Find the volume of a cone

Penguins (P): 1 H + 2 Ft

Bears (B): 1 H + 4Ft

Heads Equation:  1P + 1B = 14   → -2(1P + 1B = 14)   →  -2P - 2B = -28

Feet Equation:    2P + 4B = 30 →   1(2P + 4B = 30)  →  2P + 4B = 30

                                                                                              2B = 2

                                                                                                B = 1

Heads Equation:  1P + 1B = 14   →  1P + 1(1) = 14  →  P = 13

Answer: 13 Penguins and 1 Bear

The possible number of solutions to the equations in the system is 2. A solution is a collection of data designated to the unexplored variables.

A solution is a set of values assigned to the unknown variables that ensure the equation's equality.

To put it another way, a solution is a value or a set of values (one for each unknown) that, when substituted for the unknowns, makes the equation equal.

The given system of equation is;

[tex]x^2+y^2=9\\9x+2y=16[/tex]

The standard equation of the  circle is;

[tex]\rm (x-h)^2+(y-k)^2=r^2[/tex]

On comparing the given equation with the standard equation;

The first equation shows the center is at origin(0,0). and radius is 3.

The second equation shows the given equation is a straight line.

As we know that the straight line can only intersect a circle at a maximum of 2 points.

Hence the possible number of solutions to the equations in the system is 2.

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Answer:

39 + 5d

Step-by-step explanation:

First multiply 5 by 9 and 5 by d then subtract 6 from 45 (which you get from multiplying 5 by 9) and you get 39 and multiply 5 by d so you get 39 + 5d

let's solve:-

[tex]⇒5(9 + d) - 6(given \: equation) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ ⇒by \: bodmas \: rule \: distribute \: 5 \: with \: 9 \: nd \: d \\ \\⇒ 45 + 5d - 6 (subtracting \: like \: terms) \: \: \: \: \: \: \: \: \\ \\⇒ 39 + 5d \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ [/tex]

Answer:

6 Lollipops in 5 bags and 6 KitKat Bars in 7 bags

Step-by-step explanation: Its 6 x 5 which equals 30 and 6 x 7 that equals 42. Hope it's correct :)

Answer:

8x11/2= 44 it's 44

Step-by-step explanation:

A=44 = LW = (2W-3)W = 2W^2 -3W

2W^2-3W -44 = 0

(2W-11)(W+4) = 0

2W-11 = 0

2W = 11

W = 11/2 = 5 1/2 meters

L=2W-3 = 11-3 = 8

8x11/2= 44

length = 8 m,  width = 5 1/2 m

Answer:

79-22=8h

Step-by-step explanation:

hope this helps!

The simplification of the given expression will be  [tex](-3x^2-15x-30)[/tex].

Given expression is

[tex]-3(x+2)^2 -3+3x[/tex]

By applying  [tex](a+b)^2=a^2+2ab+b^2[/tex]  we get

[tex]-3(x^2+6x+9)-3+3x[/tex]

Multiplying by -3 into the whole bracket we get

[tex]-3x^2-18x-27-3+3x[/tex]

[tex]-3x^2-18x-30+3x[/tex]

[tex]-3x^2-15x-30[/tex]

Thus the simplification of the given expression will be  [tex](-3x^2-15x-30)[/tex]

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Answer:

B. –3x^2 – 15x – 30

Step-by-step explanation:

Answer:

8 mini muffins

Step-by-step explanation:

*Bolded is important*

1. To help you get a better feel of the wording, let me give you an example:

The Walmart Franchise costs 5$ each. If I have 10$, how much franchises can I buy? See, it becomes simpler. It's 2.

This is what it is asking here:

If he has $5.40, and he can buy 12 mini muffins, we just need to find the cost of these mini muffins to solve the second part.

2. Solve

To find the solution to this equation, I will give you another example.

If I like drinking water, and I can buy 2 Pools of water for 2 dollars, how much does each pool of water cost?

It costs $1, which is not hard to solve.

What did we do to get the answer of $1? We divided. We divided 2/2 to get one. We have to do the same in this case.

Money is x and muffins is m.

Hence the equation is:

y = x/m, or in this case,

y=5.40/12, which will give us the cost of the muffins.

5.4/12 = $0.45.

Now, since we know the cost, we can find the answer.

To find the total amount of muffins he can buy with $4, we have to

divide.

X is Money and C is Cost per muffin. Hence, the equation is:

y = x/c or,

y = 4/0.45 which equals 8.8888888888888889.

Now, you cant buy 8/9 of a muffin. You can only buy a whole.

So he can buy 8 muffins.

3. Confirm

Lets confirm that this is true for the first equation:

5.40/0.45= 12, which is what the equation states.

So 4/0.45 = 8.899 is how much he could buy, but he can only buy 8 because, again, you cant buy 8/9 of a muffin

y = 8.

According to the dimensions given, the volume of paper in the recycling bin is of 6800 cubic inches.

