please help I will give brainless.

Answer:

The fractional part of the original pizza is  [tex]\frac{1}{6}[/tex]

Step-by-step explanation:

Let

x-----> the original pizza (complete pizza)

we know that

Half a pizza represent ------> [tex]\frac{x}{2}[/tex]

Divide half a pizza by three people

[tex](\frac{x}{2})/3=\frac{x}{6}[/tex]

therefore

The fractional part of the original pizza is  [tex]\frac{1}{6}[/tex]

Answer:

255π (cm³).

Step-by-step explanation:

1. the initial formula for the required volume is V=V1-V2, where V1=π(r1)²h, V2=π(r2)²h;

h=20m=2000cm, r1=0.5*d1, r2=0.5*d2;

d1=1cm., d2=0.7 cm.

2. the final formula of the required volume is

[tex]V=\frac{ \pi*h}{4} (d_1^2-d_2^2);[/tex]

3. if to substitute the values of d1, d2 and h, then

[tex]V=\frac{ \pi*2000}{4} (1-0.49)=500 \pi*0.51=255 \pi \ (cm^3).[/tex]

Answer:

[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]

Step-by-step explanation:

Given: [tex]y^2+3y=-1[/tex]

To solve for [tex]y[/tex], we need to get everything on one side of the equal sign and set it to zero. We can do this by adding 1 to both sides. We then get:

[tex]y^2+3y+1=0[/tex]

We can solve for [tex]y[/tex] by using the quadratic formula:

[tex]y=\frac{-b+\sqrt{(b)^2-4(a)(c)}}{2a}[/tex] AND [tex]y=\frac{-b-\sqrt{(b)^2-4(a)(c)}}{2a}[/tex]

Let's identify our values:

[tex]a: 1\\b: 3\\c: 1[/tex]

Plug in the values and simplify.

[tex]y=\frac{-3+\sqrt{(3)^2-4(1)(1)}}{2(1)}\\y=\frac{-3+\sqrt{5}}{2}\\-------------------------\\y=\frac{-3-\sqrt{(3)^2-4(1)(1)}}{2(1)}\\\\y=\frac{-3-\sqrt{5}}{2}\\[/tex]

Your final answers are:

[tex]y=-\frac{3+\sqrt{5}}{2}[/tex] AND [tex]y=-\frac{3-\sqrt{5}}{2}[/tex]

Answer:

y = x^2 +2x -35

Step-by-step explanation:

Multiply the binomials. The distributive property is helpful.

y = x(x -5) +7(x -5) . . . . the terms of the first binomial multiplied by the second

= x^2 -5x +7x -35 . . . . eliminate parenthses

y = x^2 +2x -35 . . . . . . collect terms

Out of 170 students in 12th grade, 27+23 = 50 students have more than 1 college in mind.

So 50/170, or 29% is your answer.

Answer:

29%

Step-by-step explanation:

I see no actual question, but I'm assuming that you want to find the dimensions of the rectangle.

In general, the area of a rectangle with width [tex]w[/tex] and length[tex]l[/tex] is

[tex] A = wl [/tex]

In this case, we know that the width is one-fourth of its length, which means [tex] w = \frac{1}{4}l[/tex]

If we plug this expression for w in the formula for the area, we get

[tex] A = wl = \dfrac{1}{4}l\cdot l = \dfrac{1}{4}l^2 [/tex]

We also know that the area is 9 squared units, so we have

[tex] 9 = \dfrac{1}{4}l^2 [/tex]

If we multiply both sides by 4, we get

[tex] l^2 = 36 [/tex]

Consider the square root of both sides (we only accept the positive solution, since a negative length would make no sense:

[tex] l = \sqrt{36} = 6 [/tex]

So, the length is 6, and the width is one-fourth of 6, i.e.

[tex]\dfrac{1}{4} \cdot 6 = \dfrac{6}{4} = \dfrac{3}{2} = 1.5[/tex]

Answer:

1.5

Step-by-step explanation:

Answer:

A. lim [x ⇒ -∞] g(x) = -5 . . . . . . written in text form, not typeset

Step-by-step explanation:

A horizontal asymptote is a line that the function approaches but never reaches. It represents the limiting value that the function can have. (The function can come as close to that value as you like for some value of x, but can never actually reach that value.)

