How do you determine if the line segments are congruent

Answers

Answer 1

Answer: You must calculate the length of the segments.

Suppose segments AB and CD
Being A (m, n), B (p, q) C(r,s) and D(t,u)

They are congruent if:

$\boxed{(p-m)^2+(q-n)^2=(t-r)^2+(u-s)^2}$

Answer 2

Answer: You can know if they are congruent by the length of both lines!

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Point M lies between points L and N on Line segment L N .The space between L and M is 10 x + 8. The space between M and N is 5 x minus 4.
If LN = 12x + 16, what is the length of Line segment L N in units?

16 units
40 units
48 units
64 units

Answers

Answer:

64 units

Step-by-step explanation:

Given:

Point M lies between points L and N on Line segment LN.

Length of segment LM is given as = $10x+8$

Length of segment MN is given as = $5x-4$

Length of segment LN is given as = $12x+16$

From the information given we can conclude that the points L,M and N ar co-linear and

$LM+MN=LN$ [ Segment addition postulate as M lies in between L and N]

Substituting the values given to find $x$ .

$10x+8+5x-4=12x+16$

Combining like terms.

$15x+4=12x+16$

Subtracting both sides by $12x$

$15x+4-12x=12x+16-12x$

$3x+4=16$

Subtracting both sides by 4.

$3x+4-4=16-4$

$3x=12$

Dividing both sides by 3.

$(3x)/(3)=(12)/(3)$

∴ $x=4$

Length of segment LN can be found out by substituting $x=4$ in the expression for segment.

⇒ $12(4)+16$

⇒ $48+16$

⇒ $64$

Length of segment LN = 64 units (Answer)

Answer:

Step-by-step explanation:

$290, 12.5%, 6 months

Answers

The information shown here only shows a principal sum, a rate of interest and a period or time. There is no question as to what is needed. But suppose the need is for simple interest, then we calculate using the given information and the formula:I = PRTwhere I is simple interest, P is the principal, R is the rate per year, and T is timeP = 290, T is 6 months which is 0.5 years, R = 12.5 % which is written as 0.125 in decimal fraction.I = 290 × 0.125 x 0.5 → I = 18.125Therefore after 6 months , the interest earned will be 18. 125 dollars

A cone has a base radius of 7 centimeters and a height of 21 centimeters.What is the volume of the cone?

A.
28π cm3

B.
49π cm3

C.
147π cm3

D.
343π cm3

Answers

D is the answer...........

How does P minus 13 equals -2

Answers

Hey there!
Let's do this step by step:

1. P-13=2 -------Write out the equation

2. P-13+13=-2+13 ------- Undo the operations

3. $(p)/(1)$ = $(11)/(1)$ ------- What you get

4. P=11

(If you feel that my answer has helped you, please consider rating it and giving it a thank you! Also, feel free to make the best answer, the brainliest answer!)

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the answer will be 11

A new truck costs $32,000. The car’s value will depreciate over time, which means it will lose value. For tax purposes, depreciation is usually calculated linearly. If the truck is worth $24,500 after three years, write an explicit formula for the value of the car after n years.

Answers

Answer:

v = -2500*n + 32000

Step-by-step explanation:

Depreciation is usually calculated linearly, means that it follows the following equation (equation of a line):

v = a*n + b

where n is time after truck was new (in years), v is value of the truck (in $), and a and b are some constants.

A new truck costs $32,000, that is, when n = 0, v = 32000. Replacing into the equation:

32000 = a*0 + b

32000 = b

The truck is worth $24,500 after three years , that is, n = 3, v = 24500. Replacing into the equation:

24500 = a*3 + 32000

a*3 = 24500 - 32000

a = -7500/3 = -2500

32000 - (32000 * .2552n)

complete the synthetic division problem below -3|2 4 -4 6what is the quotient in polynomial form?

Answers

After completing the synthetic division, the quotient in polynomial form is equal to: B. 2x² - 2x + 2.

What is synthetic division?

Synthetic division can be defined as a simplified and specialized method that is used for the division of a polynomial by another polynomial of the first degree (x - n).

Also, you should use only the coefficients of the divided polynonial and its divisor and change the sign of the constant term in the divisor, in order to replace subtraction with addition.

Next, we would set up the synthetic division as follows:

-3 | 2 4 -4 6

|_________________

↓ -6 6 -6

|_________________

2 -2 2 0

Quotient = 2 -2 2 ⇒ 2x² - 2x + 2.

Read more on synthetic division here: brainly.com/question/9539278

Answer:

2x^2-2x+2

Step-by-step explanation:

Solved through synthetic division