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3 years ago

In the figure below, segment CD is parallel to segment EF and point H bisects segment DE :

Mathematics

1 answer:

Grace [21]3 years ago

4 0

Answer:

See explanation

Step-by-step explanation:

In the figure below, segment CD is parallel to segment EF, DE is a transversal, then angles DIH and HGI are congruent as alternate interior angles when two parallel lines are cut by a transversal.

Consider triangles DIH and EGH. In these triangles,

$\angle DIH\cong \angle EGH$ as alternate interior angles;
$\angle DHI\cong \angle GHE$ as vertical angles;
$DH\cong HE$ because point H bisects segment DE (given).

Thus,

$\triangle DIH\cong \triangle EGH$ by AAS postulate

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MAT 171

steposvetlana [31]

Using the Factor Theorem, the polynomials are given as follows:

1. $P(x) = x^5 + 2x^4 - 7x^3 + x^2$

2. $P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)$

3. P(x) = -0.1(x³ - 4x² - 3x + 18)

<h3>What is the Factor Theorem?</h3>

The Factor Theorem states that a polynomial function with roots $x_1, x_2, \codts, x_n$ is given by:

$f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)$

In which a is the leading coefficient.

Item a:

The parameters are:

$a = 1, x_1 = x_2 = 1, x_3 = x_4 = 0, x_5 = -4$

Hence the equation is:

P(x) = (x - 1)²x²(x + 4)

P(x) = (x² - 2x + 1)(x + 4)x²

P(x) = (x³ + 2x² - 7x + 1)x²

$P(x) = x^5 + 2x^4 - 7x^3 + x^2$

Item b:

The roots are:

$x_1 = x_2 = 4, x_3 = 0, x_4 = -4$

Hence:

P(x) = a(x - 4)²x(x + 4)

P(x) = a(x² - 16)x(x - 4)

P(x) = a(x³ - 16x)(x - 4)

$P(x) = a(x^4 - 4x^3 - 16x^2 + 64x)$

It passes through the point x = 5, P(x) = 36, hence:

45a = 36.

a = 4/5

a = 0.8

Hence:

$P(x) = 0.8(x^4 - 4x^3 - 16x^2 + 64x)$

Item 3:

The roots are:

$x_1 = x_2 = 3, x_3 = -2$

Hence:

P(x) = a(x - 3)²(x + 2)

P(x) = a(x² - 6x + 9)(x + 2)

P(x) = a(x³ - 4x² - 3x + 18)

For the y-intercept, x = 0, y = -1.8, hence:

18a = -1.8 -> a = -0.1

Thus the function is:

P(x) = -0.1(x³ - 4x² - 3x + 18)

More can be learned about the Factor Theorem at brainly.com/question/24380382

#SPJ1

5 0

2 years ago

Mr. West estimated a mass to be 265g, but upon carefully measuring it, found the actual mass to be 240g. What was the percent er

spayn [35]

Answer:

<h3>The answer is 10.42 %</h3>

Step-by-step explanation:

The percentage error of a certain measurement can be found by using the formula

$P(\%) = \frac{error}{actual \: \: number} \times 100\% \\$

From the question

actual mass = 240 g

error = 265 - 240 = 25

So we have

$p(\%) = \frac{25}{240} \times 100 \\ = 10.41666666...$

We have the final answer as

Hope this helps you

8 0

3 years ago

A copy machine can print 340 color copies every 8 minutes. Explain or show your reasoning.

mylen [45]

Step-by-step explanation:

340=8min

850=?(x)

340x=850×8

340x=6800

x=6800/340

x=20min

so..the teachertook 20 minute to print 850 copies

3 0

3 years ago

Read 2 more answers

Given data set:

Murrr4er [49]

Answer:

mean =6, median =6.5 mode = 7

Step-by-step explanation:

mean =6, median =6.5 mode = 7

hello,

to find the mean, you add all the numbers together and divide it by the total number of numbers. so that would be 66(total sum) divided by 11 (number of numbers) to get 6.

to find the median, you would organize the numbers from least to greatest and find the middle number which is 6.5

last but not least, to find the mode, just look for the number that appears most often. Therefore, the mode would be 7.

hope this helped!

7 0

3 years ago

7,8,9 ABC or D no explanation needed just answers and I’ll give brainly

victus00 [196]

Answer: b, c, 4x^2y

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers