(- 18) × (- 5) × (- 4) =

Answer:

[tex]\boxed{4x^{2} - 48x + 144}[/tex]

Step-by-step explanation:

Given expression:

To simplify the expression, we will use the formula (a - b)² = a² - 2ab + b².

[Where "a and b" are the first and second term in (a - b)²]

[tex]\rightarrowtail (2x - 12)^{2}[/tex]

In this case, the first term of (2x - 12)² is "2x" and the second term is "12".

[tex]\rightarrowtail (2x)^{2} - 2(2x)(12) + (12)^{2} \ \ \ \ \ \ \ \ \ \ \ \ \ \ [\small\text{First term = a = 2x; Second term = b = 12]}[/tex]

Now, simplify the expression.

[tex]\rightarrowtail (2x)^{2} - 2(2x)(12) + (12)^{2}[/tex]

[tex]\rightarrowtail (2x)(2x) - (4x)(12) + (12)(12)[/tex]

[tex]\rightarrowtail \boxed{4x^{2} - 48x + 144}[/tex]

Answer:

Step-by-step explanation:

Let k represent the multiplier of the ratio units that will give actual dimensions. The the height can be represented by k, the breadth by 2k, and the length by 3k. The volume of the room will be ...

  V = LBH

  V = (3k)(2k)(k) = 6k³

  3072 m³ = 6k³ . . . . . use known volume

  512 m³ = k³ . . . . . . . divide by 6

  8 m = k . . . . . . . . . take the cube root

The height of the room is 8 m, its breadth is 16 m, and its length is 24 m.

Answer:

See below ↓↓↓

Step-by-step explanation:

Given :

Solving :

Solution :

We can find the bat's wholesale cost by working backwards -

Do $41 - 9 to get $32, then we can divide the 32 by the 4 to get $8.

Therefore, the wholesale cost of the bat is $8.

Happy to help!

Answer:

The bat's wholesale cost is $8

Step-by-step explanation:

You first have to subtract 9 from 41 as that will be 4 times the wholesale cost, which is $32. Then you have to divide 32 by 4, as we want to get the wholesale cost, not 4 times of the wholesale cost, and this would give us the wholesale cost, which is $8.

The amount of energy waste, in terms of hours which a 60-watt light bulb would remain on, is 61.6 hours then the correct option is B.

A ratio is an ordered couple of numbers a and b, written as a/b where b can not equal 0. A proportion is an equation in which two ratios are set equal to each other.

Marco leaves the bathroom faucet running for 22 minutes while he gets ready in the morning.

Running the faucet for 5 minutes wastes the same amount of energy as leaving a 60-watt light bulb on for 14 hours.

Then we have

[tex]\begin{aligned} \dfrac{5\ minutes}{14 \ hours } &=\dfrac{1\ minute }{x \ hours}\\\\x &= 2.8 \ hours \end{aligned}[/tex]

So, the rate is 2.8 hours per minute.

Since macro leaves the bathroom faucet running for 22 minutes. Then the waste of energy is leaving a 60-watt light bulb will be

→22 minutes × 2.8 hours/minute = 61.6 hours.

More about the ratio and the proportion link is given below.

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Answer:

A and C :)

Have an amazing day!!

Please rate and mark brainliest!!

Answer:

1)  [tex]y=x^2+2[/tex]

2)  [tex]y=x^2-4[/tex]

3)  [tex]y=x^2[/tex]

4)  [tex]y=x^2+6x+14[/tex]

Step-by-step explanation:

Question 1

Given points:  (-2, 6)  (-1, 3)  (0, 2)  (1, 3)

This is likely to be a quadratic equation with a vertex of (0, 2) since the points (-1, 3) and (1, 3) are symmetrical about x = 0

Vertex form of quadratic equation: [tex]y=a(x-h)^2+k[/tex]

(where (h, k) is the vertex)

[tex]\implies y=a(x-0)^2+2[/tex]

[tex]\implies y=ax^2+2[/tex]

To find a, input one of the points into the equation:

[tex](1, 3)\implies a(1)^2+2=3\implies a=1[/tex]

Therefore, the equation of the graph is [tex]y=x^2+2[/tex]

Question 2

If the parabola intersects the x-axis at (-2, 0) and (2, 0) then

[tex]y=a(x+2)(x-2)[/tex]

We are told that the y-intercepts if (0, -4).  Input this into the equation to find a:

[tex]\implies a(0+2)(0-2)=-4[/tex]

[tex]\implies -4a=-4[/tex]

[tex]\implies a=1[/tex]

Therefore,

[tex]\implies y=(x+2)(x-2)[/tex]

[tex]\implies y=x^2-4[/tex]

Question 3

Given points: (-2, 4)  (-1, 1)  (0, 0)  (1, 1)

