Triangles are congruent if they have the same ______________.

Answers

Answer 1

Triangles are congruent if they have the same (Shape and Size).

Answer 2

Triangles are congruent if they have the same size and shape.

Related Questions

The quantity demanded of a certain brand of DVD player is 3000/wk when the unit price is $485. For each decrease in unit price of $40 below $485, the quantity demanded increases by 500 units. The suppliers will not market any DVD players if the unit price is $334 or lower. But at a unit price of $559, they are willing to make available 2500 units in the market. The supply equation is also known to be linear.

Answers

Given that the quantity demanded of a certain brand of DVD player is 3000/wk when the unit price is $485. For each decrease in unit price of $40 below $485, the quantity demanded increases by 500 units. The suppliers will not market any DVD players if the unit price is $334 or lower. But at a unit price of $559, they are willing to make available 2500 units in the market. The supply equation is also known to be linear.

Part (a): Find the demand equation.
To find the demand equation, we notice that the demand function is linear because we were told that for each decrease in unit price of $40 below $485, the quantity demanded increases by 500 units.

Given that at a price of $485, the quantity demanded is 3,000 and given that for each decrease in unit price of $40 below $485, the quantity demanded increases by 500 units. Then for a price of $485 - $40 = $445, the quantity demanded is 3,000 + 500 = 3,500 units

Thus, using the formula for the equation of a straight line and the points (3,000, 485) and (3,500, 445), we find the demand equation as follows:

[tex] \frac{p-485}{q-3,000} = \frac{445-485}{3,500-3,000} \\ \\ \Rightarrow \frac{p-485}{q-3,000}= \frac{-40}{500} =- \frac{2}{25} \\ \\ \Rightarrow25(p-485)=-2(q-3,000) \\ \\ \Rightarrow25p-12,125=-2q+6,000 \\ \\ \Rightarrow25p+2q=18,125[/tex]

Part (b): Find the supply equation.
To find the supply equation, given that the supply function is linear and that the suppliers will not market any DVD players if the unit price is $334 or lower. But at a unit price of $559, they are willing to make available 2500 units in the market.

Thus, using the formula for the equation of a straight line and the points (0, 334) and (2,500, 559), we find the demand equation as follows:

[tex] \frac{p-334}{q-0} = \frac{559-334}{2,500-0} \\ \\ \Rightarrow \frac{p-334}{q}= \frac{225}{2,500} =\frac{9}{100} \\ \\ \Rightarrow100(p-334)=9q \\ \\ \Rightarrow100p-33,400=9q \\ \\ \Rightarrow100p-9q=33,400[/tex]

(c) Find the equilibrium quantity and price.
The equilibruim quantity and price is given by the quantity and price at which the quantity demanded is equal to the quantity supplied. It is obtained by equating the demand and the supply equations.

i.e.
From demand equation, we have
[tex]25p+2q=18,125 \\ \\ \Rightarrow25p=-2q+18,125 \\ \\ \Rightarrow p= -\frac{2}{25}q +725 \ . \ . \ . (1)[/tex]

From supply equation, we have
[tex]100p-9q=33,400 \\ \\ \Rightarrow100p=9q+33,400 \\ \\ \Rightarrow p= \frac{9}{100} q+334 \ . \ . \ . (2)[/tex]

Equating equations (1) and (2), we have
[tex]-\frac{2}{25}q +725=\frac{9}{100} q+334 \\ \\ \Rightarrow\frac{9}{100} q+\frac{2}{25}q=725-334 \\ \\ \Rightarrow \frac{17}{100} q=391 \\ \\ \Rightarrow q= \frac{391\times100}{17} =2,300[/tex]

Substituting for q into equation (1), we have
[tex]-\frac{2}{25}(2,300) +725=-184+725=541[/tex]

Therefore, the equilibruim quantity is 2,300 units at a price of $541.

£2292.84 rounded to 2DP

Answers

The rounded solution of £2292.84 , is to two decimal places is £2292.84.

What is round off?