Here, you're told the asymptote for negative x values is -5. That means g(x) gets closer and closer to -5 for values of x that are more and more negative. That is, as x approaches infinity, g(x) approaches -5. We say -5 is the limit of g(x) as x approaches negative infinity.

___

The attached graph shows a function that has characteristics like those of g(x).

___

This question is about vocabulary: what is the meaning of "asymptote" and "limit", and how do you read a description of a limit written using math language.

Answer:

  73

Step-by-step explanation:

Put the values of the variables where the variables are, then do the arithmetic.

  (2·5)^2 -3·3^2 = 10^2 -3·9 = 100 -27 = 73

___

Or, you can let a calculator or spreadsheet evaluate the function for you.

Answer:

Step-by-step explanation:

After you've worked a couple of "optimum cylinder" problems, you find that the cylinder with the least surface area for a given volume has a height that is equal to its diameter. So, the volume equation becomes ...

  V = πr²·h = 2πr³ = 39 in³

Then the radius is ...

  r = ∛(39/(2π)) in ≈ 1.83779 in ≈ 1.84 in

  h = 2r = 3.67557 in ≈ 3.68 in

_____

The total surface area of a cylinder is ...

  S = 2πr² + 2πrh

For a given volume, V, this becomes ...

  S = 2π(r² +r·(V/(πr²))) = 2πr² +2V/r

The derivative of this with respect to r is ...

  S' = 4πr -2V/r²

Setting this to zero and multiplying by r²/2 gives ...

  0 = 2πr³ -V

  r = ∛(V/(2π)) . . . . . . . . looks a lot like the expression above for r

__

If we substitute the equation for V into the equation just above this last one, we have ...

  0 = 2πr³ - πr²·h

Dividing by πr² gives ...

  0 = 2r - h

  h = 2r . . . . . generic solution for cylinder optimization problems

Answer:

No

Step-by-step explanation:

A parallelogram may have a right angle (making it a rectangle), but may not.

The [tex]z[/tex]-score for a height of 16.4 feet is

[tex]z=\dfrac{16.4-14.2}{2.15}\approx1.023[/tex]

So

[tex]P(\text{height}>16.4\,\mathrm{ft})=P(Z>1.023)=1-F_Z(1.023)\approx0.153[/tex]

where [tex]F_Z(z)=P(Z\le z)[/tex] is the cumulative distribution function for the standard normal distribution.

Answer:

  cot(x) = 3

Step-by-step explanation:

The cotangent is the reciprocal of the tangent.

  cot(x) = 1/tan(x) = 1/(1/3) = 3

_____

It is helpful to memorize the relationships between the trig functions: SOH CAH TOA is a mnemonic that relates triangle sides to trig function values. The remaining relationships you need to know are ...

  secant = 1/cosine . . . . . . so cosine = 1/secant

  cosecant = 1/sine . . . . . so sine = 1/cosecant

  cotangent = 1/tangent . . . . . so tangent = 1/cotangent

It is also helpful to realize that ...

  tan = sin/cos

  sin² + cos² = 1 . . . the "Pythagorean" relationship between sine and cosine

  sec² = 1 + tan²

  csc² = 1 + cot²

Answer:

s= 15x+3x and s=18x

Step-by-step explanation:

Answer:

The total cost for the special would be $15.45

Step-by-step explanation:

One equation would be 15 x 1.03 = 15.45

Second equation would be (15 x .03) + 15 = $15.45

Answer:

x = 5 and y = 35

OR

x = -4 and y = 8.

Step-by-step explanation:

Equate the right-hand side of the two equations:

x² + 2 x = y = 3 x + 20.

x² + 2 x - 3 x - 20 = 0.

x² - x - 20 = 0.

Quadratic discriminant

Δ = b² - 4 a · c

= (-1)² - 4 × 1 × (-20)

= 81.

There are two roots:

x₁ = (-b + [tex]\sqrt{\Delta}[/tex]) / (2 a)

= (- (-1) + [tex]\sqrt{81}[/tex]) / (2 × 1)

= (1 + 9) / 2

= 10 / 2

= 5

and

x₂ = (-b - [tex]\sqrt{\Delta}[/tex]) / (2 a)

= (1 - 9) / 2

= -4.

