Alan draws the two triangles below.



Alan claims that the two triangles are similar. Which of the following methods could he use to prove his claim? Select TWO that apply.
A
show that all pairs of corresponding sides are congruent

B
show that the triangles are congruent, as all congruent triangles are similar

C
show that a sequence of rigid motions and dilations carries one triangle onto the other triangle

D
show that all pairs of corresponding angles are congruent and all corresponding sides are

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

Explanation:

Let x and y be two positive whole numbers. They may or may not be equal.

The first bag has the ratio of red to blue as 3:5, which scales up to 3x:5x after multiplying both parts by x. We have 3x red and 5x blue.

The second bag has the ratio 3:2 which scales up to 3y:2y. This bag has 3y red and 2y blue.

We can make a handy table to keep track of all the expressions

[tex]\begin{array}{|c|c|c|}\cline{1-3}\text{ } & \text{Red} & \text{Blue}\\ \cline{1-3}\text{bag 1} & 3x & 5x\\ \cline{1-3}\text{bag 2} & 3y & 2y\\ \cline{1-3}\end{array}[/tex]

Based on that, we can then say:

Effectively, I added down along each column of that table.

Divide the two expressions for R and B to lead to the fraction 11/9, which is directly from the ratio 11:9

So,

(total red)/(total blue) = 11/9

R/B = 11/9

(3x+3y)/(5x+2y) = 11/9

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

Let's cross multiply and then solve for y

(3x+3y)/(5x+2y) = 11/9

9(3x+3y) = 11(5x+2y)

27x+27y = 55x+22y

27y-22y = 55x-27x

5y = 28x

y = 28x/5

y = (28/5)x

y = 5.6x

We'll keep this in mind for later.

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

Now let:

Recall that we had 3x red and 5x blue for the first bag. That means we have 3x+5x = 8x marbles in the first bag. Therefore, F = 8x.

Also, we had 3y red and 2y blue for the second bag.

So we have S = 3y+2y = 5y

Then we can apply further substitution to say

S = 5y

S = 5(5.6x) .... plug in y = 5.6x

S = 28x

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

In short,

for some positive whole number x. We don't have enough info to pin down what x is exactly; however, it doesn't really matter. This is because the x variable will cancel when dividing F over S

F/S = (8x)/(28x) = 8/28 = 2/7

The fraction 2/7 leads directly to the final answer of the ratio 2:7

In other words, the ratio 8x:28x simplifies fully to 2:7 after dividing both parts by 4x.

The ratio between the total marbles of the first bag and the second bag is 2:7.

An equation is a mathematical statement that is made up of two expressions connected by an equal sign.

Example:

2x + 4 = 9 is an equation.

We have,

x marbles in the first bag.

red marbles = 3x

blue marbles = 5x

y marbles in the second bag.

red marbles = 3y

blue marbles = 2y

Now,

Total red marbles in both bags.

3x + 3y = 11 _____(1)

3x = 11 - 3y

x = (11 - 3y) / 3

Total blue marbles in both bags.

5x + 2y = 9 ______(2)

From (1) and (2) we get,

Multiply 2 in (1).

6x + 6y = 22

6y = 22 - 6x _____(3)

Multiply 3 in (2)

15x + 6y = 27 ______(4)

Putting (3) in (4)

15x + 22 - 6x = 27

9x = 27 - 22

9x = 5

x = 5/9

Now,

x = 5/9 in (3)

6y = 22 - 6(5/9)

6y = 22 - 10/3

6y = (66 - 10)/3

y = 56/18

y = 28/9

Now,

First bag.

Red marbles = 3x = 3 x 5/9 = 5/3

Blue marbles = 5x = 5 x 5/9 = 25/9

Total marbles = 5/3 + 25/9 = (15 + 25)/9 = 40/9

Second bag.

Red marbles = 3y = 3 x 28/9 = 28/3

Blue marbles = 2y = 2 x 28/9 = 56/9

Total marbles = 28/3 + 56/9 = (84 + 56)/9 = 140/9

Now,

The ratio between the total marbles of the first bag and the second bag.

= 40 :140

= 4:14

= 2:7

Thus,

The ratio is 2:7.

