A (5,3) and B(3,-2) are two fixed points. Find the equation of the locus of P, so that the
area of triangle PAB is 9.​

Answers

Answer 1

Answer:

[tex]37=5x-2y,\,1=5x-2y[/tex]

Step-by-step explanation:

If [tex](x_1,y_1),\,(x_2,y_2),\,(x_3,y_3)[/tex] are coordinates of a triangle then area of a triangle is equal to [tex]\frac{1}{2}|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|[/tex]

Let point P be [tex](x,y)[/tex]

Put [tex](x_1,y_1)=(5,3),\,(x_2,y_2)=(3,-2),\,(x_3,y_3)=(x,y)[/tex]

Area of a triangle = [tex]\frac{1}{2}|5(-2-y)+3(y-3)+x(3+2)|[/tex]

[tex]=\frac{1}{2}|-10-5y+3y-9+5x|\\\\=\frac{1}{2}|-19+5x-2y|[/tex]

Also,

Area of a triangle = 9 square units

[tex]9=\frac{1}{2}|-19+5x-2y|\\\\18=|-19+5x-2y|[/tex]

±18 = -19 + 5x - 2y

[tex]18=-19+5x-2y,\,-18=-19+5x-2y\\\\37=5x-2y,\,1=5x-2y[/tex]


Related Questions

There 12 sports drinks, 7 cans of orange juice, and 5
sodas in a cooler. If a drink is selected at random from
the cooler, what are the chances that it is not a orange
juice?
A. 1/2
B. 17/24
C. 7/24
D. 19/24

Answers

17/24
add up all the numbers together to give you 24
there’s 7 orange juice cans so subtract 7 from 24 to give you 17/24

Helpppppppppppppppp​

Answers

Answer:

tjrjrkrkrkrkurjrjrjrjrnr s jkalsmrnrnd

i gotta brand new whip

Answers

Answer:

no keys

Step-by-step explanation:

Brenda’s school is selling tickets to a spring musical. On the first day of ticket sales the school sold 6 adult tickets and 9 child tickets for a total of $108. The school took in $111 on the second day by selling 9 adult tickets and 5 child tickets. What is the price of each type of ticket?

Answers

Answer:

42 dollars

Step-by-step explanation:

HELP ASAP. What is the area of this trapezoid and the formula. Please explain your reason.

Answers

Answer:

base 1 + base 2 times height times half (basically dividing by 2) is the formula of a trapezoid. 25 + 35 = 60 x 21 = 1260 divided by 2 is 630

Simplify the following expression: 3(2x+7) *
O 6x + 7
O 6x + 10
O 6x + 21
O 5x + 10

Answers

3 x 2x = 6x

3 x 7 = 21

6x+21

the answer is c 6x+21

Write the equation of the line in either point-slope form or slope-intercept form.

Write the equation of a line that has a slope of -3 and passes through the point (1.25, -4).

Use the drop-down menus to select the appropriate values in the equation.

y = _ x + _

Answers

Answer:

here you go hope this helps

Step-by-step explanation:

y= -3x + -4

Answer:

answer  in picture

Step-by-step explanation:

Math 143 flooring lab​

Answers

Answer:

eeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Step-by-step explanation:

HELP ASAP PLS ANSWER THE QUESTION IN THE PIC I GIV BRAINLEST AND LOTS OF POINTS TO CORRECT ANSWER

Answers

65+3x+2x=180
5x=115
x=23

Points D and E are midpoints of the sides of triangle
ABC. The perimeter of the triangle is 48 units.
What is the value of t?
2
3
6
8

*ANSWER IS 2 just took the test*

Answers

Answer:

A. 2

Step-by-step explanation:

From the diagram, it is indicated;

AD = DB = 3t,

AC = 7t + 6

CE = EB = 4t

Perimeter = 48 units

Perimeter = AD + DB + AC + CE + EB

Plug in the values

48 = 3t + 3t + 7t + 6 + 4t + 4t

Add like terms

48 = 21x + 6

48 - 6 = 21x + 6 - 6

42 = 21x

42/21 = 21x/21

2 = x

x = 2

2.
It took you 30 minutes (min) to walk
from home to school with the
distance of 500 meters. What is the
average speed?​

Answers

If it’s per hour it would be 1000 m per hour

Answer:

0.27778m/s woulb be my average speed

How to add fraction 3/7+ 3/9=

Answers

[tex] \large \sf \pink{Answer: }[/tex]

