Which congruence criteria is met in the following scenario?
SAS
SSS
AAS
HL
ASA

The given equation

x/2 = y/3 = z/4

can be broken into three separate equations which I'll call equations (A), (B) and (C)

We'll start off solving for z in equation (C)

x/2 = z/4

4x = 2z ... cross multiply

2z = 4x

z = 4x/2 ... divide both sides by 2

z = 2x

Now let's solve for y in equation (A)

x/2 = y/3

3x = 2y

2y = 3x

y = 3x/2

y = (3/2)x

y = 1.5x

The results of z = 2x and y = 1.5x both have the right hand sides in terms of x. This will allow us to replace the variables y and z with something in terms of x, which means we'll have some overall expression with x only. The idea is that expression should simplify to 3 if we played our cards right.

We won't be using equation (B) at all.

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

The key takeaway from the last section is that

Let's plug those items into the expression (2x-y+5z)/(3y-x) to get the following:

(2x-y+5z)/(3y-x)

(2x-y+5(2x))/(3y-x) ..... plug in z = 2x

(2x-y+10x)/(3y-x)

(12x-y)/(3y-x)

(12x-1.5x)/(3(1.5x)-x) .... plug in y = 1.5x

(12x-1.5x)/(4.5x-x)

(10.5x)/(3.5x)

(10.5)/(3.5)

3

We've shown that plugging z = 2x and y = 1.5x into the expression above simplifies to 3. Therefore, the equation (2x-y+5z)/(3y-x) = 3 is true when x/2 = y/3 = z/4. This concludes the proof.

Answer:

No solutions since they are two variables and it supposed to be solved simultaneously

Answer:

Point R is at (−40, −30), a distance of 60 units from point Q

Step-by-step explanation:

Correct option is ,

Point R is at (-40, 30) , a distance of 60 units from Point Q.

hope this answer helps you dear take care!

Answer:

4- true

5-true

6-false

7-false

8-true

9-true

Step-by-step explanation:

Follow the letters and the sign of congruence

≅

Answer:

[tex]x=k\pi[/tex] for any integer [tex]k[/tex]

Step-by-step explanation:

To solve the problem we must know about the sine function.

In [tex]y= sin(k\pi)[/tex], the value of k will be any integer to form a circle.

Given in the question :

Among all the options given,

[tex]y= sin(k\pi)[/tex] will always give 0, since the value of [tex]\pi[/tex] is [tex]360^0[/tex]. So, if you multiply any integer to [tex]\pi[/tex] the result will always give a full circle.

therefore, the value of  [tex]sin(k\pi)[/tex] will always remains 0.

Hence, In [tex]y= sin(k\pi)[/tex], the value of k will be any integer to form a circle.

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Answer:

x=42

Step-by-step explanation:

Answer: x ≤ 10

Step-by-step explanation:

20 + 13x ≤ 150

13x ≤ 150 - 20

13x ≤ 130

x ≤ 130 ÷ 13

x ≤ 10

Answer:

5.4 as a fraction is 27/5.

Step-by-step explanation:

Learned in 5th grade

2,000 Sorry That Was I Know #carryonlearning

Answer:

84cm cubic.

Step-by-step explanation:

That is how it is done.Hope it will help.

Answer:

Part A:

LCM of 7 and 8 is 56.

7*8 = 56

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

Part B:

GCF of 54 and 81 is 27.

54: 1, 2, 3, 6, 9, 18, 27, 54.

81: 1, 3, 9, 27, 81.

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

Part C:

GCF of 54 and 81 is 27.

54 / 27 = 2

81 / 27 = 3

Final expression: 27(2 + 3)

Answer:

Part A: 56

Work:

7: 7, 14, 21, 28, 35, 42, 49, 56

8: 8, 16, 24, 32, 40, 48, 56, 64

Part B: 27

Work:

54: 54, 27, 9, 3, 1

81: 81, 27, 9, 3, 1

Part C: 27(2+3)

Work:

27×2 = 54    

27×3 = 81

(27×2)+(27×3) = 54+81

(27×2)+(27×3)=27(2+3)

Explaining work:

First you find the numbers that multiply the GCF by to get the product (for 54 it is 2 and for 81 it is 3). Then you replace the the products with the equations (27×2) for 54 and (27×3) for 81 to get (27×2)+(27×3). Then simplify to get 27(2+3).

Answer:

Step-by-step explanation:

We are being asked for times, so we can express the rate in terms of seconds per meter.

