Which of the following is the correct factorization of the polynomial below?

2x^2 - 12x + 18

A. 2(x - 3)^2

B. 2(x + 6)(x + 3)

C. (2x + 6)(x + 3)

D. The polynomial is irreducible.

⠀

Explanation :

⠀

We know,

[tex]{ \longrightarrow{\qquad \pmb {\sf Volume_{(Sphere)} = \dfrac{4}{3} \pi {r}^{3} }}}[/tex]

⠀

Here,

⠀

Substituting the values in the formula :

⠀

[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times3.14 \times {\bigg(7 \bigg)}^{3} }}}[/tex]

⠀

[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4}{3} \times 3.14 \times 343 }}}[/tex]

⠀

[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4 \times 3.14 \times 343}{3} }}}[/tex]

⠀

[tex]{ \longrightarrow {\qquad {\sf Volume_{(Sphere)} = \dfrac{4308.08}{3}}}}[/tex]

⠀

[tex]{ \longrightarrow{\qquad \pmb {\sf Volume_{(Sphere)} = 1436.02 }}}[/tex]

⠀

Therefore,

Answer:

[tex]\textsf{A.} \quad \textsf{The slope of the line is }\boxed{\dfrac12}[/tex]

Step-by-step explanation:

[tex]\textsf{let}\:(x_1,y_1)=(12,0)[/tex]

[tex]\textsf{let}\:(x_2,y_2)=(2,-5)[/tex]

[tex]\textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-5-0}{2-12}=\dfrac12[/tex]

[tex]\textsf{The slope of the line is }\boxed{\dfrac12}[/tex]

Answer:

  385.6 m²

Step-by-step explanation:

The surface area of a prism is the sum of the surface areas of each of the faces. A triangular prism has two triangular faces and three rectangular faces. The areas of the rectangular faces will have a total equal to the perimeter of the triangle times the height of the prism.

__

  Area = 2×triangle area + lateral area

  = 2(1/2)(bh) +PH

  = (16 m)(5.6 m) + (6 +15 +16 m)(8 m)

  = 89.6 m² +296 m² = 385.6 m²

The surface area of the triangular prism is 385.6 square meters.

_____

Additional comment

In the above formula, we have used ...

Answer:

multicultural

Step-by-step explanation:

Answer:

A. Multicultural

Step-by-step explanation:

It shows later in the sentence that they ate Thai noodles and Egyptian falafel those come from different cultures so it must be multicultural

Answer:

Step-by-step explanation:

The ratios of the numbers shown in the table are all ...

  y/x = 16/4 = 20/5 = 4

Then the missing y-value is ...

  y = 4x

  y = 4(2) = 8

__

And the missing x-value is ...

  36 = 4x

  36/4 = x = 9

_____

Additional comment

The x- and y-values in a "ratio table" are proportional to each other. That means the y corresponding to half an x-value will be half the y-value. In other words, the y for x=2 will be half the y for x=4, or 16/2 = 8.

Also, the values add. We notice that y=36 is the sum of y=16 and y=20. This means the corresponding x-value for y=36 will be the sum of x=4 and x=5, or x = 4+5 = 9.

Answer:

12.6 = c

Step-by-step explanation:

The Pythagorean therom is a^2 + b^2 = c^2

We already know 2 varibles (12 and 4) so we can just plug them in.

12^2 + 4^2 = c^2

144 + 16 = c^2

160 = c^2

[tex]\sqrt{160}[/tex] = [tex]\sqrt{c^2}[/tex]

12.6 = c

Hope this helps :)

Answer:

-4 < x < -1 or x > 1 (the third option)

Step-by-step explanation:

hope this helps

Answer:

P=90°

R=45°

Step-by-step explanation:

PQR=180°

180°-45°=135°

R=45°(iscoles triangle)

P=90°

Answer:

  y = 1.36x

Step-by-step explanation:

There will be no touchdown throws if no games are played. The y-intercept must be zero. That is, the number of touchdown throws is considered to be proportional to the number of games, with the constant of proportionality being 1.36:

  y = 1.36x

Answer: 4,000

Step-by-step explanation:

The only logical choice there because of the rate of others

Answer: c is the answer

Step-by-step explanation:

Answer:

