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melisa1 [442]
3 years ago
9

What are ways using coordinate geometry, that I could determine that this is a trapezoid?

Mathematics
1 answer:
NemiM [27]3 years ago
3 0

One method to see it's a trapezoid is to find the slope of lines BC and AD.

The slope formula is

m = (y2-y1)/(x2-x1)

You should find that BC and AD both have the same slope (of -1), so that means the lines are parallel. That proves we have a trapezoid.

-----------------------

To prove this trapezoid is isosceles, you can use the distance formula

d = \sqrt{ \left(x_1-x_2\right)^2 + \left(y_1-y_2\right)^2}

to find the lengths of AB and CD (the two non-parallel sides). You should find that AB = CD.

Because AB and CD are horizontal and vertical respectively, this means you can simply count out the spaces to find that AB and CD are 3 units each. For any other rotated version of this trapezoid, use the distance formula instead.

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What are the factors of the equation 24x^2=9-30x?
Dennis_Churaev [7]

Answer:

3(4x - 1)(2x + 3)

Step-by-step explanation:

Rearrange the equation into standard form

Subtract 9 - 30x from both sides

24x² + 30x - 9 = 0 ← in standard form

Take out 3 as a common factor

3(8x² + 10x - 3) = 0 ← factor the quadratic

Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x term

product = 8 × - 3 = - 24, sum = 10

The factors are - 2 and + 12

Use these factors to replace the x- term, that is

8x² - 2x + 12x - 3 ( factor the first/second and third/fourth terms )

2x(4x - 1) + 3(4x - 1) ← take out the common factor (4x - 1)

(4x - 1)(2x + 3)

24x² + 30x - 9 = 3(4x - 1)(2x + 3) ← in factored form

7 0
3 years ago
During a field trip, 60 students are put into equal-sized groups. Describe two ways to interpret 60 ÷ 5 in this problem *
sergeinik [125]

Answer:

    x=12 groups

This will give 5 Students each in 12 different equally sized groups

    x'=5groups

This also shows that students can grouped in equal groups of 12 in 5 places

Step-by-step explanation:

From the question we are told that

60 children in equal sized groups

Generally interpreting 60\div 5 can be mathematically represented as

a)

    x=\frac{60}{5}

    x=12 groups

This will give 5 Students each in 12 different equally sized groups

b)

    x'=\frac{60}{12}

    x'=5groups

This also shows that students can grouped in equal groups of 12 in 5 places

6 0
3 years ago
Selena drove at an average speed of 50.55 miles per hour for 1.75 hours. She stopped at a rest stop and then drove at an average
frez [133]
50.55 x 1.75 = 88
45.2 x 2.25 = 94

Selena drove more miles after (how many) 6

I hope this helped :)
3 0
4 years ago
Read 2 more answers
At its highest​ point, the elevation of a county is 5,764 feet above sea level. At its lowest​ point, the elevation of the count
Feliz [49]

Answer:

Difference = 5757\ feet

Step-by-step explanation:

Given

Highest\ Point = 5764\ feet

Lowest\ Point = 7\ feet

Required

Determine the difference between the points

The difference is calculated as follows:

Difference = Highest - Lowest

Difference = 5764\ feet - 7\ feet

Difference = 5757\ feet

8 0
3 years ago
True or False:<br> There are an infinite number of answers for this equation:<br> 63 - X = 34
Shtirlitz [24]

Answer: No, the answer is 29, this is false.

Step-by-step explanation: 63-x=34

subtract 63 from both sides

34-63= -29

-x=-29

divide both sides by the negative and you get 29

plug in 29 for x, 63-29=34

8 0
3 years ago
Read 2 more answers
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