[tex] \large \purple{ \boxed{ \frac{16}{21}}}[/tex]

[tex] \large \sf \pink{Explanation:}[/tex]

[tex] \sf \large{ \frac{3}{7} + \frac{3}{9}}[/tex]

[tex] \sf \large{ \frac{3}{7} + \frac{1 \times 3}{3 \times 3}}[/tex]

[tex] \sf \large{ \frac{3}{7} + \frac{1}{3}} [/tex]

[tex] \sf \large\frac{3 \times 3}{21} + \frac{1 \times 7}{21}[/tex]

[tex] \sf \large{ \frac{9}{21} + \frac{7}{21}}[/tex]

[tex] \sf \large{ \frac{(9 + 7)}{21}}[/tex]

[tex] \sf \large \purple{ = \frac{16}{21}}[/tex]

An igloo has a circular floor with a diameter of 4 yards. What is the floor's area? Use 3.14 for π​

Answers

Step-by-step explanation:

the answer is A=12.57

A=πr^2

3.14 • 2^2 = 12.57

Tiffany surveyed some of her classmates to find the number of times they wrote the weekly spelling words. She also found the number of words they missed on the spelling test. The scatterplot shows the results of Tiffany’s survey. Which statement does NOT match Tiffany’s scatterplot?

Answers

Options :

A.) A student who missed 2 words on the test wrote each word 4 times.

B.) A student who wrote each word once missed 6 words on the test.

C.) A student who did not write the words missed 8 words on the test.

D.) A student who missed 4 words on the test wrote each word 3 times.

Answer:

A student who did not write the words missed 8 words on the test.

Step-by-step explanation:

From the scatter plot, we could identify all the other points except that of option C.

For option A : (4, 2) is a marked point on the graph

For option B : (1, 6) is also a marked point on the graph

For option C : (0, 8) is not a marked point on the graph and hence, does not match Tiffany's scatter plot.

What is the next term of the arithmetic sequence?
-8, -14, -20,–26,

Answers

Answer:

-8, -14, -20, -26, -32, -38

Step-by-step explanation:

if we do this equation:

14 - 8 = 6

20 - 14 = 6

26 - 20 = 6  and you will do this until you get the answer you want.

so the arithmatic squence is -8, -14, -20, -26, -32, -38

Alex is building a square sandbox with sides 2 feet long and 3 feet deep he wants to fill it 2/3 full how much sand should he order

Answers

Answer:

8 cubic feet

Step-by-step explanation:

First find the volume of the sand box

2 x 2 x 3 = 12

then multiply the total volume by 2/3

12 x 2/3 = 8

That leaves you with the total cubic feet of sand he would need.

A television news program asks its viewers to call in to give their opinions on an upcoming ballot question. What type of sampling method does this represent?

Answers

Answer:

This is an example of self selecting sampling

Step-by-step explanation:

This is an example of self selecting sampling because the news program is asking viewed to give their opinions. The viewers themselves have a choice of participating in the sample therefore is self selecting.

The art club at a community college is selling burgers at lunchtime as a fundraiser. The club spends $8 for condiments and supplies. The cost of the meat and bun for each burger is $0.65. Express the total​ cost, C, as a function of the number of burgers​made, x.

Answers

Answer:

C(x)=0.65x+8

Step-by-step explanation:

According to the information given, you can say that the total cost would be equal to the result of multiplying the cost of the meat and bun per burger for the number of burgers made plus the amount spent on condiments and supplies, which can be expressed as:

C(x)=0.65x+8, where:

C(x) is the total cost

x is the number of burgers made

-2(3+m)=
Solve the question

Answers

The answer is -6-2m

Have a wonderful day

6+4/a+b/3 when a=4 and b=3

Answers

Answer:

8

Step-by-step explanation:

Plug in a =4 and b=3 into  6+4/a +b/3

6 + 4/4 + 3/3

= 6 + 1 + 1

= 8

Which of these is an example of a random sample?
A.
Customers buying a new cell phone are surveyed about cell phone plans.

B.
A phone plan company surveys people on the beach to see how well they are receiving service, and uses this information in future advertising.

C.
Every twentieth caller to an independent radio station receives tickets to a concert.

D.
A phone survey is conducted using twenty names randomly taken from the phone book.

Answers

B I believe is a good sample

multplying binomals anyone know this?

