triangle abc has an area of 6 and a perimeter of 12. if the triangle is dilated by a scale factor of 3 centered at the origin, what is the area and perimeter of its image, triangle a'b'c'?

The equivalent equations of [tex]2x+ 4y = 14[/tex] and [tex]4x + y = 20[/tex]

are [tex]2x+ 4y = 14[/tex] and[tex]-16x -4y = -80[/tex]

The system of equations is given as:

[tex]2x+ 4y = 14[/tex]

[tex]4x + y = 20[/tex]

Multiply both sides of the equations by -4.

So, we have:

[tex]-4 \times (4x + y) = -4 \times 20[/tex]

Distribute the expression

[tex]-4 \times 4x -4 \times y = -4 \times 20[/tex]

Evaluate all products

[tex]-16x -4y = -80[/tex]

So, we have the following system of equations

[tex]2x+ 4y = 14[/tex]

[tex]-16x -4y = -80[/tex]

Hence, the equivalent equations are [tex]2x+ 4y = 14[/tex] and[tex]-16x -4y = -80[/tex]

Read more about equivalent equations at:

https://brainly.com/question/9603710

Answer:

Step-by-step explanation:

To write fractions with a common denominator, you will most likely need to scale some numbers up! I will explain how.

Let's try it with the fractions

2

3

and

3

12

12 is larger than 3, so we will have to multiply the 3 by some number to equal 12. (We are really finding the Least Common Multiple of the two denominators!) To do this, you have to multiply the 3 by 4, because 3x4=12. But now the numerator doesn't match the denominator. When you scale the denominator up, you have to scale the numerator up too! So the 2 must be multiplied by 4 also.

Now you have the following:

8

12

and

3

12

These fractions now have common denominators! Now they're all set for adding or subtracting fractions.

Try another:

2

6

and

3

5

: The least common multiple of 6 and 5 is 30. (the product of the denominators)

Transform each fraction by multiplying by "1":

2

6

⋅

5

5

=

10

30

and

3

5

⋅

6

6

=

18

30

One last problem:

4

9

and

7

6

What is the least common multiple of 9 and 6? Could you use 54? Absolutely, but it is not the LEAST number that you could use. How about 18? YES!

4

9

⋅

2

2

=

8

18

and

7

6

⋅

3

3

=

21

18

Ready to go...

Hope this helped!

Answer:

12000000000

Step-by-step explanation:

did I add too many zeros????

10 to the 5 is multiply by 10 five times (100,000)

100,000 x 3 = 300,000

For the second thing, 10 to the 4 = 10,000

10,000 x 4 = 40,000

300,000 x 40,000 = 12000000000

Answer:

  7) y +5 = -(x -3)

  8) y -2 = 5/3(x -3)

Step-by-step explanation:

The point-slope form of the equation for a line is ...

  y -k = m(x -h) . . . . . line with slope m through point (h, k)

__

7) y +5 = -(x -3)

8) y -2 = 5/3(x -3)

Answer:

Percentage of one lap around the track of

the total race = 0.25%

It will take 300 laps to complete 75% of the race.

Step-by-step explanation:

1.2/480=0.0025

0.0025*100=0.25

480/100*75= 360

360/1.2=300

Answer:

Step-by-step explanation:

8 lbs of apples on the x-intercept

10lbs of peaches on y-intercept

Answer:

2

Step-by-step explanation:

3:1=6:2

They buy 2 pepperoni pizzas.

Answer:

the correct answer is supposed to be 120, your almost there :)

Step-by-step explanation:

Step-by-step explanation:

4⁵ × 4^-7 / 4^-2

it is important to understand that a negative exponent means 1/...

a^-n = 1/(a^n)

in that sense we have therefore

4⁵ × 1/4⁷ × 4² (as (1/ 1/a^n) = a^n)

4⁵ × 4² × 1/4⁷ = 4⁷ × 1/4⁷ = 1

so, "1" is the fully simplified expression equal to the original expression.

Answer:

  600 kl

Step-by-step explanation:

The volume represented by a length of 20 m, a breadth of 10 m, and a depth of 3 m is ...

  V = (20 m)(10 m)(3 m) = 600 m³

1 m³ = 1 kl

The volume of water that should be removed is 600 kl.

Answer

55$

Step-by-step explanation:

Answer:

A) 32 and 28

Step-by-step explanation:

A= √4².√2

= √16.√2

= √32

m= 32

B= √2². √7

=√4.√7

=√28

n= 28

Answer:

(-1,-6.5)

Step-by-step explanation:

midpoint formula: (x_m, y_m) = (x1+x2)/2),(y1+y2)/2)

(2-4)/2=-1, -9-4=-13/2=-6.5

=(-1,-6.5)

The value of y in the cyclic quadrilateral with ∠AOC(142°) is 38°

The diagram above represents a cyclic quadrilateral.

A cyclic quadrilateral has all it vertices on the circumference of the circle.

Therefore,

Opposite angles are supplementary. This means they add up to 180 degrees.

Therefore,

142° + y° = 180°

subtract 142 from both sides of the equation

142 - 142 + y = 180 - 142

y = 38°

learn more about circle theorem here: https://brainly.com/question/24795394

The answer is 6 per team with 2 left over, as (6 x 3) + 2 = 20

I thought of the largest amount that could be multiplied by 3, but the product would be less or equal to 20, that's how I got 6.

