Find the value of x such that the area of a triangle whose vertices have coordinates (6, 5), (8, 2) and (x, 11) is 15 square units.

Answers

Answer 1

Answer:

[tex]x =12\ or\ -8[/tex]

Step-by-step explanation:

Given

[tex](x_1,y_1) = (6,5)[/tex]

[tex](x_2,y_2) = (8,2)[/tex]

[tex](x_3,y_3) = (x,11)[/tex]

[tex]Area = 15[/tex]

Required

Find x

The area is calculated as thus:

[tex]Area = \frac{1}{2}|x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|[/tex]

Substitute values

[tex]15 = \frac{1}{2}|6*(2 - 11) + 8*(11 - 5) + x(5 - 2)|[/tex]

[tex]15 = \frac{1}{2}|6*(-9) + 8*(6) + x(3)|[/tex]

[tex]15 = \frac{1}{2}|-54 + 48 + 3x|[/tex]

[tex]15 = \frac{1}{2}|-6 + 3x|[/tex]

Multiply through by 2

[tex]2 * 15 = \frac{1}{2}|-6 + 3x| * 2[/tex]

[tex]30 = |-6 + 3x|[/tex]

Remove absolute sign

[tex]30 = -6 + 3x\ or\ -30 = -6 + 3x[/tex]

Add 6 to both sides

[tex]36 = 3x\ or\ -24 = 3x[/tex]

Divide by 3

[tex]12 = x\ or\ -8 = x[/tex]

[tex]x =12\ or\ -8[/tex]

So, the coordinates are (-8, 11) or (12,11)


Related Questions

I need help please!

Answers

Answer:

x=-7

Step-by-step explanation:

75+x+52+67+x=180

2x+194=180

2x=-14

x=-7

Answer:

x = -7

Step-by-step explanation:

total angle of triangle is 180°

nake an equation.

180°= 75 + (x+52) + (67+x)

180-75-52-67=2x

-14 =2x

Divide both sides by 2 to get the value of x

X= -7

Find the area of the shaded region. Round your answer to the nearest tenth if needed.

Answers

Area of rectangle is A1
A1=l•w
A1=3.5 • 2.4
A1=8.4 m^2

Area of triangle is A2
d=2.4
r=d/2
r=2.4/2=1.2 m
A2= π•r^2
A2=3.14 • (1.2)^2
A2=3.14 • 1.44
A2=4.5216 m^2

Area of shaded region A=A1+A2
A=8.4+4.5216
A=12.9216
A~12.9 m^2

What is the perimeter of JKLM?

Answers

Start with the 60, 60, 60 degree triangle, one of the sides are 12 so all the other sides are 12. So we have 12+12+12+9=45


Eva has some money in her wallet. She spent $18.62 buying groceries and had $43.55 left. How much money did she have in her wallet before she bought the groceries? *

$20.48
$62.17
$35.93
$62.10

Answers

Answer:

Step-by-step explanation:

62.17

Help please <3 Might give brainiest if the answer is correct

Answers

Answer:

c

Step-by-step explanation:

The general form of a reciprocal function is r(x) = a / (x - h) + k. The graphs of reciprocal functions are made up of branches, which are the two main parts of the graph; and asymptotes, which are horizontal and vertical lines that the graph approaches but doesn't touch.

Answer:

I'm pretty sure it's graph C

Can someone help me with this problem?

Answers

Answer:

147

Step-by-step explanation:

add the 2 sides together 19+14=33 then take 33 and subtract from 180. bc thats the rule btw. So 180-33= 147 hope this helps :))

ILL MARK AS BRAINLESS PLS HELP

Answers

Answer 0.01

Step-by-step explanation:

Help me with this!!!!!

Answers

Answer:

yes

Step-by-step explanation:

the answer is true!.

In ΔIJK, i = 850 inches, j = 250 inches and ∠K=80°. Find the length of k, to the nearest inch.

Answers

Answer:

886 inches

Step-by-step explanation:

Because we know the length for sides I and J, we can use the pythagorean theorem to get K. 850^2 + 250^2=KY^2. 850^2 = 722,500, and 250^2 = 62,500. 722,500 + 62,500 = 785,000. 785,000 to the square root rounded to the nearest inch is 886 inches.

Answer: 843

Step-by-step explanation:


The table above represents what type of function?
A. neither linear nor nonlinear
B. nonlinear
C. linear and nonlinear
D. linear

Answers

Answer:linear

Step-by-step explanation:

When plotting the dots a line is seen

find the slope between the point (a+b,4m-n) and (a-b,m+2n)​

Answers

Answer:

m = -3m+3n/-2b

Step-by-step explanation:

Slope is expressed as;

m = y2-y1/x2-x1

Given the coordinates (a+b,4m-n) and (a-b,m+2n)​

m = (m+2n)-(4m-n)/(a-b)-(a+b)

m = m+2n-4m+n/a-b-a-b

m = m-4m+2n+n/a-a-b-b

m = -3m+3n/-2b

Hence the required slope is m = -3m+3n/-2b

A number minus the product of 36 and its reciprocal is less than zero. Find the numbers which satsify this condition​

Answers

Answer:

A number minus the product of

4

and its reciprocal is less than zero. Find the numbers which satisfy this condition.

