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3 years ago

How to prove quadrilaterals are parallelograms?

Mathematics

1 answer:

nignag [31]3 years ago

6 0

Answer:

AB: 24

BC: 15

CD: 24

AD: 15

Step-by-step explanation:

A quadrilateral is any shape with four sides. A parallelogram has four sides, therefore it is classified as a quadrilateral.

The opposite sides of a parallelogram are equal to each other, so make the opposite sides of this parallelogram equal to each other in an equation.

AB = DC

2y + 2 = 3y - 9

AD = BC

3x + 6 = y + 4

Now you have a system of equations that you can solve by substitution.

Solve for y in the first equation by subtracting 2 from both sides.

2y = 3y - 11

Subtract 3y from both sides of the equation.

-y = -11

Divide both sides of the equation by negative 1 to make y a positive number.

y = 11

Substitute this value of y into the second equation we made.

3x + 6 = (11) + 4

Combine like terms on the right side of the equation then subtract 6 from what you get.

3x = 9

Divide both sides of the equation by 3.

x = 3

To find the length of each side of the parallelogram, substitute x into AD and y into AB.

AD: 3(3) + 6 = 15
AB: 2(11) + 2 = 24

Since AD = BC and AB = DC, you know the lengths for these sides as well.

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2 1/3 x (-3 2/7) what does it equal I’m doing “multiplying signed fractions”

aksik [14]

The answer to this question is -32

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3 years ago

A polygon has an interior angle sum of 9000. How many sides does it have

SSSSS [86.1K]

Answer:

Step-by-step explanation:

The sum of the interior angles of a polygon is

sum = 180° (n - 2) ← n is the number of sides

Here the sum = 9000°, thus

180° (n - 2) = 9000° ( divide both sides by 180° )

n - 2 = 50 ( add 2 to both sides )

n = 52

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3 years ago

A ball is shot straight up from the top of a 15-story building. The motion of the ball could be described by the function: h(t)=

viktelen [127]

Answer:

After 4 seconds the height is 480 meters.
The maximum height is 484 meters.
The ball hits the ground after 10 seconds

Step-by-step explanation:

The height after four seconds is h(4) = -16 * r² + 144*4+160 = 480

The maximum height of the ball is the value it takes at its vertex 'v = -b/2a'. In this case a = -16 and b = 144, so the v = -144/-32 = 4.5. The maximum height of the ball as a result is h(4.5) = -16 (4.5)² + 144*4.5 + 160 = 484

To find the moment the ball hits the ground, we need to find when h takes the value 0 by using the quadratic formula, with a = -16, b = 144 and c = 160.

$r_1,r_2 = \frac{-144 \, ^+_- \sqrt{144^2-4*(-16)*160}}{2*(-16)} = \frac{-144 \, ^+_- \sqrt{30976}}{-32} = \frac{-144 \, ^+_- 176}{-32} = -1, 10$

Since t cant take negative values, then the correct value is 10. The ball hits the ground after 10 seconds.

7 0

3 years ago

I need help with this geometry question, matching the right ones to each other.

8090 [49]

The transformations and their respective descriptions are:

A. (x, y) ⇒ (3x, y) implies horizontal stretch by a scale factor of 3

B. (x, y) ⇒ (x+3, y) implies translation 3 units right

C. (x, y) ⇒ (x, 3y) implies vertical stretch by a factor of 3

D. (x, y) ⇒ (x, y+3) implies implies translation 3 units up

E. (x, y) ⇒ (3x, 3y) implies dilation with a scale factor 3

<h3>What is Translation?</h3>

Translation is an algebraic transformation of a shape by moving the vertices some units along the x or y axis.

When a shape is translated it may move to a new position depending on the orientation of the translation.

Analysis:

For A, the x coordinate was transformed three times its initial value stretching it horizontally.

For B, the x coordinate moved 3 units further away from its initial value making the new value x+3 and y remaining the same.

For C, the y coordinated was transformed to a value three times what it was, making it to be stretched vertically, since the y-axis is a vertical axis.

For D, the y coordinate was moves 3 units away from its initial position making it to be translated up, since 3 is positive.

For E, both coordinates were stretched 3 units as much as their original value making the shape to dilate.

Learn more about linear transformations: brainly.com/question/13005179

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3 0

2 years ago

What is the equation of y=2x-6 in standard form?

prisoha [69]

Answer:

2x - y = 6

Step-by-step explanation:

The equation of a line in standard form is

Ax + By = C ( A is a positive integer and B, C are integers )

Given

y = 2x - 6 ( add 6 to both sides )

y + 6 = 2x ( subtract y from both sides )

6 = 2x - y, that is

2x - y = 6 ← in standard form

3 0

3 years ago

Read 2 more answers