Rounding off means a number is made simpler by keeping its value intact but closer to the next number. It is done for whole numbers, and for decimals at various places of hundreds, tens, tenths, etc.

here, we have,

given that,

£2292.84

its upto two decimal point.

so, rounded to two decimal point = £2292.84

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The number £2292.84, when rounded to two decimal places, remains unchanged as £2292.84 because the third digit after the decimal point is less than 5.

The student has asked to round the number £2292.84 to two decimal places. To round to two decimal places (2DP), you look at the third digit after the decimal point, which in this case is a 4. Since the third digit is less than 5, the second digit after the decimal point remains the same, and the number £2292.84 is already at two decimal places. Therefore, the rounded number is £2292.84.

Eduardo is 16. Eduardo’s dad takes him and his younger sister to a soccer match. Tickets are $17 for adults and $13 for children (18 and under). Write an expression for the total cost of the tickets. What is the total cost of the tickets?

Answers

X= 17a + 13c
X is total cost
a is the total number of adult tickets being bought
c is the total number of child tickets being bought

In the world problem, we learn Eduardo's dad is purchasing 1 adult ticket and 2 child tickets. This gives us: X= 17(1) + 13(2)
X= 17 + 26

X= 43

$43 was the total cost of the tickets

How many multiples of 5 are there between 81 and 358?

Answers

there are 55 multiples of 5 between 81 and 358

358-81 = 277

277/5 = 55.4

there are 55 multiples

Anton bought a picnic cooler. His total bill, with tax, was $7.95. He paid 6 percent sales tax. How much did he pay for the cooler alone without the tax?
For the cost of the cooler, solve:
106% of cost of cooler = $7.95

To find the total bill in terms of the cost of the cooler :
100% of cooler price
+ 6% of cooler price (tax)
--------------------------------------------
106% of cost (7.95)

Now, solve this problem.

106% of $ _______ = $7.95

Answers

106% of $ _______ = $7.95

this means that 1.06 of the price of the cooler is 7.95

so we can assume th
at the cooler price is x

then:

1.06 x = 7.95

Divide both sides by 1.06, we get:

x = 7.5

The price of the cooler itself without tax is $7.5

----.----.----

to check you answer:

7.5 + 7.5*6%= 7.5 + 7.5*0.06 = 7.5 + 0.45 = 7.95$

Correct!! :)

Answer:

I JUST did the test and got it right so the answer is:

Step-by-step explanation:

7.95

In the diagram which we must be true for point P to be the centroid of the triangle

Answers

The centroid is the point where the 3 medians intersect:

JM = ML, LO = OK, KN = NJ (3rd answer)

A quick guess would be A but I'm not sure since I don't really remember.

Two angles in standard position that have the same terminal side are

Answers

An angle is instandard position if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the x-axis is called the initial side and the other ray is called the terminal side.

The volume of a rectangular prism is 2,058cm. The Length of the prism is 3 times the width. The height is twice the width. Find the height of the prism?

Answers

v = l x w x h

v = 2058

width = x

height = 2x

length = 3x

2058 = 3x*2x*x =

2058 = 6x^3=

343 = x^3

x = 7

2*7 = 14

3*7 = 21

21*14*7 = 2058

height is 14 cm

Find the square root of 25.

Answers

The square root of 25, is 5.

The square root of 25 is 5

at 3:00a.m,the temperature is -5°F. Between 3:00a.m. and 6:00 a.m.,the temperature drops by 12°F. Between 6:00a.m. and 9:00a.m., the temperature rises by 4°F. What is the temperature at 9:00a.m.?

Answers

-13°F is the correct answer.

Which point best approximates square root of 45

Answers

The square root of 45 is approximately 6.7. So your answer would be C.

Answer:

The point best approximates √45 is C = 6.72

Step-by-step explanation:

We have to show the approximate square value of √45.

By solving √45 = √(5×9) = √5×√9 = 3√5 = 3×2.24 = 6.72

6.72 can be represented as point C on the given number line.