AAny number less than

2

or between

0

and

2

BAny number between

2

and

2

CAny number less than

2

DAny number between

0

and

2

Solution

Let the number be x

Then

x

(

4

×

1

x

)

0

x

4

x

x

2

4

|

x

|

2

2

x

2

Step-by-step explanation:

The numbers which satisfy this condition is less than 1. it will be 0, - 1, -2, 0, -3, -4, -5, -6, -7..................

let

the number  = x

The reciprocal of 36 = 1 / 36

Therefore, a number minus the product of 36 and it's reciprocal can be express below

x - 36 × 1 / 36

Then when it is less than zero, it can be express as follows

x - 36 × 1 / 36 < 0 x - 1 < 0

The number(x) which satisfy this condition (x - 1 < 0) is less than 1. This means the numbers are 0 to negative infinity.

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kurt cut pizza wedges into 40 degrees. If each person eats one piece how many people can he feed with 2 whole pizzas

Answers

Answer:

18 people.

Step-by-step explanation:

Are you going to lay a protractor on the pizza and measure 40° ?) Multiply that by two(because theres two pizzas) so 18 people.

Can someone help me please!!

Answers

Answer:

Im pretty sure it's C

Step-by-step explanation:

Tell me if im wrong


4x + 3y = 17
5x – 2y = 4

Answers

Answer:

I solved with substitution since you weren't specific on how to answer it but I got ( 2,3 )

[x  =  2  , y  =  3]

Answer:

x=2

y=3

Step-by-step explanation:

[tex]\left \{{4x+3y=17{} \atop{5x-2y=4}} \right.[/tex]

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

4x+3y=17,5x−2y=4

To make 4x and 5x equal, multiply all terms on each side of the first equation by 5 and all terms on each side of the second by 4.

5×4x+5×3y=5×17,4×5x+4(−2)y=4×4

Simplify.

20x+15y=85,20x−8y=16

Subtract 20x−8y=16 from 20x+15y=85 by subtracting like terms on each side of the equal sign.

20x−20x+15y+8y=85−16

Add 20x to −20x. Terms 20x and −20x cancel out, leaving an equation with only one variable that can be solved.

15y+8y=85−16

Add 15y to 8y.

23y=85−16

Add 85 to −16.

23y=69

Divide both sides by 23.

y=3

Substitute 3 for y in 5x−2y=4. Because the resulting equation contains only one variable, you can solve for x directly.

5x−2×3=4

Multiply −2 times 3.

5x−6=4

Add 6 to both sides of the equation.

5x=10

Divide both sides by 5.

x=2

The system is now solved.

x=2,y=3

HELPPPPPP PLZZZZ OMG :(

Answers

Answer:

1. C

2. A

Step-by-step explanation:

The answer is A for the first one the second one is B -1

Please help!!!
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator. 45 : 63

Answers

Answer:

5:7

Step-by-step explanation:

In AUVW, the measure of ZW=90°, UV = 4.7 feet, and WU = 2.2 feet.
Find the measure of ZU to the nearest degree.

Answers

Answer:62∘

Step-by-step explanation:

SOH-CAH-TOA

\cos U = \frac{\text{adjacent}}{\text{hypotenuse}}=\frac{2.2}{4.7}

cosU=

hypotenuse

adjacent

=

4.7

2.2

\cos U = \frac{2.2}{4.7}

cosU=

4.7

2.2

U=\cos^{-1}(\frac{2.2}{4.7})

U=cos

−1

(

4.7

2.2

)

U=62.09\approx 62^{\circ}

U=62.09≈62

Answer: 62

Step-by-step explanation:

The sides LM, MN, and LN of LMN have lengths of 3, 4, and 5 respectively. Which triangle is congruent to LMN (edge)

Answers

Answer:

Its the third one

Step-by-step explanation:

i got it right of edg

Place the Decimal!
1. Santonio bought a box of cookies for $3.84. If there are 24 cookies
in the box, how much did Santonio pay per cookie?

Answers

0.16 so 16 cents per cookies

A cylinder has a base radius of 7in and a height of 3in. What is its volume in cubic in,
to the nearest tenths place?

Answers

The volume would be 461.8 in^3
The equation to find the volume of a cylinder is V=pi*r^2*h
Plug in the numbers provided above to give you V=pi*7^2*3 after plugging it into a calculator you get 461.8 in^3

The volume of the cylinder having a radius 7 in and a height 3 in is 461.8 cubic inches.

