find a polynomial equation of the lowest degree with rational coefficients whose one root is (cbrt 2 + 3*cbrt 4)

Step-by-step explanation:

it is a combination of a cone and half a sphere.

the volume of a cone is

ground area × height / 3

the ground area is a circle, so we have

pi×r²×h/3

in our case

pi×(10/2)²×12/3 = pi×5²×4 = pi×25×4 = 100pi

the volume of a sphere is

4/3 × pi×r³

and half a sphere is then

4/3 / 2 × pi×r³ = 4/6 × pi×r³ = 2/3 × pi×r³

in our case

2/3 × pi×5³ =2/3 × pi×125 = 250/3 × pi

together we get

100pi + 250/3 × pi = 300/3 × pi + 250/3 × pi =

= 550/3 × pi = 575.9586532... cm³ ≈ 576 cm³

if we use 3.14 for pi we get

575.6666666... cm³ ≈ 576 cm³

Step-by-step explanation:

ok but wheres the question? these are just statements.

Answer:

B

Step-by-step explanation:

Square both sides, and get s^2 = k3/p

next multiply both sides by p and get (s^2)(p)=k3

Therefore k3 equals s^2 times p

Answer:

100

Step-by-step explanation:

because 100 showed twice more then the others

Answer:

To find the mode of this question. You look for the number that showed up the most out of the values given. In this case you answer is 100.

Step-by-step explanation:

Answer:

9(x-1)(x-1) or 9(x-1)²

Step-by-step explanation:

9x² - 18x + 9

factor out a 9

9(x² - 2x + 1)

use middle term factorization to factor x² - 2x + 1

9(x-1)(x-1) or 9(x-1)²

Middle term factorization explained:

For x² - 2x + 1, you want to find 2 numbers that multiply to +1 and add to -2. You then split x² to x and x and add the 2 numbers individually to x.

It should look something like (x+1st number)(x+2nd number)

the two numbers that multiply to get to 1 and add to get to -2 are -1 and -1

( -1 × -1 = 1 and -1 + -1 = 2 )

so we then add the number to the split x² to get (x-1)(x-1) which is the same as (x-1)², the 9 is then added to the factored form to get 9(x-1)(x-1) or 9(x-1)²

Answer:

RSTU is a parallelogram, quadrilateral, rectangle, rhombus, and square. NOT trapezoid.

Step-by-step explanation:

The shape has four sides, so it's a quadrilateral.

It has four equal sides so its a rhombus.

It has four right angles so its a rectangle.

It has four equal sides AND right angles so its a square.

And if all the sides are parallel (well, two pairs of parallel sides) its a parallelogram.

The value of x in the equation [tex]64^{3x} = 512^{2x}[/tex] is infinite

The equation is given as:

[tex]64^{3x} = 512^{2x}[/tex]

Rewrite [tex]64^{3x}[/tex] and [tex]512^{2x}[/tex] in base 2

[tex]2^{6*3x} = 2^{9*2x}[/tex]

Evaluate 6 * 3x and 9 * 2x

[tex]2^{18x} = 2^{18x}[/tex]

By comparing the exponents, we have:

18x = 18x

Divide both sides by 18x

1 = 1

Hence, the value of x in the equation is infinite

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Answer:

D) No Solution

Step-by-step explanation:

Answer: 30 6/29

Step-by-step explanation: 6132 \ 203 is 30 and 42/203. 42/203 simplified is 6/29

Answer:

should be 512 inches because l x w x h (8x8x8) is 512

Answer:c

Step-by-step explanation:

Step-by-step explanation:

Since radii of a circle are congruent, UT is congruent to WT.

Since angles opposite congruent sides in a triangle are congruent, angles UWT and WUT are congruent.

This means the measure of UTV is 180-57-57=66 degrees

Answer: A

Step-by-step explanation:

Answer:

320

Step-by-step explanation:

cheerleaders =1

football team members=2

2+1=3

football team members= 480 ×2/3

=320

The weight of sand in the mixture when the weight of the clay in the mixture is 6.25 pounds is 4.69 pounds.

The equation can be represented as follows:

3c = 4s

3c = 4s

where

Hence,

3c = 4s

4s = 3c

let's make s the subject of the formula, since, we want to find s when c = 6.25 pounds

s = 3 / 4 c

s = 3 / 4 × 6.25

s = 18.75 / 4

s = 4.6875

s = 4.69 pounds

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Check the picture below.

so the volume is really just the product of the trapezoidal face and the length, and we know is 464.75 ft³.