This is likely to be a quadratic equation with a vertex of (0, 0) since the points (-1, 1) and (1, 1) are symmetrical about x = 0

Vertex form of quadratic equation: [tex]y=a(x-h)^2+k[/tex]

(where (h, k) is the vertex)

[tex]\implies y=a(x-0)^2+0[/tex]

[tex]\implies y=ax^2[/tex]

To find a, input one of the points into the equation:

[tex](-2,4)\implies a(-2)^2=4\implies a=1[/tex]

Therefore, the equation of the graph is [tex]y=x^2[/tex]

Question 4

[tex]f(x) = x^2 + 5[/tex]

If we wish to move the function to the left by 3 units, we substitute x for [tex]x+3[/tex]:

[tex]\begin{aligned}\implies f(x+3) & =(x+3)^2+5\\ & = x^2+6x+9+5\\ & = x^2+6x+14\end{aligned}[/tex]

[tex]\implies y=(x+3)^2+5[/tex]

Assuming there are 7. 5 gallons of liquid per cubic foot. The volume of the cup is: 1,193.8 gallons.

Using this formula

V =πh/3 [(r base)²+ ( r base) (r top) + (r top) ²]

Where:

height of cup (h)= 8 feet

radius of base of cup (r base)= 4 feet/2=2 feet

radius of top of cup (r top)= 6 feet/2=3 feet

Let plug in the formula

V =πh/3 [(8)²+ (2) (3) + (3) ²]

V =πh/3×8×19

V=152 π/3

Hence:

Volume of the cup in gallons=152 π/3 ×7.5

Volume of the cup in gallons=477.52208334564/3×7.5

Volume of the cup in gallons=1,193.8gallons

Therefore the volume of the cup is: 1,193.8 gallons.

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Answer:

b) Show that c= 52 and a =18 is a solution to

tickets sold and a represents the number of

this equation (not system).

Linear equation that models the given equation is 4c + 10a = 388 where c is the number of children ticket sold and a is the number of adult ticket sold. c = 52 and a = 18 is a solution to the linear equation. Multiplying a constant on both sides of the equation won't affect its solutions.

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line. This is the reason why it is named as a 'linear equation'.

Let number of children ticket sold be c.

Let number of adult ticket sold be a.

Cost of one children ticket = $4.

Cost of one adult ticket = $10.

Total sales = $388

Linear equation that models the above equation: 4c + 10a = 388

Checking if a = 18 and c = 52 is a solution of the equation. It can be done by substituting the values.

LHS: 4c + 10a = 4*52 + 10*18 = 388

RHS: 388

Hence, c = 52 and a = 18 is a solution to the linear equation.

Multiplying 2 to both sides of the equation:

2(4c + 10a) = 2(388)

8c + 20a = 776

Substituting c = 52 and a = 18.

8(52) + 20(18) = 776

c = 52 and a = 18 is still a solution to the linear equation.

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The probability is the ratio of the favorable event to the total number of events. Then the probability is 0.76%.

Probability means possibility. It deals with the occurrence of a random event. The value of probability can only be from 0 to 1. Its basic meaning is something is likely to happen.

The Art Club is displaying the students' works in the main hallway. In a row of 12 randomly ordered paintings.

Then the probability that Tim's and Abby's paintings are in the 6th and 7th positions will be

[tex]P = \dfrac{1}{^{12}P_2} \\\\\\P = \dfrac{1}{\dfrac{12!}{(12-2)!}}\\\\\\P = \dfrac{1}{132}\\\\\\P= 0.007575 \approx 0.0076 \ or \ 0.76 \%[/tex]

More about the probability link is given below.

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By definition of probability, the probability that a person surveyed was either male or had a cell phone is [tex]\frac{450}{600}[/tex]= 0.75

Probability is the greater or lesser possibility that a certain event will occur.

In other words, the probability is the possibility that a phenomenon or an event will happen, given certain circumstances. It is expressed as a percentage.

The union of events, AUB, is the event formed by all the elements of A and B. That is, the event AUB is verified when one of the two, A or B, or both occurs. AUB is read as "A or B".

The probability of the union of two compatible events is calculated as the sum of their probabilities subtracting the probability of their intersection:

P(A∪B)= P(A) + P(B) -P(A∩B)

The intersection of events, A ∩ B, is the event formed by all the elements that are, at the same time, from A and B. That is, the event A ∩ B is verified when A and B occur simultaneously.

