The bottom part of this block is a rectangular prism. The top part is a square
pyramid. You want to cover the block entirely with paper. How much paper do you
need? Use pencil and paper to explain your reasoning.

9514 1404 393

Answer:

  A. (1, - 3/2)

Step-by-step explanation:

The coordinate of the midpoint is the average of the endpoint coordinates.

  M = (A +B)/2

  M = ((1, 2) +(1, -5))/2 = (1+1, 2-5)/2 = (2, -3)/2

  M = (1, -3/2) . . . . . matches choice A

Answer:

A. (1, - 3/2)

Step-by-step explanation:

A)
i) the inequality to show the number of ballons that the dance committee can buy is: 0.80b + 65 ≤ 125

ii)  solving the inequality above, we arrive at b ≤ 75
B) The graph is attached accordingly.

C) See the description of the solution below.

Let's start by defining our variables. Let b be the number of balloons that the dance committee could buy.

The cost of b balloons is $0.80b. We want to make sure that the cost of the balloons plus the amount already spent on decorations ($65) is less than or equal to the budget of $125. So we can write the following inequality:

0.80b + 65 ≤ 125

Now we can solve for b:

0.80b + 65 ≤ 125

0.80b ≤ 125 - 65

0.80b ≤ 60

b ≤ 75

Therefore, the dance committee can buy up to 75 balloons to stay within their budget.

To graph the solution set, we can plot b on the horizontal axis and shade the region to the left of b = 75, since b must be less than or equal to 75.

The solution set represents all possible values of b that satisfy the inequality. In this case, the solution set is b ≤ 75, which means that the dance committee can buy up to 75 balloons and still stay within their budget.

As the number of balloons increases, the cost of the balloons also increases, and the amount of money left in the budget decreases.

Therefore, the more balloons the dance committee buys, the less money they will have left for other decorations or expenses.

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Full Question:


Since the above question is incomplete, it appears you are referring to the question below.


The dance committee has a budget of $125 to decorate the gym for a spring dance. They already spent $65. Some members want to buy helium balloons that cost $0.80 each.

A) Write and solve an inequality to show the number of balloons that the dance committee could buy.

B) Graph the solution set for the inequality.
C) Describe what the solution means and how the number of balloons affects the amount in the budget.

Answer:

314.16 in²

Step-by-step explanation:

Answer:

\(A\) ≈ \(314.16\)

Step-by-step explanation:

\(A=\pi r^2\)

\(A = \pi (10)^2\)

\(A = \pi (100)\)

\(A\) ≈ \(314.16\)

Each package has 18 granola bars.

This problem can be solved through a system of linear equations.

Let "x" be the total number of granola bars that each pack of granola has. Let "y" be the total amount of granola bars that each cafeteria has.

For cafeteria A: \(7x+12=y\)

For cafeteria B: \(3x+84=y\)

Since both equations are solved for y, we may take the argument at the left of the equal sign from both equations and equal them.

\(7x+12=3x+84\).

\(7x+12=3x+84\)

\(7x-3x=84-12\) --> Substract 3x and 12 from both sides.

\(4x=72\) --> Simplify by solving the substraction.

\(\frac{4x}{4} =\frac{72}{4}\)--> Divide both sides by 4.

\(x= 18\)

\(y=7(18)+12\\ \\y=138.\)

If a system of linear equations was created, where 2 equations that gave the number of granola bars that each cafeteria has, then the x value obtained when the system was solved, indicates the amount of granola bars that each cafeteria has in each package. Each package has 18 granola bars.

Answer:

-48

Step-by-step explanation:

\(x+15=-33 \\ \\ x=-33-15 \\ \\ x=-48\)

Answer:

0.69 rounded to the nearest tenth is 0.7

Answer:

I'm pretty sure its 90° rotation clockwise

9514 1404 393

Answer:

  is a function

Step-by-step explanation:

The graph passes the vertical line test, so the relation is a function of x.

Answer:25

Step-by-step explanation:

Answer:

Part A: $3,415.50

B: 11.34%

Step-by-step explanation:

Part A: $31,000 is within the values 10,276≤x≤41,175, so use f(x)=0.12x-205.50

Part B: For the effective tax rate, divide the amount in part A by the taxable income

Part C: Compare both the taxable income and the effective tax rate to the income domains given and the % multiplier. This one is mostly about how you describe the situation, so I'll leave that up to you.

