Evaluate. −64125−−−−√3

The given line segment has a midpoint at (3,1)

masya89 [10]

Answer:

$y=\frac{1}{3}x$

Step-by-step explanation:

We have been given an image of a line segment and we are asked to find the equation of perpendicular bisector of our given line segment in slope-intercept form.

Since we know that the slope of perpendicular line to a given line is negative reciprocal of the slope of the given line.

Let us find the slope of our given line using slope formula.

$\text{Slope}=\frac{y_2-y_1}{x_2-x_1}$ , where,

$y_2-y_1$ = Difference between two y-coordinates,

$x_2-x_1$ = Difference between two x-coordinates of same y-coordinates.

Upon substituting the coordinates of points (2,4) and (4,-2) in slope formula we will get,

$\text{Slope}=\frac{-2-4}{4-2}$

$\text{Slope}=\frac{-6}{2}$

$\text{Slope}=-3$

Now we will find negative reciprocal of $-3$ to get the slope of perpendicular line.

$\text{Negative reciprocal of }-3=-(-\frac{1}{3})=\frac{1}{3}$

Since point (3,1) lies on the perpendicular line, so we will substitute coordinates of point (3,1) in slope-intercept form of equation $(y=mx+b)$ .

$1=\frac{1}{3}\times 3+b$

$1=1+b$

$1-1=1-1+b$

$b=0$

Therefore, the equation of perpendicular line will be $y=\frac{1}{3}x+0=\frac{1}{3}x$ and option A is the correct choice.

5 0

3 years ago

Read 2 more answers

2x - 4y = -2<br>2x + 3y = 12

Iteru [2.4K]

Answer: x=3 and y=2

Your welcome

8 0

3 years ago

Read 2 more answers

What is the value of x in the equation −x = 4 − 3x + 6?<br><br> 5<br> 10<br> −5<br> −10

ddd [48]

Combine like terms

-x = 4 + 6 - 3x
-x = 10 - 3x

Isolate the x, add 3x to both sides

-x (+3x) = 10 - 3x (+3x)

-x + 3x = 10

Simplify. Combine like terms

-x + 3x = 10

2x = 10

Isolate the x, divide 2 from both sides

2x/2 = 10/2

x = 10/2

x = 5

x = 5, or A is your answer

hope this helps

8 0

3 years ago

Read 2 more answers

Account A and Account B both have a principal of $2,000 and an annual interest rate of 2%. No additional deposits or withdrawals

GuDViN [60]

Answer:

Account B earns more interest.

After 20 years, account B will have earned $171.89 more.

Step-by-step explanation:

Let's calculate the total for each account.

Account A:

Account A earns simple interest. We know that the principal value is $2000 and the interest rate is 2% or 0.02. We can use the simple interest formula:

$A=P(1+rt)$

Where A is the future value, P is the principal, r is the rate, and t is the time in years.

So, let's substitute 2000 for P, 0.02 for r, and 20 for t. This yields:

$A=2000(1+0.02(20))$

Multiply and add:

$A=2000(1+0.4)=2000(1.4)$

Multiply. So, the total amount of money in Account A after 20 years is:

$A=\$2800$

Since we initially deposited $2000 and our total is now $2800, this means that we earned an interest of $2800-2000=\$ 800$

Account B:

Account B earns compound interest. Like Account A, Account B has a principal value of $2000 and the interest rate is 2% or 0.02. We also know that it's compounded annually, so once per year. We can use the compound interest formula:

$B=P(1+\frac{r}{n}})^{nt}$

Where B is the future value, P is the principal, r is the rate, n is the times compounded per year, and t is the time in years.

So, let's substitute 2000 for P, 0.02 for r, n for 1 (since it's compounded annually), and t for 20. This yields:

$B=2000(1+\frac{0.02}{1})^{(1)(20)}$

Simplify this to acquire:

$B=2000(1.02)^{20}$

Evaluate. Use a calculator. So, after 20 years, the amount of money in Account B is:

$B\approx\$2971.89$

Since our principal was $2000, this means that we earned an interest of approximately $2971.89-2000=\$ 971.89$ .

So, Account A earned an interest of $800 and Account B earned an approximate interest of $971.89.

So, Account B earned more interest.

And it earned $971.89-800=\$ 171.89$ more than Account A.

And we're done!

5 0

3 years ago

An Archer shoots an arrow horizontally at 250 feet per second. The bullseye on the target and the arrow are initially at the sam

Genrish500 [490]

Answer:

Step-by-step explanation:

Using the formula for finding range in projectile, Since range is the distance covered in the horizontal direction;

Range $R = U\sqrt{\frac{H}{g} }$

U is the velocity of the arrow

H is the maximum height reached = distance below the bullseye reached by the arrow.

R is the horizontal distance covered i.e the distance of the target from the archer.

g is the acceleration due to gravity.

Given R = 60ft, U = 250ft/s, g = 32ft/s H = ?

On substitution,

$60 = 250\sqrt{\frac{H}{32}} \\\frac{60}{250} = \sqrt{\frac{H}{32}}\\\frac{6}{25} = \sqrt{\frac{H}{32}$

Squaring both sides we have;

$(\frac{6}{25} )^{2} = (\sqrt{\frac{H}{32} } )^{2} \\\frac{36}{625} = \frac{H}{32} \\625H = 36*32\\H = \frac{36*32}{625} \\H = 1.84feet$

The arrow will hit the target 1.84feet below the bullseye.

5 0

3 years ago