PLS HELP ME ASAP WITH A-C (CORRECT ANSWERS PLS!!) THANK YOU SM!!!!

Answers

a--> as the distance increases, the weight decreases

b-->(shown in attached picture)

c--> 18ft ~ 5125lbs
30ft ~ 3125lbs
72ft ~ 1250lbs

A(n) _____ is a two dimensional diagram that can be folded to form a three dimensional figure?

A. net

B. orthographic drawing

C. isometric drawing

D. geometric solid

Answers

Answer:

The answer is option A.

Step-by-step explanation:

A net is a two dimensional diagram that can be folded to form a three dimensional figure.

A net is a pattern made when a 3 d figure is put flat on the surface, showing each face of the figure.

A solid has different nets.

Answer:

Step-by-step explanation:

1.A

2.A

3.B

4.B

5.C

6.D

7.C

8.B

9.A

10.D

11.C

12.C

13.C

14.B

15.D

Find the distance between the given points. C(7, 1) and D(4, -6) Distance =

Answers

[tex] \sqrt{( x_{2}- x_{1}) ^{2}+( y_{2}- y_{1}) ^{2[/tex]

Plug and chug

Answer: [tex] \sqrt{34} [/tex]

Answer:

√58

Step-by-step explanation:

When Lou started his current job, his employer told him that he would receive two vocation days for each full year he worked. How long will it take him to earn 18 paid vacation days?

Answers

9 years. 2 divided by 18 is 9

By solving a linear equation, we will see that he needs to work for 9 years.

How long will take Lou to earn 18 vacation days?

We know that for each year that he works, he gets 2 vacation days.

So we can write the linear equation:

y = 2*x

Where y is the number of vacation days, and x is the number of years that he worked.

We want to find the value of x such that y = 18, then we need to solve:

18 = 2*x

Solving for x w get:

18/2 = x = 9

This means that to get 18 vacation days, he needs to work for 9 years.

If you want to learn more about linear equations, you can read:

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Solve for L: S = B + 1/2L

Answers

First get L on the side by itself by subtracting B from both sides. S-B=1/2L. Then multiply both sides by 2. 2S-2B=L

Isolating L, it is found that the solution for L is given by:

[tex]L = 2(S - B)[/tex]

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

The equation is:

[tex]S = B + \frac{1}{2}L[/tex]

Leaving everything with L on one side, everything without on the other.

[tex]\frac{L}{2} = S - B[/tex]

[tex]L = 2(S - B)[/tex]

Which is the solution for L.

A similar problem is given at https://brainly.com/question/5123313

A school offers two summer sports: lacrosse and tennis. There are 438 students in all. Of this number, 52 participate in lacrosse and 94 participate in tennis. Nobody does both. What fraction of the students participate in a sport? Write the fraction in simplest terms.

Answers

52 + 94 = 146

146/438
1/3

Hope this helped!

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

We have been given that there are 438 students in all. Of this number, 52 participate in lacrosse and 94 participate in tennis.

Our required fraction would be:

[tex]\frac{\text{Students participant in lacrosse + Tennis}}{\text{Total students}}[/tex]

[tex]\frac{52+94}{438}[/tex]

[tex]\frac{146}{438}[/tex]

[tex]\frac{146*1}{146*3}[/tex]

[tex]\frac{1}{3}[/tex]

Therefore, our required fraction would be [tex]\frac{1}{3}[/tex].

A block of wood is 0.2 meters (m) by 0.1 m by 0.5 m. find its dimensions in centimeters

Answers

1m=100cm

0.2m=100(0.2)cm=20cm
0.1m=100(0.1)cm=10cm
0.5m=100(0.5)cm=50cm

it's dimetions are 20cm by 10cm by 50cm

The area of the irregular polygon is ____ square units.

