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Considering the definition of axis of symmetry, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.

An axis of symmetry is an imaginary reference line that, when dividing any shape into two parts, its opposite points are equidistant from each other, that is, they are symmetrical.

In other words, the axis of symmetry is a vertical line that divides the parabola into two congruent halves.

The axis of symmetry is the line perpendicular to the "x" axis that contains the vertex of the function, that is, it always passes through the vertex of the parabola. So the x-coordinate of the vertex is the equation of the axis of symmetry.

That is, in a quadratic function that has the form:

f(x)= ax² + bx + c

the axis of symmetry is a vertical line and it is defined as [tex]x=\frac{-b}{2a}[/tex].

In this case, you know:

Replacing in the definition of axis of symmetry:

[tex]x=\frac{-12}{2x3}[/tex]

Solving:

[tex]x=\frac{-12}{6}[/tex]

x= -2

Finally, the axis of symmetry of the graph of the function f(x) = 3x²+ 12x+ 9 is x=-2.

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(4x−101)(2x+3)

Apply the distributive property by multiplying each term of 4x−101 by each term of 2x+3.

8x²+12x−202x−303

Combine 12x and −202x.

8x²−190x−303

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We are asked to find the value of x in [tex]\mathrm{(4x-101)(2x+3)}[/tex].

◈ Note:

⇛ We can't find the value of x, but we can simplify this expression.

This is how we'll simplify it:

◆ Multiply 4x times 2x and 3 first:

[tex]\large\pmb{4x\times2x=8x^2}[/tex]

[tex]\large\pmb{4x\times3=12x}[/tex]

Add the terms:

[tex]\large\pmb{8x^2+12x}[/tex]

Now, do the same thing with -101 - multiply that times 2x and 3:

[tex]\large\pmb{-101\times2x=-202x}[/tex]

[tex]\large\pmb{-101\times3=-303}[/tex]

Add the terms:

[tex]\large\pmb{-202x-303}[/tex]

Put all 4 of the terms together:

[tex]\large\pmb{8x^2+12x-202x-303}[/tex]

Combine like terms (12x and -202x):

[tex]\large\pmb{8x^2-190x-303}[/tex]

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The numbers between 10 and 50  when they are divided by 5 then the remainder is 2 is shown in the form of description method and in set-builder form is {12, 17, 22, 27, 32, 37, 42, 47}.

A set is a collection of clearly - defined unique items. The term "well-defined" applies to a property that makes it simple to establish whether an entity actually belongs to a set. The term 'unique' denotes that all the objects in a set must be different.

We have:

The set of numbers between 10 and 50 when they are divided by 5 then the remainder is 2

The numbers are:

12, 17, 22, 27, 32, 37, 42, 47

By description method:

1      2     3    4      5     6      7      8  

12   17   22   27    32    37   42    47  

By set builder form:

s = {12, 17, 22, 27, 32, 37, 42, 47}

Thus, the numbers between 10 and 50  when they are divided by 5 then the remainder is 2 is shown in the form of description method and in set-builder form is {12, 17, 22, 27, 32, 37, 42, 47}.

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If f(x) and f¹(x) are inverse functions of each other then value of ƒ˜¹ (8) = 3/2.

In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.

We have,

f(x) = 2x + 5

Let us consider f(x) as y

So, y= 2x + 5

Now replace x to y and y to x

x= 2y+ 5

Solving for y we get

2y = x - 5

y = (x - 5)/2

[tex]f^{-1[/tex](x) = (x - 5)/2

Now, [tex]f^{-1[/tex](8) = (8 - 5)/2

[tex]f^{-1[/tex](x) = 3/2

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Answer:

43 percent

Step-by-step explanation:

When you divide 43 by 100 you get .43 which is 43%

Answer:

43%

Step-by-step explanation:

Because if you divide 43  by 100 you get, .43 and so there you have it, 43% Hope you understand <3

Answer:

16

Step-by-step explanation:

Answer:24

Step-by-step explanation:

Answer:

14 inch ^2

Step-by-step explanation:

Area of a trapezium= (a+b) 2 times h

so side a= 5 inches

    side b= 9 inches

then times by 2 times the height (2)

you can rearrange the formula to this- a + b/ 2 times height.

