Use the law of detachment to determine what you can conclude from the given information if three points lie on the same line then they are collinear points A B and C lie on the line M

Answer:

a) y = 2x -2

b) Equation: q = 2p - 2  ----(1)

p² + q² = 4   ----(2)

The coordinates of C may be (0, -2) or (6/5, 8/5)

Step-by-step explanation:

a) Step 1: Find the coordinates of midpoint, P of AB

x-co-ordinate of P = (x₁ + x₂)/2 = (-1 + 7)/2 = 3

y- co-ordinate of P = (y₁ + y₂)/2 = (6 + 2)/2 = 4

Step 2: Determine the gradient, m₂ of perpendicular bisector of AB

For perpendicular lines, m₁ * m₂ = -1 where m₁ is slope of AB

m₁ = (2 - 6)/(7 - -1) = -4/8 = -1/2

-1/2 * m₂ = -1

m₂ = 2

Step 3: Deriving the equation of the perpendicular bisector in the form y = mx + c

y - y₁ = m(x - x₁); substituting the values of the midpoints of the line

y - 4 = 2(x - 3)

y - 4 = 2x - 6

y = 2x -2

b) Step 1: Derive the values of the p and using the formula of distance between two points:

y = 2x - 2

therefore q = 2p - 2  ----(1)

OC = √(x₂ -x₁)² + (y₂ - y₁)²

2 = √(p - 0)² + ( q - 0)²

2 = √p² + q²

squaring both sides

p² + q² = 4   ----(2)

Substituting (1) in (2)

p² + (2p - 2)² = 4

p² + 4p² - 8p + 4 = 4

5p² - 8p = 0

p(5p - 8) = 0

Therefore p = 0 or 5p - 8 = 0

p = 0 or p = 8/5

Substituting p = 0 in (1)

q = -2

substituting p = 8/5 in (1)

q = 2(8/5) - 2

q = 16/5 - 2

q = 6/5

Hence the coordinates of C may be (0, -2) or (6/5, 8/5)

Answer:

l;k

Step-by-step explanation:

qwdefr

Answer:

a= -7, b= 4

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer:

[tex]30x^2+45x[/tex]

Step-by-step explanation:

The answer is

[tex]48^{9} - 72x^{7} +36x^{5}[/tex]

Answer:

6.729

Step-by-step explanation:

Integers only include plsitive and negative numbers and zero. 6.729 is a number alright but it is a fractional or decimal number.

Answer:48

Step-by-step explanation:add up all the sidees

Step-by-step explanation:

divide them by using long polynomial division.

d

Answer:

i believe its B,C, and E

Step-by-step explanation:

Answer:

r =10

Step-by-step explanation:

5(r + 3) = 3r + 35.

Distribute

5r+15 = 3r+35

Subtract 3r from each side

5r+15-3r = 3r+35-3r

Combine like terms

2r +15 = 35

Subtract 15 from each side

2r+15-15 =35-15

2r = 20

Divide by 2

2r/2 =20/2

r =10

Answer:

6.8

Step-by-step explanation:

Answer:6.7850 also it's thousandth :)

Step-by-step explanation:

Answer:

Explanation:

Lets just say the amount her mom gave her is c

and the months is a

the equation would be

c + 25a = 250

we can plug in 8 for a, cause we know its been 8 months,

c + 25(8)= 250

then do the parentheses

c + 200 = 250

subtract the 200 to isolate the variable c

c = 50

then you get c = 50,

Karen's mom gave her a check for $50.

(why karen btw. i would never give $50 to a karen)

The linear equation to calculate the amount from Karen's mother is

A + 25x = 250

where A is the amount and x is the number of months

The amount from Karen's mother is $ 50

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the amount given to Karen by her mother be = A

Let the total number of months be = x

The value of x is = 8 months

The total amount Karen has after 8 months = $ 250

The amount Karen saves per month = $ 25

Now , the equation will be

Total amount Karen has after 8 months = amount given to Karen by her mother + ( amount Karen saves per month x total number of months )

Substituting the values in the equation , we get

250 = A + 25x

On simplifying the equation , we get

A + 25x = 250

when x = 8

A + 25 ( 8 ) = 250

A + 200 = 250

Subtracting 200 on both sides of the equation , we get

A = $ 50

Therefore , the value of A is $ 50

Hence , The linear equation to calculate the amount from Karen's mother is  A + 25x = 250

where A is the amount and x is the number of months

The amount from Karen's mother is $ 50

To learn more about equations click :

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Answer:

Options 1 and 4 are the only other parallel lines

Step-by-step explanation:

Plug the equation into a graphing calculator and observe your results.

