Wally uses his own recipe for mixing glittered paints. He recently mixed 3 1/3 cups of glitter to make 2 1/2 gallons of paint. How much glitter does Wally use in each gallon of paint

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]

Answer:

2 rides & 4 games

Step-by-step explanation:

2 rides=$8

4 games=$8

8+8=$16

Point (4,2), represents that Victoria played 4 games (x = 4) and went on 2 rides (y = 2).

A graph can be defined as a pictorial representation or a diagram that represents data or values.

The number of games Victoria played, x, and the number of rides Victoria went on, y.

Each game costs $2 and each ride costs $4, so we can set up the following system of equations:

2x + 4y = 16

x + y = 6

To graphically solve this system of equations, we can plot the equations on the same coordinate plane and find the point where they intersect. This point will represent the values of x and y that satisfy both equations.

To plot the equations, we can first graph the equation 2x + 4y = 16.

The slope is 2 and the y-intercept is 4, so we can plot the line by starting at the point (0,4) and moving 2 units up and 1 unit to the right to find the next point on the line.

We can then connect this point to the first point with a straight line to complete the graph of the equation.

Next, we can graph the equation x + y = 6 similarly.

The point will represent the values of x and y that satisfy both equations.

In this case, we can see that the lines intersect at point (4,2), which means that Victoria played 4 games (x = 4) and went on 2 rides (y = 2).

Learn more about the graphs here:

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Answer:

98 since vertical angels have same angles

Step-by-step explanation:

Answer:

B: x = -5

Step-by-step explanation:

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.

Answer:

g

Step-by-step explanation:

Answer:

80 potatoes

Step-by-step explanation:

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

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:

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;

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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:

Step-by-step explanation:

If the center of the circle is at the origin, the general formula for the circle is

x^2 + y^2 = r^2.

Since r  = 2 units in this particular problem, the equation of the circle is:

x^2 + y^2 = 2^2,  or  x^2 + y^2 = 4

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:

that's a good color to wear

Step-by-step explanation:

:)

Answer:

each number plus itself so it will be 06,144

Answer:

6.633249581 and I would say it's irrational

Step-by-step explanation:

:)

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:

x = 4, y = 4 or you can say (4, 4)

Step-by-step explanation:

let third angle be x

60° + 60° + x = 180° (Δ sum property)

x = 60°

so, this is a equilateral triangle (all Δ equal)

in equilateral triangle --> all sides are equal

so, therefore =>>

7x + 19 = 11x - 89

19 + 89 = 11x - 7x

108 = 4x

108 ÷ 4 = x

27 = x

so variable

1.) 7x + 19

= 7(27) + 19

= 189 + 19

= 208

2.) 11x - 89

= 11(27) - 89

= 297 - 89

= 208

Answer:

Step-by-step explanation:

Answer:

You can try searching it up or going to math.way

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:

Speed = distance / time

= 6/3 =2 ft/sec

Time = distance / speed

= 60/2

= 30 seconds

Answer:

C.

Step-by-step explanation:

B. is your answer

≈Godbless

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: 9 hours

Step-by-step explanation:

13.5 hours / 1.5 hours = 9 hours