Endpoints of segment MN have coordinates (0, 0), (5, 1). The endpoints of segment AB have coordinates (1 1/22 , 2 1/4 ) and (−2 1/4 , k). What value of k makes these segments perpendicular?

Answers

Answer 1

Answer: [tex]k=18\dfrac{8}{11}[/tex].

Step-by-step explanation:

If a line passing through two points, then

[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Endpoints of segment MN have coordinates (0, 0) and (5, 1).

Slope of MN [tex]=\dfrac{1-0}{5-0}=\dfrac{1}{5}[/tex]

The endpoints of segment AB have coordinates [tex]\left(1\dfrac{1}{22} , 2\dfrac{1}{4}\right)[/tex] and  [tex]\left(-2\dfrac{1}{4} , k\right)[/tex].

[tex]A=\left(1\dfrac{1}{22} , 2\dfrac{1}{4}\right)=\left(\dfrac{23}{22} ,\dfrac{9}{4}\right)[/tex]

[tex]B=\left(-2\dfrac{1}{4} , k\right)=\left(-\dfrac{9}{4} , k\right)[/tex].

Slope of AB [tex]=\dfrac{k-\frac{9}{4}}{-\frac{9}{4}-\dfrac{23}{22}}[/tex]

[tex]=\dfrac{\frac{4k-9}{4}}{\frac{-99-46}{44}}[/tex]

[tex]=\dfrac{4k-9}{4}\times \dfrac{44}{-145}[/tex]

[tex]=4k-9\times \dfrac{11}{-145}[/tex]

[tex]=\dfrac{44k-99}{-145}[/tex]

Product of slopes of two perpendicular segments is -1.

Slope of MN × Slope of AB = -1

[tex]\dfrac{1}{5}\times \dfrac{44k-99}{-145}=-1[/tex]

[tex]\dfrac{44k-99}{-725}=-1[/tex]

[tex]44k-99=725[/tex]

[tex]44k=725+99[/tex]

[tex]k=\dfrac{824}{44}[/tex]

[tex]k=\dfrac{206}{11}[/tex]

[tex]k=18\dfrac{8}{11}[/tex]

Therefore, the value of k is [tex]k=18\dfrac{8}{11}[/tex].

Answer 2

Answer:

k=21

Step-by-step explanation:

Find the slope of MN which is 1/5, (use the slope formula.)

Use the slope formula for AB using k as y_2

Substitute and you get k=21

21-2.25/-2.25-1.5=-5

The lines are perpendicular because the slopes are the negative reciprocal of one another.


Related Questions

Find the length of the missing side. Sorry, I’m just really bad with algebra!

Answers

217 will be the answer

{{3x + 6}/2- 4}/2 + 12/2=10
the solution for x is:
A). x = 4
B). x = -4
C). x = -2
D). x = 2

Answers

Answer:

The answer is D). x=2

Step-by-step explanation:

Which expression is equivalent to 3.7 x + (0.5-6y)+0.8-(1.7x+1-2.3y)?

Answers

Answer:

2.0x-8.3y+2.3

Step-by-step explanation:

Give the expression 3.7 x + (0.5-6y)+0.8-(1.7x+1-2.3y), to get the equivalent expression we will follow thw steps;

open the parenthesis

3.7 x + 0.5-6y+0.8-1.7x+1-2.3y

collect like terms

= 3.7 x -1.7x -6y-2.3y+0.5+0.8+1

= 2.0x-8.3y+1.3+1

= 2.0x-8.3y+2.3

Hence the equivalent expression is 2.0x-8.3y+2.3

your cell phone plan cost $39.99 per month plus $0.13 for each text message you send or receive. you have a most $46 to spend on your cell phone bill. what is the maximum number of text messages that you can send or receive next month?​

Answers

Answer:

55.87

Step-by-step explanation:

Answer:

46 messages.

Step-by-step explanation:

The top got cut off a bit, it says "Make the same/similar inequality as the other problem:"

What’s the formula for motion?

