Mr. Jones is building the garage shown below. What is the volume of the garage?

The roots of a quadratic equation and the zeroes of a quadratic equation are related in the following form: [tex]\sum\limits_{i= 0}^{2} c_{i}\cdot x^{i} = \prod \limits_{j= 1}^{2} (x-r_{j}) = 0[/tex].

Polynomials are algebraic entities that satisfy the following condition:

[tex]p(x) = \sum\limits_{i= 0}^{n} c_{i}\cdot x^{i} = \prod \limits_{j= 1}^{n} (x-r_{j})[/tex]   (1)

Where:

If we have that [tex]p(x) = 0[/tex], then there are n values of x such that the equation is satisfied and those values are called zeroes. For the case of a quadratic equation, there are two zeroes.

[tex]\sum\limits_{i= 0}^{2} c_{i}\cdot x^{i} = \prod \limits_{j= 1}^{2} (x-r_{j}) = 0[/tex]   (2)

Please note that the right part of (2) contains the roots of the polynomial and (2) represents a relationship based on the closure properties for algebraic fields.

Therefore, the roots of a quadratic equation and the zeroes of a quadratic equation are related in the following form: [tex]\sum\limits_{i= 0}^{2} c_{i}\cdot x^{i} = \prod \limits_{j= 1}^{2} (x-r_{j}) = 0[/tex].

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Answer:

Your answer would be 8,770.

Step-by-step explanation:

the numbers list as 0,085-0,785-0,870-7,780-8,750-8,770 so you would be correct saying that 8,770 is the largest number.

Answer:

[tex]\tt B)\;93^o[/tex]

Step-by-step explanation:

[tex]\tt 2(19x+1)+(19x+1)+15x=360[/tex]

[tex]\tt 38x+2+19x-2+15x=360[/tex]

[tex]\tt 38x+19x+15x+2-2=360[/tex] (Add similar elements)

[tex]\tt 72x+2-2=360[/tex] (2-2=0)

[tex]\tt 72x=360[/tex]

[tex]\tt \cfrac{72x}{72}=\cfrac{360}{72}[/tex] ( Divide both sides by 72)

[tex]\tt x=5[/tex]

Now,

m∠km:-

[tex]\tt 19x-2[/tex]

[tex]\tt 19(5)-2[/tex] (Multiply 19*5= 95)

[tex]\tt =95-2[/tex] (Subtract)

[tex]\tt = 93[/tex]

Therefore, m∠km=93° is the answer.

_____

Answer:

Step-by-step explanation:

In the first equation, -4 x -b should be postive 4b, so +4b, because a negative times a negative equals a postive

Answer: 7

Step-by-step explanation: -4(6 - b) = 4

-24 + 4b = 4

The negative turns into a postive for 4b because two negatives make a postive.

4b (positive) = 28

b = 7

Answer:

8 3/4

Step-by-step explanation:

because each serving is 04 cups all you need to do is divide 3 1/2 by 0.4.

first convert 3 1/2 into decimal which would be 3.5. then divide 3.5 by 0.4

3.5/0.4

=3.5x10/0.4x10

=35/4

=8 3/4

The first player using Xs does indeed have a strategy to always win by placing an X in the Middle right box.

When the first player places an X in the middle right spot, the second player will have to place an O in two places to avoid the first player winning.

They would have to place an O in the middle left space and in the bottom right space. Seeing as they can't place an O in two boxes at once, the first player will be able to place an X in the empty box out of the two, and win.

In conclusion, there is a winning strategy.

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Step-by-step explanation:

The first player has two possible winning moves.

Regardles the next move the first player has one of the two options next: middle left or bottom right box

Regardles the next move the first player has one of the two options next: middle right or top left box

Answer:

Step-by-step explanation:

Isolate the term of x from one side of the equation.

First, add by 9 from both sides.

x-9+9=-21+9

Solve.

-21+9=-12

X=-12

Switch sides.

x+10=112

Subtract by 10 from both sides.

x+10-10=112-10

Solve.

112-10=102

X=102

Switch sides.

x-30=14

Add by 30 from both sides.

x-30+30=14+30

Solve.

x=44

Switch sides.

x-12=3

Add by 12 from both sides.

x-12+12=3+12

Solve.

Add the numbers from left to right.

3+12=15

x=15

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

486 square inches.

Step-by-step explanation:

126 = w + 6w + w + 6w

126 = 14w

width = 9 inches

A = wl

A = (9)(9*6)

A = 486 square inches

Answer:

y=-3x

Step-by-step explanation:

Answer:

I believe D should be the correct answer

Step-by-step explanation:

so, they want to sell 200,000 tickets (and we assume they can really sell all of these).

they have to pay the prize money afterwards :

1 × $8,000 = $8,000

10 × $300 = $3,000

75 × $50 = $3,750

--------------

$14,750

and they have to pay for the ticket production at the beginning.

this is not really well defined, but I assume the following :

C(20) = 4500 + 6x

x = units of 10,000 tickets (because of the functional argument of 20, and we have to deal with 200,000 tickets).

