If 2x - 3y = 24 and 3x + 4y = 2, what is the value of x - y ?

Answer:

(-1.875, -1.625)

Step-by-step explanation:

We want to find the point on the equation 2*x + 6*y + 1 = 0 which is closest to the point (-5, -3)

Remember that the distance between two points (a, b) and (c, d) is:

D = √( (a - c)^2 + (b - d)^2)

First we can write our equation as a line in the slope intercept form:

y = -(2/6)*x - 1

Now we could minimize the equation:

D = √( (x - (-5))^2 + (y - (-3))^2) = √( (x + 5)^2 + (y + 3)^2)

D = √(  ( x + 5)^2 + (  -(2/6)*x - 1 + 3) ^2)

Then we can minimize:

D^2 = (x + 5)^2 + ( -(2/6)*x + 2)^2

       = x^2 + 10*x + 25  + (4/36)*x^2  - (8/6)*x + 4

       =  (1 + 4/36)*x^2 + (10 - 8/6)*x + 29

        = (40/36)*x^2 + (52/6)*x + 29

This is a quadratic equation whose leading coefficient is positive, then the minimum of this equation is at the vertex.

The vertex is at the x-value such that (D^2)' = 0

Then:

(D^2)' = 2*(40/36)*x + (52/6)

This needs to be zero then:

0 = 2*(40/36)*x + (52/6)

-52/6 = (80/36)*x

(-52/6)*(36/80) = x

-1.875 = x

And the y-value when x = -1.875 is:

y = -(2/6)*-1.875 - 1

y = -1.625

Then the point on the line 2x+6y+1=0 that is closest to (-5,-3) is the point (-1.875, -1.625)

Answer:

x = -2 and y = 1

Step-by-step explanation:

→ Rearrange x - y = -3 to make y the subject

-y = - x - 3 so y = x + 3

→ Substitute into 2x + y = -3

2x + x + 3 = -3

→ Simplify

3x + 3 = -3

→ Minus 3 from both sides

3x = -6

→ Divide both sides by 3

x = -2

→ Substitute x value into first equation

-4 + y = -3

→ Add -4 to both sides

y = 1

Answer:

Speed = distance / time

= 6/3 =2 ft/sec

Time = distance / speed

= 60/2

= 30 seconds

Answer:

Step-by-step explanation:

help me The science teacher brought a goldfish to her room at school. A total of 36 students voted on the name of the goldfish. The results of the vote are shown in the circle graph.

A circle graph with three sections is shown. The sections are labeled: Goldy, sixty degrees, Slinky, one hundred twenty degrees, Finny, one hundred eighty degrees.

Answer:

A

Step-by-step explanation:

Answer:

Ethnically diverse people loving in the same area

Answer:

[tex]T_7 = 11[/tex]

[tex]T_n = 2n- 3[/tex]

Step-by-step explanation:

Given

[tex]S_n = n^2 -2n[/tex]

[tex]T_n = S_n - S_{n-1}[/tex]

Solving (a): T7

Substitute 7 for n in [tex]T_n = S_n - S_{n-1}[/tex]

[tex]T_7 = S_7 - S_{7-1}[/tex]

[tex]T_7 = S_7 - S_6[/tex]

Calculate S7 and S6

[tex]S_n = n^2 -2n[/tex]

[tex]S_7 = 7^2 - 2 * 7 = 35[/tex]

[tex]S_6 = 6^2 - 2 * 6 = 24[/tex]

So:

[tex]T_7 = 35 -24[/tex]

[tex]T_7 = 11[/tex]

Solving (b): Tn

[tex]T_n = S_n - S_{n-1}[/tex]

Where [tex]S_n = n^2 -2n[/tex]

Calculate[tex]S_{n-1}[/tex]

We have:

[tex]S_{n-1} =(n-1)^2 - 2(n-1)[/tex]

Open brackets

[tex]S_{n-1} = n^2 -2n + 1 -2n +2[/tex]

[tex]S_{n-1} = n^2 -2n-2n + 1 +2[/tex]

[tex]S_{n-1} = n^2 -4n + 3[/tex]

So:

[tex]T_n = S_n - S_{n-1}[/tex]

[tex]T_n = n^2 - 2n - (n^2 -4n + 3)[/tex]

[tex]T_n = n^2 - 2n - n^2 +4n - 3[/tex]

Collect Like Terms

[tex]T_n = n^2 - n^2- 2n +4n - 3[/tex]

[tex]T_n = 2n- 3[/tex]

Uhm... I’m sorry I don’t really know the answer to your question I’m just answering it for points....

