Prove Triangle ABC is congruent to Triangle CDA.

Prove Triangle ABC Is Congruent To Triangle CDA.

Answers

Answer 1

The triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.

What is the similarity?

If two triangles are congruent, this means they are the same shape and the same size. By definition, all corresponding angles of two congruent triangles are congruent. Additionally, all corresponding sides of two congruent triangles are congruent.

In the given triangles we can see that:-

Angle BAC is congruent to Angle DCA Angle B and Angle D are congruent.The two triangles are sharing common side which is AC.

Therefore we can see that the triangle ABC and triangle CDA are congruent by AAS [Angle - Angle-Side] property.

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Related Questions

The statement “a > 2 and a < 5” is true when a is equal to
A. 5
B. 3
C. 10
D. 2

Answers

Answer:

B

Step-by-step explanation:

because > means greater than or more than

and < means less than

the answer is B because 3 is more than 2 and the same time less than 5

indicate whether the statement is true of false.
please provide a explanation


A linear system with three variables and three equations has a unique solution.

Answers

The statement is false, as the system can have no solutions or infinite solutions.

Is the statement true or false?

The statement says that a system of linear equations with 3 variables and 3 equations has one solution.

If the variables are x, y, and z, then the system can be written as:

[tex]a_1*x + b_1*y + c_1*z = d_1\\\\a_2*x + b_2*y + c_2*z = d_2\\\\a_3*x + b_3*y + c_3*z = d_3[/tex]

Now, the statement is clearly false. Suppose that we have:

[tex]a_1 = a_2 = a_3\\b_1 = b_2 = b_3\\c_1 = c_2 = c_3\\\\d_1 \neq d_2 \neq d_3[/tex]

Then we have 3 parallel equations. Parallel equations never do intercept, then this system has no solutions.

Then there are systems of 3 variables with 3 equations where there are no solutions, so the statement is false.

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Tan + Cos / 1 + Sin = Sec

Answers

[tex]\tan x+\frac{\cos x}{1+\sin x}\\\\ =\frac{\sin x}{\cos x}+\frac{\cos x}{1+\sin x}\\\\=\frac{\sin x(1+\sin x)+\cos^{2} x}{\cos x(1+\sin x)}\\\\=\frac{\sin^{2} x+\cos^{2} x+\sin x}{\cos x(1+\sin x)}\\\\=\frac{1+\sin x}{\cos x(1+\sin x)}\\\\=\frac{1}{\cos x}\\\\=\sec x[/tex]

Which of the following terms best describes a vertical line that the graph of a function approaches but never intersects

Answers

Answer: an asymptote is, essentially, a line that a graph approaches , but     does not intersect.      

Step-by-step explanation:

for example , in the following graph of y =1x y=1x the line approaches the x- axis (y=0) but never touches it

The following are scores for students in Ms. Kennedy's math class.What is the range of the scores?
451
560
600
422
603
514
A 109
B 149
C 178
D181

Answers

Answer:

The answer will be D. 181

Step-by-step explanation:

603 - 422 = 181

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21% of hospital patients stay for less than 1 day. If 1,134 patients in January stay less than 1 day what total of number of patients did the hospital treat in January?

Answers

Fifty-four hundred is the answer

Determine if an exponential would be an appropriate model for the data shown in each scatter plot. Select one that applies.

Answers

Answer:

Graph 1: No, a linear model would be more appropriate.Graph 2: YesGraph 3: No, a quadratic model would be more appropriate.

Please answer these questions!!!!

Answers

Answer:

BEC = C. 50

BCD = A. 120

Step-by-step explanation:

BEC

65 + 65 = 130

180 - 130 = 50

BCD = 180 - 60 = 120

BEC is 50

A) 120°

Explanation: The angle ACD shows 180°. We are given 60°. 180°-60°=120°, Hope this helped! :D

The equation for the pH of a substance is pH = -log[H*], where H+ is the concentration of hydrogen ions. A basic
solution has a pH of 11.2. An acidic solution has a pH of 2.4. What is the approximate difference in the concentratic
of hydrogen ions between the two solutions?
1.6x10-9
O4.0x10-3
O 6.7x10-1
O 1.6x10¹11

Answers

The approximate difference in the concentration of hydrogen ions between the two solutions is 4.0×10⁻³

What is pH value?