that means the cost for these 200,000 tickets is then

4500 + 6×20 = $4,620

$4,500 are fixed costs insurgent of the number of tickets (like for creating the design, configuring the printing machines for the design, ...).

and 6×20 = $120 are the cost of actuality printing the tickets ($6 per 10,000 ticket prints).

so, the total expenses are

$14,750 + $4,620 = $19,370

under the assumption they can sell all 200,000 tickets to just break even, the prize for each ticket must be

19,370 / 200,000 = $ 0.09685 ≈ $0.10

if my assumptions are wrong, please adapt the numbers in the calculations i showed you here.

for example, what if the x in the printing cost is per ticket and not per 10,000 tickets ?

then the printing costs would be

4500 + 6×200000 = $1,204,500

and the total expenses would be

$14,750 + $1,204,500 = $1,219,250

and the prize per ticket would have to be

1,219,250 / 200,000 = $ 6.09625 ≈ $6.10

The total amount of all the prize money is $14,750, and the price of each of the 200,000 raffle tickets in order to break even should be $0.08.

Given that to raise money for malaria research the New York City Rotary Club is going to sell 200,000 raffle tickets, and one ticket will have an 8000 dollar prize attached to it, while ten tickets will have a 300 dollar prize attached to it, and seventy-five tickets will have a 50 dollar prize, to determine what is the total amount of all the prize money and what should be the price of each of the 200,000 raffle tickets in order to break even, the following calculation must be made:

Therefore, the total amount of all the prize money is $14,750, and the price of each of the 200,000 raffle tickets in order to break even should be $0.08.

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Answer:

Answer: the equation of the line is y=−3.

Step-by-step explanation:

Since the slope equals 0, then the line is horizontal.

This means that the equation of the line doesn't contain x.

Thus, the equation of the line is y=−3.

Answer:

2 7/24

Step-by-step explanation:

First we have to add the gallons of two cow of each owner:

Hank's cows: 4 3/4 + 4 1/8

Add the whole numbers:

4 + 4 = 8

Now for 3/4 and 1/8

Find common

6/8 + 1/8

= 7/8

Put together :

8 7/8

Debra's cows: 5 1/2 + 5 2/3

Add the whole number

5 + 5 = 10

Now for 1/2 and 2/3

3/6 + 4/6

1 1/6

10 + 1 1/6

= 11 1/6

Since now we know that:

Hank - 8 7/8

Debra - 11 1/6

we can solve the question:

How many more gallons of milk did Debra's two cows produce on that compared to Hank's two cows?

Solution:

11 1/6 - 8 7/8

Subtract whole number

11 - 8 = 3

Now for 1/6 and 7/8

4/24 - 21/24

4-21/24

-17/24

2 7/24

~lenvy~

Answer:

2 7/24

Step-by-step explanation:

Hank Cows:

4 3/4 and 4 1/8

Debra Cows:

5 1/2 and 5 2/3

To find the difference between Hank cows and Debra cows..

we first have to add both cows together:

4 3/4 + 4 1/8 = 8 7/8  {Hank}

5 1/2 + 5 2/3 = 11 1/6  {Debra}

Since now we know Hank and Debra total gallons of milk we can solve and find out the difference.

11 1/6 - 8 7/8 = 2 7/24

Hence, Debra have 2 7/24 more gallons of milk than Hank.

[RevyBreeze]

The probability of choosing a number that is not a multiple of 2 is P = 0.44

We need to count the number of options for each digit.

The total number of combinations is the product between the numbers of options:

C = 8*9*9 = 648

If we want our number to not be a multiple of 2 then it must end in a odd digit, the combinations that meet that condition are:

C = 8*9*4 = 288

Then the probability of selecting a 3 digit number that is not a multiple of 2 is:

P = 288/648 = 0.44

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Answer:

Option C.

Step-by-step explanation:

Perimeter = 2L + 2h

[tex]P=2(5x^{2}y) +2(3y^{3} )=10x^{2} y+6y^{3}[/tex]

Hope this helps

Answer:

  tan(S) = 12/5

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you the tangent ratio is ...

  Tan = Opposite/Adjacent

In the given triangle, the side opposite angle S is RT, which has length 12. The side adjacent to angle S is ST, which has length 5. Then the tangent of angle S is ...

  tan(S) = RT/ST

  tan(S) = 12/5

_____

Additional comment

The rest of the trig functions in this triangle are ...

  sin(S) = 12/13

  cos(S) = 5/13

  tan(R) = 5/12

  sin(R) = 5/13

  cos(R) = 12/13

Answer:

tan(S) = [tex]\frac{12}{5}[/tex]

Step-by-step explanation:

Hi there!

We are given ΔRST, where ST=5, RT=12, and RS=13

We want to find the tangent of angle S (the notation tan(S) means "tangent of angle S")

In trigonometry, tangent refers to the ratio of the opposite side/adjacent side.

The opposite side is the side that is opposite to the angle that we are referencing (in this case, angle S); in this case, that side is RT, which is 12

The adjacent side is the leg that is adjacent to the opposite side; in this case, that side is ST, which we were given as 5

Therefore, tan(S) will be [tex]\frac{RT}{ST}[/tex], or [tex]\frac{12}{5}[/tex].

