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3 years ago

Find the value of x for which ABCD must be a parallelogram.

Mathematics

1 answer:

densk [106]3 years ago

4 0

For a parallelogram, the parallel sides must be the same length. This means you can set their lengths equal to each other. Get like terms on the same side to calculate x.

3x-5=2x+3
3x-5+5=2x+3+5
3x=2x+8
3x-2x=2x-2x+8
x=8

x=8

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Parallel / Perpendicular Practice

deff fn [24]

The slope and intercept form is the form of the straight line equation that includes the value of the slope of the line

Neither
║
Neither
⊥
║
Neither
Neither
Neither

Reason:

The slope and intercept form is the form y = m·x + c

Where;

m = The slope

Two equations are parallel if their slopes are equal

Two equations are perpendicular if the relationship between their slopes, m₁, and m₂ are; $m_1 = -\dfrac{1}{m_2}$

1. The given equations are in the slope and intercept form

$\ y = 3 \cdot x + 1$

The slope, m₁ = 3

$y = \dfrac{1}{3} \cdot x + 1$

The slope, m₂ = $\dfrac{1}{3}$

Therefore, the equations are neither parallel or perpendicular

Neither

2. y = 5·x - 3

10·x - 2·y = 7

The second equation can be rewritten in the slope and intercept form as follows;

$y = 5 \cdot x -\dfrac{7}{2}$

Therefore, the two equations are parallel

3. The given equations are;

-2·x - 4·y = -8

-2·x + 4·y = -8

The given equations in slope and intercept form are;

$y = 2 -\dfrac{1}{2} \cdot x$

Slope, m₁ = $-\dfrac{1}{2}$

$y = \dfrac{1}{2} \cdot x - 2$

Slope, m₂ = $\dfrac{1}{2}$

The slopes

Therefore, m₁ ≠ m₂

$m_1 \neq -\dfrac{1}{m_2}$

The lines are Neither parallel nor perpendicular

Neither

4. The given equations are;

2·y - x = 2

$y = \dfrac{1}{2} \cdot x +1$

m₁ = $\dfrac{1}{2}$

y = -2·x + 4

m₂ = -2

Therefore;

$m_1 \neq -\dfrac{1}{m_2}$

Therefore, the lines are perpendicular

5. The given equations are;

4·y = 3·x + 12

-3·x + 4·y = 2

Which gives;

First equation, $y = \dfrac{3}{4} \cdot x + 3$

Second equation, $y = \dfrac{3}{4} \cdot x + \dfrac{1}{2}$

Therefore, m₁ = m₂, the lines are parallel

6. The given equations are;

8·x - 4·y = 16

Which gives; y = 2·x - 4

5·y - 10 = 3, therefore, y = $\dfrac{13}{5}$

Therefore, the two equations are neither parallel nor perpendicular

Neither

7. The equations are;

2·x + 6·y = -3

Which gives $y = -\dfrac{1}{3} \cdot x - \dfrac{1}{2}$

12·y = 4·x + 20

Which gives

$y = \dfrac{1}{3} \cdot x + \dfrac{5}{3}$

m₁ ≠ m₂

$m_1 \neq -\dfrac{1}{m_2}$

Neither

8. 2·x - 5·y = -3

Which gives; $y = \dfrac{2}{5} \cdot x +\dfrac{3}{5}$

5·x + 27 = 6

$x = -\dfrac{21}{5}$

Therefore, the slopes are not equal, or perpendicular, the correct option is Neither

Learn more here:

brainly.com/question/16732089

6 0

3 years ago

The quotient of the sum of 3 and a number and 6 is less than -2

GalinKa [24]

Answer: 3 + n / 6 is less than -2

Explanation:

It’s an inequality:

Quotient: division

Sum: addition

A number: the variable, n

7 0

3 years ago

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5 friends go out to lunch and order 4 pizzas. The friend divides the pizzas evenly. Find how much pizza each friend got as a dec

vichka [17]

Each friend gets 0.8 of a pizza.

7 0

3 years ago

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mariarad [96]

Answer:

From my understanding of the question its 104.58 for the first picture (8.3x3x4.2)

Step-by-step explanation:

All you need to do is multiply the length width and height. it will give you the volume of the object. For your understanding, you can try the second one as practice for these type of problems.

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3 years ago

Solve the inequality and graph the solution. 60 ≥ 4x

Luda [366]

Answer: isolate the variable by dividing each side by factors that don't contain the variable.

x is less than or equal to 15

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