Answers

To find the area of this shape youd have to break it up. If you broke it into the left section and the right bottom section youd get 2 rectangles and the area of a rectangle is defined as A=Length*Width. The left would be a 3*4 rectangle making its area 12 units^2 and the right would have a height of (3-2) units and a length of (7-4) units making its area 1*3 or just 3 units^2, if you add both areas you get the total area, which is 15 units^2

break it up into chunks: the small rectangle and the big rectangle.
subtract 7 and 4 to get the big side of the rectangle, and subtract 3 and 2 to get the small side. then find the area of the big rectangle and small rectangle to get the area of the entire rectangle. area equals 15 units^2

Determine the measures of the unknown labeled angles in the diagrams below:

Answers

check the picture below.

thus, angle "a" is just 180 - 102 - 42.

and angle "b" is just 180 - 44.

keeping in mind that, for the second triangle, for two equal sides, departing from the same vertex, they'd make up equal angles on the other end, thus the red 68°.

If x=2 then 2=x what’s the definition

Answers

Answer:

The symmetric property of equality.

Step-by-step explanation:

The symmetric property of equality says that if a=b, then b=a. Here, we have x substituted for "a" and 2 substituted for "b" to get ...

if x = 2, then 2 = x. . . . . . . symmetric property of equality

i need help please
what is the missing reason in the proof

Answers

There's a lot going on, but the main thing to focus on really is the equation
AE+EB = CF+FD

and on the equation
EB = CF

Because the second equation (shown above) is true, we can effectively replace the "EB" with "CF" like so
AE+EB = CF+FD
AE+CF = CF+FD

Then we can subtract CF from both sides
AE+CF = CF+FD
AE+CF-CF = CF+FD-CF
AE = FD

When I subtracted CF from both sides, I used the Subtraction Property of Equality, which is the answer needed to go into the blank.

Help me with this math man

Answers

= 7m(3m^6 - m^4 + 7)
or

= 7m(3m^6 + (-m^4) + 7)

hope it helps

see attached picture for solution:

What is the measure of FSM

Answers

m<FSM = m<WSU
7x+ 8 = 5x + 32
2x = 24
x = 12

m<FSM = 7x+ 8 = 7(12) + 8 = 84 + 8 = 92

answer
A 92

The measure of angle FSM 92 degrees.

The given problem can be solved using the concept of Intersecting Lines, specifically the fact that vertical angles are equal.

Here, the angles WSU and FSM form vertical angles at point 'S' as the lines WM and FU intersect at this point.

Given that WSU = (5x+32) degrees and FSM = (7x+8) degrees, since they are vertical angles, we can set them equal to each other.

This gives, 5x + 32 = 7x + 8.

Now, by subtracting 5x from each side, we get 2x = 24.

Thus, dividing by 2 on both sides, we obtain 'x' as 12.

Substitute 'x' values in FSM = (7x+8) degree. So, FSM = (7*12+8) = 92 degrees.

Therefore, the measure of angle FSM is 92 degrees which makes the answer option A. Correct answer.

Learn more about Intersecting Lines here:

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The probable question may be:

Line WM and Line FU intersects each other at common point S

The angle between WSU is (5x+32) degree

The angle between FSM is (7x+8) degree

What is the measure of FSM

A. 92degree

B. 93 degree

C. 95 degree

D. 94 degree

There are two jars. One jar contains 2 red gum balls , 3 green gum balls ,and 1 yellow gumball.the other jar contains 2 blue balloons and 3 purple balloons . Jeff randomly draws one gumball and then balloon .what is the probability that he will draw a green gumball and a blue balloon?
A.1/15
B.2/15
C.1/5
D.3/10

Answers

There are 3 green gumballs out of 6 in total. So, the odds of Jeff pulling out a green gum ball is 3/6, or 1/2.

There are 2 blue balloons out of 5 in total. So, the odds of Jeff pulling out a blue balloon is 2/5.

Therefore, the combined odds of Jeff pulling out a green gum and a blue balloon is 1/2 multiplied by 2/5, which is 2/10, or 1/5, Making the answer C.

TL;DR: The answer’s C.

