The diameter of a cone is 34 ft. The height is 16 ft. What is the volume in cubic ft?

Answer:

4

Step-by-step explanation:

i dont really know how to explain i used an algebra calculator

Answer:

Given,  

The ratio of the three numbers are 1:2:3 . Let the numbers are x , 2x and 3x.

According to the question,

x³+(2x)³+(3x)³=4,500  

⟹x³+8x³+27x³=4,500  

⟹36x³=4500  

⟹x³=4,50036  

⟹x³=125  

⟹x=125−−−√3  

⟹x=5  

So the numbers are 5,5×2=10,5×3=15  

Therefore, 5 is the smallest number.

https://www.quora.com/Three-numbers-are-in-the-ratio-1-2-3-and-the-sum-of-their-cubes-is-4-500-What-is-the-smallest-number

Answer:

[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]

Step-by-step explanation:

We are given the two functions:

[tex]\displaystyle r(x) = -x^2 + 3x \text{ and } s(x) = 2x + 1[/tex]

And we want to find:

[tex]\displaystyle (s-r)(x)[/tex]

This is equivalent to:

[tex]\displaystyle (s-r)(x) = s(x) - r(x)[/tex]

Substitute and simplify:

[tex]\displaystyle \begin{aligned}(s-r)(x) & = s(x) - r(x) \\ \\ & = (2x+1)-(-x^2+3x) \\ \\ & = (2x+1)+(x^2-3x) \\ \\ & = x^2 +(2x-3x) + 1 \\ \\ & = x^2 - x + 1 \end{aligned}[/tex]

In conclusion:

[tex]\displaystyle (s-r)(x) = x^2 - x + 1[/tex]

Answer:

Step-by-step explanation:

4 person =  1575 bags

1 person  = 1575:4 = 393.75 bags

40 min = 1 bag

393,75 bags = 40 min•393,75 = 15 750 min

Answer:

1 : 400

Step-by-step explanation:

[tex]\frac{3.5 x 10^{3} }{3.5 x 10^{3} } : \frac{1.4 x 10^{6 } }{3.5 x 10^{3} }[/tex]

1 : .4 x [tex]10^{3}[/tex]

1 : 4 x [tex]10^{2}[/tex]

1 : 400

Answer:

Step-by-step explanation:

2(75)=150 that's the amount due in total for two months so

400-150= 250 they will owe $250 after two months payment

Answer:

c

Step-by-step explanation:

x³ - y³ ← is a difference of cubes and factors as

x³ - y³ = (x - y)(x² + xy + y²)

Given

[tex]\frac{x}{y}[/tex] + [tex]\frac{y}{x}[/tex] = - 1

Multiply through by xy to clear the fractions

x² + y² = - xy ← substitute into second factor of expansion

x³ - y³ = (x - y)(- xy + xy) = (x - y) × 0 = 0 → c

Answer:

The answer is C. 0

Step-by-step explanation:

since

[tex] \frac{x}{y} + \frac{y}{x } = - 1[/tex]

we multiply both sides by xy to cancel their denominators and multiply -1 by xy

so we have

[tex]xy( \frac{x}{y}) + xy( \frac{x}{y} ) = xy \times - 1[/tex]

we get our answer as

[tex] {x}^{2} + {y}^{2} = - xy[/tex]

we were given the difference of cubes that is

[tex] {x}^{3} - {y}^{3} [/tex]

which is =

[tex](x - y)( {x}^{2} + xy + {y}^{2} )[/tex]

so since,

[tex] {x}^{2} + {y}^{2} = - xy[/tex]

we substitute,

[tex](x - y)( - xy + xy) = (x - y)(0) = 0[/tex]

Answer:

b. The science students

Step-by-step explanation:

If you count the dots, they are the same for both class (9 people) but the range of the science students' scores are higher than the range for the math students, which means that the sum of their scores will be larger than the math students' and since they have the same number of people, the number being divided for the average would be the same, so the science students' average would be greater than the math's.

I hope this helped! ;D

Answer:

31

Step-by-step explanation:

Given

x² + 5x - 3 = 0

with a = 1, b = 5, c= - 3 , then

sum of roots x₁ + x₂ = - [tex]\frac{b}{a}[/tex] = - [tex]\frac{5}{1}[/tex] = - 5

product of roots = [tex]\frac{c}{a}[/tex] = [tex]\frac{-3}{1}[/tex] = - 3

Now

(x₁ + x₂)² = x₁² + 2x₁x₂ + x₂² , that is

(- 5)² = x₁² + 2(- 3) + x₂²

25 = x₁² - 6 + x₂² ( add 6 to both sides ), then

x₁² + x₂² = 31

Answer:

A,B,C

explanation:

i got it right on edge

Answer:

D. Positively skewed

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

it is defined for all values so D=R

also we can get any value

so Range =R

Answer:

B

Step-by-step explanation:

because that's odd power function it can take both, negative and positive values

( − 2 ) ( 3+ 2 2 − − 2 )

Hope this helps, have a great day!

