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3 years ago

Which equation has infinitely many solutions?

Mathematics

1 answer:

liubo4ka [24]3 years ago

6 0

Answer:

Step-by-step explanation:

i dont really have an explanation but i got it right

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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

Nana76 [90]

Answer: $k=18\dfrac{8}{11}$ .

Step-by-step explanation:

If a line passing through two points, then

$Slope=\dfrac{y_2-y_1}{x_2-x_1}$

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

Slope of MN $=\dfrac{1-0}{5-0}=\dfrac{1}{5}$

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

$A=\left(1\dfrac{1}{22} , 2\dfrac{1}{4}\right)=\left(\dfrac{23}{22} ,\dfrac{9}{4}\right)$

$B=\left(-2\dfrac{1}{4} , k\right)=\left(-\dfrac{9}{4} , k\right)$ .

Slope of AB $=\dfrac{k-\frac{9}{4}}{-\frac{9}{4}-\dfrac{23}{22}}$

$=\dfrac{\frac{4k-9}{4}}{\frac{-99-46}{44}}$

$=\dfrac{4k-9}{4}\times \dfrac{44}{-145}$

$=4k-9\times \dfrac{11}{-145}$

$=\dfrac{44k-99}{-145}$

Product of slopes of two perpendicular segments is -1.

Slope of MN × Slope of AB = -1

$\dfrac{1}{5}\times \dfrac{44k-99}{-145}=-1$

$\dfrac{44k-99}{-725}=-1$

$44k-99=725$

$44k=725+99$

$k=\dfrac{824}{44}$

$k=\dfrac{206}{11}$

$k=18\dfrac{8}{11}$

Therefore, the value of k is $k=18\dfrac{8}{11}$ .

8 0

3 years ago

Read 2 more answers

The length of one side of a square is 3n+2. The perimeter of the square is 4(3n+2). Which expression is equivalent to the perime

deff fn [24]

Answer:

4(3n + 2)

Step-by-step explanation:

as we know perimeter of a square is 4 x side

one side is 3n + 2

4 sides = 4(3n +2)

8 0

3 years ago

Find the area of the following shapes:

Annette [7]

Answer:

24 square units

Step-by-step explanation:

You apply area of a trapezium

5 0

2 years ago

What is the meaning of the slope of the line ?

Mila [183]

Step-by-step explanation: In algebra, we use the word slope to describe how steep a line is and slope can be found using the ratio rise/run between any two points that are on that line.

The ratio rise/run is the equal to the rate of change

or the change in y/change in x.

In algebra, the rate of change or the change in y/change in x or

the rise/run is also called the slope of a line.

4 0

2 years ago

Write an equation of the circle with center (4,5) and radius 9.

mixer [17]

Answer:

I'm going to write both of these because maybe you have a fill in the blank question. I don't know.

$(x-4)^2+(y-5)^2=9^2$

Simplify:

$(x-4)^2+(y-5)^2=81$

Step-by-step explanation:

$(x-h)^2+(y-k)^2=r^2$ is the equation of a circle with center (h,k) and radius r.

You are given (h,k)=(4,5) because that is the center.

You are given r=9 because it says radius 9.

Let's plug this in.

$(x-4)^2+(y-5)^2=9^2$

Simplify:

$(x-4)^2+(y-5)^2=81$

6 0

3 years ago

Read 2 more answers