What is the volume?

The volume of the rectangular prism is defined as the space in three-dimension covered by the rectangular prism having the sides Length, Width, and Height.

For the cylinder, the volume will be calculated by the radius and the height of the cylinder.

Given that the height of the cylinder is 3 in and the radius of the cylinder is 7 in.

The volume of the cylinder will be calculated as:-

V = πr²l

V = π x ( 7 )² x 3

V = 461.8 cubic nches

Therefore, the cylinder will have a volume of 461.8 inches.

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Please help fast I got to turn it in

Answers

613, hope this helps

- If you can answer this calculus thing, you are the Brainliest -

The function f(x) has values as given in the table below.

A 2-column table with 6 rows. Column 1 is labeled x with entries 1.99, 1.999, 1.9999, 2.0001, 2.001, 2.01. Column 2 is labeled f (x) with entries 0.505, negative 0.827, 0.306, negative 0.306, 0.827, negative 0.506.

Find Limit of f (x) as x approaches 2 f(x), if it exists.

2
0.3
0
DNE

*The clock is ticking*

Answers

Answer:

D

Step-by-step explanation:

Edge

Answer:

d

Step-by-step explanation:

Pls Help Me With This Question! It's 8th Grade Math!

Answers

Answer:

y= 4/3x

Step-by-step explanation:

Answer:

y= 4/3x

Step-by-step explanation:

A restaurant charges $5.00 for a slice of pizza that is 1/3 of a pizza and $4.50 for a slice that is 1/5 of a pizza. One day they cooked 8 pizzas that were all the same size. If they sell all the slices, would they make more money by slicing each pizza into thirds or fifths? How much more? Explain.​

Answers

Answer:

5ths

Step-by-step explanation:

Given that:

Price of whole pizza (A) = 5 × 3 = $15Price of whole pizza (B) = 4.50 × 5 = $22.50

They make 8 whole pizzas.

Therefore

Thirds (A) = 15 × 8 = $120Fifths (B) = 22.50 × 8 = $180

They'll make more money if they slice it into fifths.

180 - 120 = $60

Because if they slice it into thirds, total profit will be $60 less

____________________

#IndonesianPride - kexcvi

If John gets paid $340 a week and needs $29482 for a house. How many weeks will it take to save enough money.​

Answers

87 weeks of saving, yikes!

Answer:

86.71 or 87 weeks

Step-by-step explanation:

29482/340= 86.71

5. A 200g packet of Oreo's costs $3, Calculate How much would a 50g packet cost?

Guyss helpppp plss

Answers

Answer:

1$ because yo cut it down AND get your answer

the answer is $0.75 :)

When a football is punted, it goes up in the air, reaches a maximum altitude, and then comes back down. We can assume that the football follows a parabolic path. When the ball was kicked it was one foot above the ground. One second later, it was 20 feet above the ground. Four seconds after it was kicked it was 35 feet above the field.

What is the quadratic equation?

Answers

Answer

look ate image i just send u that´s the answer on the pice of paper

Step-by-step explanation:

The equation of the parabola is given by y=x²+19

What are quadratic equations?

A quadratic equation can be written in the standard form as ax2 + bx + c = 0, where a, b, c are constants and x is the variable. The values of x that satisfy the equation are called solutions of the equation, and a quadratic equation has at most two solutions.

Given here: In t=1 sec the football's height was 20 feet and for t=4 the height of the football was 35 feet.

Let the path of the football be a parabola and facing downward.

Thus the equation of the parabola must be y=-4ax²+c

But the parabola passes through the points (1,20) and (4,35)

Thus substituting the points on the equation of the parabola we get

20=-4×1²×a+c & 35=-4×4²a+c

20=-4a+c &35=-64a+c

Solving for a we get

          a=-1/4

Thus c=19

∴The equation of the parabola is given by

y=x²+19

Hence, The equation of the parabola is given by y=x²+19

Learn more about the quadratic equation here:

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Which Superhero has the greater miles to second ratio
------------------------------------------------------------------------------------------
Choices are:
------------------------------------------------------------------------------------------
A) Super-Man
B) Iron-man
C)Neither they are both equivalent
------------------------------------------------------------------------------------------

Answers

Answer:

Super Man

Have a great day!

Rewrite 8x - 7 as the product of two factors

Answers

Answer:

factors are any group of number or expressions which, when multiplied, produce another number or expression.

Basic example:  4 can be broken into 2 factors---2 and 2.  2 times 2 = 4

Example using an unknown:

2X + 6 = 2 * (X + 3)

In the given problem, there is no whole-number common factor.  A normal convention would be to factor based on the unknown term----thus 8X is factored into 8 and X.

So:  8X + 7 = 8 ( X + 7/8 )

The following would also be correct:

8X + 7 = 4 ( 2X + 7/4 )

Step-by-step explanation:

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