Answer:

291 cm³

Does the answer help you?

Answer:

k=10BY DPING PROCESS IT BECOME

Answer:

x^2+3x-4

Step-by-step explanation:

(x-1)(x+4)

x^2+4x-x-4

x^2+3x-4

Hope this helps ;) ❤❤❤

Answer:

y = x² + 3x -4

Step-by-step explanation:

we can use the FOIL formula

(x-1) (x+4)

x² + 4x - x -4

x² + 3x -4

therefore, the standard form would be y = x² + 3x -4

Answer:

{x | x is a real number}

Step-by-step explanation:

f(x) = 5x – 7

There are no restrictions on the value that x can take

The domain is all real numbers

Answer:

In the given expression, that is, f (x) = 5x - 7, we can say:

x satisfies all the real values starting from -∞ to ∞.

domain of 5x-7

Interval notation for f (x):

(- ∞ , ∞)

So, the domain will be all real numbers, as the function is a straight line, with no discontinuities, thus undefined at no value of x.

Answer:

the function is a y-intercept

Step-by-step explanation:

y=mx+b is the slope intercept formula, m being the slope and b being the y-intercept, meaning y=b, so b=-9/4.

Because it says y=-9/4, we can assume that m, or the slope equals 0.

so when you plug it in, you get

y=0x-9/4

y=-9/4

Answer:

mean is adding up all the numbers.

range means the difference between the Lowest and highest value.

Step-by-step explanation:

when we add the answer is 240.6.

divide it to 12..do the final answer is 20.05

range is 25.4_16.3

9.1

Answer:

Mean: 20.05

Range: 9.1

Step-by-step explanation:

To find the mean in this problem, first you add all the following numbers together then subtract by the quantity.

20.1 + 19.6 + 18.0 + 17.8 + 25.2 + 18.7 + 21.9 + 16.3 + 25.4 + 20.5 +17.8 + 19.3

= 240.6

Now, divide by the quantity which is 12 since there's 12 numbers.

240.6 divided by 12 = 20.05.

The mean is 20.05.

To find the range in the problem, you must subtract the smallest value from the largest value.

In this case, 16.3 is the smallest value and 25.4 is the largest.

25.4 - 16.3 = 9.1

9.1 is the range.

Hope this helps you!

Answer:

(x-12)² + (y-6)² = 36 (Option C)

Step-by-step explanation:

use circle formula

(x-h)² + (y-k)²= r²

h= 12 and k= 6 and r= 6

(x-12)² + (y-6)² = 6²

6 squared = 36 (6·6)

(x-12)² + (y-6)² = 36

Answer:

  GH = 16; CH = 12

Step-by-step explanation:

First of all, you need to understand the meaning of "perpendicular bisector." It means that GH is divided into two equal parts by line AC, and that AC makes a right angle to GH.

The right angle is marked.

(a) The length of one of the halves of GH is marked as being 8 units long, so the other half will also be 8 units long. Of course, the length of GH is the sum of its two halves:

  GH = GB +BH = 8 + 8

  GH = 16

__

(b) Triangles CBG and CBH share side CB, so have that length in common. They have equal lengths BG and BH because BC bisects GH. They have a right-angle at B in common, so can be considered congruent by SAS, the fact that two congruent sides have a congruent angle between them.

Since triangles CBG and CBH are congruent, their corresponding sides CG and CH are also congruent. Side CG is marked 12 units long, so CH will be 12 units long, also.

  CH = 12

You could shortcut all of the congruent triangle logic by recognizing that an altitude (CB) is a perpendicular bisector of the base (GH) if and only if the triangle is isosceles. The sides of an isosceles triangle are always congruent, so CG = CH = 12.

__

In part (c), you're supposed to choose possible theorems for demonstrating the congruence of the triangles we described above.

Answer:

16x^2 + 24x + 9  

Step-by-step explanation:

perfect square trinomial is of the form

a^2 + 2 * a * b + b^2

9x^2 + 9x + 1   = (3x)^2 + 3*3x*1 + 1^2  not a perfect square trinomial

36b^2 − 24b + 8  = ( 6b)^2  -2 * 6b *2 + ( 2 sqrt(2)) ^2  not a perfect square trinomial

16x^2 + 24x + 9  = ( 4x) ^2 + 2 * ( 4x) * 3 + 3^2 = perfect square trinomial

4a^2 − 10a + 25 = ( 2a) ^2 -  1 * 2a *5 + 5^2   not a perfect square trinomial

Answer:

The third answer listed:

[tex]16x^2+24x+9[/tex]

Step-by-step explanation:

The trinomial:  

[tex]16x^2+24x+9[/tex]

can be factored out as follows:

[tex]16x^2+24x+9\\(4x)^2+24x+3^2\\(4x)^2+12x+12x+3^2\\4x(4x+3)+3(4x+3)\\(4x+3)\,(4x+3)\\(4x+3)^2[/tex]

which as can be seen,is the perfect square of a binomial, so this trinomial is what is called a perfect square trinomial.