5+9/2 times 2= 14

I hope this helps, have a lovely day.

Answer:

Area of Circle  = 346.5 cm².

Area of square = 272.25 cm ² .

Step-by-step explanation:

So , 2πR = 66

2 × 22 / 7 × R = 66

R comes out is 21/2 cm .

Area of Circle = 22/7 × 21/2 × 21/2 = 33×21/2

= 693 / 2 = 346.5 cm².

If bent into the shape of a square ;

4 a = 66

a = 33/2 . ( Side of a square )

Area of square = a ² = 33×33/4 = 1089/4

= 272.25 cm ² .

[tex](\frac{4m^5n^2}{m^2n})^3 = (\frac{4m^5n^2}{m^2n})(\frac{4m^5n^2}{m^2n})(\frac{4m^5n^2}{m^2n})[/tex]

---Essentially, we're taking the given expression and multiplying it by itself three times. So, we can solve the problem by multiplying fractions or simply distributing the 3 to each term. Remember, we will be multiplying the existing exponents by the 3, not adding 3.

[4^3 m^15 n^6] / [m^6 n^3]

---Now, we need to simplify the expression. Since there are 15 m's on the top, and 6 m's on the bottom, we can take 15 - 6 to now have only 9 m's on the top.

64 m^9 n^3

Answer: A

Hope this helps!

Answer:

185 anle with the postive measure and a negative measure

The computation of (TR)546 - (TR)540 will give a value of 3261.

TR(546)  =  546(546 + 1)/2  =  273 * 547

TR (540)  =  540(540 + 1)/2  =  270 * 541

273 * 547  = (270 + 3)(541 + 6)

= 270*541  + 270*6  + 541 *3  +  18

= 270*541  + 1620  + 1623  +  18

= 270*541  + 3261

TR(546) -TR (540)   = 270*541  + 3261  - 270 * 541

= 3261  

TR(546) -TR (540)   = 3261  

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Answer: 346.19cm²

Step-by-step explanation:

π= 3.14

Divide 21 (the diameter) by 2 to get the radius( it 's half of the diameter). so the radius is 10.5

Area= πr²

       = 3.14x10.5x10.5

       = 346.185

So next round up the value you got to the nearest tenth, so when u round up to the nearest tenth you get 346.19

Based on the result from the box plot, the number of blue marbles is equal to the median of the data set and this is equal to 40.

A boxplot is a type of chart that can be used to graphically represent the five-number summary of a data set with respect to locality, skewness, and spread. Also, the five-number summary include the following:

For this exercise, we would create a box plot (see attachment) for the marbles in a bag of 100 marbles. By critically observing the box plot, we can logically deduce that the number of blue marbles is equal to the median of the data set and this is given by:

Median = 4 × 10

Median = 40.

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Answer:

solution;

21=7x-4x

21=3x

21x/3x

Then finalay aneswer is 7x

The number of students who come to school through other modes o transportation is 1,165.

The number of students who come to school through other modes o transportation can be calculated as follows:

A = Number of girls that uses other modes o transportation = (100% - 40%) * 950 = 570

B = Number of boys that uses other modes o transportation = (100% - 30%) * (1800 - 950) = 595

C = Total number of studens that uses other modes o transportation = A + B = 570 + 595 = 1,165

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Answer:

The triangles are not similar.

Step-by-step explanation:

First, what's all the information we know?
We know we're trying to prove that triangle BAC is similar to triangle DEC.
We know AC=12 and EC =12 (proving 1 side equal).
We know angle BCA and angle DCE or equal.
However, we do not know any information further than this, and there is no postulate/theorem for AS. Therefore, the triangles are not similar.

