Select the correct answer from each drop-down menu.

1.

The new system of equivalent equations are 4x + 6y = 8 and 12x + 3y = 1

To get an equivalent equation, we multiply the original equation by a constant and replace it with the new equation.

So, 2x + 3y = 4 (1)

12x + 3y = 1 (2)

We multiply equation (1) by 2

So, 2x + 3y = 4 (1) × 2

⇒4x + 6y = 8 (3)

Replacing (1) by (3), we have

4x + 6y = 8 (3)

12x + 3y = 1 (2)

So, the new system of equivalent equations are 4x + 6y = 8 and 12x + 3y = 1.

2.

The new system of equivalent equations are 3x - 21y = 24 and 5x + 4y = 20

To get an equivalent equation, we multiply the original equation by a constant and replace it with the new equation.

So,

x - 7y = 8  (1)

5x + 4y = 20 (2)

We multiply equation (1) by 3, we have

So, x - 7y = 8 (1) × 3

⇒3x - 21y = 24 (3)

Replacing (1) by (3), we have

3x - 21y = 24 (3)

5x + 4y = 20 (2)

So, the new system of equivalent equations are 3x - 21y = 24 and 5x + 4y = 20.

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Answer:

that's the correct answers

Step-by-step explanation:

thanks for your

To translate the statement "A number is less than 15" into an inequality using the variable x, we write:

x < 15

This inequality indicates that the value of x is any number that is smaller than 15. In other words, x can be any real number in the open interval (-∞, 15). It represents a wide range of values from negative infinity up to, but not including, 15.

This statement is not restrictive and allows for infinite possibilities for x, as long as it is smaller than 15. The inequality x < 15 leaves ample room for a wide variety of numerical solutions.

Therefore, to translate the statement "A number is less than 15" into an inequality using the variable x, we write:

x < 15

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Answer: 4.15

Step-by-step explanation:

Answer: B

Step-by-step explanation:

Reflection does preserve side length and dilation preserves angles.

The solution is Option B.

The reflection preserves the side lengths of the triangle ABC and the dilation preserves angles but not side lengths

Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.

The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

Given data ,

Let the triangle be represented as ΔABC

Now , Triangle ABC is reflected across the y-axis and then dilated by a factor of 2 centered at the origin

And , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).

So , only the x coordinate of the point changes and there is no change in the angles or the side lengths

Now , dilation changes the side lengths of the triangle by a factor of 2

But there is no change in the angles of the triangle after a dilation

Hence , reflection preserves the angles and side lengths of a triangle

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Answer:

(x+1)(x−2)(x+3)(x−4)

Apply the distributive property by multiplying each term of x+1 by each term of x−2.

(x  

2

−2x+x−2)(x+3)(x−4)

Combine −2x and x to get −x.

(x  

2

−x−2)(x+3)(x−4)

Apply the distributive property by multiplying each term of x  

2

−x−2 by each term of x+3.

(x  

3

+3x  

2

−x  

2

−3x−2x−6)(x−4)

Combine 3x  

2

 and −x  

2

 to get 2x  

2

.

(x  

3

+2x  

2

−3x−2x−6)(x−4)

Combine −3x and −2x to get −5x.

(x  

3

+2x  

2

−5x−6)(x−4)

Apply the distributive property by multiplying each term of x  

3

+2x  

2

−5x−6 by each term of x−4.

x  

4

−4x  

3

+2x  

3

−8x  

2

−5x  

2

+20x−6x+24

Combine −4x  

3

 and 2x  

3

 to get −2x  

3

.

x  

4

−2x  

3

−8x  

2

−5x  

2

+20x−6x+24

Combine −8x  

2

 and −5x  

2

 to get −13x  

2

.

x  

4

−2x  

3

−13x  

2

+20x−6x+24

Combine 20x and −6x to get 14x.

x  

4

−2x  

3

−13x  

2

+14x+24

Step-by-step explanation:

i really dont know

Answer:

Option A

Step-by-step explanation:

Given equation is:

[tex]x^2+1=2x-3[/tex]

Setting it up as a quadratic equation.

[tex]x^2+1-2x+3=0\\\\x^2-2x+4=0[/tex]

Comparing it with quadratic equation [tex]ax^2+bx+c=0[/tex], we get:

a = 1 , b = -2 , c = 4

Putting the values in quadratic equation:

[tex]\displaystyle x = \frac{-b +-\sqrt{b^2-4ac} }{2a} \\\\x = \frac{-(-2)+-\sqrt{(-2)^2-4(1)(4)} }{2(1)}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

A

Step-by-step explanation:

a = 1, b = -2, and c =4

d = -b +- sqrt (b^2 - 4*a*b)

= - (-2) +- sqrt ((-2)^2 - 4*1*4)

Answer:

108 g of water

Hope This Helps!!!

Answer:

y=4

Step-by-step explanation:

x1=4,y1=4,m=0

Equation of a line: y-y1=m(x-x1)

y-4=0(x-4)

y-4=0

y=4

2% of 350 is 7, so Bentley sold 7 cards on Mother's Day

Step-by-step explanation:

when we have multiplications of fractions, we can simply "break" the multiplications apart, simplify every fraction, and then combine the results again.