[tex]\textit{area of a trapezoid}\\\\ A=\cfrac{h(a+b)}{2}~~ \begin{cases} h=height\\ a,b=\stackrel{parallel~sides}{bases}\\[-0.5em] \hrulefill\\ h=5\\ b=8\\ a=5 \end{cases}\implies A=\cfrac{5(5+8)}{2}\implies A=\cfrac{65}{2}~ft^2 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\large volume of the prism}}{\stackrel{\textit{area of trapezoid}}{\left( \cfrac{65}{2} \right)} \stackrel{length}{(x)}}~~ = ~~464.75\implies \cfrac{65x}{2}=464.75 \\\\\\ 65x=(2)464.75\implies x=\cfrac{(2)464.75}{65}\implies x=14.3[/tex]

Answer:

A us right of first one and d is the right of another one

Answer:

The volume is 110

Answer:

110

Step-by-step explanation:

10x2x5.5=110

Transforming the function f(x) would change its formula to g(x)

The transformation of f(x) to g(x) are

The function is given as:

f(x) = e^x

Shift the function 2 units left

f'(x) = e^x + 2

Shift the function 3 units up

f''(x) = e^x + 2 + 3

Rewrite as:

g(x) = e^x + 2 + 3

Hence, the transformation of f(x) to g(x) are (b) and (c)

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Answer:

Simplifying

2.5x + -5 = 5

Reorder the terms:

-5 + 2.5x = 5

Solving

-5 + 2.5x = 5

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.

-5 + 5 + 2.5x = 5 + 5

Combine like terms: -5 + 5 = 0

0 + 2.5x = 5 + 5

2.5x = 5 + 5

Combine like terms: 5 + 5 = 10

2.5x = 10

Divide each side by '2.5'.

x = 4

Simplifying

x = 4

Step-by-step explanation:

Answer:

x=4

Step-by-step explanation:

2.5x-5=5

isolate the variable to find your answer

2.5x-5=5

      +5>+5

2.5x=10

divide by 2.5

10/2.5=4

x=4

let's keep in mind that the shapes are both congruent, and let's also notice the letters sequence, KLMN is congruent with with its corresponding sides and angles at PQRS, so the PS side will be corresponding with the NK side, and the angle at M is the same as the angle at R, Check the picture below.

Answer:

(4,2)

Step-by-step explanation:

It's parallel, so all of them have to be on the same way.

The last point has to be at the same distance from the one right above it

Answer:

C. (4, 2)

Step-by-step explanation:

(x, y)

if you put the last dot on (4, 2) and connected all of them, it would create a perfect parallelogram

Answer:

Step-by-step explanation:

The expanded form of 30 is 30+ 0. 2. How can write a 30 number in expanded fraction form? In the expanded fraction form, you can write 30 as (3 x 10) + (0 x 1).

Answer:

the answer for the first is 3/4

and the answer for the second is 2x/x+5

Answer:

64 cm^2

Step-by-step explanation:

Split the figure into two parts (top and bottom rectangle)

TR : 2 x (12-5)*

   2 x 7 = 14

*= Since there are a few ways to split it up but I chose to make the top one shorter so you have to subtract 5 from 12

BR : 10x5 = 50

Add together

14 + 50 =

64 cm^2

Hope this helps :)

Answer: 1. Smaller than 8 SQUARE ft. 8 ft on one side and 7/8 ft one one side does NOT equal 8 square ft, it is less. It is actually 7ft. 2. 50,343 is the answer to the second question, so less than the number. Explanation: When you multiply a number by a fraction you get less than the number you started with.

Hope this helps

Answer:

7. Option 2 smaller than 8 sq.ft.

8. Less than 67.24

Step-by-step explanation:

7. the fraction 7/8 is proper, i.e. less than the unit, Any number multiplied by a proper fraction is less (reduced).

8. the same reason as the previous one, 3/4 is a proper fraction.

Hope this helps

The expression that represents the perimeter of the given triangle in centimeters is;  14n + 10p + 14q

We are given the  side lengths of the triangle as;

5n + p; 9n + 8q; 6q + 9p

Now, the formula for perimeter of a triangle is;

Perimeter = a + b + c

where a, b and c are side lengths of the triangle. Thus;

Perimeter = 5n + p + 9n + 8q + 6q + 9p

Perimeter = 14n + 10p + 14q

In conclusion, we can sa that the perimeter of the given triangle is 14n + 10p + 14q.

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Answer:

For problem 1...                                                    For problem 2...

Here are the solutions for a.                               Here are the solutions for b.

[tex]\left[\begin{array}{ccc}5&6\\7&8&9\end{array}\right][/tex]                                                            [tex]\left[\begin{array}{ccc}3\\4&5&6\\7&8&9\end{array}\right][/tex]

There are only 5 to infinity solutions.                Here, there are 7 to infinity.

                            What can we base off of these data sets?

   We can create many more numerical comparisons, as well as ineqaulities.

Examples of those ineqaulities include...

What have we learned?

Answer:

a is 4.5, and b is 3.

Step-by-step explanation:

These numbers are the averages for the numbers shown.

4+5 = 9

9/2 = 4.5

2+4 = 6

6/2 = 3

That is how you can find the average of two numbers.

Answer:

K ∩ L = {a, e, i, n, q, t, u}

K ∪ L = {a, e, i, l, n, o, q, t, u, y}

Step-by-step explanation:

Write the sets in alphabetical order

K = {a, e, i, n, o, q, t, u}

L = {a, e, i, l, n, q, t, u, y}

Set of all values that are members of both sets:

K ∩ L = {a, e, i, n, q, t, u}

Set of all values that are members of K, or L, or both:

K ∪ L = {a, e, i, l, n, o, q, t, u, y}