Find the value of y in both case.

y₁ = 3 × 5 + 20 = 35.

y₂ = 3 × (-4) + 20 = 8.

The solution to the system of equations is [tex]\( x = 5 \)[/tex] with [tex]\( y = 35 \)[/tex] and [tex]\( x = -4 \)[/tex] with [tex]\( y = 8 \)[/tex].

To solve these equations algebraically, we'll set them equal to each other since they both represent [tex]\( y \)[/tex].

Given equations:

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

[tex]\[ y = 3x + 20 \][/tex]

Setting them equal to each other:

[tex]\[ x^2 + 2x = 3x + 20 \][/tex]

Now, let's rearrange this equation to solve for \( x \):

[tex]\[ x^2 + 2x = 3x + 20 \[/tex]

[tex]x^2 + 2x - 3x - 20 = 0 \[/tex]

[tex]x^2 - x - 20 = 0[/tex]

This is a quadratic equation in the form [tex]\( ax^2 + bx + c = 0 \)[/tex]. We need to factorize or use the quadratic formula to solve for [tex]\( x \)[/tex]. Factoring might work here:

[tex]x^2 - x - 20 = 0[/tex]

[tex](x - 5)(x + 4) = 0[/tex]

Setting each factor equal to zero:

[tex]\[ x - 5 = 0 \] or \( x + 4 = 0 \)[/tex]

Solving for [tex]\( x \)[/tex] in each case:

[tex]\[ x = 5 \] or \( x = -4 \)[/tex]

Now that we have found the potential values of [tex]\( x \)[/tex], let's find the corresponding [tex]\( y \)[/tex] values using either of the original equations. Let's use [tex]\( y = x^2 + 2x \)[/tex]:

For [tex]\( x = 5 \)[/tex]:

[tex]y = 5^2 + 2(5)[/tex]

[tex]y = 25 + 10[/tex]

[tex]y = 35[/tex]

For [tex]\( x = -4 \)[/tex]:

[tex]y = (-4)^2 + 2(-4)[/tex]

[tex]y = 16 - 8[/tex]

[tex]y = 8[/tex]

Therefore, the solution to the system of equations is [tex]\( x = 5 \)[/tex] with [tex]\( y = 35 \)[/tex] and [tex]\( x = -4 \)[/tex] with [tex]\( y = 8 \)[/tex].

Answer:

1/4

Step-by-step explanation:

3 x 1 = 3

4 x 3 = 12

3/12 simplified is 1/4

The quotient of the numbers 3/4 and 1/3 will be 9/4.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

Making anything easier to accomplish or comprehend, as well as making it less difficult, is the definition of simplification.

The numbers are given below.

3/4 and 1/3

The quotient of the numbers 3/4 and 1/3 is given by the number 3/4 divided by 1/3. Then we have

⇒ (3/4) / (1/3)

Simplify the expression, then we have

⇒ (3/4) x (3/1)

⇒ 9 / 4

The quotient of the numbers 3/4 and 1/3 will be 9/4.

More about the division link is given below.

https://brainly.com/question/369266

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Answer:

Step-by-step explanation:

When you have a non-trivial number of sets of equations to solve, it can be useful to let a machine solve them for you. Here, suitable equations for chair cost (c) and table cost (t) can be written as ...

___

I find a graphing calculator easy to use for solving such equations.

___

A spreadsheet programmed with Cramer's Rule can do it, too. The second attachment shows the spreadsheet formulas used to solve the standard-form linear equations of the kind that can be written for this problem. The third attachment shows the solution(s).

Answer:

430

Step-by-step explanation:

All you have to do is add up all the sides So 80+80+250+20=430 And there you have it!

