Colin, Michael, and John are among 15 singers
in the community choir. Three members of the
choir will be selected at random to sing the
national anthem at the next city council meeting.
What is the probability that Colin, Michael, and
John will be the 3 singers chosen?
A.
1/910

B.
2/1125

C.
1/455

D.
1/5

Given the function w:

[tex] \displaystyle \large{w(x) = {x}^{2} + 1 }[/tex]

Since we want to find w(x+3), the input would be x+3.

Substitute x = x+3 in.

[tex] \displaystyle \large{w(x + 3) = {(x + 3)}^{2} + 1 }[/tex]

Alternate Solution

The answer above works if you want it in vertex form. For this alternate solution, I will convert the function in standard form.

As we know:

[tex] \displaystyle \large{ {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} }[/tex]

Therefore:

[tex] \displaystyle \large{ {(x + 3)}^{2} = {x}^{2} + 2(x)(3) + {3}^{2} } \\ \displaystyle \large{ {(x + 3)}^{2} = {x}^{2} + 6x+ 9}[/tex]

Now for function w:

[tex] \displaystyle \large{w(x + 3) = {x}^{2} + 6x + 9+ 1 } \\ \displaystyle \large{w(x + 3) = {x}^{2} + 6x + 10}[/tex]

Hence:

Answer:

Step-by-step explanation:

[tex]x^2+8x=38\\\\x^2+8x-38=0\\\\\Delta=8^2+4*38=216=6^3\\\\x=\dfrac{-8-6\sqrt{6} }{2} \ or\ x=\dfrac{-8+6\sqrt{6} }{2}\\\\x=-4-3\sqrt{6} \ or\ x=-4+3\sqrt{6}\\\\a=-4\\b=3\\c=6\\[/tex]

y = 2x + 5

Answer:

-16

Step-by-step explanation:

7)

y= mc+c ------gradient formula

y: y-intercept

m: gradient

c: y-axis

y= -2(6)+(-4)

= -12-4

= -16

Answer:

D. quadratic; y = 2.5x2

Step-by-step explanation:

Answer:

A. quadratic; y = 2.5x2

Step-by-step explanation:

Answer:

Option (1)

Step-by-step explanation:

x               -2              -1                 0                    1                   2

y               10            2.5                0                  2.5                3.0

Ist difference,

   = -2.5

  = 2.5

  = 7.5

2nd difference,

   = 5

  = 5

  = 5

Since 2nd difference is common, given table represents a quadratic equation.

Let the equation is,

y = ax²+ bx + c

For a point (0, 0) passing through the quadratic equation,

0 = c

Therefore, quadratic equation is y = ax² + bx

Since ordered pair (-1, 2.5) passes through the graph of the function,

2.5 = a(-1)² + b(-1)

a - b = 2.5 ------(1)

For another point (1, 2.5)

2.5 = a(1)² + b(1)

a + b = 2.5 ------(2)

By adding equations (1) and (2),

2a = 5

a = 2.5

and from equation (2)→ y = 0

Therefore, equation of the quadratic function given in the table is y = 2.5x²

Option (1) is the answer.

Answer: B) Use distributive property to multiply 5(x + 8).

Step-by-step explanation:

trust me its right

The first step in solving this equation 6x = 4 + 5(x + 8) is,

⇒ Use distributive property to multiply 5(x + 8).

Option B is true.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ 6x = 4 + 5(x + 8)

Now, We can solve the expression as;

⇒ 6x = 4 + 5(x + 8)

⇒ 6x = 4 + 5x + 40

⇒ 6x - 5x = 44

⇒ x = 44

Thus, The first step in solving this equation is,

⇒ Use distributive property to multiply 5(x + 8).

Learn more about the mathematical expression visit:

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#SPJ2

Answer:

7(x+7)(5x+18)

Step-by-step explanation:

Answer:

factors are (5n + 8)(n + 7)

Step-by-step explanation:

[tex] {35n}^{2} + 371n + 882 \\{ \sf{sum = \frac{371}{35} \: and \: product = \frac{882}{35} }} \\ factors= (5n + 8)(n + 7)[/tex]

Answer:

{1,3,5,6,7,8}

Step-by-step explanation:

U={1,2,3,4,5,6,7,8}

B={2,4}

B is even factors so you won't start with one

The complement of set B will be {1, 3, 5, 6, 7}

A set is an arrangement or collection of numbers. Given the universal sets:

Natural numbers are positive integers starting from 1. Hence the universal set will be:

U = {1, 2, 3, 4, 5, 6, 7, 8}

Factors of 8 are 1, 2, 4 and 8

Set of even factors of 8 will be 2, 4 and 8

B = {2, 4, 8}

Compliment of a set B are sets that are in the universal set but not in set B. Hence the complement of B will be {1, 3, 5, 6, 7}

Learn more here: https://brainly.com/question/18203375

Answer:

I will help ukshagaakavlabsbakakahsjskmdlslsbsbs skshsvs

Answer:

18

hope it helps

Answer:

undefined

Step-by-step explanation:

4 - 9 = x - 2

-5 = x - 2

-3 = x

this is a vertical line (parallel to the y-axis) at x = -3.

that means the slope of this line is "undefined". or some would call it "infinite".

as the slope is the ratio of y/x describing how many units y changes, when x changes a certain amount of units.

now the change of x for this line is constant 0.

so, we have a slope y/0, which is undefined.

