Find the volume of the prism.

Answer:

4 m squared minus 20 m n + 25 n squared; a perfect square trinomial

Step-by-step explanation:

(-2m+5n)(-2m+5n)

4[tex]m^{2}[/tex]-20mn+25[tex]n^{2}[/tex]

By expanding the given expression, we conclude that the equivalent expression will be the perfect square trinomial:

4m^2 + 20m*n + 25n^2

We have a polynomial given by the expression:

(2m + 5n)^2

If we expand the binomial (binomial means that it hastwo terms), we will get:

(2m)^2 + 2*(2m)*(5n) + (5n)^2

= 4m^2 + 20m*n + 25n^2

This is a perfect square trinomial (trinomial because has 3 terms and perfect square because is the square of a binomial).

If you want to learn more about polynomials, you can read:

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Answer

x=1 +[tex]\sqrt{2} ,x=1 - \sqrt{2}[/tex]

Step-by-step explanation:

x.1,2=[tex]\frac{-(-2)+ \sqrt{(-2)^2-4.1(-1)} }{2.1}[/tex]

apply rule -(-a)=a

[tex]\sqrt{(-2)^2+4.1.1}[/tex]

[tex]x1,2=\frac{-(-2)+2\sqrt{2} }{2.1}[/tex]

x=1 +[tex]\sqrt{2} ,x=1 - \sqrt{2}[/tex]

Answer:

Step-by-step explanation:

It was confusing

Answer:

[tex](x+1)^2 + (y + 1)^2 = 13[/tex]

Step-by-step explanation:

To find the centre of the circle, find the mid - point of PQ :

[tex]Centre =( \frac{x_1+x_2}{2} \ , \ \frac{y_1 + y_2}{2}) = (\frac{-2}{2} \ , \ \frac{-2}{2}) = (-1, -1)[/tex]

Diameter = 2 x Radius , To Find the diameter, find distance between P and Q:

[tex]Distance , PQ = \sqrt{(2 - (-4))^2 + (1 -(-3))^2}[/tex]

                   [tex]= \sqrt{6^2 + 4^2} = \sqrt{36+ 16} = \sqrt{52} = \sqrt{4 \times 13} = 2 \times \sqrt{13}[/tex]

PQ is the diameter , therefore radius :

                                                [tex]r = \frac{1}{2} \times 2 \sqrt{13} = \sqrt{13}[/tex]

Equation of a circle :

                              [tex](x + 1)^2 + (y + 1)^2 = 13[/tex]

Answer:

(x - 1)2 + (y - 1)2 = 13

Step-by-step explanation:

This is the answer for Acellus users

Answer:

sin x = a/b

cos x = c/b

tan x = a/c

Answer:

sin x = a/b

cos x = c/b

tan x = a/c

Step-by-step explanation:

We know,

So, in this right triangle, the opposite is a

                                          "   hypotenuse is b

                                          "   adjacent is c

So, sin x = a/b

      cos x = c/b

      tan x = a/c          

Answer:

Step-by-step explanation:

( - ∞ , - 3 ) ∪ [ - 1 , ∞ )

Answer:

[tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5} = 0[/tex]

General Formulas and Concepts:

Algebra I

Terms/Coefficients

Calculus

Limits

Limit Rule [Variable Direct Substitution]:                                                             [tex]\displaystyle \lim_{x \to c} x = c[/tex]

Step-by-step explanation:

Step 1: Define

Identify

[tex]\displaystyle \lim_{x \to 5} \frac{x^2 - 25}{x + 5}[/tex]

Step 2: Evaluate

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Limits

Answer:

[tex] \frac{1}{2} \: as \: a \: decimal = \\ 0.5[/tex]

Step-by-step explanation:

thats the answer

The decimal form, the mixed fraction can be written as 112.5.

To find out mixed fraction in the form of decimal.

A fraction is a part of a whole. In arithmetic, the number is expressed as a quotient, in which the numerator is divided by the denominator. In a simple fraction, both are integers. A complex fraction has a fraction in the numerator or denominator. In a proper fraction, the numerator is less than the denominator.

Given that:

The mixed fraction is a fraction whose nominator is greater than its denominator or improper fraction is a fraction in which the denominator is always less than the numerator.