-9/-15 = 3/5

x^-1/x⁵ = 1/x¹x⁵ = 1/x⁶

y^-9/y^-3 = y³/y⁹ = 1/y⁶

so, when we multiply the 3 fractions again, we get

3/(5x⁶y⁶)

which is the second answer option.

Answer:

20 More Periods

Step-by-step explanation:

Just Divide 200/10 and you get 20.

Step-by-step explanation:

first you need to find the height

V = L×W×H

the volume your given is 880mm³

length is 22mm

width is 8mm

height is unknown

furthermore

V=L×W×H

880mm³= 22mm×8mm×H

880mm³= 176mm²×H

880mm³/176mm²=176mm²/176mm²×H

5mm=H

H=5mm

therefore S.A=2(L×W+ W×H +L×H)

=2(22mm×8mm+8mm×5mm+22mm×5mm)

=2(176mm²+40mm²+ 110mm²)

=352mm²+80mm²+220mm²

=652mm²

Answer:

292 acres.

Step-by-step explanation:

OK so if there are 73,000 acres of trees in total and 0.4% are old we would simply calculate what 0.4% of 73,000 which is 292. So of those 73,000 acres of trees 292 acres of them would be "old-growth trees".

Answer

$835,25

Explanation

Total sales = $6425

Commission = 13%

100%  - $6425

13%     -  x

13 * 6425 = 83525

83525 \ 100 = 835,25

Answer:

  $53.61

Step-by-step explanation:

It looks like the rate of change is supposed to be -2 2/5% = -2.4% per year. That means the "growth factor" is ...

  growth factor = 1 + growth rate

  growth factor = 1 -2.4% = 1 -0.024 = 0.976

Each year, Charisse's cactus salt and pepper shakers will have their value multiplied by this factor. After 2 years, their value will be ...

  ($56.28)(0.976)(0.976) = $56.28×0.976^2 ≈ $53.61

The value is projected to be $53.61 in 2 years.

Answer:

4096

Step-by-step explanation:

Answer:

Arc Length = θ × (π/180) × r, where θ is in degree.

The Arc length of the given partial circle is 4π units or 12.56 units .

Step-by-step explanation:

Answer:

4π

Step-by-step explanation:

Hope this helps!

Answer:

Plain is $7 and Holiday is $15

Step-by-step explanation:

Castel: 2p + 5h = 89

Kali: 9p + 10h = 213

Double Castel's: 4p + 10h = 178

Subtract fro Kali's   9p + 10h = 213

                              - 4p + 10h = 178

5p = 35

p = 7  Plain is $7

Substitute 7 into one of the equations and solve for h:

2(7) + 5h = 89

14 + 5h = 89

5h = 75

h = 15  Holiday is $15

Answer:

33.3%

Step-by-step explanation:

1. Formula: difference/original

2. 120 - 80 = 40

3. 40/120

4. 1/3

5. 1/3 = 33.3%

Answer:

Step-by-step explanation:

the answer is -480

Answer:

x = -24

Step-by-step explanation:

First, transpose 6 to the right and remember that 6 must change sign if you transpose it, that'll give you

- 3/8x = 15-6

-3/8x = 9

Divide both sides by - 3/8

Then x = - 24

area=147 cm squared

7 x 7 = 49

49 x 3 = 147

Answer:

[tex]\frac{12}5[/tex]

Step-by-step explanation:

The easiest way to find the tangent is to calculate the ratio of opposite side over the adjacent, or [tex]\frac{12}5[/tex]

We know

[tex]\\ \sf{:}\Rrightarrow tan\Theta=\dfrac{Perpendicular}{Base}[/tex]

Now

[tex]\\ \sf{:}\Rrightarrow tanT=\dfrac{SU}{TU}[/tex]

[tex]\\ \sf{:}\Rrightarrow tanT=\dfrac{12}{5}[/tex]

Answer:

Their are many answers for that seqence such as

1,6,11,16,21, etc..

Answer:

6,11,16,21,26,31,36...

Step-by-step explanation:

5x1=5 +1=6

5x2=10+1=11

...

Answer:

Step 1: 10 group(s) of 23 = 230

Step 2: 6 group(s) of 23 = 138

Step 3: Add the partial quotients: 10 + 6 = 16

Step-by-step explanation:

For step one you can tell that 230/10 is 23. You can tell this because of the zero at the end of the number. Anything multiplied by 10 is that number but  with a zero at the end. For step 2 you kind of have to do long division, or you can use a calculator. You will end up with 6. When you add the partial quotients, it means add the answers to steps 1 and 2 together and get 16. This should be right hope it helps!

Answer

From the results, we can conclude:





​

230=23×10

138=23×6

​

Therefore:



Step 1: 10 groups of 23 = 230

Step 2: 6 groups of 23 = 138



Step 3: Add the partial quotients: 10 + 6 = 16

answer 10 + 6 = 16

When multiplying the same variable to different exponents add the exponents and multiply the constant numbers:

3x x 2x = 6x

^2 + ^3 = ^5

Answer is a. 6x^5

Answer:

x+2y=-3

Step-by-step explanation:

Answer:

y = 7x -26

Step-by-step explanation:

[tex]y-9=7(x-5)[/tex]

[tex]y=7x-35+9[/tex]

[tex]y=7x-26[/tex]

Hope this helps