  (15 seconds)/(14 meters) = (15/14) seconds per meter = 1 1/14 seconds/meter

__

1) It will take Robot A 1 1/14 seconds to go 1 meter.

2) it will take Robot A 4 2/7 seconds to go 4 meters. (4 times as long)

Answer:

fluid space that contains DNA, ribosomes, and other enzymes

Step-by-step explanation:

B is points towards the "empty" space, meaning its Stroma.

Stroma defintion: involved in the synthesis of organic molecules from carbon dioxide and water or the fluid of the chloroplast surrounding the thylakoid membrane;

Let's look at the answer choices.

A. enclosed space containing proteins used in ATP formation

B. membranes enclosing open space

C. layered stacks of membranes

D. fluid space that contains DNA, ribosomes, and other enzymes

Obviously not C.

A is Synthase.

B is the whole thing.

It is D.

(BTW THIS IS MATH!! Not science!! Just in case you have more questions!)

Answer:

raw

Step-by-step explanation:

Answer:

Step-by-step explanation:

Essentially, we can use the pythagorean rule that:

a^2+b^2=c^2

c^2 resembles the hypotenuse, which is almost always the largest number. therefore, we simply have to find two which equal the largest side:

9^2+40^2=41^2

81+1600=1681

1681=1681

Based on this math, A is our right angle!

Hope this helps!

Answer:

(8, 0)

(-2, 0)

(-3, 0)

Step-by-step explanation:

x - 8 = 0

x = 8

x + 2 = 0

x = -2

x + 3 = 0

x = -3

[tex](x-8)(x+2)(x+3) =0\\\\\implies x -8 =0~~~ \text{or}~~~x+2 =0 ~~~ \text{or}~~~x+3 = 0\\\\\implies x = 8 ~~~~~~~~ \text{or}~~~~~~x = -2 ~~~ \text{or}~~~ x = -3\\\\\\\text{Hence the roots are}~ 8, -2 ~\text{and} ~-3[/tex]

Answer:

the answer to the question is 210

Answer:

Name:

Grade & Section:

Date Submitted: 12/14/2021

Advent: Use it

Christmas: Open gifts under the tree left by Santa

Ordinary Time:

Lent: Celebrate Jesus.

Paschal Triduum: The Proper day to Celebrate Jesus

Easter: It is a Holiday where you celebrate a bunny and get candy.

Step-by-step explanation:

So is what you do here is you enter your Name, Grade & Section, and Date which i've already given you. So your assignment is about how you will participate in the seasonal activity. So Advent looks like it would be a Advent Calendar.

Christmas You wanna open gifts

Now I left Ordinary Time blank because you need to put what time you would regularly open gifts or if you do not celebrate Christmas put what time you'd like to open gifts at.

Lent: is where you celebrate Jesus and what he did on his time being on Earth.

Paschal Triduum is basically the same as Lent but it is the proper day you celebrate Jesus Which starts April 13 & Ends Saturday, April 16

Easter: Is where you usually get candy but it is in a hunt form

Angles theorem and Reflexive property of congurence

The solution is

Each diagonal of a parallelogram separates it into two congruent triangles

So , ΔABC ≅ ΔCDA

Opposite angles are congruent

So , ∠B ≅ ∠D

What is a Parallelogram?

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the parallelogram be ABCD

Now , AC is a diagonal of the parallelogram

According to the postulates of parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

And ,

From the figure , we can deduct that ΔABC ≅ ΔCDA by

Angle A is congruent to angle C, and angle D is congruent to angle B

So , from congruent triangle theorem ΔABC ≅ ΔCDA

And ,

∠B ≅ ∠D

Because Opposite angles are congruent of a parallelogram

Hence , Each diagonal of a parallelogram separates it into two congruent triangles

So , ΔABC ≅ ΔCDA

Opposite angles are congruent

So , ∠B ≅ ∠D

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[tex]y +11 = -2(x+1.5)\\\\\implies y = -2x -3 -11\\\\\implies y = -2x - 14\\\\\text{The above equation is in a form of y = mx +b,}~\text{where}~~ b = -14~\text{ is the y-intercept.}[/tex]

Answer:

61.9

Step-by-step explanation:

mark me as brainliest

Answer:

  62°

Step-by-step explanation:

The law of cosines is used to find the length of side k:

  k² = i² +j² -2i·j·cos(K)

  k² = 40² +80² -2·40·80·cos(92°) ≈ 8223.3568

  k ≈ 90.6827 . . . . . . . take the square root

Then the law of sines is used to find angle J.

  sin(J)/j = sin(K)/k

  J = arcsin(j/k·sin(K)) = arcsin(80/90.6827·sin(92°)) ≈ 61.84°

  J ≈ 62°

Emika's monthly budget is $60.