He needs 20 more unit cubes to completely fill the prism

The dimension of the prism is given as;

4 by 3 by 3

The volume is calculated as:

Volume = 4 * 3 * 3

Volume = 36

He has already filled 16 units.

So, the units remaining is

Remaining = 36 - 16

Evaluate

Remaining = 20

Hence, he needs 20 more unit cubes to completely fill the prism

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Answer:

15 2/3

Step-by-step explanation:

4 2/3 = 14/3

11 = 33/3

14/3 + 33/3 = 47/3

47/3 = 15 2/3

Remember the shortcut way for graphing quadratic equations

#1

Vertex

As a is positive parabola facing upwards

Find y for same x distance from vertex

I took 3-1=2 and 3+1=4

Now plot vertex and these two points (2,1) and (4,1) on graph then draw a parabola by freehand

#2

Convert to vertex form

Vertex at (-1,-9)

Same take two equidistant x values

Let's take -1-1=-2 and -1+1 =0

Put (-1,-9),(-2,-8),(0,-8) on graph and draw a freehand parabola

#3.

Yes it can be verified by finding the coordinate theoretically on putting them on function then can be verified through putting them on graph whether they matches or not

Answer:

a. direct

Step-by-step explanation:

direct variation is y = kx and y = -2/5x is written in direct variation.

80 * 25 /100 = 20 .........

Answer:

20

Step-by-step explanation:

25% of 80

to turn 25% into a decimal, 25 / 100 = 0.25  

multiply 80 by 0.25, 80 x 0.25 = 20

Answer: x = 3.75 inches

Step-by-step explanation:

     We will set up a proportion to solve.

[tex]\displaystyle \frac{6 \text{ inches}}{16 \text{ feet}} =\frac{x \text{ inches}}{10 \text{ feet}}[/tex]

     Now, we will cross multiply, simplify and isolate the variable to solve your math problem.

6 * 10 = 16 * x

60  = 16x

3.75 = x

x = 3.75 inches

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Answer:

A is the answers for the question

Step-by-step explanation:

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Answer:

nth term = n(n + 2)

Step-by-step explanation:

Note that the first number in each parentheses is the sequence number n of the term. This  value of n is then multiplied by (n + 2) - for example 3 x 5

( 3 x (3+2)).

So the nth term = n(n + 2).

This is an example of a Quadratic Sequence.

The volume of the silo = volume of the hemisphere + volume of the cylinder ≈ 4,410.8 m³.

Volume of a hemisphere = 2/3πr³

Volume of cylinder = πr²h

The volume of the silo = 2/3πr³ + πr²h

Plug in the values

The volume of the silo = 2/3π(6³) + π(6²)(35) ≈ 4,410.8 m³

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Answer:

989.6 m^3

Step-by-step explanation:

refer to images hope this helps x

X=7.1cm

The solution is in the attached file

The equation that must be true about the rotation is that m∠EAE ' = m∠FAF.

Rotation is a type of transformation in which the shape of the original object is preserved and the angle of rotation is constant for all the parts of the body.

In this case, ΔDEF rotates 90° clockwise about point A to create ΔD 'E 'F, m∠EAE ' = m∠FAF.

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Answer:

w=7

Step-by-step explanation:

A parallelogram is defined as a four-sided plane rectilinear figure with opposite sides parallel. This means that GH and FE must be equivalent, and HE and GF must be equivalent. Now, we just use those equations to solve.
16w-63=7w
9w-63=0

9w=63

w=7!!!
and we can double check.

16w-81=15w-74
16w=15w+7
w=7

Answer:

Substitution. Substitution is a good method to use when one of the variables is isolated in the equation or the coefficient of one of the variables is 1 or -1. When you isolate that variable to substitute into the other equation, you will not be introducing additional fractions into the problem.

Answer:

B  isosceles with sides  sqrt (61)

Step-by-step explanation:

Find the two sides' lengths via pythagorean theorem to be

 sqrt ( 5^2 + 6^2) = sqrt (61)