In first place, let's define the following events:

The probability that a person surveyed was either male or had a cell phone is calculated as:

P(M∪C)= P(M) + P(C) -P(M∩C)

In this case, you know:

Replacing in the definition of probability:

P(M∪C)= [tex]\frac{220}{600}[/tex] + [tex]\frac{350}{600}[/tex] - [tex]\frac{120}{600}[/tex]

Solving:

P(M∪C)= [tex]\frac{220+350 -120}{600}[/tex]

P(M∪C)= [tex]\frac{450}{600}[/tex]= 0.75

Finally, the probability that a person surveyed was either male or had a cell phone is [tex]\frac{450}{600}[/tex]= 0.75

Learn more about probability:

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Answer:

H= 8 k = 11

Step-by-step explanation:

H= 8 k = 11

sqrt ( x^8 k^11) =  x^4 k^5 sqrt k

Answer:

1 over 20

Step-by-step explanation:

Given that:

a spinner and 4 cards

A Spinner ⇒ 5 equal sectors;Color: Blue,Purple,Yellow,Red,Green

Arrow point at purple

Four cards ⇒ Color : Red,Yellow,Blue,Pink

Jane spins the spinner & selects card without looking.

To Find - Probability spinner stops at purple & select pink card.

Solve:

Multiply 4 (the number of cards) with 5 (The number of equal sectors)

[tex]\frac{1}{5}\times\frac{1}{4}=\frac{1}{20}[/tex]          {1 × 1 = 1}    {5×4=20}

~lenvy~

Answer:

1 over 20

Step-by-step explanation:

Given the following:

1 spinner and 4 cards

A Spinner which has 5 equal sectors;Color: Green, Blue,Purple,Yellow,Red.

{Arrow point at purple}

Four cards ⇒ which color are Red,Yellow,Blue,Pink

Jane spins the spinner & selects card without looking.

To Find →  Probability spinner stops at purple & select pink card.

Since, purple and pink only has one in each of Spinner/card

Thus,

Spinner (5 equal sectors - 1/5}

Card {4 cards - 1/4}

1/4 × 1/5 = 1/20

Hence, probability spinner stops at purple & select pink card is [A] 1/20

[RevyBreeze]

Answer:

x=2+\sqrt{6}, :x=2-\sqrt{6}

Step-by-step explanation:

those are the 2 awnsers

Step-by-step explanation:

[tex](x - |2| ){}^{2} = 2 + {2}^{2} [/tex]

[tex]x - 2 = \sqrt{6} \\ x = + - \sqrt{6} + 2 \\ x = - \sqrt{6} + 2 \\ x = \sqrt{6} + 2[/tex]

Answer: (-1,-6)

Step-by-step explanation:

x^2+6x+3

g(x) = f(x-2)

replace all value of x in the f(x) function to (x-2)

(x-2)^2 + 6(x-2) + 34

(x-2)(x-2) + 6(x-2) + 34

expand through FOIL and distribution

x^2-4x+4+6x-12+3

combine like terms

x^2+2x-5

-b/2a = x value of vertex

-2/2(1) = x value

x value = -1

plug in -1 for all values of x in the g(x) equation to solve for y value

(-1)^2+2(-1)-5

1-2-5 = -6

y = -6

x = -1

(x,y) = (-1,-6)

The vertex of the considered function g(x) = f(x − 2) is given by: Option c: (-1,-6)

If a quadratic equation is written in the form

[tex]y=a(x-h)^2 + k[/tex]

then it is called to be in vertex form. It is called so because when you plot this equation's graph, you will see vertex point(peak point) is on (h,k)

This point (h,k) is called the vertex of the parabola that quadratic equation represents.

We first take out coefficient of x squared, and then inside the bracket, we try to make perfect square like situation.

So, we're given that:

Thus, we get:

[tex]g(x) = f(x-2) \\g(x) = (x-2)^2 + 6(x-2) + 3 \\g(x) = x^2 -4x + 4 + 6x - 12+3\\ g(x) = x^2 + 2x -5[/tex]

Converting g(x) to vertex form:

[tex]g(x) = x^2 + 2x - 5\\g(x) = x^2 + 2x + 1 - 1 -5\\g(x) = (x+1)^2 -9\\g(x) = (x - (-1) )^2 -6\\g(x) = (x-(-1))^2 + (-6)[/tex]

Comparing this with [tex]a(x-h)^2 + k[/tex], we get (h,k) = (-1,-6) as the coordinate of the vertex of the graph of g(x), as shown below.

Thus, the vertex of the considered function g(x) = f(x − 2) is given by: Option c: (-1,-6)

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1. - 3p^3 + 7p^2 - 3

2. 5a^3 - 5a^2

3. 6 + 7n^3

4. - 6n^3

5. a^2 + 2r^4

6. 9r^3 + 2r^4

7. 1

8. 6x^4 - 6x

9. - 7k^4 - 11k^2 + 6

10. 2n^5 - 2n^4 + 3n + 3

11. 14a^5 + 14a^4 - 10a^3 - 16a

12. - 14n^4 - 7n^2 + 8n + 7

13. 18x^5 + 6x^4 + 12x^3

14. 7r^3 - 3r^2 + 20r

15. 8n - 8n^4

16. - 2x^5 + 10x^4 + 5x + 14

17. 4x^5 - 15x^3 - 11x - 1

18. 5a^5 + 23a^2 - 11a

19. 15v^5 + 4v^3 - 24v^2

20. 2b^4 + 15b^3 - 3

Answer:

B

Step-by-step explanation:

20 × 2/5 = 8

15 × 2/5 = 6

5 × 2/5 = 2

p/s : the pic is for question no 7. i thought that you want the number 7 so i solved it first. then i reread your question. then i realized u actually want number six. so...

yeah, your welcome :)

Answer:

I think is B: 40.