It is given by the multiplication of the base area by the height, that is:

[tex]V = S_bh[/tex]

In this problem, we have that the measures in square inches and inches, respectively, are given by:

[tex]S_b = 400, h = 17[/tex]

Hence:

[tex]V = 400 \times 17 = 6800[/tex]

The volume of paper in the recycling bin is of 6800 cubic inches.

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Answer:

6800

Step-by-step explanation:

Answer:

Step-by-step explanatio

may not be real numbers. Our final theorem in the section gives us an upper bound on the number

of real zeros.

Theorem 3.7. Suppose f is a polynomial of degree n ≥ 1. Then f has at most n real zeros,

counting multiplicities.

Theorem 3.7 is a consequence of the Factor Theorem and polynomial multiplication. Every zero c

of f gives us a factor of the form (x − c) for f (x). Since f has degree n, there can be at most n of

these factors. The next section provides us some tools which not only help us determine where the

real zeros are to be found, but which real numbers they may be.

We close this section with a summary of several concepts previously presented. You should take

the time to look back through the text to see where each concept was first introduced and where

each connection to the other concepts was made.

Connections Between Zeros, Factors and Graphs of Polynomial Functions

Suppose p is a polynomial function of degree n ≥ 1. The following statements are equivalent:

• The real number c is a zero of p

• p(c) = 0

• x = c is a solution to the polynomial equation p(x) = 0

• (x − c) is a factor of p(x)

• The point (c, 0) is an x-intercept of the graph of y = p(x)

3.2 The Factor Theorem and The Remainder Theorem 265

3.2.1 Exercises

In Exercises 1 - 6, use polynomial long division to perform the indicated

Answer:

C The Item cost more than mona was able to pay

Step-by-step explanation:

I took the test

Answer:

■ Sales tax: $36.00

■ Cost/Price before ST: $719.99

■ Total Cost/Price including ST: $755.99

Step-by-step explanation:

Answer: $755.99

Step-by-step explanation: The first step in finding how much an item or product costs with tax is to take the price of the product and multiply it by the percentage of sales tax to find out how much the tax costs. The next step is to take this cost of the tax and add it to the original price of the product. This gives you your final cost. This gives us the following equations.

In this problem the sales tax is 5%, which is equal to 0.05

(719.99) (0.05) = 35.9995

35 + 719.99 = 755.9895

The answer we get from the equations is 755.9895. Rounding to the nearest penny, or hundredth space, gives us our final answer of $755.99

Answer:

height = 50 ft (nearest foot)

Step-by-step explanation:

This creates a right triangle, where:

Use the tan trig ratio to find the height.

[tex]\mathsf{\tan\theta=\dfrac{opposite \ side}{adjacent\ side}}[/tex]

[tex]\implies \mathsf{\tan(34.6)=\dfrac{height}{72}}[/tex]

[tex]\implies \mathsf{height=72\tan(34.6)}[/tex]

[tex]\implies \mathsf{height=50 \ ft \ (nearest\ foot)}[/tex]

[tex]\\ \rm\Rrightarrow tan\theta=\dfrac{Perpendicular}{Base}[/tex]

[tex]\\ \rm\Rrightarrow tan34.6=\dfrac{x}{72}[/tex]

[tex]\\ \rm\Rrightarrow x=72tan34.6[/tex]

[tex]\\ \rm\Rrightarrow x=72(0.689)[/tex]

[tex]\\ \rm\Rrightarrow x=49.61ft[/tex]

Answer:

Bottom left

Step-by-step explanation:

The limit as x approaches infinity is 3, so there is a horizontal asymptote at 3. So eliminate top left and bottom right.

Also, the fraction 2/(x-1) is undefined when x=1 (since the denominator is 0), so there is a vertical asymptote at x=1. Eliminate top right

So, your answer is the bottom left graph.

Answer:

between 3 and 4 around 3[tex]\frac{3\\}{4}[/tex]

Answer: 3.5

Step-by-step explanation:

You want to choose two numbers that have perfect roots. One above 14, and one below 14. The nearest two perfect roots to 14 is 9 and 16. We have the following inequality:

[tex]\sqrt{9} < \sqrt{14} < \sqrt{16}[/tex]

[tex]3 < \sqrt{14} < 4[/tex]

This means the square root of 14 is somewhere between 3 and 4. A good estimate would be 3.5

Answer:

y =mx

Step-by-step explanation:

The second one is for the gradient

The third one is pythogras theorm

The last one is for the slope of a line(i'm not that sure about this one, sorry if its wrong)

Answer : 6

Explanation : 6 Is The Smallest  Number Which Is The Sum Of 1, 2, And 3. Other Perfect Numbers Are 28, 496, And 8,128.