The pH of a solution is a measurement of the concentration of hydrogen ions in the solution, as well as its acidity or alkalinity. Normally, the pH scale ranges from 0 to 14.

pH value for basic solution = 11.2

pH value for acidic solution = 2.4

Concentration for a basic solution:

[tex]\rm = 10^{-11.2}[/tex]

[tex]= 6.309\times10^{-12}[/tex]

Concentration for an acidic solution:

[tex]\rm = 10^{-2.4}[/tex]

[tex]= 3.981\times10^{-3}[/tex]

Difference between the concentration:

[tex]= 3.981\times10^{-3}- 6.309\times10^{-12}[/tex]

[tex]= 3.98\times10^{-3}[/tex]

[tex]= 4\times10^{-3}[/tex]

Thus, the approximate difference in the concentration of hydrogen ions between the two solutions is 4.0×10⁻³

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A 13 ​-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the​ house, the base is moving away at the rate of 15 ​ft/sec.
a. What is the rate of change of the height of the top of the​ ladder?
b. At what rate is the area of the triangle formed by the​ ladder, wall, and ground changing​ then?
c. At what rate is the angle between the ladder and the ground changing​ then?

Answers

I think the answer is B because all the air other answers are incorrect

how do you simplify

−(12st3+34s3t+t2−1)

Answers

Answer:

-34s^3t - 12st^3 - t^2 + 1

Step-by-step explanation:

hope this helps

what are the intercepts of x^2 +8x+16​

Answers

Answers:

x intercept = -4

y intercept = 16

The graph is shown below.

=======================================================

Explanation:

To determine the x intercept(s), we set the expression equal to zero and solve for x. In other words, we plug in y = 0 and solve for x.

y = x^2 +8x+16​

0 = x^2 +8x+16​

x^2 +8x+16​ = 0

(x+4)^2 = 0

x+4 = 0

x = -4

There's only one x intercept. It's located at the vertex of the parabola.

The location of the x intercept is the point (-4,0)

------------

To find the y intercept, we plug in x = 0 and compute like so:

y = x^2 +8x+16​

y = (0)^2 +8(0)+16​

y = 16

The y intercept is 16 which is located at (0,16)

Check out the graph below. It was made using the free app Desmos.

Help please and thank you!! :)

Answers

Answer:

33 elements

Step-by-step explanation:

Set A has 59 elements. Set A and Set B share 26 elements.

This means that 26 out of the 59 elements in Set A are also in set B.

Therefore, to find the number of elements not in Set B, you need to subtract the common elements from the total amount of elements in Set A.

59 (total in Set A) - 26 (common in Set A) = 33 (unshared elements).

I think it’s thirty three

Word Problem 3 Priscilla works 43 hours a week for eight weeks. If she makes $14.73 per hour, how much money did she make in the eight weeks? Operation(s): Math sentence(s): Solution: Word Problem 3 Priscilla works 43 hours a week for eight weeks . If she makes $ 14.73 per hour , how much money did she make in the eight weeks ? Operation ( s ) : Math sentence ( s ) : Solution :​

Answers

Answer:

$5067,12

Step-by-step explanation:

14,73*43*8

The required money Priscilla will earn in 8 weeks is $5067.12.

As mentioned in the question, Priscilla works 43 hours a week for eight weeks. If she makes $14.73 per hour,

What is simplification?

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Let the amount earned be x,
According to the condition,
x = 8 × 43 × 14.73
x =  $5067.12.

Thus, the required money Priscilla will earn in 8 weeks is $5067.12.

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what is it asap please​

Answers

There is a 70% probability that a pupil who uses the swimming pool and gym will be selected. How do I know this? Well, since 30 pupils use neither, this means at least 50/80 pupils use both. This reduces to 5/8, so 5/8 pupils use both the gym and swimming pool. 5/8 as a decimal is equal to 70%, because 80% would be 6/8, 90% would be 7/8, and 100% would be 8/8.

That’s one way to do it.


Another way to solve this is as follows:

Since 22 pupils use the swimming pool and 34 use the gym, that means 56 pupils use both total. 56/80 reduces to 7/10, which as a decimal is 70% or 0.7.

Your final answer: Probability = 70%

If you need more help, let me know and I will gladly assist you!

A clock was reading the time accurately on Friday at noon. On Monday at 6pm the clock was running late by 468 seconds. On average, how many seconds did the clock skip every 30 minutes?

Answers

The clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.

The clock was still accurate by Friday noon. The clock was late by 468 seconds by Monday, 6 pm.

To solve the problem, we must:

Know how many 30-minutes have passed during the time period.

1 day = 24 hours

1 hour = 60 minutes = 2 × (30 minutes)

1 day = 24 hours × 2 × (30 minutes)

1 day = 48 × (30 minutes)

Thus, there are 48, 30-minutes in a day. On Friday, however, we start counting at noon, which is half of the day. Moreover, on Monday, the mark is only up to 6 pm, which is three-fourths of the day.