Answer: 3/10 I had the same problem on a test and this was correct

−7x−50≤−1 AND−6x+70>−2

Answers

wrong it would be -7 greater than sign x another greater than sign 12

After solving the compound inequalities we get

[tex]-7\leq x<12[/tex]

Given :

[tex]-7x-50\leq -1 and -6x+70>-2[/tex]

solve each inequality using algebraic operations

[tex]-7x-50\leq -1\\-7x\leq -1+50\\-7x\leq 49\\Divide \; by \; -7\\x\geq -7[/tex]

Now we solve the next inequality

[tex]-6x+70>-2\\-6x>-2-70\\-6x>-72\\Divide \; by \; -6\\x<12[/tex]

From both inequalities we get

[tex]-7\leq x<12[/tex]

Solution for the given inequality is [tex]-7\leq x<12[/tex]

Learn more : brainly.com/question/234674

What is the simplified expression for

Select one:
a. 3 over 2
b. 3 to the power of 2 over 2 to the power of 2
c. 3 to the power of 2 over 2
d. 2 to the power of 4 over 3

Answers

c because it's telling you

RS=5y+5, ST=3y+7, and RT=12y-20 what is the value of y?

Answers

since S is a point on the line RT, therefore:
RS+ST = RT
5y+5+3y+7 = 12y-20
separate the variables and solve to get thevalue of y as follows:
5+7+20 = 12y-3y-5y
32=4y
y = 8

substitute in the equation of each line to get its length as follows:
RS = 5y+5 = 5(8)+5 = 45
ST = 3y+7 = 3(8)+7 = 31
RT = 12y-20 = 12(8)-20 = 76

Answer:

-12 or 8

Step-by-step explanation:

Kevin is six years older than his twin sisters. The sum of the three children’s ages is the same as their 42 year old dad’s age. How old are the children?

Answers

Let the age of Kevin be x,

age of twin sisters = x - 6
sum of children's age = x + x - 6 + x - 6
= 3x - 12
3x - 12 = 42
3x = 54
x = 54/3
= 18
age of twin sisters = x - 6
= 18 - 6
= 12

Kevin is 18 years old whereas the twin sisters are both 12 years old.

Final answer:

The question involves solving a basic algebra problem to determine the ages of three children. By setting up an equation based on the given information, we find that each twin sister is 12 years old and Kevin is 18 years old.

Explanation:

The question revolves around finding the ages of three children, Kevin and his twin sisters, given that Kevin is six years older than his twin sisters and the sum of their ages equals their father's age, who is 42 years old. First, let's denote the age of each twin sister as x. Since Kevin is six years older, his age will be x + 6. The sum of their ages equals their father's age, which is given as 42 years. Therefore, the equation to find their ages will be:

[tex]x + x + (x + 6) = 42[/tex]

This simplifies to:

3x + 6 = 42

Subtracting 6 from both sides gives:

3x = 36

Dividing by 3:

x = 12

So, the age of each twin sister is 12 years, and Kevin's age is 12 + 6 = 18 years.

ABCD is a square. What is the measure of angle BAC?

A. 90°
B. 45°
C. 15°
D. 135°

Answers

a corner in a square is 90%

the angle BAC is half that

90/2 = 45 degrees

Answer:

The correct option is B.

Step-by-step explanation:

Given information: ABCD is a square.

According to the property of square,

1. The measure of all interior angles of the square is 90°.

2. Diagonals are angle bisector.

In the given figure ABCD is square, so

[tex]\angle DAB=90^{\circ}[/tex]

AC is a diagonal of ABCD.

[tex]\angle DAC=\angle BAC[/tex]

We can say that

[tex]\angle DAB=\angle DAC+\angle BAC[/tex]

[tex]\angle DAB=\angle BAC+\angle BAC[/tex]

[tex]\angle DAB=2\angle BAC[/tex]

[tex]90^{\circ}=2\angle BAC[/tex]

Divide both sides by 90.

[tex]\frac{90^{\circ}}{2}=\angle BAC[/tex]

[tex]35^{\circ}=\angle BAC[/tex]

The measure of angle BAC is 45°. Therefore the correct option is B.

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