Answers

F=ma is the formula



hope this helps!

The width of a rectangle measures 9.7 X -4.7 centimetersAnd the length measures 2.9 X +6.4 cm which expression represents the perimeter in centimeters of the rectangle

Answers

Answer:

25.2X + 3.4 centimeters.

Step-by-step explanation:

The formula for the perimeter of a rectangle

= 2L + 2W

= 2(L + W)

From the question:

Width of a rectangle (W) = 9.7 X - 4.7 centimeters

Length of a rectangle (L) = 2.9 X + 6.4 centimeters

Imputing it into the formula

2(L + W)

2( 9.7X - 4.7 + 2.9X + 6.4)

2 (9.7X + 2.9X - 4.7 + 6.4)

2( 12.6X + 1.7)

= 25.2X + 3.4 centimeters.

Therefore, the perimeter of the rectangle = 25.2X + 3.4 centimeters.

Please help with this math problem:)

Answers

Answer:

See SBS Explanation

Step-by-step explanation:

1. Produces a number that can be classified as an Irrational number.

A:  Square root of 2.

2. Produces a number that an be classified as a Rational number.

A: Square root of 4.

3. Rational number that can be classified as an integer.

A: Negative 2/1 (-2/1)

4. Rational number that produces a repeating decimal.

A: 5/9 (Decimal is 0.5 repeating or 0.555....)

5. Rational number that produces a terminating decimal.

A: 1/4 (Decimal is 0.25)

6) -4(3 + 5x) + 10(8x + 4)

Answers

Answer:60x+28

Step-by-step explanation:

60x+28
That would be the correct answer

The perimeter of a square picture froame is 48 inches. One side length of the frame si 30.48 centimeters, how many centimeters are in an inch?

Answers

4

Step-by-step explanation:

simplify the expression by combining like terms; 4z+4-z+5

Answers

Answer:

3z+9

Step-by-step explanation:

=4z+4-z+5

=4z-z+4+5

=3z+9

In a study of 600 community college students, 200 of them indicated that they are part-time students. What percent of the students are part-time students?

Answers

That’s 1/3 of the students, so 33.3333...%

Alvin is 9 years older than Elga. The sum of their ages is 89. What is Elga's age?

Answers

Answer:

Alvin: 49

Elga: 40

Step-by-step explanation:

The equation is 89 = x + (x-9).Remove the parenthesis and combine the like terms. 89 = 2x - 9Add 9 on both sides. 98 = 2x Divide by 2 on both sides. x = 4949 is the age of Alvin. (49-9) 40 is the age of Elga.

Hey there!☺

[tex]Answer:\boxed{40}[/tex]

[tex]Explanation:[/tex]

Elga's age can be represented as "x". If Elga is x years old, then Alvin's age would be represented as "x+9", since Alvin is 9 years older than Elga.

Their combined age is 89. If you were to write that as an equation in terms of "x", you would have the following equation.

[tex]x+x+9=89[/tex]

Since the question is asking for Elga's age, which is x, you're going to be solving the equation for the value of x.

First add like terms: [tex]x+x+9=89 \rightarrow 2x+9=89[/tex]

Subtract both sides by 9 to leave x alone: [tex]2x+9-9=89-9 \rightarrow 2x=80[/tex]

Divide both sides by 2 to find x: [tex]\frac{2x}{2} = \frac{80}{2} \rightarrow x=40[/tex]

Since x is equal to 40, Elga is 40 years old, and Alvin would be 49 years old.

You can also check if the answer is correct by adding their ages.

[tex]40+49=89\ \br \checkmark[/tex]

Elga is 40 years old.

Hope this helps!

[tex]\text{-TestedHyperr}[/tex]

Sara has $1.30 less than double what Billy does. Sara has $53.72. How much money does Billy have?​

Answers

Answer:

Billy has $27.51

Step-by-step explanation:

First let's set up an equation to solve this problem.