Answers

Answer:

Yes I know this material.

(x+2)(x+1) x^2+x+2x+2 So the answer is x^2+3x+2 Hope this helps
you use the distribution method
i cant do all but hopefully this will help
(x+2)(x+1)
=x^2+1x+2x+2
=x^2+3x+2

(x+3)(x+4)
=x^2+4x+3x+12
=x^2+7x+12

Find the equation of the circle touching both axes and has centre on the line 3x - 5y = 4.​

Answers

Step-by-step explanation:

Look at the picture.

can I be brainliest

have a nice day

Write an exponential function to model the following situation: A population starting at 740 animals
decreases at an annual rate of 12%. Use your function to determine about how many animals there will
be after 5 years.
A. 390
B. 150
CC. 680
D. 340

Answers

Answer:

A. 390

Step-by-step explanation:

An exponential function can be written in the form [tex]f(n)=a\times b^n[/tex], where [tex]a[/tex] is your starting population, [tex]b[/tex] is the factor by which the population increases, and [tex]n[/tex] is the number of terms. In this case, [tex]a=740[/tex], [tex]b=0.88[/tex] because the population decreases by 12 percent (1-0.12=0.88), and [tex]n=5[/tex].

Thus, [tex]f(5)=740 \times 0.88^5[/tex], which is roughly equal to 390.

Gina is wrapping gifts for her daughter's birthday how many square inches of wrapping paper does Gina use to wrap a box 3 inches 8 inches tall 14 inches​

Answers

Answer:

336 inches

Step-by-step explanation:

What is the area of this figure?

Enter your answer in the box.

Answers

Answer:

24

Step-by-step explanation:

Area of the 1st upright rectangle: 3x4=12

Area of 2nd rectangle: rectangle: 6x1=6

area of triangle: ((1st leg)x(2nd leg))/2=(4x3)/2=6

1st leg=4

2nd leg=6-3=3

12+6+6

24=area

Hope this helps :)

You are in charge of monitoring the pressure of a compressed air tank in a processing plant. After repeating the pressure measurement a large number of times, you found that the pressure values have Gaussian distribution with a mean value of 69 psi and a standard deviation of 10 psi. If it is important that the pressure stays below 86 psi, what is the probability (in percent) that the pressure will exceed this value? (Provide your answer as a percentage using two decimal places. Do not include the % symbol in your answer)

Answers

Answer:

4.46% probability that the pressure will exceed this value.

Step-by-step explanation:

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Gaussian distribution with a mean value of 69 psi and a standard deviation of 10 psi.

Gaussian distribution = normal.

This means that [tex]\mu = 69, \sigma = 10[/tex]

If it is important that the pressure stays below 86 psi, what is the probability (in percent) that the pressure will exceed this value?

As a proportion, this probability is 1 subtracted by the pvalue of Z when X = 86. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

[tex]Z = \frac{86 - 69}{10}[/tex]

[tex]Z = 1.7[/tex]

[tex]Z = 1.7[/tex] has a pvalue of 0.9554

1 - 0.9554 = 0.0446

0.0446*100 = 4.46%

4.46% probability that the pressure will exceed this value.

Find the value of x and the measure of each angle:

Answers

Answer:

m<M= 85° m<N= 85°

Step-by-step explanation:

To find the value of x we should...

Sum of all angles = 360°

95+95+10x-5+8x+13 = 360

198+18x = 360

18x = 360-198

18x = 162

x = 162÷18

x = 9

m<M = (10×9)-5 = 90-5 = 85°

m<N = (8×9)+13 = 72+13 = 85°

PLZZZ MARK ME AS BRAINLIEST PLZZZ

Answer:

x = 9

∠M = 85°

∠N = 85°

Step-by-step explanation:

360 = 95 + 95 + (10x-5) + (8x + 13)

reduce:

18x = 162

x = 9

∠M = 85°

∠N = 85°

an angle measures 66° less than the measure of its complementary angle. what is the measure of each angle

Answers

Answer:

12 and 78

Step-by-step explanation:

The sum of complementary angles is 90 degrees

X+(x-66) = 90

2x = 156    x =  78

78-66 = 12

besties if your looking for 50+ points and brainliest plz answer this correctly thanks

Answers

A: -0.7
B: 0.9
C: (given)
D: -0.1
E: -0.9
F: 0.7

hope this helps!! :)
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