Answer:

The answers are y = −4x, 16x + 4y = 9, and y = −4x + 15

Step-by-step explanation:

y=-4x has the -4 as slope so it parallel

y = −4x + 15 also has the -4 as a slope so it parallel

16x + 4y = 9 u have to solve.

4y=-16x+9 First step is to subtract -16 both sides (which just tosses -16 to the other side where the 9 is.

y=-4x+2.25 Divide everything by 4

REMEMBER TO MARK ALL THREE TO GET FULL CREDIT

Answer:

$5.35

Step-by-step explanation:

.85+4.50= 5.35

Answer:

5.35$

Step-by-step explanation:

add 4.50+0.85

Answer:

I belive the number you are searching for is 35.

Step-by-step explanation:

Simply divide 142.20 by 6 to get the hourly wage(23.70). Divide 829.50 by the hourly wage to get the answer. (35)

Answer:2 is the answer.

Step-by-step explanation:

The integers are the whole numbers, their opposites, and 0 . From the given numbers, −7 and 8 are integers.

Answer:

There is not enough evidence suggesting that the mean processing time exceeds 2 minutes.

Step-by-step explanation:

The hypothesis can be defined as follows:

H₀: The mean processing time is 2 minutes, i.e. μ = 2.

Hₐ: The mean processing time exceeds 2 minutes, i.e. μ > 2.

The significance level of the test is, α = 0.05.

Recorded Time (x)        (x - μ)          + Ranks             -Ranks

        1.4                          -0.6                                           8

        2.1                            0.1                   1

        1.9                           -0.1                                           1

        1.7                           -0.3                                          6

       2.4                            0.4                  7

       2.9                            0.9                10

       1.8                            -0.2                                          4

       1.9                            -0.1                                           1

       2.6                            0.6                 8

       2.2                            0.2                 4

    TOTAL                                              30                    20

Sum of +Ranks = 30

Sum of -Ranks = 20

Test statistic = Min (∑+Ranks, ∑-Ranks)

                     = Min (30, 20)

                     = 20

Compute the critical value using the Wilcoxon Signed-rank test table.

Critical value = 11

As the test statistic value is more than the critical value, the null hypothesis was failed to be rejected.

Thus, there is not enough evidence suggesting that the mean processing time exceeds 2 minutes.

Answer:

1. 1 real solution

2. 2 real solutions

3. Two complex solutions

Step-by-step explanation:

y = 3x^2- 6x + 3

This has 1 real solutions.

y= -x^2 - 4x + 7

This has 2 real solutions.

y = -2x^2 + 9x – 11

This has 2 complex solutions.

The number of unique solutions each equation has is required.

[tex]y=3x^2-6x+3[/tex] has one real solution.

[tex]y=-x^2-4x+7[/tex] has two real solutions.

[tex]y=-2x^2+9x-11[/tex] has two complex solutions.

The number of solutions is determined by the value of the discriminant.

Let us find the determinant of each equation

[tex]y=3x^2-6x+3[/tex]

[tex]D=b^2-4ac\\\Rightarrow D=6^2-4\times 3\times 3\\\Rightarrow D=36-36\\\Rightarrow D=0[/tex]

The equation has one real solution.

[tex]y=-x^2-4x+7[/tex]

[tex]D=(-4)^2-4\times (-1)\times 7\\\Rightarrow D=16+28\\\Rightarrow D=44\\\Rightarrow D>0[/tex]

The equation has two real solutions.

[tex]y=-2x^2+9x-11[/tex]

[tex]D=9^2-4\times (-2)\times (-11)\\\Rightarrow D=81-88=-7\\\Rightarrow D<0[/tex]

The equation has two complex solutions.

Learn more:

https://brainly.com/question/14240415

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Answer:

0,1,2,3............

Answer:

y = x - 1

Step-by-step explanation:

slope intercept form is y = mx+b. (mx - slope, b - y-intercept)

You just subtract 1 from both sides, giving you y = x - 1

Step-by-step explanation:

Per means division so this should be 25/0.5

I think you can do the problem by yourself now!