Learn more about equations here:

https://brainly.com/question/17194269

#SPJ2

Answer:

7

Step-by-step explanation:

i know

Answer:

sqrt(10)

Step-by-step explanation:

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

Answer:s

Step-by-step explanation:

Answer:

x=2  y=3

Step-by-step explanation:

Answer:

y= 2/3x+8

Step-by-step explanation:

you add 10 to both sides then combine -2 with 10 to get 8

then 1x times 2/3 is 2/3x and -3 times 2/3 is -2

Answer:

1) 6 & 2)12

Step-by-step explanation:

Solve the equations backwards-

1) Subtract 6 from 36, and then divide by 5.

36 = 6 + 5x

(36 - 6)/5 = x

x = 6

2) Subtract 7 from 43, and then divide by 3.

43 = 7 + 3y

(43 - 7)/3 = y

y = 12

Answer:

$15

Step-by-step explanation:

20-5= 15

Answer: The range is 15 because 20 is the highest and 5 is the lowest and when you subtract them you get 15.

Hope this helps :)

Answer:

X= -1/3 or 4

Step-by-step explanation:

Answer:

x =-1/3 and x=4

Step-by-step explanation:

solve by factoring:

separate into two equations:

3x+1=0

8-2x=0

(when the products of factors equals zero, at least one factor is zero)

3x=-1

x=-1/3

-2x=-8

x=4

Answer:

6 rainy days

Step-by-step explanation:

Answer:

$72,000

Step-by-step explanation:

If we take 60,000 and then take 20 percent of it, we get 12,000. Then we add 12,000 to 60,000 and it gives us 72,000.

Answer:

no its not a function

Step-by-step explanation:

because the lines on the graph are not equal\in a straight line(the puppy is not gaining the same amount each week)

Answer:

[tex]33\%, ~\dfrac 3{10},~0.32,~ \dfrac 13[/tex]

Step-by-step explanation:

[tex]33\% <\dfrac 3{10}<0.32<\dfrac 13[/tex]

Answer:

f(x)=125k(1.05)x

Step-by-step explanation:

ommg

ok so every year it increase by 5%, aka 105%

which is 125k*105/100x which is the first one f(x)=125k(1.05)x

if u are not sure than use cross of elinimation

cant be 2nd one cause its not correct

third one ur decreasing

fourth one is just like the 2nd one

[tex]\huge \rm༆ Answer ༄[/tex]

The equivalent expression is ~

Refer to attachment for solution ~

For x such that 0 < x < [tex]\frac{\pi}{2}[/tex], the mathematical expression is:

[tex]\frac{\sqrt{1 \;-cos^2x} }{sinx} + \frac{\sqrt{1 \;-sin^2x} }{cosx} = 1+1=2[/tex]

Given the following data:

In Trigonometry, you should take note of the following mathematical expression:

[tex]sin^2x + cos^2x = 1[/tex]

Therefore, we can obtain the following:

[tex]sin^2x = 1 - cos^2x[/tex]   ...equation 1.

[tex]cos^2x = 1 - sin^2x[/tex]    ...equation 2.

Substituting the equations respectively, we have:

[tex]\frac{\sqrt{1 \;-cos^2x} }{sinx} + \frac{\sqrt{1 \;-sin^2x} }{cosx} = \frac{\sqrt{sin^2x} }{sinx} + \frac{\sqrt{cos^2x} }{cosx}\\\\[/tex]

Taking the square roots, we have:

[tex]\frac{sinx}{sinx} + \frac{cosx}{cosx} = 1 +1\\\\1+1=2[/tex]

Therefore, for x such that 0 < x < [tex]\frac{\pi}{2}[/tex], the expression is:

[tex]\frac{\sqrt{1 \;-cos^2x} }{sinx} + \frac{\sqrt{1 \;-sin^2x} }{cosx} = 1+1=2[/tex]

Read more on trigonometry here: https://brainly.com/question/4515552

Answer:

If you are not in Iceland, then you are not in Reykjavik.

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

The contrapositive of a statement is as follows:

"Switching the hypothesis and conclusion of a conditional statement and negating both. For example, the contrapositive of "If it is raining then the grass is wet" is "If the grass is not wet then it is not raining."

So, for this one, we need to switch as well!

If you are in Reykjavik, then you are in Iceland.

If you are NOT in Iceland, then you are not in Reykjavik.

