The lines 2x=ky+2 and (k+1)x=6y-3 have same gradient. Find possible values of k
I need the answers ASAP please!

Answers

Answer 1

Answer:

k = 3 or k = -4

(Anyone can correct me if I'm wrong)

Step-by-step explanation:

[tex]2x=ky+2\to\ eq1\\(k+1)x=6y-3\to\ eq2\\$Change to this form: $y=mx+c\\ky=2x-2\\y=\frac{2x-2}{k}\\$gradient of eq1: $\frac{2}{k}\\6y=(k+1)x+3\\y=\frac{(k+1)x+3}{6}\\y=\frac{k+1}{6} x+\frac{3}{6}\\y= \frac{k+1}{6} x+\frac{1}{2}\\$gradient of eq1: $\frac{k+1}{6}\\$Since gradient, m, is the same for both lines,$\\\frac{2}{k}=\frac{k+1}{6}\\12=k^{2}+k\\k^{2}+k-12=0\\(k-3)(k+4)=0\\k=3 $ or $ k=-4[/tex]


Related Questions


#6thgrademath plz help

Answers

Answer:

Check pdf

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

40,404x40=1,616,160

57,616x40=2,304,640

2,304,640-1,616,160=688,480

I need help plssssssss

Answers

Answer: x = 0

is basically

4,6,9, ...
Find the 8th term.

Answers

Answer:

39

Step-by-step explanation:

Answer:

39

Step-by-step explanation:

the answer is going up by the numbers 1,2,3,4...

you start with 4 and go up by 2

you then get 6 that's when you count up 3

you get 9 and then count up 4

which is 13 count up 5

18 count up 6

24 count up 7

31 count up 8

39

If a total of 100 people bought drinks at the
stadium on Monday, how many could be expected to
have ordered a small, medium or a large?

Answers

Answer:

33.33333

Step-by-step explanation:

You really don't know what they could've ordered, just divide by 3, to get an average of each.

PLEASE HELP

A circular hot tub has a diameter of 3 feet. What is the approximate
circumference of the hot tub?
9.42
15.70
18.84
25.12

Answers

The answer is 9.42. All you need to do is multiply 3 by pi (3x3.14)

Using the information provided, identify the
domain and range.

I really need help I don’t understand this

Answers

Answer:

Domain: x>=-5

Range: y>=-6

Step-by-step explanation:

10x + 4x 3 – 4 Write the polynomial in standard form. Then name the polynomial based on its degree and number of terms.

Answers

Guessing that the 3 was suppose to be an exponent.

The answer written in standard form is :
4x^3 + 10x - 4

This is called a cubic trinomial.

help vvvvvvvvvvvvvvvvvvv

Answers

i think C would be it

Need step to step answer
(2.7×10^-3) ÷ (9×10^7)​

Answers

Answer:

243,000

Step-by-step explanation:

(2.7×10^-3) ÷ (9×10^7) | Given (thanks for proper formatting :')

(2.7 × 0.001) ÷ (9 × 10,000,000) | Start with exponents

0.0027 ÷ 90,000,000 | Multiply what's in the parenthesis

243,000 | Divide these numbers

Neal buys a board game. He pays for the board game and pays $1.54 in sales tax. The sales tax rate is 5.5%.What is the original price of the board game, before tax?

Answers

Answer:

28

Step-by-step explanation:

1.54 divided by 0.055 = 28

A pen stand costs ₹120. How many pen stand can be bought for ₹1440​

Answers

1440 divided by 120 = 12 pen stands

hope it helps:))

find the cost of 24 opera tickets at 112 each​

Answers

Answer:

2688

Step-by-step explanation:

Answer:

The answer is - 2688

Step-by-step explanation:

24×112=2688

In ΔPQR, r = 870 cm, p = 410 cm and ∠Q=142°. Find ∠R, to the nearest degree.

Answers

Answer: 26

Step-by-step explanation:

Ryan bought a brand new car for $18,000. It's value depreciated at a rate of 1.2% write a function to represent the value of the car as a function of time

Answers

Answer:

gds

Step-by-step explanation:

hgfdz

b

Which statement is best supported by the information in the box plots?
A. The interquartile range for Orchard G is greater than the interquartile range for Orchard H
B. The median number of baskets harvested from trees in Orchard G is less than the median number of baskets harvested from trees in Orchard H.
C. The minimum number of baskets harvested from trees in Orchard H is less than the minimum number of baskets harvested from trees in Orchard G.
D. The data for Orchard H are more symmetrical than the data for Orchard G.