Hope this helps!

Answer:

  1982.0 ft³

Step-by-step explanation:

The composite figure can be decomposed into a cube and a square pyramid. The volume is the sum of the volumes of these.

__

The square base of the pyramid is 12 ft on each side, so the diagonal of the base is 12√2 feet. (The diagonal of a square is √2 times the side length.) Then the distance from a corner to the center of the base is half that, or 6√2 feet.

That distance and the height of the pyramid form a right triangle whose hypotenuse is the given 10 ft measure of the length of the edge of a face of the pyramid. Then the height can be found using the Pythagorean theorem:

  h² +(6√2)² = 10²

  h² = 100 -72 = 28

  h = 2√7 ≈ 5.291503 . . . ft

The volume of the pyramid is ...

  V = 1/3Bh = 1/3s²h

  V = 1/3(12 ft)²(5.2910503 ft) ≈ 253.992 ft³

__

The volume of a cube is given by ...

  V = s³

  V = (12 ft)³ = 1728 ft³

__

The total volume of the figure is the sum of the pyramid volume and the cube volume:

  total volume = 253.992 ft³ +1728 ft³ = 1981.992 ft³

The volume of the figure is about 1982.0 ft³.

_____

Additional comment

Your figure for the volume seems to assume the height of the pyramid is 8 feet. That length is the slant height of one face of the pyramid. It would be the hypotenuse of a right triangle whose other legs are 6 ft and the height of the pyramid. Then we would have ...

  h² +6² = 8²

  h² = 64 -36 = 28 . . . . as above

The pyramid height is the perpendicular distance from the plane of the base to the peak. It is measured through the middle of the volume, not along one face.

Answer:

66.42 degrees

Step-by-step explanation:

Cos(angle B) = adj / hyp = 2/5

arc cos (2/5) = angle B = 66.4 2 degrees

Answer:

The

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Answer:

1/5

Step-by-step explanation:

jack + 4 friends = 5 people

5 people would each get 1 slice

Answer:

3.15g

Step-by-step explanation:

2.2 g of the​ substance, to the nearest tenth of a​ gram, will be present after 9 ​yr.

The formula for exponential growth is y = y₀.e^(kt).

The formula for exponential decay is y = y₀.e^(-kt).

Given, 10g of a radioactive substance is present initially and 4 yr later only 5.0g​ remain.

∴ y₄ = y₀.e^(kt).

5 = 10.e^(4k).

e^(4k) = 1/2.

lne^(4k) = ln(1/2).

4k = - 0.69.

k = - 0.69/4.

k = - 0.17.

At this rate after 9 years later the amount of substance left will be,

y₉ = 10.e^(-0.17×9).

y₉ = 10.e^(-1.53).

y₉ = 10/e^(1.53).

y₉ = 10/4.62.

y₉ = 2.16 g.

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Step-by-step explanation: please see attached to PDF document.

Answer:

a) 6

b) 1/3

c) 2

Step-by-step explanation:

a) 3 ( x + 1 ) - x = 15. expand the bracket

3x + 3 - x = 15

2x + 3 = 15. collect the like terms

2x = 15 - 3.

2x = 12.

x = 12/2 = 6

b) 5 ( x + 2 ) - 2x = 11. expand the bracket

5x + 10 - 2x = 11

3x + 10 = 11. collect the like terms

3x = 11 - 10

3x = 1

x = 1/3

c) 6 ( 1 - 2x ) = - 4 - 7x. expand the bracket

6 - 12x = -4 -7x. collect the like terms

6 + 4 = -7x + 12x

10 = 5x

or

5x =. 10

x = 10/5 = 2

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The probability of on-time arrival in class given that the subject is biology is, 82.4%.

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that;

The probabilities by subject of on-time assignment submission and on-time arrival in class are given in the table.

Here, the table is,

Subject:      On-time Assignment:     On-time Arrival to Class:

PHYSICS                  89.7%                                     82.3%

MATH                        88.2%                                     88.7%

CHEMISTRY             89.4%                                     83.1%

BIOLOGY                  90.1%                                     82.4%

TOTAL                       88.5%                                     84.7%

Now, from table;

The probability of on-time arrival in class given that the subject is biology is, 82.4%.

Hence, the probability of on-time arrival in class given that the subject is biology is, 82.4%.

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Answer:

99.9 [tex]cm^{2}[/tex]

Step-by-step explanation:

Given, AB=13 cm, BC=4 cm

AC is the diagonal of parallelogram ABCD.

Also AC=16 cm

We know, △ABC≅△ACD     [S−S−S Congruence]

Also, area of parallelogram ABCD = Area of △ABC + Area of △ACD

                                            = 2 × Area of △ABC

                                            = [tex]2\sqrt{s(s-13)(s-4)(s-15)}[/tex]

         [tex]s= \frac{13+15+4}{2}[/tex]                 = [tex]2\sqrt{16(16-13)(16-4)(16-15)}[/tex]

             = 16                          = 99.9

Answer:

3/8

Step-by-step explanation:

Values we are given :

We know that :

Therefore,