Friday = 48 × [tex]\frac{1}{2}[/tex] = 24

Saturday = 48

Sunday = 48

Monday = 48 × [tex]\frac{3}{4}[/tex] = 36

TOTAL = 24 + 48 + 48 + 36 = 156

Therefore, the total number of 30-minutes that have passed is 156. There were 156, 30-minutes that passed during the time period.

Divide the number of total seconds late by the number of 30-minutes passed.

That is, the number of total seconds late= 468 seconds ÷ 156

= 3 seconds  

Therefore, the clock was skipping 3 seconds every 30 minutes from Friday noon to Monday 6 pm.

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Where does billy bob johns

Answers

Answer:

in ur moms house

Step-by-step explanation:

Answer:

he doesn't

Step-by-step explanation:

Follow the steps to find the area of the shaded region.


First use the formula below to find the area of the whole sector.


Sector Area= ( angle of sector/360). R2


Sector Area = ? Cm^2
Round to four decimal places.

14 cm

46°

14 cm

Answers

The area of the sector, to 4 decimal places, is 78.6794 cm².

We have given that,

Sector Area= ( angle of sector/360). R2

We have to determine the Sector Area

What is the Area of a Sector of a Circle?

Area of sector = ∅/360 × πr².

We have given the following:

∅ = 46°

Radius (r) = 14 cm

Area of sector = 46/360 × π(14²)

Area of sector ≈ 78.6794 cm²

The area of the sector is approximately 78.6794 cm².

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urgent help wanted/ needed

Answers

The equation in slope-intercept form is: y = -x + 5

The equation in point-slope form is: y - 3 = -1(x - 2)

How to Find the Equation of a Line in Point-Slope Form and Slope-intercept Form?Where (a, b) is a point on the line and m is the slope of the line, the equation in point-slope form for such line would be: y - b = m(x - a).Where b = y-intercept and m = slope, the slope-intercept form for the equation of the line is expressed as: y = mx + b.

Slope (m) = rise/run = -(2/2) = -1

Y-intercept (b) = 5 (where the line intercepts the y-axis)

Using a point, (2, 3) = (a, b) and m = -1, the equation in point-slope form is:

y - 3 = -1(x - 2)

Rewrite in slope-intercept form:

y - 3 = -x + 2

y = -x + 2 + 3

y = -x + 5

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Finding the Domain and Range of a Graph
Determine the domain and range for the graph below. Write your answer in interval notation.

Answers

Answer:

Domain: [tex][-3, 1)[/tex]Range: [tex][-5, 4][/tex]

Step-by-step explanation:

The domain is the set of x-values and the range is the set of y-values.

A company had the following purchases and sales during its first year of operations:


Purchases Sales
January: 10 units at $120 6 units
February: 20 units at $125 5 units
May: 15 units at $130 9 units
September: 12 units at $135 8 units
November: 10 units at $140 13 units

Answers

The final answer of the Inventory is $3540.

What is Inventory?

The term inventory refers to the raw materials used in production as well as the goods produced that are available for sale.

FIFO means first in, first out. It means that it is the first purchased inventory that is the first to be sold

Ending inventory comprises of goods bought in May, September and November

cost of the ending inventory :

(4 x $130) + (12 x $135) + (10 x$140) = $3540

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what is (x^2y^3)^1/3 / 3 sqrt x^2

Answers

Answer:  y/(3x^1/3)

Step-by-step explanation:

Which expression is equivalent to One-fifth (150 x minus 80 y + 50 minus 50 x minus 25 y + 20)?

20 x minus 21 y + 14

20 x + 11 y + 14

20 x minus 11 y + 6

20 x + 21 y + 6

Answers

Answer:

150 x - 80 y + 50 - 50 x - 25 y + 20

Arranging like terms

150 x - 50 x -25 y - 80y + 50 + 20

100x - 105 y + 70

5 ( 20x - 21y + 14)

Answer:

20x - 21y + 14

Explanation:

[tex]\rightarrow \sf \dfrac{1}{5} (150x - 80y + 50 - 50x - 25y + 20)[/tex]

collect like terms

[tex]\rightarrow \sf \dfrac{1}{5} (150x-50x - 80y -25y + 50 + 20)[/tex]

add/subtract like terms

[tex]\rightarrow \sf \dfrac{1}{5} (100x - 105y+70)[/tex]

distribute inside parenthesis

[tex]\rightarrow \sf \dfrac{1}{5} (100x) + \dfrac{1}{5}( - 105y) + \dfrac{1}{5}(70)[/tex]

simplify the following

[tex]\rightarrow \sf 20x -21y + 14[/tex]

Please help me answer this mathematics question

Answers

Answer:

[tex]x = 172.75[/tex]

Hope this help!!!