37 5/7

Step-by-step explanation:

use formular it will be 2pie -22/7 ×radius

since we have been given only radius it will be

2×22/7×6=37 5/7

[tex]\qquad\qquad\huge\underline{{\sf Answer}}♨[/tex]

Let's find the circumference of given circle ~

Circumference :

[tex] \qquad \tt  \dashrightarrow \: 2\pi{r}^{} [/tex]

where, r = radius

Now, let's calculate it ~

[tex] \qquad \tt  \dashrightarrow \: c = 2×\pi{}^{}×6 [/tex]

[tex] \qquad \tt  \dashrightarrow \: c = 12\pi\: \: m[/tex]

That's the answer I terms of π, but we can also plug in the approximate value of pi as 3.14

[tex] \qquad \tt  \dashrightarrow \: c = 12 \times 3.14{}^{} [/tex]

[tex] \qquad \tt  \dashrightarrow \: c = 37.68\: \: m[/tex]

[tex] \qquad \tt  \dashrightarrow \: c \approx 37.7\: \: m[/tex]

The Total Number of socks is 10 in all, bear in mind that there is no blue socks hence it will not add to the total amount of socks

Note : 1 pais = 2 socks

Given Data

The statement " 6 times as many pairs of blue socks" is equivalent to no socks, since we have no blue socks, hence 6*0 = 0

Let us find the total socks

= 8+0+2

= 10 socks

Learn more about addition here:

https://brainly.com/question/25421984

Step-by-step explanation:

Using distance formula,

Let the distance between point E and F = ef,

[tex]ef = \sqrt{{(7 - 1)}^{2} + {(2 - 9)}^{2} } \\ ef = \sqrt{85} \\ = 9.219544457[/tex]

Answer:

a

Step-by-step explanation:

An asteroid is a minor planet of the inner Solar System. Historically, these terms have been applied to any astronomical object orbiting the Sun that did not resolve into a disc in a telescope and was not observed to have characteristics of an active comet such as a tail.

Answer:

The answer should be 15, since each week the number goes up by 15.

I see a pattern here! Let me show you - multiply 15 by the week number (1, 2, 3, 4, ...), and you have y.

For example, 15 x 3 (for week 3) is 45, as shown by the y value.

So all we must do is multiply 15 by 5, and voila! We'll have our answer. Which, by the way, is 75.

I hope this answers your question!

-Toremi

Answer:y=4+x

Step-by-step explanation:

You are adding gallons not *,/,-,. So it's y=4+x.

The required equation is y = 4 + x. The correct answer would be an option (A).

The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.

Jayne stopped for gas before embarking on a road trip. There were already 4 gallons of gas in the tank.

As per the question, the required equation would be as:

y = 4 + x

This equation relates the total amount of gasoline in the tank, y, to the number of gallons that she put in the tank, x. The total amount of gasoline in the tank, y, is equal to the number of gallons that she put in the tank, x, plus the 4 gallons that were already in the tank.

Learn more about the equation here:

brainly.com/question/10413253

#SPJ2

Answer:

$318

Step-by-step explanation:

6% x 300 = 18

300 + 18 = 318

Answer:

B. 6 cookies

Step-by-step explanation:

Given :

Number of chocolate chip

Answer:

See below in bold.

Step-by-step explanation:

Let the length of the shortest side be x, then the longest side = 2x.

Also  x + y = 2x  + 1   where y = length of the middle side,

Simplifying:

2x - x - y = -1

x - y = -1        (A)

Also as the perimeter = 7:

x + 2x + y = 7

3x + y = 7       (B)

Adding (A) and (B):

4x + 0 = 6

x = 6/4 = 1.5

Plug x = 1.5 into equation B:

3(1.5) + y = 7

y = 7 - 4.5 = 2.5.

Answer:

So the shortest side = 1.5, middle = 2.5 and longest = 2*1.5 = 3.

Answer:

8√3

Step-by-step explanation:

Let a, b = the positive numbers, and the sum = s,

(1)---- ab = 192

(2)--- a + b = s

Since we want to find the minimum sum, we'll have to substitute one of the variables (either a or b) from (1) to (2), I'll choose b,

From (1), b = 192/a

Substitute b = 192/a into (2),

s = a + 192/a

Now, we are able to use a concept of calculus (maximum & minimum) to solve it, just remember 2 steps in finding the values of x in maxima minima question:

1) find dy/dx

2) Find x from dy/dx = 0

ds/da = 1 - 192/a²

When ds/da = 0,

1 - 192/a² = 0

a² = 192

a = ±√192

a = 8√3 , -8√3

Since a is positive, a = 8√3

Substitute a into (1),

b = 192/(8√3)

b = 8√3

Therefore, the two positive numbers are 8√3... and 8√3

I assume 3π/2 < x < 2π, so that x is in the 4th quadrant. For angles x terminating in Q4, we have sin(x) < 0 and cos(x) > 0, so tan(x) = sin(x)/cos(x) < 0.