Answer:

I think that it might be (−∞,1/2)

hope it was any help ^^

Answer:

[tex]this \: a \: complex \: equation \: so \: compare \\ \: real \: term \: and \: imaginary \: term \\ so \\ 18 = 3x \: \: and \: 22i = - 2yi \\ x = \frac{18}{3} \: \: \: \: and \: y = \frac{22i}{ - 2i} \\ x = 6 \: \: \: y = - 11 \\ then \: 6 \times 3 - - 2 \times 11i \\ = 18 + 22i \\ thank \: you[/tex]

Answer: Area = 17.5 unit²

Concept:

Here, we need to know how to calculate the area of a triangle.

Area (triangle) = b · h · (1/2)

b = base

h = height

Solve:

Given information (By counting grids on the graph)

b (AB) = 7

h (BC) = 5

Given expression

Area = b · h · (1/2)

Substitute values into the expression

Area = (7) · (5) · (1/2)

Simplify by multiplication

Area = (35) · (1/2)

Area = [tex]\boxed{17.5}[/tex]

Hope this helps!! :)

Please let me know if you have any quesitons

Answer: A

Step-by-step explanation:

Answer:

Step-by-step explanation:

c

Answer:

The greatest common factor for 18,42 and 96 is 6.

Step-by-step explanation:

6 X 3 = 18

6 X 7 = 42

6 X 16 = 96  

making 6 your largest common factor.

Answer:

don't u just add the side lengths and then get the answer?

9514 1404 393

Answer:

Step-by-step explanation:

The prime factorization of 1458 is ...

  1458 = 2·3^6

The exponent of 3 is even, but we need another factor of 2 to make the exponent of that factor even. You will get a perfect square by multiplying by 2.

  √(2·1458) = √2916 = 54

Multiplying by 2 will give the square of 54.

Answer:

x ≥ -1

Step-by-step explanation:

The domain is all the possible x-values of the function.

Reading from left to right, the first x-value is x = -1 (which is included because the dot is filled in.) From there, the graph goes to the right, towards infinity.

So x is greater than or equal to -1.

x ≥ -1

Step-by-step explanation:

1)8x-2x=35-17

6x=18

x=18/6

x=3

2)7k-2k=-37-8

5k=-45

k=-45/5

k=-9

3)m-9m=-13-3

-8m=-16

8m=16

m=16/8

m=2

4)-4y+3y=12-6

-y=6

y=-6

5)6a-2a=-40

4a=-40

a=-40/4

a=-10

6)5w+2w=55+29

7w=84

w=84/7

w=12

7)5p-13p=-43+11

-8p=-32

8p=32

p=32/8

p=4

8)-c-5c=-2+50

-6c=48

c=-48/6

c=-8

Answer:

1. 12x+19

2.11x+16

3.54

4.3x+5x+8

Step-by-step explanation:

I first wrote the question and grouped like terms.So after grouping these you will get x+2x+8x +x +7 + 2+10 .When you simplify you wil get 12x+19 . If you don't understand comment me

Answer:

338

Step-by-step explanation:

ok

Answer:

The answer is 14.28cm

Answer:

x= -3, y= 13

Step-by-step explanation:

The idea is that x and y in both equations are the same numbers and that the equations are like rules that need to be followed both in the same time.

We take the y from one equation and use it in the other equation because is the same y .

3x+y =4 , subtract 3x from both sides

y=  -3x+4

2x+y =7 , substitute y with the y = -3x+4 from the first equation

2x -3x+4 = 7, subtract 4 from both sides

2x-3x = 7-4, combine like terms

-x = 3  so x = -3

We know that x= -3 so we can substitute it in y= -3x+4 to find y

y=  -3x+4

y= -3 (-3) +4

y= 9+4 = 13

y= 13

Answer:

It is 7x + 12

Step-by-step explanation:

[tex]5(3x + 2) - 2(4x - 1)[/tex]

open brackets:

[tex] = 15x + 10 - 8x + 2[/tex]

group like terms together:

[tex] = (15x - 8x) + (10 + 2)[/tex]

factorise out x :

[tex] = x(15 - 8) + 12 \\ = 7x + 12[/tex]

Answer:

the difference is £0.3 because I have calculated 25% of £1.20 and got£0.3 meaning the Doughnuts at the second shop costs £1.5 which is the sum of 25% of £1.2 and £1.2 and the difference between£1.5 and £1.2 is £0.3