The answer would be D

Answer:

10:24

Step-by-step explanation:

if school starts at 7:15 and you stay in the first 4 periods for 47 minutes each, that totals 3 hours, 8 minutes

7:16 + 3 hrs, 8 min = 10:24

Answer:

(7,-2)

Step-by-step explanation:

Answer:

(7, - 2 )

Step-by-step explanation:

x - y = 9 ( add y to both sides )

x = y + 9 → (1)

2x + 5y = 4 → (2)

Substitute x = y + 9 into (2)

2(y + 9) + 5y = 4 ← distribute parenthesis and simplify left side

2y + 18 + 5y = 4

7y + 18 = 4 ( subtract 18 from both sides )

7y = - 14 ( divide both sides by 7 )

y = - 2

Substitute y = - 2 into (1)

x = - 2 + 9 = 7

solution is (7, - 2 )

Answer:

y =47.5.

Step-by-step explanation:

First eliminate the fractions by multiplying through by the LCM of 7 and 3 which is 21:

21* 6[y-2]/7-21*12 = 21*2[y-7]/3

18(y - 2) - 252 = 14(y - 7)

18y -36 - 252 = 14y - 98

18y - 14y = -98 + 36 + 252

4y = 190

y = 190/4

y = 47.5.

Answer:

25452664637378381234

Answer:

2b+7

Step-by-step explanation:

sorry for the dimwit who typed random numbers

Answer:

y = x + 7

Step-by-step explanation:

If the slope is 1, the original equation is y = mx + b, with m being 1.

Now substitute -6 and 1 for x and y and solve for b

1 = 1(-6) + b

1 = -6 + b

7 = b

Put it all together:

y = x + 7

Answer: 4

Step-by-step explanation: If Caleb starts with 4 and subtracts 6, he'll get -2. -2 times 2, equals -4. If he starts with 4 and subtracts 8, he'll again end up with -4, meaning the original number is 4!

4-6= (-2)

-2*2= (-4)

4-8= (-4)

Answer:

Yes They Are Equivalent

Step-by-step explanation:

I checked by multiplying them.

Answer: yes, because they both equal x= -8

Step-by-step explanation:

m= -5 -3

calculate

= -8

m= -12+4

calculate

m= - 8

1, a.) The two specific conjectures are in the first image.

1, b.) The two general conjectures are in the second image.

2, a.) Two specific conjectures for this pattern are:

2, b.) From our observation two general conjecture is that the given sequence is an arithmetic sequence and the common difference is 3.

For finding its nth term we can use the formula: a(n) = a + (n-1) x d.

2, c.) A formula for the given pattern is 5 + (n-1)3, where n is the number of the term.

Step-by-step explanation:

Distributive property

Answer:

????????????????????????

Answer: 60%

Step-by-step explanation: if the question is saying the item was already 40% an ADDITIONAL (adding) 20% will make the item 60% off meaning your percentage of savings is 60%

Im pretty sure It would be a decrease

Answer: x= -2, y= 3

Step-by-step explanation:

3x+5y=9

X-y=-5

Multiply bottom equation by 5

3x+5y=9

5x-5y=-25

3x + 5x=8x

5y-5y cancels out

9-25= -16

8x= -16

X= -2

Plug -2 back into equation of choice to find y

3(-2)+5y=9

-6+5y=9

Add -6 to both sides

-6+6 cancels

9+6=15

5y=15

Y=3

Answer:

x = 14

Step-by-step explanation:

21 ÷[tex]\frac{2}{3}[/tex] = 14

Answer:

x = 31 1/2

Step-by-step explanation:

- Isolate x by multiplying 2/3 on each side, cancelling out the one of its original placement

- You can't divide by a fraction, so KCF (Keep Change Flip):

      x = 21 * 3/2

      = 63/2 or 31 1/2

Answer:

Step-by-step explanation:

[tex]\sf 2x+4=3(x-4)[/tex]

[tex]\sf 2x+4=3x-12[/tex]

[tex]\sf 2x+4-4=3x-12-4[/tex]

[tex]\sf 2x=3x-16[/tex]

[tex]\sf 2x-3x=3x-16-3x[/tex]

[tex]\sf -x=-16[/tex]

[tex]\sf \cfrac{-x}{-1}=\cfrac{-16}{-1}[/tex]

[tex]\sf x=16[/tex]

solve the equation below :-

2x+4=3(x-4)

x = 16

=> 2x+4 = 3(x-4)

=> 2x+4 = 3x-12

=> 2x+4 - 4 = 3x-12 - 4 (Subtract 4 on both the sides)

=> 2x = 3x-16

=> 2x-3x = -16

=> -x = -16

=> -x/-1 = -16/-1

=> x = 16