To calculate the taxes owed on a taxable income of $31,000, we use the appropriate equation for the tax bracket it falls into and substitute the value of x. The effective tax rate is calculated by dividing the amount of taxes owed by the taxable income and multiplying by 100. The piecewise function represents the marginal tax rate chart by using different equations for each tax bracket.

Part A:

To calculate the amount of taxes owed on a taxable income of $31,000, we need to determine which tax bracket it falls into. Since $31,000 is greater than $10,275 but less than $41,175, it falls into tax bracket 2. To find the amount of taxes owed, we use the equation for tax bracket 2: f(x) = 0.12x - 205.50. Plugging in $31,000 for x, we get:

f(x) = 0.12 * 31000 - 205.50 = $3,574.50

Therefore, the amount of taxes owed on a taxable income of $31,000 is $3,574.50.

Part B:

To determine the effective tax rate, we divide the amount of taxes owed by the taxable income. Using the result from Part A (taxes owed = $3,574.50) and the taxable income of $31,000, we have:

Effective tax rate = (taxes owed / taxable income) * 100 = (3,574.50 / 31,000) * 100 ≈ 11.52%

Therefore, the effective tax rate on a taxable income of $31,000 is approximately 11.52%.

Part C:

The piecewise function represents the amount of taxes owed as a function of the taxable income. Each part of the function corresponds to a different tax bracket, with the equation for that tax bracket. The marginal tax rate chart is represented in the piecewise function by the different equations for each tax bracket. For example, the equation in part 1 of the function (f(x) = 0.10x) corresponds to the 10% marginal tax rate for the tax bracket $0-$10,275.

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Answer:

Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.

Step-by-step explanation:

Let \(x\) denote the number of rafts seating 3 people and \(y\) the number of rafts seating 5 people. The total number of rafts is 13, so \(x+y=13\). We can also assume that every raft is filled to the brim (it isn't stated explicitly though, but it's probably the intention of the question maker), so \(3x+5y=53\).

It's always a good idea to put these equations under each other:

\(\left \{ {{x+y = 13} \atop {3x+5y=53}} \right.\)

We can subtract the first equation three times from the second one to obtain \((3x+5y)-3(x+y) = 53 - 3(13)\\3x-3x + 5y - 3y = 53 - 39\\2y = 14\\y=\frac{14}{2} = 7\)

Now, substitute this found value for \(y\) into \(x+y = 13\) and we see that \(x=6\). We are now done: Peter rents 6 of the rafts seating 3 people, and 7 of the rafts seating 5 people.

................... rafts

the one on the bottom left

The solution of the given system is x = 0 and y = -2.

Simultaneous equations are any one or more equations that can have the same number of unknowns and be solved concurrently. The system of equations is a simultaneous equation.

Given:

A system of equations,

-5x + y = -2   {equation 1}

and -3x + 6y = -12    {equation 2}.

Multiply 6 by equation 1 and subtract equation 2 from equation 1,

we get,

-30x + 6y -(-3x + 6y) = -12 -(-12)

-27x = 0

x = 0.

Substitute the value of x into equation 1,

we get,

y = -2.

Therefore, the solution is x = 0 and y = -2.

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9514 1404 393

Answer:

  see below

Step-by-step explanation:

Add 3 to both sides of the inequality to find the solution.

  x -3 +3 > -2 +3

  x > 1

This graphs as an open circle at x=1, with shading to the right.

Answer:

y = 12 x = 12\(\sqrt{3}\)

Step-by-step explanation:

This is a 60, 90, 30. It's a special triangle.

2z = 24

z = 12

If x = z\(\sqrt{3}\)

then x = 12\(\sqrt{3}\)

y = z itself

So y = 12

Approximately 95% of housing prices are between a low price of $133,000 and a high price of $161,000.

These approximate percentages are defined by the Empirical Rule, for a normally distributed variable.

Hence the prices within two standard deviations of the mean are given as follows:

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Answer:

y=3/5x-9

this is what im learning as well

Regular: 12x-20y=180

In slope-int form: y = 3/5x - 9

Answer:

7⁸ or 1/7⁸ I hope this help

Step-by-step explanation:

7⁻⁶/7² = ⁻⁽⁻⁶⁾= 7⁶+7²= 7⁸

Answer:

Below

Step-by-step explanation:

L x W = 438

L = 438/W

L = 438/3 = 146 ft

then perimeter = 3 + 3 + 146 + 146 = 298  ft

Answer:

It should be 146

Answer:

Its c

Step-by-step explanation:

Answer:

The numbers:

-43    and     58

Step-by-step explanation:

a + b = 15

a = b - 101

then:

(b-101) + b = 15

2b = 15+101

2b = 116

b = 116/2

b = 58

a = b - 101

a = 58 - 101

a = -43

Check:

a + b = 15

-43 + 58 = 15

When edge D connects with edge X, this net is folded into a cube, which is obtained by folding the given figure in cube.