Answer:

D

Step-by-step explanation:

Because I said so ho3

Answer:

Solution : A number is divisible by 11, if the difference of sum of its digits in odd places from the right side and the sum of its digits in even places from the right side is divisible by 11. Since difference is 11 which is divisible by 11, therefore 5918 is divisible by 11.

Step-by-step explanation:

Solution : A number is divisible by 11, if the difference of sum of its digits in odd places from the right side and the sum of its digits in even places from the right side is divisible by 11. Since difference is 11 which is divisible by 11, therefore 5918 is divisible by 11.

To find the surface area, we must define what is the surface area

In this case, we have a cube

  ⇒ which means all the sides have equal areas since all the side lengths

      are equal

That means the surface area

  ⇒ is equal to ⇒ 6 * (Area of One Side)        

        '6' comes from the # of sides on a cube

Surface Area = [tex]6 *\frac{1}{9} *\frac{1}{9} = \frac{6}{9 *9} =\frac{2*3}{3*3*3*3} =[/tex] 2/27

Hoped that helped!

Answer:

2.5782963e+29

Step-by-step explanation:

basically 19 times itself 63 times

Answer:

19^63  ,  3.6431483821774E+80

Step-by-step explanation:

Answer:

(10 , 3)

Step-by-step explanation:

When you reflect over the y-axis, you are flipping the sign of the x-coordinate.

Likewise, when you reflect over the x-axis, you are flipping the sign of the y-coordinate.

In this case, you are reflecting over the y-axis, and the pair given to you is (-10, 3). When you reflect over the y-axis, you must flip the sign of the x-coordinate.

(-10 , 3) reflected over the y-axis is (10 , 3).

~

Answer:

1320

Step-by-step explanation:

The sample ad 600 chips. They wanted to test 36000 chips. 600*60=36000

If 22 out of 600 chips were defective, and 600*60=36000

Then 1320 chips were defective out of the 36000 because 22*60=1320.

Answer:

Pi is exactly [tex]3.1415926535897932384626433832795[/tex]

Pi is often used in mathematical expressions, calculating measurements, and finding circumference as well as volume.

Q has coordinates

P is 6units left

R is 7units up

Option B

Answer:

B)  P (-4, 4) and R (2, 3)

Step-by-step explanation:

Q = (2, -4)

If ΔPQR is a right triangle, then

If PQ is 6 units, then

P = (2-6, -4) = (-4, -4) or

P = (2, -4+6) = (2, 2)

If QR is 7 units, then

R = (2-7, -4) = (-5, -4) or

R = (2, -4+7) = (2, 3)

Therefore, P (-4, 4) and R (2, 3)

Answer:

466,207,795.2 cm^3

Step-by-step explanation:

The equation to find both, the volume of the sphere and cube, are given.

The sphere:

V = [tex]\frac{4}{3}[/tex]πr^3

the radius is 7 ft therefore

V =  [tex]\frac{4}{3}[/tex]π7^3

The problem says to use 3 for pie therefore

V =  [tex]\frac{4}{3}[/tex](3)7^3

7 to the power of three is

V = [tex]\frac{4}{3}[/tex](3)343

[tex]\frac{4}{3}[/tex] and 3 cancel each other out to equal 4

V = 4 × 343

V = 1,372 ------> volume of sphere

______________________________________________

The cube:

V = Legth × width × height

V = 12 × 12 × 12

V =  1,728 ------> volume of cube

_______________________________________________

Total volume:

1,372 + 1,728 = 3,100 ft^3

But the question asks for the mesurement in centimeters so convert feet to centimeters using a calculator :)

3,100 ft^3 = 87,782,080 cm^3

Answer:

100

Step-by-step explanation:

Because 127 rounded is to 100, as if it goes over 150 then round it to 200 , but if it goes lower than 150 then it's 100.

Answer:

Zahra cannot make a triangle with these angle measures.

Step-by-step explanation:

Answer:

Roy eat 4 sweets

Step-by-step explanation:

Roy =R

Mike= (R-2)

Leen= 3(R+ R-2)

R + (R-2) + 6R-6 = 24

8R-8=24

8R=32

R=4

     Mike  4-2 = 2

     Leen 3(4+2) = 18

4+2+18=24