Answers

Answer:

B is the correct

Step-by-step explanation:

choose as brinliest

the distance from Portland to Seaside is 75 miles what is the distance in inches on the map which scale of 1.25 in:25 mi

I also need help with this other one

the distance between Portland to Seaside is 75 miles what is the distance in inches on the map with a scale of 1.25 in:25mi​

Answers

Answer:

1.25in/25mi = x/75mi

25x = 93.75

x = 3.75

3.75 inches

2i^20 + i^42
i^101 - i^2

Show Work

Answers

I assume you're talking about a fraction,

(2i ²⁰ + i ⁴²) / (i ¹⁰¹ - i ²)

Remember that i ² = -1; from this it follows that

i ³ = i ² × i = -i

i ⁴ = i ³ × i = (-i ) × i = -i ² = -(-1) = 1

i ⁵ = i ⁴ × i = i

i ⁶ = i ⁵ × i = i ² = -1

and so on. In particular, raising i to some integer multiple of 4 reduces to 1.

Using the above pattern, we find

i ²⁰ = 1

i ⁴² = i ⁴⁰ × i ² = 1 × (-1) = -1

i ¹⁰¹ = i ¹⁰⁰ × i = 1 × i = i

So, we have

(2i ²⁰ + i ⁴²) / (i ¹⁰¹ - i ²) = (2 - 1) / (i - (-1)) = 1 / (i + 1)

We can stop here, but usually it's more useful to have complex numbers written in standard a + bi form. To get this result, multiply the numerator and denominator by the complex conjugate of i + 1:

(2i ²⁰ + i ⁴²) / (i ¹⁰¹ - i ²) = 1 / (i + 1) × (-i + 1) / (-i + 1)

… = (-i + 1) / (-i ² + 1²)

… = (-i + 1) / (-(-1) + 1)

… = (1 - i ) / 2

or equivalently,

… = 1/2 - 1/2 i

A model car has a length of 7.25 inches. The actual car is 14.5 feet long. What is the scale of the model car?

Answers

Answer:

1:24

Step-by-step explanation:

Convert inches to feet, 7.25 inches is 0.604 feet.

0.604:14.5 needs to become 1:something, so set up 0.604/14.5 = 1/x

Solve for x now by dividing 14.5 by 0.604. You get 24 for x, so the answer is 1:24 scale!

115
149°
What is the degree measure of v?.
A)
31°
B)
34°
58°
D)
749

Answers

THE ANSWER IS 58°...!!!!!!!!

Solve the simultaneous equations
5x + y = 11
3x - y = 9​

Answers

Answer:

Step-by-step explanation:

5x  + y = 11 -------------------(I)

3x - y = 9 -----------------(II)

Add equation (I) & (II)

   5x + y = 11

   3x - y = 9        {add and y will be eliminated and we'll get the value of x}

  8x       = 20

          x = 20/8

         x = 2.5

Plugin x = 2.5 in equation (I)

5*2.5 + y = 11

 12.5  + y = 11

            y = 11 - 12.5

            y = -1.5

After solving the equations simultaneously we get the value [tex]x=\frac{5}{2}[/tex] and [tex]y=\frac{-3}{2}[/tex].

What are equations ?

An equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign .

We have,

[tex]5x + y = 11[/tex]   [tex].......... (i)[/tex]

[tex]3x - y = 9[/tex]   [tex]...........(ii)[/tex]

To solve we will multiply equation [tex](i)[/tex] by [tex]3[/tex] and equation [tex](ii)[/tex] by [tex]5[/tex],

[tex]15x + 3y = 33[/tex]   [tex]..........(iii)[/tex]

[tex]15x -5y = 45[/tex]   [tex]..........(iv)[/tex]

Now, adding both equations [tex](iii)[/tex] and [tex](iv)[/tex] ,

We get,

[tex]8y=-12[/tex]

[tex]y=-\frac{3}{2} =1.5[/tex]

Now putting value of [tex]y=-\frac{3}{2} =1.5[/tex] in equation [tex](i)[/tex] ,

[tex]5x+(\frac{-3}{2} )=11[/tex]

[tex]x=\frac{5}{2} =2.5[/tex]

So, using the elimination method we find out the value [tex]x=\frac{5}{2}[/tex] and [tex]y=\frac{-3}{2}[/tex], which was find out simultaneously.