Answer:

3) 2/3

4) an = 162·(1/3)^(n-1)

Step-by-step explanation:

3) A geometric sequence has a common ratio between adjacent terms. Here, that ratio is ...

r = 54/162 = 18/54 = 6/18 = 1/3

Then the next two terms can be found by multiplying by the common ratio:

6 · 1/3 = 2

2 · 1/3 = 2/3 . . . . . the sixth term

____

4) The generic expression for the n-th term of a geometric sequence with first term a1 and common ratio r is ...

an = a1·r^(n-1)

We can put in the numbers for a1 and r, and we have ...

an = 162·(1/3)^(n-1)

Answer:

t = 58x or t + 7x = 65x

The expression that represents a senior citizen's total cost for the plumber in 2 different ways can be written as: Method 1: Total Cost = $65 - $7 per hour. Method 2: Total Cost = $65 - ($7 per hour x Number of hours)

The expression that represents a senior citizen's total cost for the plumber in 2 different ways can be written as:

Method 1 calculates the total cost by applying the discount of $7 per hour directly to the base rate of $65. Method 2 calculates the total cost by multiplying the discount per hour ($7) by the number of hours and subtracting it from the base rate of $65.

https://brainly.com/question/3200361

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A random supporter roots the home team with probability 0.9, and the away team with probability 0.1.

Choosing 6 out of 8 supporters who root for the home team has probability

[tex]\displaystyle\binom{8}{6}\cdot 0.9^6\cdot 0.1^2 = 28\cdot0.531441\cdot 0.01=0.14[/tex]

Answer:

Mason wins after 18 total moves

Step-by-step explanation:

Mason's optimal strategy is to keep the total number of marbles at 11n+1, so he will take 10 marbles to start. For each move Jason makes, Mason will take a number of marbles that makes the sum from the two turns be 11.

After each of Mason's 9 turns, the number of remaining marbles will be ...

89, 78, 67, 56, 45, 34, 23, 12, 1

It doesn't matter how many marbles Jason takes. He will lose on his 9th turn.

Mason's best strategy is to stay the overall variety of marbles at 11n+1, thus he can take ten marbles to begin. for every move Jason makes, Mason can take variety of marbles that creates the add from the 2 turns be eleven.

After every of Mason's nine turns, the amount of remaining marbles are

89, 78, 67, 56, 45, 34, 23, 12, 1

It doesn't matter what number marbles Jason takes. He can lose on his ninth flip.

mason will win after 18 moves

Since f(x) = -3x + 2, the slope of f(x) is greater than the slope of g(x).

Hence, the answer is (D).

The slope of f(x) is greater than the slope of g(x) because the slope of f(x) is 1 option (D) is correct.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have:

g(x) = -2x - 6

f(x) is shown in the graph

The slope of g(x), m = -2

From the graph:

(0, 2) and (-1, 1)

M = (1-2)/(-1) =  1

Thus, the slope of f(x) is greater than the slope of g(x) because the slope of f(x) is 1 option (D) is correct.

Learn more about the slope here:

brainly.com/question/3605446

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Answer:

You need to find the number of times x goes into 3x^2 which is 3x, so you write 3x as the beginning of the quotient to start the division.

Answer:

3x^2 / x.

Step-by-step explanation:

The first step is to divide 3x^2 by the first term of x - 2 ( that is x).

If [tex]b[/tex] is Ben's age and [tex]i[/tex] is Ishaan's age, then

Rewrite the second equation as

[tex]b-6=6(i-6)\implies b-6=6i-36\implies b+30=6i[/tex]

Substitute [tex]b=4i[/tex] into this equation to solve for [tex]i[/tex]:

[tex]b+30=6i\implies4i+30=6i\implies30=2i\implies i=15[/tex]

Then

[tex]b=4i\implies b=4\cdot15=60[/tex]

So Ben is 60 years old now.

Answer:

The correct answer is 2.

Step-by-step explanation:

To find this, first identify the ordered pairs at those two points. They would be (3, -2) and (6, 4). Then use the slope formula with those two points to find the rate of change.

m(slope) = (y2 - y1)/(x2 - x1)

m = (4 - - 2)/(6 - 3)

m = 6/3

m = 2

Answer:

2

Step-by-step explanation:

Rate of change on the given interval a to b is

[tex]\frac{f(b)-f(a)}{b-a}[/tex]

a=3 and b=6

f(a) and f(b) are the y values on the graph at x=3  and x=6

f(3)= -3  and f(6) is 4

Now plug in the values in the formula

[tex]rate of change =\frac{4-(-2)}{6-3} =\frac{6}{3} =2[/tex]

answer is 2

The percent that Container A is full after pumping its water into Container B until it is full is that Container A is 49.1% full after pumping water to Container B.