Assign a variable to Billy's amount. Let's make it x.

Then we just interpret the problem and solve:

2x - 1.30 = 53.72

     +1.30    +1.30

----------------------------

2x = 55.02

(Divide by 2 on both sides)

----------------------------

x = $27.51

2x = Billy's amount doubled

2x - 1.30 = Taking away 1.30 from double Billy's amount

53.72 = Sara's amount

Can someone help plz

Answers

Answer: x=-7

Step-by-step explanation:

1) The angles of a triangle are equal to 180

2) Add your angles together and set them equal to 180 like this:

x+59+x+51+84=180

3) Combine like terms:

2x+ 194 =180

4) Subtract 195 from both sides:

2x+ 194 =180

    - 194   -194

2x = -14

5) Divide by 2 on both sides

2x= -14

/2     /2

x= -7

Solve this equation for x: 3x - (5x - 9) - 7- 4(x + 1)​

Answers

Step-by-step explanation:

this is your answer..........

can someone solve 3(b+2)+2(b-3)=-5

Answers

Answer:

ofc I can.

Step-by-step explanation:

Solve for b.

By simplifying both sides of the equation, then isolating the variable.

Exact Form:

b= 27/2

Decimal Form:

b= 13.5

Mixed Number Form:

b= 13 1/2

what is 2 (x+2) + 3x =2 (x+1) + 1

Answers

Step-by-step explanation:

2x+4 +3x = 2x +2 +1

4+x= 2x+3

4-3=2x-x

1=x

x=1

2x+4+3x=2x+2+1
5x+4=2x+3
-4 -4
5x=2x-1
—=———
5 5

ANSWER :
x= 2x-1
——
5

!!30 POINTS!!
What is the intersection of planes ABG and BCD in the figure below?

Answers

d explanation: just is

Antonela is planning on painting her room. A gallon of paint covers 110 square feet.
If Antonela's room is 10 feet by 8 feet and has an 8 foot ceiling, how many gallons
would she need to buy?

Answers

She would have to buy 6 gallons of paint because 10 times 8 times 8 = 640 then divide that by 110 which equals something like 5.8 rounded up to 6

Find the distance between the two points. (round to the nearest hundredths)



distance:
please bhelopppplp;pp[

Answers

Answer: The distance between them would be 4 and 5 because if you look at it the one is at -1 and the 5 is at the top you have to count how many spaces their are between them to see what your answer would be and so in this equation it would be 4 and

Step-by-step explanation:The distance between them would be 4 and 5 because if you look at it the one is at -1 and the 5 is at the top you have to count how many spaces their are between them to see what your answer would be and so in this equation it would be 4 and

Answer: (2.5,2)

Step-by-step explanation:

12•_=4
What’s the answer?

Answers

Answer:

3

Step-by-step explanation:

1 1/3 divided by 3/5 and i wil name brainliest

Answers

Answer:

2 2/9

Step-by-step explanation:

Convert any mixed numbers to fractions.

Then your initial equation becomes:

4/3÷3/5

Applying the fractions formula for division,

=4×5

3×3

=20/9

Simplifying 20/9, the answer is

=2 2/9

Answer:

[tex]\frac{20}{9}[/tex] or [tex]2\frac{2}{9}[/tex]  or [tex]2\frac{1}{3}[/tex]

Step-by-step explanation:

[tex]1\frac{1}{3} = \frac{4}{3}[/tex] and [tex]\frac{3}{5}[/tex]

to

[tex]\frac{4}{3}[/tex] divided by [tex]\frac{3}{5}[/tex]

                    ↑

flip the second number

[tex]\frac{4}{3}[/tex] divided by [tex]\frac{5}{3}[/tex]

but instead of divison it becomes multiplication,

[tex]\frac{4}{3}[/tex] × [tex]\frac{5}{3}[/tex]

=

[tex]\frac{20}{9}[/tex]