Answer: 6

Step-by-step explanation: is A Perfect Number

The income of the amusement park is a function of the price of the ticket

The entry price that will result in no income is $24

The expression for the income is given as:

[tex]96x - 4x^2[/tex]

When the income is 0, we have the following equation

[tex]96x - 4x^2 = 0[/tex]

Factor out 4x

[tex]4x(24 - x) = 0[/tex]

Split the equation

4x = 0 or 24 - x = 0

Solve for x

x = 0 or x = 24

This means that, the entry price that will result in no income is $24

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Ali gets £10

Beth gets £25

Step-by-step explanation:

The amount is divided into 7 equal parts since 2+5=7.

since Ali's name comes first, he gets 2 of the parts as the 2 is the first number in the ratio. Beth gets 5 parts, since her name is the second.

share the £35 between the 7 parts by dividing 35 by 7.

35÷7=5

Ali gets 5× £2= £10

Beth gets 5×£5 =£25

5×5=25 (Beth's portion)

Part (a)

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

Explanation:

Multiply by 1000 to go from km to meters.

This is because 1000 m = 1 km.

Multiplying by 1000 in scientific notation means we add 3 to the exponent 5. The 3 is because 1000 = 10^3.

So the [tex]3.84 \times 10^5 \text{ km}[/tex] becomes [tex]3.84 \times 10^8 \text{ meters}[/tex]

===========================================================

Part (b)

Answer in standard form:  960,000 seconds

Answer in scientific notation: [tex]9.6\times10^{5} \text{ seconds}[/tex]

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

Work Shown:

[tex]\text{distance} = \text{rate}*\text{time}\\\\\text{time} = \frac{\text{distance}}{\text{time}}\\\\\text{time} = \frac{3.84 \times 10^8 \text{ meters}}{400 \ \text{ m}/\text{s}}\\\\\text{time} = \frac{3.84 \times 10^8}{4 \times 10^2} \text{ seconds}\\\\\text{time} = \frac{3.84}{4}*\frac{10^{8}}{10^2} \text{ seconds}\\\\\text{time} = 0.96 \times 10^{8-2} \text{ seconds}\\\\\text{time} = 0.96\times 10^{6} \text{ seconds}\\\\[/tex]

[tex]\text{time} = (9.6\times10^{-1})\times10^{6} \text{ seconds}\\\\\text{time} = 9.6\times(10^{-1}*10^{6}) \text{ seconds}\\\\\text{time} = 9.6\times10^{-1+6} \text{ seconds}\\\\\text{time} = 9.6\times10^{5} \text{ seconds}\\\\\text{time} = 960,000 \text{ seconds}\\\\[/tex]

To go from the scientific notation to standard form, move the decimal point 5 spaces to the right. The 5 is from the exponent.

Cylinder A can hold 6902.08 ft^3

Cylinder B can hold 5654.87 ft^3

6902.08 - 5654.87 = 1247.21

The amount that will be left over in container A is 1247.21

Answer:

B

Step-by-step explanation:

Answer:

200000 x 1.05^3=231525

Step-by-step explanation:

X 1.05 because the price is increasing by 5% and ^3 because there are three years between 2014 and 2017

Answer: carter has not saved any money

Step-by-step explanation:

Which of the following methods would be the easiest to use to solve x²−6=0?

[tex] \tt \: {x}^{2} - 6 = 0 \\ \tt {x}^{2} = 6 \\ \tt \: x = \pm \sqrt{6} \\ \tt \: x = - \sqrt{6} , x = \sqrt{6} [/tex]

And done, Solved!

[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]

Which of the following methods would be the easiest to use to solve x²−11=0?

[tex] \tt {x}^{2} - 11 = 0 \\ \tt \: {x}^{2} = 11 \\ \tt \: x = \pm \sqrt{11} \\ \tt \: x = - \sqrt{11} , x = \sqrt{11} [/tex]

[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]

Which equation would be the best to solve by completing the square?

[tex] \tt {x}^{2} = 49 \\ \tt \: x = \pm7 \\ \tt \: x = - 7, x = 7[/tex]

Answer:

1.

A: GI= 60

B:  MH= 14

C: IK= 23

D: HI=  46

E: MG= 24

2.

A: TU= 38

B: VY= 17

C: UZ= 15

D: WV= 15

E: TV= 30

Step-by-step explanation:

This probally isnt all right but most of it most likely is.

Cathy and Iris have 259,459,200 ways to skip countries.

Data;

To solve this problem, we would have to use a mathematical procedure known as combination.

Let us calculate the number of countries that would have to skip.

[tex]13 - 9 = 4[/tex]

To decide which country they have to skip, it would be 4 out of 13.

[tex]x = ^1^3C_4 = \frac{13!}{4!}[/tex]

Let's solve this

[tex]\frac{13!}{4!} = \frac{13*12*11*10*9*8*7*6*5*4*3*2*1}{4*3*2*1}\\ \frac{13!}{4!} = 13*12*11*10*9*8*7*6*5 = 259459200 ways[/tex]

Cathy and Iris have 259,459,200 ways to skip countries.

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