A cube is a solid shape with six square faces. Each side of a square  has the same side length, so all  faces are the same size.

A cube has 12 sides and 8 vertices. Each vertex refers to the angle where the three edges of the cube meet.

Shape Properties of  Cube  

Thus, when edge D connects with edge X, this net is folded into a cube.

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162

Step-by-step explanation:

(12 square - 15 + 17) + 16

=(144 - 15 + 17) + 16

=146 + 16

=162

Answer & Step-by-step explanation:

First, we need to know the formula for finding the distance between the two points.

\(Distance(d)=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Next, we plug in our coordinate points to their respectful places and solve for the distance.

\(Distance(d)=\sqrt{(3-1)^2+(11-5)^2}\)

\(Distance(d)=\sqrt{(2)^2+(6)^2}\)

\(Distance(d)=\sqrt{4+36}\)

\(Distance(d)=\sqrt{40}\)

We can simplify this radical.

So, the distance between the two points in the simplest radical form is 2√10

The percentage change in GDP is 2.04%

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

The formula of percentage change is given as

Percentage change =[ (New increase - old value) / old value] * 100

Percentage change = [(14.72 - 14.42) / 14.72] * 100

Percentage change = 2.04%

In this case, there is a percentage decrease of 2.04%

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\( \huge\frak{Answer:-}\)

\( \rm{cot \: x = cos \: x \: sin \: x}\)

\(\huge \mathtt \purple{Answer:-}\)

\( \sf \red{cot \: x \: = \: cos \: x \: sin \: x}\)

100 times the square root of 3 is also a possible value of a for this function.

In mathematics, the square root of a non-negative real number "a" is a non-negative real number that, when multiplied by itself, gives the original number "a". It is denoted by the symbol "√".

We can substitute each of the given values into the function f(a) = a² + 7 to determine if they are possible values of a.

Substituting the square root of 5:

f(√(5)) = (√(5))² + 7 = 5 + 7 = 12

So, the square root of 5 is not a possible value of a for this function.

Substituting the square root of 7:

f(√(7)) = (√(7))² + 7 = 7 + 7 = 14

So, the square root of 7 is a possible value of a for this function.

Substituting 100 times the square root of 3:

f(100√(3)) = (100√(3))² + 7 = 30000 + 7 = 30007

So, 100 times the square root of 3 is also a possible value of a for this function.

Therefore, the possible values of a for the given function are:

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Convert \(-1+i\) to polar form.

\(z = -1 + i \implies \begin{cases}|z| = \sqrt{(-1)^2 + 1^2} = \sqrt2 \\\\ \arg(z) = \pi + \tan^{-1}\left(\dfrac1{-1}\right) = \dfrac{3\pi}4 \end{cases}\)

By de Moivre's theorem,

\(\left(-1+i\right)^7 = \left(\sqrt2 \, e^{i\,\frac{3\pi}4}\right)^7 \\\\ ~~~~~~~~ = \left(\sqrt2\right)^7 e^{i\,\frac{21\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \, e^{-i\,\frac{3\pi}4} \\\\ ~~~~~~~~ = 8\sqrt2 \left(\cos\left(\dfrac{3\pi}4\right) - i \sin\left(\dfrac{3\pi}4\right)\right) \\\\ ~~~~~~~~ = 8\sqrt2 \left(-\dfrac1{\sqrt2} - \dfrac1{\sqrt2}\,i\right) \\\\ ~~~~~~~~ = -8 (1 + i)\)

QED

Given:

The average number of acres per farm after x years from 2000 is given by,

Explanation:

a) To find: The average number of acres per farm in 2005

Substituting x = 5 in the given function we get,

The average number of acres per farm in 2005 is 40.05.

b) To find: The average number of acres per farm in 2012

Substituting x = 12 in the given function we get,

The average number of acres per farm in 2012 is 34.62.

c) To find: The zeros

Let the average function equal zero.

Hence, the zero of the function is 45.46.

Yes, The average number of acres per farm after 45.46 years from 2000 is zero.

That is, there is no land to make forms.