Have a good day♡

If y=4 when x=12, find y when x=-24

Answers

The value of y is -8 if the x  -24 and y varies directly with x, and If y = 4 when x = 12.

What is a proportional relationship?

It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.

The question is incomplete.

The complete question is:

If y varies directly with x, and If y = 4 when x = 12, how do you find y when x = -24?

y ∝ x  (given)

y = kx

k is the constant of proportionality.

4 = 12k  (y = 4, and x = 12)

k = 1/3

y = x/3

Plug x = -24

y = -24/3

y = -8

Thus, the value of y is -8 if the x  -24 and y varies directly with x, and If y = 4 when x = 12.

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f(x) = -3 +3
Which graph represents the inverse of function ?
-3
N
-1
4
3-
2-
1-
-2+
-3-
-4+
-5+
W.
Y
54
-1-
4-
3-
2
-4
-2
N
-3
-5+
X.
Y
4-
3-
2-
-1-
3
X
e

Answers

Answer: Y

Step-by-step explanation:

Since f(x) passes through (0,3), its inverse should pass through (3,0).

This eliminates X and Z.

Also, since f(x) has a negative slope, so its inverse should also have a negative slope.

This eliminates W.

The graph of the inverse of function is shown in figure.

We have to given that,

Function is defined as,

f (x) = - 3x + 3

Hence, The inverse of function f (x) is,

f (x) = - 3x + 3

y = - 3x + 3

Solve for x,

3x = y + 3

Divide by 3;

x = (y + 3) / 3

Hence,

f⁻¹ (x) = (x + 3) / 3

f⁻¹ (x) = x/3 + 1

Therefore, The graph of the inverse of function is shown in figure.

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Analyze the diagram below and complete the instructions. Find the value of x and the value of y

Answers

The value of the variable x and y will be 15 and 5√3. Then the correct option is D.

The complete question is attached below.

What is trigonometry?

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

The right triangle is shown.

Then the value of x will be

x = 10√3 × sin 60°

x = 15

Then the value of y will be

y = 10√3 × cos 60°

y = 5√3

Then the correct option is D.

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1. The perimeter of the square is f(x) = 4x, where x is the side of the square. Find the domain of the function.

A. Set of rational numbers
B. Set of whole numbers
C. Set of integers
D. All of the choices


2. Find the domain of the function y = 3x + 8(3 - x).
A. Set of real numbers
B. Set of integers
C. Set of whole numbers
D. Set of natural numbers

Answers

Question 1

B. Set of whole numbers

Eliminate A and C because negative integers are in those sets.

Question 2

A. Set of real numbers

The equation represents a line, which has a domain of all real numbers.

If the perimeter of the square is 4x then the domain of the function will be set of rational numbers and the domain of the function y=3x+8(3-x) is set of real numbers.

Given The perimeter of the square is f(x)=4x and the function is y=3x+8(3-x)

We will first solve the first part in which we have been given that the perimeter of the square is 4x and we have to find the domain of the function.

First option is set of rational numbers which is right for the function.

Second option is set of whole numbers which is not right as whole number involves 0 also and the side of the square is not equal to 0.

Third option is set of integers which is not right as integers involve negative number also and side of square cannot be negative.

Hence the domain is set of rational numbers.

Now we will solve the second part of the question

f(x)=3x+8(3-x)

we have not told about the range of the function so we can put any value  in the function and most appropriate option will be set of real numbers as real number involve positive , negative and decimal values also.

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what is the answer please??

Answers

Answer:

See below

Step-by-step explanation:

Area of a circle = pi * r^2

  for this circle  :    Area = 3.142 * 10 * 10 =  314.2 cm^2

The formula for area of a circle is [tex]\pi r^{2}[/tex]

So using pi as 3.142, we can do 3.142 • 100 which is 314.2 when moving place values.

Even though you did not ask, the circumference formula is 2[tex]\pi[/tex]r.

If we were given the same information, where the radius is 10, and we were solving circumference, then we would do 3.14 • 20 = 62.8.

Brainliest if helpful.

Christmas bulbs made of different colours are set to light after 8seconds,10 seconds and 14 seconds. How many times will they light simultaneously in one hour if they start together​

Answers

Answer:

36 seconds will be the answer... by looking down here↓:

Step-by-step explanation:

6 secs x 6 cycles = 36 seconds

9 secs x 4 cycles = 36 secs

12 ses x 3 cycles = 36 secs

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