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34kurt
3 years ago
15

Determine whether a figure with the given vertices is a parallelogram. Use the method indicated.

Mathematics
1 answer:
aliya0001 [1]3 years ago
6 0

Answer with explanation:

The coordinates of four points of Quadrilateral ABCD are

    A(4, 5), B(–7, –10), C(–4, –9), D(7, 6)

AB=\sqrt{(4+7)^2+(5+10)^2}\\\\AB=\sqrt{121+225}\\\\AB=\sqrt{346}\\\\BC=\sqrt{(-7+4)^2+(-10+9)^2}\\\\BC=\sqrt{9+1}\\\\BC=\sqrt{10}\\\\CD=\sqrt{(4+7)^2+(5+10)^2}\\\\CD=\sqrt{121+225}\\\\CD=\sqrt{346}\\\\DA=\sqrt{(7-4)^2+(6-5)^2}\\\\DA=\sqrt{9+1}\\\\DA=\sqrt{10}

Slope between two points is given by

 m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\m_{1}=\frac{-10-5}{-7-4}\\\\=\frac{-15}{-11}\\\\m_{1}=\frac{15}{11}\\\\m_{2}=\frac{-9+10}{-4+7}\\\\m_{2}=\frac{1}{3}\\\\m_{3}=\frac{6+9}{7+4}\\\\m_{3}=\frac{15}{11}\\\\m_{4}=\frac{6-5}{7-4}\\\\m_{4}=\frac{1}{3}

As slope of opposite sides are equal and length of Opposite sides are equal.So,the given Quadrilateral is a Parallelogram.

Option A

Yes; The opposite sides are congruent and have the same slope.

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Write each equation in slope-intercept form (3,4); and (-6,-2)
Alborosie

Answer:

y = 2/3x + 2

Step-by-step explanation:

Slope intercept form is y=mx+b where m is the slope and b is the y intercept.

Given 2 points you can find the slope using (y-y1)/(x-x1)

m = (-2-4)/(-6-3) = -6/-9 = 2/3

To find b use one of the points and m and plug into the slope intercept form and then solve for b.

y=mx+b

4=2/3(3) + b

4=2 + b

b=2

Now we can write the final equation as : (plug m and b back in)

y = 2/3x + 2

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2 years ago
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5. Find the value of the 11th term of the arithmetic sequence <br> -2, 5, 12, 19, 26, ...(11th term)
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Answer:

-2, 5, 12, 19, 26, 33, 40, 47, 54, 61, 68, 75, 82, 89, 96, 103

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Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study wa
4vir4ik [10]

Using the z-distribution, it is found that since the <u>test statistic is greater than the critical value</u>, it can be concluded that the mean length of jail time has increased.

At the null hypothesis, it is <u>tested if the mean length of jail time is still of 2.5 years</u>, that is:

H_0: \mu = 2.5

At the alternative hypothesis, it is <u>tested if it has increased</u>, that is:

H_1: \mu > 2.5

We have the <u>standard deviation for the population</u>, thus, the z-distribution is used. The test statistic is given by:

z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}

The parameters are:

  • \overline{x} is the sample mean.
  • \mu is the value tested at the null hypothesis.
  • \sigma is the standard deviation of the sample.
  • n is the sample size.

For this problem, the values of the <u>parameters</u> are: \overline{x} = 3, \mu = 2.5, \sigma = 1.5, n = 26

Hence, the value of the <u>test statistic</u> is:

z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}

z = \frac{3 - 2.5}{\frac{1.5}{\sqrt{26}}}

z = 1.7

The critical value for a <u>right-tailed test</u>, as we are testing if the mean is greater than a value, with a <u>significance level of 0.05</u>, is of z^{\ast} = 1.645

Since the <u>test statistic is greater than the critical value</u>, it can be concluded that the mean length of jail time has increased.

A similar problem is given at brainly.com/question/24166849

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2 years ago
4 more than y into a algebraic expression
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3 years ago
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shaquana has a deck that measures 18 feet by 15 feet. She wants to increase each dimension by equal lengths so that its area tri
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to increase each dimension by equal lengths so that its area triples is 12 feet.

The given dimensions are 18 feet by 15 feet.

We need to find how much should each dimension increase.

Shaquana wants to increase each dimension by equal lengths so that its area triples.

Let the increased length be x.

So, length =18+x feet and width=15+x feet.

As we know, the area of a deck=Length×Width

The original area of a deck=18×15=270 square feet.

Now, the new area of a deck=(18+x )×(15+x)=3×270

⇒270+15x+18x+x²=810 square feet

⇒x²+33x-540=0

Here, a=1, b=33 and c=-540 in x=\frac{-b\±\sqrt{b^{2-4ac} } }{2a}.

⇒x=\frac{-33\±\sqrt{33^{2} -4 \times (-540)} }{2 \times 1}

⇒x=\frac{-33\±\sqrt{1089 +2160} }{2 \times 1}=\frac{-33\±57}{2}

⇒x=-45 or x=12

Length can not be a negative integer.

Therefore, to increase each dimension by equal lengths so that its area triples is 12 feet.

To learn more about the area of a rectangle visit:

brainly.com/question/20693059.

#SPJ1

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