Solve |6x + 3| = 27.
A. x = 4 and x = -5
B. x = -4 and x = -5
C. x = -4 and x = 5
D. x = 4 and x = -4.

Given:

Total number of people = 10

To find:

The number of ways in which 10 people can be divided into three groups of 2, 3, and 5 people respectively.

Solution:

We know that the number of ways to select r items form n times is:

[tex]^nC_r=\dfrac{n!}{r!(n-r)!}[/tex]

The number of ways to select 2 people from 10 is [tex]^{10}C_2[/tex].

The number of remaining people is [tex]10-2=8[/tex].

The number of ways to select 3 people from 8 is [tex]^{8}C_3[/tex].

The number of remaining people is [tex]8-3=5[/tex].

The number of ways to select 5 people from 5 is [tex]^{5}C_5[/tex].

Now, the total number of ways is:

[tex]Total=^{10}C_2\cdot ^{8}C_3\cdot ^{5}C_5[/tex]

[tex]Total=\dfrac{10!}{2!(10-2)!}\cdot \dfrac{8!}{3!(8-3)!}\cdot \dfrac{5!}{5!(5-5)!}[/tex]

[tex]Total=\dfrac{10\times 9\times 8!}{2\times 1\times 8!}\cdot \dfrac{8\times 7\times 6\times 5!}{3\times 2\times 1\times 5!}\cdot 1[/tex]

[tex]Total=45\cdot 56\cdot 1[/tex]

[tex]Total=2520[/tex]

Therefore, the total number of ways is 2520 to divide 10 people into three groups of 2, 3, and 5 people respectively.

Answer:

x = 240

Step-by-step explanation:

Using the Altitude- on- Hypotenuse theorem

(leg of large triangle)² = ( part of hypotenuse below it) × (whole hypotenuse)

x² = 144 × 400 = 57600 ( take the square root of both sides )

x = [tex]\sqrt{57600}[/tex] = 240

x = 240

Using Pythagoras' theorem on the 3 triangles of sides (as shown in the graphic - the 2 smaller inner triangles and the large main triangle) it can be shown that the height is the square root of the product of both segments of the baseline.

let's call the 2 segments p and q.

p+q = 400

p = 144

q = 400 - 144 = 256

so, as said before, height = sqrt(p×q) = sqrt(144×256) = 192

now the main Pythagoras with the smallest triangle to get x

x² = 192² + 144² = 36864 + 20736 = 57600

x = 240

now, FYI, why is that formula true ?

as we said, we called the segments of the long baseline p and q.

then we can the sides of the main triangle x and y.

and the height is simply h.

so, then we have for the main rectangular triangle

(p+q)² = x² + y²

and for the 2 smaller triangles

x² = p² + h²

y² = q² + h²

=>

p² +2pq + q² = p² + h² + q² + h²

2pq = 2h²

h² = pq

h = sqrt(pq)

and there you have it. just as simple as that.

Answer:

it is an rigjt angle triangle you shoult pythogores therom if you will know it it will be easy to you to understand this question

Step-by-step explanation:

4m+2g=p

2g=p-4m

g=(p-4m)/2

Answer:

g = p/2 - 2m

Step-by-step explanation:

4m +2g = p

Subtract 4m from each side

4m -4m +2g = p-4m

2g = p -4m

Divide each side by 2

2g/2 = p/2 - 4m/2

g = p/2 - 2m

x^2 + 3x + 2x

x^2 + 5x = Binomial

x^3 + x + 3x^2 - x

x^3 + 3x^2 = Binomial

4x^3 + x + x^2 - 2x

4x^3 + x^2 - x = Trinomial

3x^4 + x - 3x^4 - x

0 = No Polynomial/Zero Polynomial

Hope this helps!

The first given polynomial is binomial.

The second given polynomial is binomial.

The third given polynomial is binomial.

The fourth given polynomial is monomial.

Polynomials are algebraic expressions that consist of variables and coefficients.

A monomial is an algebraic expression that has only one term.

Binomial is an algebraic expression that contains two different terms connected by addition or subtraction.

A trinomial is an algebraic expression that has three non-zero terms.