Mixed number form is:

[tex]2\frac{2}{9}[/tex]

or

Simplify:

[tex]2\frac{1}{3}[/tex]

Solve the system of inequalities: a) .4x−1≤0
2.3x≥4.6

Answers

Answer:

(a) [tex]x \leq 2.5[/tex]

(b) [tex]x \geq 2[/tex]

Step-by-step explanation:

Solving (a):

[tex]0.4x - 1 \leq 0[/tex]

Add 1 to both sides

[tex]0.4x - 1 + 1\leq 0 + 1[/tex]

[tex]0.4x \leq 1[/tex]

Solve for x

[tex]x \leq 1/0.4[/tex]

[tex]x \leq 2.5[/tex]

Solving (b):

[tex]2.3x \geq 4.6[/tex]

Solve for x

[tex]x \geq 4.6/2.3[/tex]

[tex]x \geq 2[/tex]

please answer only 17 and 18 asap

Answers

Answer:

17. -1 (y2-y1/x2-x1)

18. x/8= -6-4, x= -10*8 = -80

What does 2 tenths look like?

Answers

Answer:

2/10 or 0.2

i dont know which tenths you wanted so i did both

First person to answer gets brainliest find the domain and range of the following absolute value functions. F(x)=|3x-4|

Answers

Domain:  

( − ∞ , ∞ ) , { x | x ∈ R }

Range:  

[ 0 , ∞ ) , { y |y ≥ 0 }

I am a multiple of 70. I am between 500 and 1000. My tens digit is odd. What number could I be?
Plz help also can you show the explanation too!

Answers

Answer:

Step-by-step explanation:

490 = 70 * 7

560 = 70 * 8

630 = 70  *9

700 = 70 * 10

770

840

910

You can fill in the other 3

So the number can be 630 770 or 910

Answer:

630, 770, 910

Step-by-step explanation:

They are multiples of 70 and the tens place number is odd 630, 770, 910

HELP ME PLZ!!!! I'll do ANYTHING!!!

Answers

Answer: N = 11

Step-by-step explanation:

Add 8 on both sides

-10n = -110

divide -110 by -10

Answer:

n = 11

Step-by-step explanation:

-10n - 8 = -118

Add 8 to each side

-10n - 8+8 = -118+8

-10n = -110

Divide by -10

-10n/-10 = -110/-10

n = 11

Write a fraction that is equal to 5

Answers

The fraction [tex]\dfrac{10}{2}[/tex] is equal to 5.

Important information:

The given number is 5.Fraction:

The given number can be written as:

[tex]5=\dfrac{5}{1}[/tex]

Now, multiply the numerator and denominator by the same natural number which is greater than 1, to get a fraction.

Multiply the numerator and denominator by 2.

[tex]\dfrac{5\times 2}{1\times 2}=\dfrac{10}{2}[/tex]

Therefore, the fraction [tex]\dfrac{10}{2}[/tex] is equal to 5.

Find out more about 'Fraction' here:

https://brainly.com/question/363606

The fraction 5/1 is equal to 5, 25/5, and 30/6.

We have,

When we write a whole number as a fraction, we can express it by placing the number over the denominator of 1.

This is because any number divided by 1 is equal to itself.

In the case of the number 5,

We can write it as a fraction by placing it over 1:

5/1

This fraction represents the whole number 5, where the numerator (5) indicates the quantity or value, and the denominator (1) represents a single unit.

Or,

25/5 can also be written as 5// = 5

30/6 can also be written as 5/1 = 5

Thus,

The fraction 5/1 is equal to 5, 25/5, and 30/6.

Learn more about fractions here:

https://brainly.com/question/24370499

#SPJ6

How do you solve
60 = -12r

Answers

Answer:

- 5

Step-by-step explanation:

Step 1:

60 = - 12r

Step 2:

12r = -60

Step 3:

r = - 60 ÷ 12

Answer:

r = - 5

Hope This Helps :)

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