Answer:

8a^3-64p^3-36a^2+54a-27

Step-by-step explanation:

since it no common variable so it can not be further solved

The length of the rectangular delivery box must be equal to 4 inches.

Let the length of the box be L.

Let the width of the box be W.

Let the height of the box be H.

Given the following data:

Translating the word problem into an algebraic expression;

[tex]W = 3 + L[/tex]  ......equation 1

[tex]H = 4 + L[/tex]  ......equation 2.

Mathematically, the volume of a rectangular solid is given by the formula;

[tex]Volume = length * width * height[/tex]  .....equation 3.

Substituting the values into equation, we have;

[tex]224 = L * (3 + L) * (4 + L)\\\\224 = (3L + L^{2})* (4 + L)\\\\224 = 12L + 3L^{2} + 4L^{2} + L^{3} \\\\224 = 12L + 7L^{2} + L^{3}[/tex]

Rearranging the polynomial, we have;

[tex]L^{3} + 7L^{2} + 12L - 224 = 0[/tex]

We would apply the remainder theorem to solve the polynomial.

According to the remainder theorem, if a polynomial P(x) is divided by (x - r) and there is a remainder R; then P(r) = R.

When x = 3

[tex](x - 3) = 0\\x = 3[/tex]

[tex]P(3) = 3^{3} + 7(3^{2}) + 12(3) - 224\\\\P(3) = 27 + 7(9) + 36 - 224\\\\P(3) = 27 + 63 + 36 - 224 = -98 \neq 0[/tex]

We would try with 4;

[tex]P(4) = 4^{3} + 7(4^{2}) + 12(4) - 224\\\\P(4) = 64 + 7(16) + 48 - 224\\\\P(4) = 64 + 112 + 48 - 224\\\\P(4) = 224 - 224 = 0[/tex]

Therefore, 4 is one of its roots.

Hence, the length of the rectangular delivery box must be equal to 4 inches.

Find more information on polynomial here: https://brainly.com/question/10689855

Answer:

[tex]\frac{-17}{15}[/tex]

Step-by-step explanation:

When solving this problem you must follow PEMDAS, so parentheses should go first. To solve 1/10 - 2/3, first, find the common denominator. In this case, that is 30. Then, subtract, [tex]\frac{3}{30} - \frac{20}{30}[/tex]. This equals -17/30. Finally, divide by 0.5. To do this remember that dividing by half is the same as multiplying by 2. Doing [tex]\frac{-17}{30} *2[/tex] equals [tex]\frac{-17}{15}[/tex].

Answer:

[tex] { x^2+3x-4} [/tex]

Step-by-step explanation:

Factor top and bottom.

The numerator is a difference of two squares, and the denominator is a quadratic.

[tex] \frac{ {9x}^{2} - {(x}^{2} - 4)^{2} }{4 + 3x - {x}^{2} } [/tex]

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

= [tex] \frac{ (x-1)(x+4) (1+x)(4-x) }{(1+x)(4-x)} [/tex]

If x does not equal -1 and does not equal 4, we can cancel the common factors in italics to give

= [tex] { (x-1)(x+4)} [/tex]

= [tex] { x^2+3x-4} [/tex]

Answer:

The answer is

Step-by-step explanation:

[tex] \frac{9 {x}^{2} - ( { {x}^{2} - 4})^{2} }{4 + 3x - {x}^{2} } [/tex]

To solve the expression first factorize both the numerator and the denominator

For the numerator

9x² - ( x² - 4)²

Expand the terms in the bracket using the formula

( a - b)² = a² - 2ab + b²

(x² - 4) = x⁴ - 8x² + 16

So we have

9x² - (x⁴ - 8x² + 16)

9x² - x⁴ + 8x² - 16

- x⁴ + 17x² - 16

Factorize

that's

(x² - 16)(-x² + 1)

Using the formula

a² - b² = ( a + b)(a - b)

We have

(x² - 16)(-x² + 1) = (x + 4)(x - 4)( 1 - x)(1 + x)

For the denominator

- x² + 3x + 4

Write 3x as a difference

- x² + 4x - x + 4

Factorize

That's

- ( x - 4)(x + 1)

So we now have

[tex] \frac{(x + 4)(x - 4)( 1 - x)(1 + x)}{ - (x - 4)(x + 1)} [/tex]

Simplify

[tex] \frac{ - (x + 4)(1 - x)(1 + x)}{x + 1} [/tex]

Reduce the expression by x + 1

That's

-( x + 4)( 1 - x)

Multiply the terms

We have the final answer as

Hope this helps you

Answer:

d = 19/5 or, 4.75 in decimal form

Step-by-step explanation:

Answer:

3 ft per minute

Step-by-step explanation:

Take the distance and divide by the time

3/4 ft ÷ 1/4 minute

Copy dot flip

3/4 * 4/1

Rewriting

3/1 * 4/4

3/1 *1

3 ft per minute