According to the given question.

We have some polynomials.

If we take the polynomial:

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

The above polynomial can be written as

[tex]x^{2} + 5x[/tex]

Since, the above polynomial has only two terms therefore it is  a binomial.

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

The above polynomial has only two terms. Hence, the given polynomial is binomial.

[tex]4x^{2} + x + x^{2} -2x\\=5x^{2} -x[/tex]

The given polynomial has only two terms therefore it is binomial.

[tex]3x^{4} + x - 3x^{4} -x\\= 0[/tex]

The given polynomial has only one term therefore it is monomial.

Find out more information about classification of polynomials here:

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Answer:

has been saving is the correct answer I believe

Answer:

"has been saving" is the right answer.

Answer:

22x + 21y = 0

Step-by-step explanation:

33x + 22y = 11x + y

Subtract y from both sides.

33x + 21y = 11x

Subtract 11x from both sides.

22x + 21y = 0

Answer:

Required probability:

Required probability:

At least 2 students pass:

Number of x's:

This is a point, so it has x- and y-coordinates. Both of these coordinates are positive, therefore the point must be in the first quadrant.

The pattern for the points on a unit circle is 3 - 2 - 1 starting at 0 and up to pi/2. The pattern for the radian denominators on a unit circle is 6 - 4 - 3 starting at 0 and up to pi/2.

(sqrt(3) / 2, 1/2) = pi / 6 radians

Hope this helps!

Answer:

A. pi/6 radians

Step-by-step explanation:

The ratio of the lengths of the sides of a 30-60-90 triangle is

1/2 : sqrt(3/2) : 1

sin theta = opp/hyp

tan theta = 1/2 / 1

tan theta = 1/2

theta = pi/6 radians

Answer: A. pi/6 radians

Answer:

12

Step-by-step explanation:

bc it is

Answer:

Volume of a cube is s×s×s

hence 7 cube=343

343 is the answer. Hope this helps you. Good luck^_^

Answer:

its letter c so 80

Step-by-step explanation:

I hope this help

Answer:

Step-by-step explanation: i think in my own word x+3<12 is A because it said julie only 3 notebook togerther it make itt less than 12notebook

Answer:

x^ (-19/3)

Step-by-step explanation:

x ^ (-10/3)  ÷ x^3

We know a^b ÷ a^c = a^(b-c)

x ^ (-10/3)  ÷ x^3 = x^(-10/3 - 3) = x^(-10/3 - 9/3) = x^ (-19/3)

Mình gửi bạn

Bạn xem câu cuối có sai đề không

Answer:

x = 8

Step-by-step explanation:

Given

- 4 + 3x = 20 ( add 4 to both sides )

3x = 24 ( divide both sides by 3 )

x = 8

[tex]\huge\text{Hey there!}[/tex]

[tex]\large\textsf{-4 + 3x = 20}\\\rightarrow\large\textsf{3x - 4 = 20}\\\\\large\text{ADD 4 to BOTH SIDES}\\\large\textsf{3x - 4 + 4 = 20 + 4}\\\large\text{CANCEL out: \textsf{-4 + 4} because that gives you \textsf 0}\\\large\text{KEEP: \textsf{20 + 4}} \text{ because it gives you the \textsf{x-value}}}\\\\\large\textsf{20 + 4 = \bf 24}\\\\\large\text{DIVIDE 3 to BOTH SIDES}\\\\\mathsf{\dfrac{3x}{3}= \dfrac{24}{3}}\\\large\text{CANCEL out: }\mathsf{\dfrac{3}{3}}\large\text{ because that gives you \textsf 1}[/tex]

[tex]\large\text{KEEP: }\mathsf{\dfrac{24}{3}}\large\text{ because it helps gives you the result of the \textsf{x-value}}\\\\\mathsf{x = \dfrac{24}{3}}\\\\\large\textsf{x= 24}\div \large\textsf{3}}\\\large\textsf{x = \bf 8}\\\\\boxed{\boxed{\huge\text{Therefore, your answer is: \textsf{x = 8}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

~[tex]\frak{Amphitrite1040:)}[/tex]

Answer:

3.1°

Step-by-step explanation:

Given the temperature values :

12 degrees, -2 degrees, -6 degrees, and 8.4 degrees

To obtain the average temperature, take the sum of the temperatures and divide by the number of days

Sum of temperature values : (12 + (-2) + (-6) + 8.4) = 12.4 degree

Sum of temperature / 4

= 12.4 / 4

Average temperature = 3.1 degrees

Answer

6372 - power 4

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

f(x) + 2 is it I am not sure but do not lie

Answer:

I think it's D or C, but am leaning towards D. Don't take my word for it though.

