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2 years ago

Multiply 3x ( x + 2y)

Mathematics

1 answer:

11Alexandr11 [23.1K]2 years ago

4 0

Answer:

3x^2 + 6x

Step-by-step explanation:

Just distribute

3x(x + 2)

3x(x) = 3x^2

3x(2) = 6x

3x^2 + 6x

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100 Points! What are the classifications of each system?

alexdok [17]

Answer:

Part 1) Is a inconsistent system

Part 2) Is a consistent independent system

Part 3) Is a consistent dependent system

see the attached figure

Step-by-step explanation:

we know that

If a system has at least one solution, it is said to be consistent .

If a consistent system has exactly one solution, it is independent .

If a consistent system has an infinite number of solutions, it is dependent

If a system not have solution, it is said to be inconsistent

Part 1) we have

$x+5y=-2\\x+5y=4$

This system of linear equations has two parallel lines (their slopes are equal) with different y-intercept

The lines don't intersect

The system has no solution

therefore

Is a inconsistent system

Part 2) we have

$y=3x+4\\-2x+y=4$

we know that

If two lines have different slopes, then the lines intersect at one point and the system of equations has one solution

In this problem, the lines have different slopes (m=3 and m=2)

The lines intersect at one point

The system has one solution

therefore

Is a consistent independent system

Part 3) we have

$3x+y=4$ ----> equation A

$-6x-2y=-8$ ----> equation B

Multiply equation A by -2 both sides

$-2(3x+y)=-2(4)$

$-6x-2y=-8$ ----> equation C

Compare equation B and equation C

Are identical lines

The system has infinity solutions

therefore

Is a consistent dependent system

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3 years ago

The.......... is an appropriate unit to measure the capacity of a hand sanitizer bottle

Yuri [45]

Liters can probably be the unit to measure the capacity of a hand sanitizer bottle

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3 years ago

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Ivenika [448]

Answer:-68 i think

Step-by-step explanation:

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2 years ago

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What is the inverse (opposite) of addition?

madam [21]

Answer:

Subtraction is the inverse (opposite operation) of addition

Step-by-step explanation:

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3 years ago

Which describes how triangle FGH could be transformed to triangle F prime G prime H prime in two steps? On a coordinate plane, t

charle [14.2K]

Answer:

A dilation by a scale factor of 4 and then a reflection across the x-axis

Explanation:

1. Vertices of triangle FGH:

F: (-2,1)
G: (-3,3)
H: (0,1)

2. Vertices of triangle F'G'H':

F': (-8,-4)
G': (-12,-12)
H': (0, -4)

3. Solution:

Look at the coordinates of the point H and H': to transform (0,1) to (0,-4) you can muliply each coordinate by 4 and then change the y-coordinate from 4 to -4. That is a dilation by a scale factor of 4 and a reflection across the x-axis. This is the proof:

Rule for a dilation by a scale factor of 4: (x,y) → 4(x,y)

(0,1) → 4(0,1) = (0,4)

Rule for a reflection across the x-axis:{ (x,y) → (x, -y)

(0,4) → (0,-4)

Verfiy the transformations of the other vertices with the same rule:

Dilation by a scale factor of 4: multiply each coordinate by 4

4(-2,1) → (-8,4)

4(-3,3) → (-12,12)

Relfection across the x-axis: keep the x-coordinate and negate the y-coordinate

(-8,4) → (-8,-4) ⇒ F'

(-12,12) → (-12,-12) ⇒ G'

Therefore, the three points follow the rules for a dilation by a scale factor of 4 and then a reflection across the x-axis.

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3 years ago

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