 112 1/2

= (2 x 112 + 1)/2

= (224 + 1)/2

= 225/2

To divide the 225 by 2 ,we get

=112.5

So,  the decimal form, the mixed fraction can be written as 112.5

Learn more about fraction here:

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Did you manage to solve it?

Answer:

[tex]14. \\841\rightarrow 800\\\\15.\\750[/tex]

Step-by-step explanation:

14:

Round the highest place means keeping the farther non-zero digit to the left, then rounding. Therefore, there should only be one non-zero digit in our final answer. The only answer choice that follows this and correctly rounds is [tex]\boxed{841\rightarrow 800}[/tex]

15:

There are 30 days in November. Therefore, the number of pages typed is equal to [tex]30\cdot 25=\boxed{750}[/tex]

Answer:

.

Step-by-step explanation:

9514 1404 393

Answer:

Step-by-step explanation:

a) ac is the product of the leading coefficient (16) and the constant (-1).

  ac = (16)(-1) = -16

__

b) b is the coefficient of x. There is no x term, so ...

  b = 0

__

c) Two factors that add to give zero must be opposites. That is, they must be the square root of the opposite of -16, and the opposite of that.

  the two numbers are -4 and 4

__

d) The factored form for the two numbers p and q just found is ...

  ax^2 +bx +c = (ax +p)(ax +q)/a

  = (16x -4)(16x +4)/16

  = (4x -1)(4x +1) . . . . factored form of 16x^2 -1

Answer:

Consider the polynomial 16x2 – 1.

*)   What is the value of ac?  

–16

**)     What is the value of b?  

0

***)    What two numbers multiply to get ac and add to get b?  

–4 and 4

****)    The factored form of 16x2 – 1 is  

(4x– 1)(4x+ 1)

.

Step-by-step explanation:

Edge 2021

Answer:

8 and 2/5 is 42/5 and its reciprocal is 5/42

Step-by-step explanation:

[tex]Reciprocal \: of \: \frac{42}{5} \: is \: \frac{5}{42} [/tex].

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex]8 \frac{2}{5} \\ \\ = \frac{42}{5} [/tex]

[tex]Hence, \:the\: reciprocal \: of \: \frac{42}{5} \: is \: \frac{5}{42}.[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer:

just took it, 15%

Step-by-step explanation:

I just took it online on ed

Answer:

30/100 × Y= 234

Y= 234÷30=7.8

7.8×100= 780

So the money is $780

Step-by-step explanation:

a. 60/100× 780 = $468

b. 90/100× 780 = $702

c. 15/100× 780= $117

d. 3/100 × 780= $23.4

Answer:

5

Step-by-step explanation:

Given :

Y α 1/x

Y = k/x

Where, k = constant of proportionality ;

y = 3 ; x = 10

3 = k / 10

k = 10 * 3

k = 30

Equation becomes :

Y = 30/x

Y =? ; when x = 6

Y = 30 / 6

Y = 5

Answer:

625 miles

Step-by-step explanation:

250/4=62.5

62.5*10 = 625

Answer:

Below.

Step-by-step explanation:

There are 6 * 10 minutes in 1 hour and 4*6 = 24  10minutes in 4 hours.

So in 10 minutes she travels 250 / 24

= 10.417 miles to nearest thousandth.

9514 1404 393

Answer:

  (a)  145

Step-by-step explanation:

The measure of the angle marked x° is half the sum of the intercepted arcs:

  (90° +200°)/2 = x° = 145°

Answer:

A: SA = 46 cm^2; V = 11 cm^3

B: SA = 46 cm^2; V = 14 cm^3

C: SA = 46 cm^2; V = 15 cm^3

Step-by-step explanation:

SA = 2B + PH = 2LW + PH

where SA = total surface area,

B = area of a base

P = perimeter of the base

H = height of the prism

L = length of the base

W = width of the base

V = LWH

Prism A:

SA = 2(11 cm)(1 cm) + 2(11 cm + 1 cm)(1 cm)

SA = 46 cm^2

V = (11 cm)(1 cm)(1 cm) = 11 cm^3

Prism B:

SA = 2(7 cm)(2 cm) + 2(7 cm + 2 cm)(1 cm)

SA = 46 cm^2

V = (7 cm)(2 cm)(1 cm) = 14 cm^3

Prism C:

SA = 2(5 cm)(3 cm) + 2(5 cm + 3 cm)(1 cm)

SA = 46 cm^2

V = (5 cm)(3 cm)(1 cm) = 15 cm^3

Answer:

uₙ₊₁ = uₙ + ¹/₂

Step-by-step explanation:

uₙ₊₁ = uₙ + d

u₈ = 3

u₁₀₀ = 49

We can establish the following:

u₉ = 3 + d

u₁₀ = (3 + d) + d = 3 + 2d

u₁₁ = (3 + 2d) + d = 3 + 3d

so...

u₈₊ₐ = 3 + ad

u₁₀₀ = u₈₊₉₂ = 3 + 92d

3 + 92d = 49

92d = 46

d = ¹/₂

∴ uₙ₊₁ = uₙ + ¹/₂

Answer:

1.33

Step-by-step explanation:

so mean is the average

so what you have to do is add the numbers for each person and then divide by the amount of numbers present. the question is asking for the difference so subtract the numbers for each from person.

mia's mean= 34.33

sophia's mean= 35.667

sophia-mia= 1.33

(check my work, and if you need help just comment)

Answer:

No

Step-by-step explanation:

To be a function, each input can only go to one output

0 goes to 1 and 2 so it cannot be a functions

Answer:

[tex]-4x^{2} +11[/tex] is a parabola. The coefficient in front of the highest term (-4 in front of the [tex]x^{2}[/tex]) is negative, meaning both of the ends go towards negative infinity (point downward). So, as x approaches positive or negative infinity, y approaches negative infinity.

The end behavior of the function is being divergent for [tex]x \to \pm \infty[/tex].

According to theory of limits and differential calculus, all polynomial functions are continuous and differentiable function with no limits for [tex]x \to \pm \infty[/tex]. Therefore, we can conclude that function [tex]h(x) = -4\cdot x^{2}+11[/tex] diverges to [tex]-\infty[/tex] for [tex]x > 0[/tex] or [tex]x < 0[/tex].

That is,

[tex]x \to +\infty[/tex]

[tex]\lim_{x \to +\infty} -4\cdot x^{2} + 11 = -4 \cdot \lim_{x \to +\infty} x^{2} + \lim_{x \to +\infty} 11[/tex]

[tex]\lim_{x \to +\infty} -4\cdot x^{2} + 11 = N.E. + 11[/tex]

[tex]\lim_{x \to +\infty} -4\cdot x^{2} + 11 = N.E.[/tex]

[tex]x \to -\infty[/tex]

[tex]\lim_{x \to -\infty} -4\cdot x^{2} + 11 = -4 \cdot \lim_{x \to -\infty} x^{2} + \lim_{x \to -\infty} 11[/tex]

[tex]\lim_{x \to -\infty} -4\cdot x^{2} + 11 = N.E. + 11[/tex]

[tex]\lim_{x \to -\infty} -4\cdot x^{2} + 11 = N.E.[/tex]

Hence, the end behavior of the function is being divergent for [tex]x \to \pm \infty[/tex].

We kindly invite you to check this question related to limits: https://brainly.com/question/12383180

Answer:

8,9,10

Step-by-step explanation:

Let x be the first integer

x+1 is the next consecutive integer

x+2 is the third consecutive integer

The sum is 27

x + (x+1) + (x+2) = 27

Combine like terms

3x+3 = 27

Subtract 3 from each side

3x+3-3 =27-3

3x =24

Divide by 3

3x/3 = 24/3

x=8

The integers are

x=8

x+1 =9

X+2 =10

Answer: the top one

Step-by-step explanation:

Answer:

[tex]63\frac{6}{9}[/tex]

Step-by-step explanation:

[tex](212-4-5)[/tex] ÷ [tex]3-4=[/tex]

[tex]203[/tex] ÷ [tex]3-4=[/tex]

[tex]67\frac{6}{9}-4=[/tex]

[tex]=63\frac{6}{9}[/tex]

Hope this helps

OPTION C is the correct answer.