Step-by-step explanation:

f(x-2)

(Do not use my answer though as I am not completely sure since the parent function f(x) might be looking for a certain location where the plus-minus 2 is.)

My reasoning is that I went to a graphing calculator and the first two choices are incorrect where it is something like f(x) + 2 or - 2.

The graph is lower than the parent function meaning it probably involves a negative or positive since the graph is much steeper.

Answer:

The choose (D)

D. Circle

I hope I helped you^_^

The required cross-section for a cone is a circle. Option D is correct.

A conic section is a geometric shape that is obtained by intersecting a cone with a plane. Conic sections include circles, ellipses, parabolas, and hyperbolas.

The type of conic section that is formed depends on the angle of the plane relative to the axis of the cone, as well as the distance of the plane from the vertex of the cone.

Here,
The cross-section of a cone is a circle.

A cross-section is a shape that you get when you slice a 3D object with a plane. If you slice a cone parallel to its base, you get a circle as the cross-section.

Therefore, the correct answer is option D.

Learn more about the conic section here;

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Answer: y=80/5x+80

Step-by-step explanation:

At one point graph goes from (0,400) to (25,800). So the y intercept is 400 because that’s where the line was at x=0. 0 to 25 is 25. 400 to 800 is 400. So the equation would be y=400/25x+400. But you can divide all of it by 5 to get y=80/5x+80.

Step-by-step explanation:

Bob's salary : $35000 per year plus 10% after one year

100% = 35000

1% = 100%/100 = 35000/100 = $350

10% = 10×1% = 10×350 = $3500

so in total, his salary will be $35000+$3500 = $38500 after one year.

Sam's salary : $3842.42 per month plus 5% after one year.

100% = $3842.42 per month. but to make it comparable to Bob's salary, we need to calculate the annual salary.

so, 100% 12×3842.42 = $46109.04

1% = 100%/100 = 46109.04/100 = $461.09

5% = 5×1% = 5×461.09 = $2305.45

so, in total, his salary will be $46109.04+$2305.45 = $

Answer:

3 = 3(x² - 1) We know, any Function f(x) decrease s in interval [a, b] when f'(x) < 0 ... -1 < x < 1. Hence, function f(x) = x³ - 3x - 2 , is decreased in (-1, 1).

Answer:

y = 3 + 0.40x

Step-by-step explanation:

Fixed cost of taxi fare = $3

Additional cost = $0.40

Let

y = Total cost

x = number of kilometers

The equation:

Total cost = Fixed cost of taxi fare + (Additional cost * number of kilometers)

y = 3 + 0.40x

Answer:

obviously sus island

Step-by-step explanation:

Answer:

A. 75.40 m³

Step-by-step explanation:

Diameter of cylinder (d) = 4 m

Radius (r) = ½(d) = ½(4) = 2 m

Height (h) = 3 × r = 3 × 2 = 6 m

Volume of cylinder = πr²h

Substitute the values

Volume of cylinder = π*2²*6

Volume of cylinder = π*4*6

Volume = π*24

Volume = 75.40 m³

Step-by-step explanation:

let,the sum of the ages of chukwu & Caroline be X & Y.

now,

X+y=45

X-y=3

(+) (+) (-)

__________

2x=42

or,X=42/2

or,X=21

putting the value of X,

X+y=45

or, 21+y=45

or,y=45-21

or,y=24

therefore,X=21

y=24

Answer:

hello,

Step-by-step explanation:

12²=(x-16)*16

9=x-16

x=25

Relation metric in a right triangle