Answer:

6.633249581 and I would say it's irrational

Step-by-step explanation:

:)

9514 1404 393

Answer:

  1. 1/3 × 3/7 = 1/7

  2. 1/2×(1 -1/4) = 3/8

Step-by-step explanation:

Attached is my attempt at the required drawings. Yours may be different, based on the methods used by your teacher.

Answer: y=x+60

So y=mx+b is slope intercept form

y=x+60

m=1/1 because we go equally up as we go right so just put x

b=60 because we start at 60

Hope this helps

Answer:

80 potatoes

Step-by-step explanation:

Answer:

3:5

Step-by-step explanation:

To find the simplest ratio, divide each number by 2:

6/2

= 3

10/2

= 5

So, the simplest ratio of triangles to squares is 3:5

Answer:

3 inches

Step-by-step explanation:

1. Volume of a sphere

V = 4/3πr^3

2. Plug in numbers

V = 36π

r = ?

36π = 4/3πr^3

27=r^3

[tex]r=\sqrt[3]{27}[/tex]

r = 3

Answer:

98 since vertical angels have same angles

Step-by-step explanation:

Answer:

B: x = -5

Step-by-step explanation:

Answer:19

Step-by-step explanation:perimeter is everything added since it’s a rectangle 10 on both length sides will be 20 so 58-20 is 38 divide that by 2 and that’s your answer.

Answer:

11. 78

12. 4x² - 3x - 1

Step-by-step explanation:

11. Sum of n whole numbers = ½(n² + n)

Multiply

½*n² + ½*n

= n²/2 + n/2

To find the sum of the first 12 whole number, substitute 12 for n into the equation.

= 12²/2 + 12/2

= 144/2 + 12/2

= 72 + 6

= 78

12. Area of trapezoid = ½(a + b)*h

Where,

a = 5x - 4

b = 3x + 2

h = x + 1

Area = ½(5x - 4 + 3x + 2)*(x + 1)

Area = ½(8x - 2)*(x + 1)

Area = ½[8x(x + 1) -2(x + 1)]

= ½[8x² + 8x - 2x - 2]

Add like terms

= ½(8x² - 6x - 2)

= ½(8x²) - ½(6x) - ½(2)

= 4x² - 3x - 1

Answer:

27

Step-by-step explanation:

Carlotta can feed 3 times her dog with leftover in this bag of dog food

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. If an event can occur in m different ways and if following it, a second event can occur in n different ways, then the two events in succession can occur in m × n different ways.

WE have been given that Carlotta has 2/3 of a bag of dog food  and She gives her dog 2/9 of the bag at each feeding.

The bag of dog food = 2/3

Let she feed her dog with leftover in this bag of dog food = X

Therefore, X = 2/3 × 9/2

X = 18 / 6

X = 3

Hence, Carlotta can feed 3 times her dog with leftover in this bag of dog food

Learn more about the unitary method, please visit the link given below;

https://brainly.com/question/23423168

#SPJ5

Answer:

g

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

Answer:

Y=-1

Step-by-step explanation:

2(-1)+3=y

-2+3= -1

Answer:

The lateral surface of an object is all of the sides of the object, excluding its base and top. The lateral surface area is the area of the lateral surface

Step-by-step explanation:

Answer:

m<FCE = 45°

Step-by-step explanation:

Given that ∆ABD ≅ ∆FEC, therefore,

<A ≅ <F

<B ≅ <E

<ADB ≅ <FCE

m<ADB = 45°

Therefore,

m<ADB = m<FCE = 45°

m<FCE = 45°

9514 1404 393

Answer:

  Chun is correct

Step-by-step explanation:

The angle bisector divides the sides of the triangle proportionally. Any proportion that is written should equate ratios of corresponding sides.

Chun's proportion correctly relates the top-side measures to their corresponding bottom-side measures:

  top short : bottom short = top long : bottom long

  5 / 8 = 15 / x

__

Traci's error is that she mixes top-side and bottom-side measures. Her incorrect relation is ...

  top short : bottom long = bottom short : top long

She has used top:bottom for short measures and bottom:top for long measures. This mixing will give Traci an incorrect solution.

__

Chun's proportion correctly gives x=24.

Answer:

Step-by-step explanation:

Chun; by the Triangle Angle Bisector Theorem, the correct proportion is  58=15x.