Hence, we can say that after solving the equations simultaneously we get the value [tex]x=\frac{5}{2}[/tex] and [tex]y=\frac{-3}{2}[/tex].

To know more about equations click here

https://brainly.com/question/20380548

#SPJ2

Work out the cheapest way to buy 48 cans of cola

Answers

Answer:

Where is the image? I did something like this so if you are looking for that answer they are both the first one.

Which numbers from the list below are irrational numbers?

Your answer:

fraction numerator square root of 3 over denominator 7 end fraction


square root of 2.3 end root


8.5353...


fraction numerator negative 2 over denominator 5 end fraction

Answers

Answer:

1st and 2nd option are the correct answers.

Gerald recorded the gains and losses for each play on the football field. Gains were marked with a + and losses with a –. Play 1 2 3 4 Yards +4 –6 –2 +3

Answers

Answer:

Play 3

Step-by-step explanation:

Given:

[tex]\left\begin{array}{ccccc}{Play}&{1}&{2}&{3}&{4}&{Yards}&{+4}&{-6}&{-2}&{+3}\end{array}\right[/tex]

Required [Missing from the question]:

Determine the play with the least change in yard?

To do this, we ignore the sign in front of each yard before we analyze.

So, we have:

Play 1 has a change of 4

Play 2 has 6

Play 3 has 2

Play 4 has 3

From the above analysis, play has the least (which is 2)

What is a quadratic function that has zeros of x=-1 and x=-2?
Write in factored form.

Answers

Answer:

f(x) = (x + 1)(x + 2)

Step-by-step explanation:

Zero x = -1 corresponds to factor x + 1, and zero x = -2 to x + 2.  Thus, the quadratic in question is

f(x) = (x + 1)(x + 2)

[Image: Vertical number line ranging from negative 5 to 5.]

On this number line, zero represents sea level. Plot the following points based on the description provided.

• absolute value of 1


(worth 100 pts

Answers

Answer:

Step-by-step explanation:

since the absolute values do not apply to positive numbers because the absolute value of say 5 is still five. But the absolute value of -5 is 5.

the absolute value of 1 is 1.

so it is 1 unit above sea level

|_._._._._._._._._._._._|

-5,-4,-3,-2,-1,0,1,2,3,4,5

                       ^

                       ||

Answer:

If on a number line, to the right of zero but if not and you're trying to oppose it, it's -1.

Step-by-step explanation:

Caroline owns 3 fewer T shirts than chase. Let k Represent the number of chase’s T shirt. What expression can be used? A. 3k B. 3-k C. K+3
D. K-3 Real quick please!

Answers

Answer:

D

Step-by-step explanation:

Hope this helps

A color document measures 10 by 15 inches. It must be reduced so that the longest side measures 3 inches. What will the dimensions of the document be once it is resized?

Answers

The dimensions would be 2 by 3 because 15 divided by 5 would be there and 10 divided by 5 would be 2 so the final answer would be 2 by 3 :)

Answer:

C

Step-by-step explanation:

Please give me the correct answer.Only answer if you're good at math.​

Answers

answer:

the 1st hour is 14 euros and each hour after that is 2 euros

step-by-step explanation:

so usually when renting something there is an upfront fee you have to pay first. in this case, that fee is 14 euros. now, sometimes you also have to pay a relatively small amount of money for each hour you're using it, in your case that is the 2 euros.

good luck :)

hopefully, this helps

have a great day !!

Answer:

The first hour is 14 euros and each hour after that is 2 euros.

Step-by-step explanation:

I hope I get brainliest. I answered without looking at the other person's answer. I just want to help.

Find the value of x.
A) 3 √3
B) 6 √3
C) 12 √3
D) 6

Answers

Answer:

x=6√3

Step-by-step explanation:

I hope this helps.

Answer:

use trigonometric ratios. I think you use tan whereby tan is opposite over adjacent. the opposite side is X and the adjacent side is 6 . we looking for X you gonna calculate

X=6tan60

=6√3

PLEASE HELP!!!!
Identify the following

Answers

Answer:

definitions

Step-by-step explanation:

central angle

interior angle

diameter

chord

tangent

arc

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