A percentage can be described as the fraction of a number multiplied by 100. The sign used to represent percentages is %.

Let Emika's cell phone bill budget be represented with x.

In order to determine his monthly budget, divide $60 by 120%

x = $60 / 120%

x = $60 / 1.20

x = $50

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Answer:

[tex]y=-8x+80[/tex]

Step-by-step explanation:

[tex]Slope=\frac{y_2-y_1}{x_2-x_1}=\frac{32-64}{6-2}=\frac{-32}{4}=-8[/tex]

[tex]y=mx+b[/tex]

[tex]y=-8x+b[/tex]

[tex]64=-8(2)+b[/tex]

[tex]64=-16+b[/tex]

[tex]80=b[/tex]

Therefore, the estimated line of best fit is [tex]y=-8x+80[/tex]

The sub duplicate ratio of 16:9 is

4: 3

The sub-duplicate ratio is found by finding the square root of both the numerator and denominator

The given ratio is 16:9

Find the square root of 16

[tex] \sqrt{16} = 4[/tex]

Find the square root of 9

[tex] \sqrt{9} = 3[/tex]

Combining the two square roots that were found, the sub duplicate is:

[tex] \frac{4}{3} [/tex]

Therefore, the sub duplicate ratio of 16:9 is

4: 3

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Answer:

Inverse Property of Multiplication

Step-by-step explanation:

Inverse Property of Multiplication is when you do inverse operations to get rid of a multiplied number (if that makes any sense). to solve 8x = 80 you do the inverse of multiplying by 8 (divide both sides of the equal sign by 8) to get x=10.

Answer:

9

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

Step-by-step explanation:

11x - 47 = 6x - 2                  Corresponding angle. Add 47 to both sides

11x = 6x + 47 - 2                 Combine

11x = 6x + 45                      Subtract 6x from both sides

11x - 6x = 45                       Combine

5x = 45                              Divide by 5

5x/5 = 45/5

x = 9

Answer:

On average, the workers dig 4.75ft each day. Also, what x and y questions?

Step-by-step explanation:

Take [tex]38/8=4.75[/tex]

I hope you have a great day and make me the brainliest.

The drilling team digs 4.75 feet every day, as per the given conditions, and y and x-intercept represent the depth and days respectively.

Given that,
A drilling team detected water 38 feet below the ground. if it took workers 8 days to be able to dig and pull up the water,

the equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

here,
The total depth of dig = 38 feet
Total time took to dig 38 feet = 8 days
For 1 day, the depth of the dig = 38 / 8 = 4.75
Now,
Let x is the number of days,
while y be the depth left to dig in feet,
y = 38 - 4.75x

The drilling team digs 4.75 feet every day, as per the given conditions, and y and x-intercept represent the depth and days respectively.

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Answer:

60/8 = 7.5 mins per mile

Step-by-step explanation:

Answer:

No, it is not possible.

Step-by-step explanation:

A system of linear equations with infinitely many solutions must meet at every single point. That means they have both the same y-intercept and the same slope. If either one of those are different, there cannot be infinitely many solutions.

Answer:

r = 6

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

The compounded interest is applied to the amount in the account at end

of a period specified in the rate of compounding.

Reasons:

The interest paid on the account = 4% compounding

Amount with which she opened the account = $10,000

Amount she makes as deposit at the end of each quarter = $1,000

Therefore;

The interest per quarter = 4% ÷ 4 = 1%

Amount in the account after the end first quarter, A₁, is therefore;

A₁ = 10,000 × 0.01 + 10,000 + 1,000 = 11,100

The amount in the second quarter, A₂, is given as follows;

A₂ = 11,100 × 0.01 + 11,100 + 1,000 = 12211

A₃ = 12211 × 0.01 + 12211 + 1,000 = 13333.11

A₄ = 13333.11 × 0.01 + 13333.11 + 1,000 = 14466.4411

A₅ = 14466.4411 × 0.01 + 14466.4411 + 1,000 = 15611.105511

At the end of the 6th quarter, we have;

A₆ = 15611.105511 × 0.01 + 15611.105511 + 1,000 = 16767.2165991

The amount in the account at the end of 6 quarters, A₆ ≈ $16,767.2

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