrilateral ABCD is given,

Line segment AC divides quadrilateral ABCD into two triangles namely

ABC and ADC, and both have a common side AC.

m∠BAC ≅ m∠DAC and m∠BCA ≅ m∠DAC.

Therefore, Triangle ABC and ADC are congruent by ASA, with two angles and a side included between them.

learn more about congruency here :

https://brainly.com/question/7888063

#SPJ7

Answer:

Step-by-step explanation:

Answer:

substitute means to use or add in place of something.

Step-by-step explanation:

Example: Substitute 1 for x: therefore x now is equal to 1.

Answer:

(3x + 4)^2

Step-by-step explanation:

9x^2 + 24x + 16

Let's use middle term break method to factor this polynomial.

In Quadratic Factorization using Splitting of Middle Term which is x term is the sum of two factors and product equal to last term. Factor each pair by finding common factors.

we nee two number which give 144 wh3n multiplied and 24 when added.So, 12 and 12 is the number because 12*12=144 and 12+12=24.

9x^2 + (12+12)x +16

9x^2 +12x +12x +16

take common

3x(3x + 4) +4(3x +4)

take (3x + 4) as common

(3x +4)(3x*1 +4*1)

(3x +4)(3x +4)

(3x +4)^2

Answer:

2 (17+12x)

Step-by-step explanation:

See image below:)

Answer:

1/6x1/2=1/12

Step-by-step explanation:

Answer:

The average rate of change is 28.57

Step-by-step explanation:

Given

See attachment for graph

Required

The average rate of change from 0 to maximum profit

At 0, we have:

[tex](x_1,y_1) = (32,0)[/tex]

At maximum, we have:

[tex](x_2,y_2) = (60,800)\\\\[/tex]

The average rate of change (m) is calculatd as:

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

So, we have:

[tex]m = \frac{800 - 0}{60 - 32}[/tex]

[tex]m = \frac{800}{28}[/tex]

[tex]m = 28.57[/tex] --- approximated