Then to find the left over remaining balls that are given out I subtracted 20-18 = 2.

Answer:

The Principle of Zero Products states that if the product of two numbers is 0, then at least one of the factors is 0.

Step-by-step explanation:

Answer:

when using the zero product rule you know at least one of the factors must equal 0 because and most places anything that is put with zero equal zero because zero have no value

Step-by-step explanation:

The atom's place on the table is determined solely by its number of protons

Since the atomic number is equal to the number of protons an element contains, hence we can conclude that the atom's place on the table is determined solely by its number of protons

Learn more about periodic table here;https://brainly.com/question/14514242

Answer:

number of protons

Step-by-step explanation:

hope this helps. leave a comment if you have a question.

Hello there!

[tex]( - 12x) ÷ ( - 2)[/tex]

This is an algebraic expression.We need to find the result of it.

[tex]\sf \longmapsto (- 12x) \div ( - 2)[/tex]

This algebraic expression may be rewritten as:-

[tex]\sf \longmapsto \: \dfrac{ - 12x}{2} [/tex]

Cancel the minus (-) sign:-

[tex]\sf \longmapsto \dfrac{ \cancel - 12x}{ \cancel - 2} [/tex]

Then,cancel 12 and 2 by 2, 12 ÷ 2 results 6. (Don't cancel x):-

[tex]\sf \longmapsto \: \dfrac{ \cancel {12}x}{ \cancel{2}} [/tex]

[tex]\sf \longmapsto6x[/tex]

Option A

______________________________________

Henceforth the value of the algebraic expression is:

[tex]\boxed{\boxed{\displaystyle \huge 6x}}[/tex]

Option A is correct!

______________________________________

I hope this helps!

Please let me know if you have any questions.

~MisterBrian

Answer:

s/3

Step-by-step explanation:

The quotient means you divide the two values.

Answer:

V = 87.92 cubic cm

Step-by-step explanation:

V(cyl) = πr²h

V = 3.14(2²)(7)

V = 87.92

Rearrange the equation by writing

x² + x - 90 = 0

x² + x = 90

x² + x + 1/4 = 90 + 1/4

Recall that (a + b)² = a² + 2ab + b². Then

x² + 2 • x/2 + (1/2)² = 361/4

(x + 1/2)² = 361/4

x + 1/2 = ± √(361/4)

x = -1/2 ± 19/2

x = 9   or   x = -10

Answer:

y = 14x

Step-by-step explanation:

First Way of Finding the Equation:

We can find the equation for this proportional relationship by subtracting two of the y-values from each other and then dividing that by the difference of two of the x-values. For now, I'll use the points (2, 28) and (1, 14).

[tex]\frac{28-14}{2-1} =\frac{14}{1} =14[/tex]

So, this proportional relationship has an equation of y = 14x.

Second Way of Finding the Equation:

Another way of finding the equation is to simply examine the table given. What are all the x-values multiplied by to get to their corresponding y-values? Well, one easy way of answering this question is looking at the point (1, 14) - 1 × 14 = 14, so the constant of proportionality must be 14.

From this information, we know that the equation must be y = 14x.

Hopefully that's helpful! :)

Answer:

Yes

Domain: 1, -1, 0, -3, 3

Range: 1, -1, 6

Step-by-step explanation:

The domain is in the left oval, the range is in the right oval. To find if its a function you have to make sure the domain (left side) doesn't "cheat". One number in the domain cant have more than one number in the range (right side), BUT (for future reference) the range can cheat. As shown, the right side numbers 1 and 6 have two different arrow pointed at them. As long as the domain doesnt "cheat" it is a function

Answer:

D) Impossible

Step-by-step explanation:

This would be B. It is certain that there is a 0% chance of the earth being the closest planet to the sun. Mercury is the closest. Earth is the third closest behind Mercury and Venus. Hope that helps.

Answer:

3 + 21 = 24 and they are the product to the factors of 63

Step-by-step explanation:

Answer:

it is c

Step-by-step explanation:

Given :-

To find :-

Solution :-

According to the Question ,

[tex]\dashrightarrow[/tex] Passing marks = 40% .

[tex]\dashrightarrow[/tex] Seema's marks = 130 .

Let us take the maximum marks be x . Then ,

[tex]\dashrightarrow[/tex] Passing marks = 130 + 2

[tex]\dashrightarrow[/tex] Passing marks = 132

And , by question ,

[tex]\dashrightarrow[/tex] 40x/100 = 132

[tex]\dashrightarrow[/tex] x = 132 * 100/40

[tex]\dashrightarrow[/tex] x = 330

Hence the maximum marks for the exam is 330.

Given :

So, Let us assume the maximum marks as x .

Also,

Passing marks = 132 [ ∵ Seema got 130 marks and she failed by 2 marks ]

According to the question :

[tex] \\ \tt : \implies\dfrac{40x}{100} = 132 \\ \\ \tt : \implies\dfrac{4 \cancel{0}x}{10 \cancel{0}} = 132 \\ \\ \: \: \: \tt \: : \implies 4x = 132 \times 10 \\ \\ \tt : \implies \: 4x = 1320 \\ \\ \tt : \implies \: x = \frac{1320}{4} \\ \\ \tt : \implies \: x = 330 \: \: \\ [/tex]

Hence, The total marks is 330 .

Answer: No, this relation is not a function.

Step-by-step explanation:

Two of the points with the same Y axis have different X values (as stated in answer A)