The problem asks us to determine what percent of Container A is full after Container B is full when water is transferred from Container A to Container B. We start by calculating the volume of both cylinders. The volume of a cylinder is given by the formula V = π r² h where V is volume, r is radius, and h is height.

Container A has a radius of 13 feet and a height of 13 feet, so:

π r² h ≈ 6985.3 cubic feet

Container B has a radius of 9 feet and a height of 14 feet, so:

π r² h≈ 3553.0 cubic feet

After filling Container B completely, the volume of water left in Container A is the original volume of Container A minus the volume of Container B. Therefore, the remaining volume in Container A is (6985.3 - 3553.0) cubic feet ≈ 3432.3 cubic feet.

To find the percentage full, we divide this remaining volume by the total volume of Container A and multiply by 100:

Percentage = (3432.3 / 6985.3) * 100 ≈ 49.1%.

After the pumping is complete, Container A is 48.4% full.

Calculate the volume of each container

The volume  of a cylinder is given by the formula:

[tex]\[V = \pi r^2 h\][/tex]

Volume of Container A

- Radius [tex]\( r_A = 13 \)[/tex]feet

- Height [tex]\( h_A = 13 \)[/tex] feet

[tex]\[V_A = \pi (13)^2 (13) = \pi (169)(13) = 2197\pi \text{ cubic feet}\][/tex]

Volume of Container B

- Radius [tex]\( r_B = 9 \)[/tex]feet

- Height [tex]\( h_B = 14 \)[/tex] feet

[tex]\[V_B = \pi (9)^2 (14) = \pi (81)(14) = 1134\pi \text{ cubic feet}\][/tex]

Calculate the remaining volume of water in Container A

Since Container A is initially full and the water is pumped into Container B until Container B is full, the remaining volume of water in Container A is:

[tex]\[V_{\text{remaining}} = V_A - V_B = 2197\pi - 1134\pi = (2197 - 1134)\pi = 1063\pi \text{ cubic feet}\][/tex]

Calculate the percent of Container A that is still full

The percent of Container A that is full is given by:

[tex]\[\text{Percent full} = \left( \frac{V_{\text{remaining}}}{V_A} \right) \times 100\%\][/tex]

Substituting the volumes we calculated:

[tex]\[\text{Percent full} = \left( \frac{1063\pi}{2197\pi} \right) \times 100\% = \left( \frac{1063}{2197} \right) \times 100\%\][/tex]

Simplifying the fraction:

[tex]\[\text{Percent full} = 0.484 \times 100\% = 48.4\%\][/tex]

Answer:

  59.0°

Step-by-step explanation:

Many triangle solvers are available for your phone, tablet, or browser. The attachments show the input and output of one of them.

___

You can use the law of cosines to compute the result yourself.

  b^2 = a^2 + c^2 - 2ac·cos(B)

  cos(B) = (a^2 +c^2 -b^2)/(2ac) = (22^2 +18^2 -20^2)/(2·22·18) = 408/792

  B = arccos(408/792) ≈ 58.9924° ≈ 59.0°

Answer:

3.5 pounds of nuts; 6.5 pounds of M&Ms

Step-by-step explanation:

Let m represent the number of pounds of M&Ms to use. Then 10-m is the number of pounds of nuts, and the cost of the mix is ...

6·m + 3·(10-m) = 4.95·10 . . . . . cost = cost per pound times pounds

3m +30 = 49.5 . . . . . . simplify

3m = 19.5 . . . . . . . . . . . subtract 30

m = 6.5 . . . . . . . . . . . . . divide by 3

Then 10-m = 10-6.5 = 3.5.

The manager should use 3.5 pounds of nuts and 6.5 pounds of M&Ms in the mix.

Answer:

First account (simple interest)

Step-by-step explanation:

The amount of interest earned by the first account is ...

I = Prt = $2000·0.04·7 = $2000·0.28 = $560

The amount in the second account at the end of 7 year is ...

FV = P·(1+r)^t = $2000·1.02^7 = $2297.37

so you have earned $297.37 in interest on the second account.

$560 is more than $297, so the First Account (simple interest) earns more money.

The second one is d I’m pretty sure

Answer:

#23, A

#24, D

Hope this helped!!

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