Am I right or wrong can you let me know so i can know if im doing it the right way

Let us have four distinct collinear points $a,$ $b,$ $c,$ and $d$ on the cartesian plane. the point $c$ is such that $\dfrac{ab}

Deffense [45]

Start with a line segment connecting two points, A and B. $\dfrac{DA}{BA}=3$ means DA is 3 times longer than BA. Clearly, D cannot fall between A and B because that would mean DA is shorter than BA. So there are two possible locations where D can be placed on the line relative to A and B.

But with $\dfrac{DB}{BA}=2$ , or the fact that DB is 2 times longer than BA, we can rule out one of these positions; referring to the attachment, if we place D to the left of A, then DB would be 4 times longer than BA.

Finally, $\dfrac{AB}{CB}=\dfrac12$ , so that CB is 2 times longer than AB. Again we have two possible locations for point C (it cannot fall between A and B), but one of them forces C to occupy the same point as D. However, A, B, C, D are distinct, so C must fall to the left of A.

Now let $d$ be the length of AB. Then the length of CD in terms of $d$ is $4d$ . We have the coordinates of C and D, and the distance between them is $\sqrt{(4-0)^2+(0-4)^2}=4\sqrt2$ . So

$4d=4\sqrt2\implies d=\sqrt2$

The slope of the line through C and D is

$\dfrac{0-4}{4-0}=-1$

and so the equation of the line through these points is

$y-4=-(x-0)\implies x+y=4$

So the coordinates of A are $(x,y)=(x,4-x)$ . The distance between C and A is $d=\sqrt2$ , so we have

$\sqrt{(x-0)^2+(4-x-4)^2}=\sqrt{2x^2}=|x|\sqrt2=\sqrt2\implies|x|=1$

Since A falls to the right of C (in the $x,y$ plane, not just in the sketch), we know to take the positive value $x=1$ . Then the $y$ coordinate is $y=4-1=3$ .

All this to say that A is the point (1, 3), so

$2x+y=2+3=5$

5 0

3 years ago

many credit card companies charge a compound interest of 1.8% per month on a credit card balance. Miriam owes 750 on a credit ca

nadya68 [22]

Answer:

Most credit card companies also apply a late payment penalty if you owe a balance and do not make a payment. Ignoring that fee, Miriam's balance will increase as:

B(n) = 750(1.018)^n

where B(n) is Miriam's balance after n months. The progression will be:

$750.00

$763.50

$777.24

$791.23

$805.48

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Determine which of the indicated column vectors are eigenvectors of the given matrix

gladu [14]

]Eigenvectors are found by the equation $(A-\lambda I) \vec{v} = 0$$ implying that $\det(A-\lambda I) = 0$ . We then can write:

$A-\lambda I = \left [ \begin{array}{cc} 4-\lambda & 2 \\ 5 & 1-\lambda \end{array}\right ]$

And:

$\det(A-\lambda I) = (4-\lambda)(1-\lambda) - 10 = 0$

Gives us the characteristic polynomial:

$\lambda^2 - 5 \lambda -6 = 0 \implies \lambda_1 = -1, \lambda_2 = 6$

So, solving for each eigenvector subspace:

$\left [ \begin{array}{cc} 4 & 2 \\ 5 & 1 \end{array} \right ] \left [ \begin{array}{c} x \\ y \end{array} \right ] = \left [ \begin{array}{c} -x \\ -y \end{array} \right ]$

Gives us the system of equations:

$4x + 2y = -x \newline 5x + y = - y$

Producing the subspace along the line $y = -\frac{5}{2} x$

We can see then that 3 is the answer.

7 0

3 years ago

The x co-ordinate of any point lying on the Y axis is: please help urgent

olchik [2.2K]

Answer:

x-coordinate = 0

Step-by-step explanation:

In a coordinate plan there are two perpendicular lines one is x-axis and another is y-axis

x-axis is a horizontal line and y-axis is a vertical line.

Both lines intersect each other at (0,0).

On x-axis, y-coordinate remains same , i.e., y=0.

On y-axis, x-coordinate remains same , i.e., x=0.

Therefore, the x co-ordinate of any point lying on the y axis is 0.

8 0

2 years ago

Find the value of x if a rectangle has a perimeter of 154 cm with a length of 18 cm and a width of 2x cm

scZoUnD [109]

Answer:

X = 59

Step-by-step explanation:

2 × 59 = 118

18 + 18 + 59 + 59 = 154

8 0

3 years ago