This means that, using the Pythagorean identity,

cos(x) = + √(1 - sin²(x)) = 4/5

tan(x) = (-3/5) / (4/5) = -3/4

Recall the double angle identities:

sin(2x) = 2 sin(x) cos(x) = 2 (-3/5) (4/5) = -24/25

cos(2x) = 2 cos²(x) - 1 = 2 (4/5)² - 1 = 7/25

tan(2x) = 2 tan(x) / (1 - tan²(x)) = 2 (-3/4) / (1 - (-3/4)²) = -24/7

Answer:

[tex]\boxed{\sf{x=\dfrac{25}{2}=12.5}}[/tex]

Step-by-step explanation:

Solve the logarithm function.

Put the logarithm function on one side of the equation and x on the other.

[tex]\sf{\log _{10}(x)+\log _{10}(8)=2}[/tex]

First, subtract by log₁₀(8) from both sides.

[tex]\sf{\log _{10}(x)+\log _{10}(8)-\log _{10}(8)=2-\log _{10}(8)}[/tex]

Solve.

[tex]\sf{\log _{10}(x)=2-\log _{10}(8)}[/tex]

[tex]\sf{\log _{10}(x)=2-\log _{10}(8)=\boxed{\sf{x=\dfrac{25}{2} }}[/tex]

I hope this helps you! Let me know if my answer is wrong or not.

Step-by-step explanation:

it is 300,000 for a 3 day contract

Answer:

B. 46 ft²

Step-by-step explanation:

Two sides are rectangles 3.1 ft by 5 ft.

One side is a rectangle 5 ft by 3 ft.

area = 2(3.1 ft × 5 ft) + (5 ft × 3 ft)

area = 46 ft²

x is equal to 3 ..

Step-by-step explanation:

hope this helps

Answer:

y = (4/3)x

Step-by-step explanation:

Two points on the line are the origen (0, 0) and the given (9, 12).

Starting at the origin and moving to (9,  12), we see the change in x being 9 and that in y being 12.  Thus, the slope of the line through these two points is m = rise/run = 12/9 = 4/3.

Thus the equation of the line in slope-intercept form is y = (4/3)x + 0, or

just y = (4/3)x

The different recital programs that are possible is 80,730 ways

Permutation has to do with arrangement while combination has to do with the selection.

According to the question, a pianist plans to play 5 pieces at a recital from her repertoire of 27 pieces, this shows that he can select the 5 pieces in any form.

The number of ways this can be done is given as:
[tex]27C_5=\frac{27!}{(27-5)!5!}\\ 27C_5=80,730[/tex]

Hence the different recital programs that are possible is 80,730 ways

Learn more on combination here: https://brainly.com/question/11732255

Answer:y=x^2 translated 3 to the right gives

y=(x-3)^2,   the vertex shifts from (0,0) to (3,0)

translate it 4 up by adding 4

y=(x-3)^2 + 4, this shifts the vertex up to (3,4)

f(x) = (x-3)^2 + 4   or call it

g(x) = (x-3)^2 + 4  if you want to distinguish it from the original f(x) function

Step-by-step explanation:In this question we have been given a function f(x) = |x|

When we perform a translation of 4 units right then the translated form of the function becomes f(x) = |x - 4|

And when we we translate the function up by 2 units then the transformed form is f(x) = |x - 4| + 2

Therefore the given graph in option B is the correct option.

[tex] \frac{(1 - \cos(a))(1 + \cos(a)) }{(1 - \sin(a) )(1 + \sin(a)) } = \\ [/tex]

[tex] \frac{1 - {cos}^{2}(a) }{1 - {sin}^{2}(a) } = \\ [/tex]

[tex] \frac{ {sin}^{2}(a) }{ {cos}^{2}(a) } = \\ [/tex]

[tex] {tan}^{2} (a)[/tex]