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1 year ago

Plzzzz help me In ΔABC, . Complete the proof showing that is parallel to .

Mathematics

2 answers:

Luden [163]1 year ago

5 0

AD*EB=CE*DB because cross multiplication

pychu [463]1 year ago

3 0

Answer: First option of STATEMENT and third option of REASON are correct.

Step-by-step explanation:

Since we have given that

$\frac{AD}{DB}=\frac{CE}{EB}$

We need to prove that DE is parallel to AB.

For this we need to use the converse of BPT theorem.

which states that if the corresponding parts of the triangle is in same ratio, then the line joining the points of other two sides parallel to the third side.

So, we have ,

$\frac{AD}{DB}=\frac{CE}{EB}\\\\\frac{AD}{DB}+1=\frac{CE}{EB}+1(\text{ Addition property of equality)}\\\\\frac{AD+DB}{DE}=\frac{EC+EB}{EB}\\\\\frac{AB}{DB}=\frac{BC}{EB}$

Hence, First option of STATEMENT and third option of REASON are correct.

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In quadrilateral ABDC, AB ∥ CD. Which additional piece of information is needed to determine that ABDC is a parallelogram? AB ≅

siniylev [52]

For any quadrilateral to be a parallelogram

i) either both the pairs of opposite sides must be equal

ii) Both the pairs of opposite sides must be parallel

iii) Opposite pairs of angles must be equal

iv) Diagonals must bisect each other.

v) A pair of opposite sides must be parallel and equal

Here we are already given that AB || CD

So either we should be given that AD || BC

or we must be given that AB = CD

Here it is given AB = CD as an option.

So Option A) or the first option is the right answer that AB ≅CD is needed to prove ABCD is a parallelogram.

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2 years ago

Read 2 more answers

A manufacturer of paper coffee cups would like to estimate the proportion of cups that are defective (tears, broken seems, etc.)

Maksim231197 [3]

Answer:

The 95% confidence interval is $0.0503 < p < 0.1297$

The sample proportion is $\r p = 0.09$

The critical value is $Z_{\frac{\alpha }{2} } = 1.96$

The standard error is $SE =0.020$

Step-by-step explanation:

From the question we are told that

The sample size is n = 200

The number of defective is k = 18

The null hypothesis is $H_o : p = 0.08$

The alternative hypothesis is $H_a : p > 0.08$

Generally the sample proportion is mathematically evaluated as

$\r p = \frac{18}{200}$

$\r p = 0.09$

Given that the confidence level is 95% then the level of significance is mathematically evaluated as

$\alpha = 100 - 95$

$\alpha = 5\%$

$\alpha = 0.05$

Next we obtain the critical value of $\frac{ \alpha }{2}$ from the normal distribution table, the value is

$Z_{\frac{\alpha }{2} } = 1.96$

Generally the standard of error is mathematically represented as

$SE = \sqrt{\frac{\r p (1 - \r p)}{n} }$

substituting values

$SE = \sqrt{\frac{0.09 (1 - 0.09)}{200} }$

$SE =0.020$

The margin of error is

$E = Z_{\frac{ \alpha }{2} } * SE$

=> $E = 1.96 * 0.020$

=> $E = 0.0397$

The 95% confidence interval is mathematically represented as

$\r p - E < \mu < p < \r p + E$

=> $0.09 - 0.0397 < \mu < p < 0.09 + 0.0397$

=> $0.0503 < p < 0.1297$

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1 year ago

What is the correlation coefficient for the data shown in the table?

Leviafan [203]

we know that

<u>The correlation coefficient</u> is a number between $-1$ and $+1$ that represent the linear dependence of two variables or sets of data

Using the function CORREL in a excel tool, calculate the correlation coefficient (r)

see the attached table

the correlation coefficient for the data in the table is equal to $1$

therefore

<u>the answer is</u>

$r=1$

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1 year ago

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A fitted multiple regression equation is Y = 28 + 5X1 - 4X2 + 7X3 + 2X4. When X1 increases 2 units and X2 increases 2 units as w

ad-work [718]

Answer:

A. Increase by 2

Step-by-step explanation:

Given that a fitted multiple regression equation is

$Y = 28 + 5X_1 -4X_2 + 7X_3 + 2X_4$

This is a multiple regression line with dependent variable y and independent variables x1, x2, x3 and x4

The coefficients of independent variables represent the slope.

In other words the coefficients represent the rate of change of y when xi is changed by 1 unit.

Given that x3 and x4 remain unchanged and x1 increases by 2 and x2 by 2 units

Since slope of x1 is 5, we find for one unit change in x1 we can have 5 units change in y

i.e. for 2 units change in x1, we expect 10 units change in Y

Similarly for 2 units change in x2, we expect -2(4) units change in Y

Put together we have

$10-8 =2$ change in y

Since positive 2, there is an increase by 2

A. Increase by 2

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1 year ago

Dan bought a new computer for $900. Each year, the value of the computer decreased by 25% of the previous year’s value. At this

lys-0071 [83]

Answer:

$120.14

Step-by-step explanation:

This question is an example of a compound percentage decrease.

To work this out you would first need to convert the percentage of 25 into a decimal. You can do this by dividing the percentage of 25 by 100, this gives you 0.25. This is because percentages are out of 100.

The next step is to minus 0.25 from 1, this gives you 0.75. This is because we are working out the percentage decrease.

The final step is to multiply the amount of 900 by 0.75 to the power of 7, this gives you $120.14.

1) Divide 25 by 100.

$25/100=0.25$

2) Minus 0.25 from 1.

$1-025=0.75$

3) Multiply 900 by 0.75 to the power of 7.

$900*0.75^7=120.14$

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2 years ago