Hope this helps <3

Answer:

-15

Step-by-step explanation:

x= -8   (-8)-7= -15

Answer:

The answer would be

[tex]x=\frac{-7}{2}[/tex]

Answer:

-3.5

Step-by-step explanation:

Answer:

a) P(A) = 0,4607     or   P(A) = 46,07 %

b) P(B) = 0,7120   or 71,2 %

c) P(C) = 0,2055  or P(C) = 20,55 %

Step-by-step explanation:

We will use two concepts in solving this problem.

1.- The probability of an event (A) is for definition:

P(A) = Number of favorable events/ Total number of events FE/TE

2.- If A and B are complementary events ( the sum of them is equal to 1) then:

P(A) = 1 - P(B)

a) The total number of events is:

C ( 24,4) = 24! / 4! ( 24 - 4 )!    ⇒  C ( 24,4) = 24! / 4! * 20!

C ( 24,4) = 24*23*22*21*20! / 4! * 20!  

C ( 24,4) = 24*23*22*21/4*3*2

C ( 24,4) = 24*23*22*21/4*3*2    ⇒  C ( 24,4) =  10626

TE = 10626

Splitting the group of tanks in two 6 with h-v  and 24-6 (18) without h-v

we get that total number of favorable events is the product of:

FE = 6* C ( 18, 3)  = 6 * 18! / 3!*15!  =  18*17*16*15!/15!

FE =  4896

Then P(A) ( 1 tank in the sample contains h-v material is:

P(A) = 4896/10626

P(A) = 0,4607     or   P(A) = 46,07 %

b) P(B) will be the probability of at least 1 tank contains h-v

P(B) = 1 - P ( no one tank with h-v)

Again Total number of events is 10626

The total number of favorable events for the ocurrence of P is C (18,4)

FE = C (18,4) = 18! / 14!*4! = 18*17*16*15*14!/14!*4!

FE = 18*17*16*15/4*3*2  = 3060

Then P = 3060/10626

P = 0,2879

And the probability we are looking for is

P(B) = 1 - 0,2879

P(B) = 0,7120   or 71,2 %

c) We call P(C) the probability of finding exactly 1 tank with h-v and t-i

having 4 with t-i tanks is:

reasoning the same way but now having 4 with t-i (impurities) number of favorable events is:

FE = 6*4* C(14,2) = 24 * 14!/12!*2!

FE = 24* 14*13*12! / 12!*2

FE = 24*14*13/2    ⇒  FE = 2184

And again as the TE = 10626

P(C) = 2184/ 10626

P(C) = 0,2055  or P(C) = 20,55 %

Answer:

3/8

Step-by-step explanation:

1/8 got a A

1/2 got a B

1/2 is = to 4/8

4/8 + 1/8 = 5/8

1(8/8) - 5/8 = 3/8

Answer:  see below

Step-by-step explanation:

A normal distribution is shaped like a negative parabola  →  ∩

The midpoint of the parabola is the median and represents 50% of the data.

Therefore, there is equal distribution to the left and to the right of the 50% mark.

Answer:

Normal distributions are symmetric and the mean, medium, mode. The shape of used is a bell curve. We can also use normal distributions for the height, weight.

Answer:

A complementary angle is an angle that adds up to 90 degrees. supplementary angles add up to 180 degrees. So a supplementary angle lies on a single, straight line, and a complementary angle is a right angle.

Step-by-step explanation:

hopes this helps

Answer:

Step-by-step explanation:

Supplementary is when all the angles add up to 180. Complementary is when all the angles add up to 90.

Answer:

Step-by-step explanation:

ok you have to find which one by

one i mean ( C or L ) DESCRIBES the best

( C ) that is library and u have to find out wut is ( L )

Answer:

the values of angle;

a=61

b=61

c=29

Answer: All of the angles combined are 180 degrees. Since b and its adjacent angle is 90 degrees, you would subtract 90-29, which gives you 61. b=61. You would then use both angle measures to determine the other two. You would need to find two values that add up to 90 degrees for c and a. Angle b+c would be equal to 90 degrees, and angle a and d (I used d to represent the 29 degree angle) would be equal to 90 degrees, equaling a total of 180 degrees. Angle a would be equal to 61, and angle c would be equal to 29. Hope this helps.