Please answer the question correctly

Find the distance from P to l. Line l contains points (-4,2) and (3,-5).Point P has coordinates (1,2).

Annette [7]

Hello,

A=(-4,2)
B=(3,-5)
AB≡y-2=(x+4)(-7)/7==>y=-x-2

Slope of the perpendicular: 1

y-2=(x-1)1==>y=x+1 is the equation of the perpendicular.

Intersection: y=x+1 and y=-x-2 ==>(-3/2,-1/2)=Q

|PQ|²=(-1/2-2)²+(1+3/2)²=25/2
|PQ|=5√2/2≈3.5355339059....

7 0

3 years ago

Find the equation of the line that is parallel to the given line and passes through the given point

Sati [7]

Answer:

$\huge\boxed{y=-\dfrac{1}{4}x-1\to x+4y=-4}$

Step-by-step explanation:

$\text{Let}\ k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\==========================\\\\\text{We have}\ x+4y=-6.\\\text{Convert to the slope-intercept form:}\\\\x+4y=-6\qquad\text{subtract}\ x\ \text{from both sides}\\\\4y=-x-6\qquad\text{divide both sides by 4}\\\\y=\dfrac{-x}{4}-\dfrac{6}{4}\\\\y=-\dfrac{1}{4}x-\dfrac{3}{2}\to m_1=-\dfrac{1}{4}$

$\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (9,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}\\\\x=9,\ y=-3\\\\-3=-\dfrac{1}{4}(9)+b\\\\-3=-\dfrac{9}{4}+b\qquad\text{add}\ \dfrac{9}{4}\ \text{to both sides}\\\\-\dfrac{12}{4}+\dfrac{9}{4}=b\to b=-\dfrac{3}{4}$

$\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (8,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}$

$x=8,\ y=-3\\\\-3=-\dfrac{1}{4}(8)+b\\\\-3=-2+b\qquad\text{add 2 to both sides}\\\\-1=b\to b=-1$

$\text{Therefore the equation is:}\ y=-\dfrac{1}{4}x-1.\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y=-\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4y=-x-4\qquad\text{add}\ x\ \text{to both sides}\\\\x+4y=-4$

5 0

3 years ago

Jared surf for one third of the nine hours he was at the beach he spent the rest of the time building a sandcastle how many hour

WINSTONCH [101]

9 dived by 3 = 3
so he surfed for 3 hours = 1/3 of 9
and there are 6 hours left

so he spent 6 hours building a sandcastle

8 0

2 years ago

Read 2 more answers

At the AoPS office, mice vary inversely with cats, that is, $\text{mice}=\frac{k}{\text{cats}}$, for some value of $k$. When the

lesya692 [45]

Answer:

540

Step-by-step explanation:

im terrible at explaining so-

5 0

2 years ago

Say that you (or your parents) are purchasing a used car for $19,850. The sales tax is 7.5%, the down payment is $1,000.00, and

IgorLugansk [536]

We are NOT told 1) the finance charge and 2) the amount of time
 19,850.00 Car Price
+1,488.75 Sales Tax 
 -1,000.00 Down Payment
 20,338.75 This is the amount being financed

Using a loan calculator http://www.1728.org/calcloan.htm
We see that if the loan is for 9.382% and it is for 5 years,
Then the monthly payment is $425.98
We will make 60 (12 months * 5) monthly payments resulting in a total loan cost of 425.98 * 60 =
 25,558.80 Total Loan Cost
-20,338.75 Money Being Financed

5,220.05 Five Year's Interest
********************************************************************
THIS ISN'T EXACTLY RIGHT - SCROLL TO THE BOTTOM
So, 5,220.05 / 60 = Interest Paid each month.
= $87.00

So,
425.98
-87.00
 338.98 Each month goes toward the principal.
******************************************************************************************
Although, the monthly payment remains exactly the same each month, the amount going toward interest and the amount going to equity (what you own), changes drastically each month.
See the mortgage calculator
http://www.1728.org/mortmnts.htm

So, your first payment, of 452.98 pays for $159.02 in interest and $266.95 in principal.

5 0

3 years ago

Read 2 more answers