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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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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:

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)

The data value that is an outlier in the data for boxes of cookies is: E. 56.

The simple rule is that values lower than Q1 - 1.5 × IQR and values greater than Q3 + 1.5 × IQR are outliers of a data distribution.

Given the data, 20, 23, 18, 4, 17, 21, 15, 56, find the Q1, Q3, and IQR of the data distribution:

First Quartile (Q1) = 15.5

Third Quartile (Q3) = 22.5

Interquartile Range (IQR) = 22.5 - 15.5 = 7

Q1 - 1.5 × IQR = 15.5 - 1.5 × 7 = 5

Q3 + 1.5 × IQR = 33

None of the values are lower than 5.

However, the only value that is greater than 33 is 56.

The outlier in the data is: E. 56.

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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:

16

Step-by-step explanation:

Answer:24

Step-by-step explanation:

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:

solution;

21=7x-4x

21=3x

21x/3x

Then finalay aneswer is 7x

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.

Answer:

y=-x+6

Step-by-step explanation:

Start by graphing y=-x+5.  Then mark the point (2,4) for easier reference.  A parallel line just has the same slope, so if you make another line with the same slope, and change the y-intercept until the line goes through (2,4), you will have the answer.

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

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the objects. The polar coordinate of the coordinate (1, -3) is (√10, 288.435).

A coordinate system in geometry is a system that employs one or more integers, or coordinates, to define the position of points or other geometric components on a manifold such as Euclidean space.

The polar coordinate of the coordinate (1, -3) are,

r = √(x² + y²) = √[(1)²+(-3)²] = √10

θ = tan⁻¹(-3/1) = -71.565 = 288.435

Hence, The polar coordinate of the coordinate (1, -3) is (√10, 288.435).

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Answer:

A is the answers for the question

Step-by-step explanation:

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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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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:

185 anle with the postive measure and a negative measure

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:

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:

6 hours 30 minutes

Step-by-step explanation:

10 subtract 4 is 6

55 subtract 25 is 30

The slope of the line is [tex]\frac{6-0}{0-6}=-1[/tex]. so in point-slope form, the equation of the line is [tex]y=-x+6[/tex].

In standard form, this is [tex]\boxed{x+y=6}[/tex]

The angle the longer chain makes with the ceiling is 38.5°

The two chains and ceiling form a triangle and with two sides and an angle, we use the sine rule to find the other angle

The sine rule states in any triangle with sides a, b, c and angles A, B and C, repsectively, we have that

a/sinA = b/sinB = c/sinC

Since one chain is 46cm long and forms an angle of 60° with the ceiling. the other chain 64cm long. So, we find the other angle.

So, a/sinA = b/sinB  where

Making A subject of the formula, we have

A = sin⁻¹(asinB/b)

So, substituting the values of the variables into the equation, we have

A = sin⁻¹(asinB/b)

A = sin⁻¹(46 cm × sin60/64 cm)

A = sin⁻¹(46 cm × 0.8660/64 cm)

A = sin⁻¹(39.84 cm/64 cm)

A = sin⁻¹(0.6225)

A = 38.49°

A ≅ 38.5°

So, the angle the longer chain makes with the ceiling is 38.5°

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Answer:

[tex]\sf M=\left(-\dfrac{1}{2},0\right)[/tex]

Step-by-step explanation:

Let (x₁, y₁) = Point A = (-2, 1)

Let (x₂, y₂) = Point B = (1, -1)

[tex]\sf Midpoint=\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)[/tex]

[tex]\implies \sf Midpoint=\left(\dfrac{-2+1}{2},\dfrac{1+(-1)}{2}\right)[/tex]

[tex]\implies \sf Midpoint=\left(-\dfrac{1}{2},0\right)[/tex]

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.

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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When we try to compute gamma, for this problem, the value of gamma is 1

To answer the question, we need to know what time dilation is.

Time dilation is a phenomenon in special relativity in which there is an elongation of time due to the motion of an object.

Now, the time is given by t = γt₀ where

Since we need to compute gamma when the speed of the automobile moving past you is 30 m/s.

Given that

Substiting these into γ, we have

γ = 1/√[1 - (v/c)²]

γ = 1/√[1 - (30 m/s/3 × 10⁸ m/s)²]

γ = 1/√[1 - (1/1 × 10⁷)²]

γ = 1/√[1 - (1 × 10⁻⁷)²]

γ = 1/√[1 - (1 × 10⁻¹⁴)]

γ = 1/√[1 - 0.00000000000001]

γ = 1/√0.99999999999999

γ = 1/1

γ = 1

So, when we try to compute gamma, the value of gamma is 1

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The number of books Alisha did not sell after making a profit of £490 is 45 books

How to find how many book she sell base on the profit?

She buys 200 books costing £3 each.

Therefore,

cost = 3 × 200 = £600

Hence,

She sells 2/5 of the books at £8 each.

total amount = 2 / 5 of 200 × 8

total amount = 80 × 8

total amount = £640

Alisha then reduces the price of the remaining books by a quarter.

She then sells some of the remaining books.

Therefore,

the remaining book = 120

She sold some of the remaining books.

profit = selling price - cost price

490  = selling price - 600

selling price = 490 + 600

selling price = £1090

Therefore,

the cost of the remaining book she sold = 1090 - 640 = £450

Hence,

let

x = number of book sold

6(x) = 450

x = 450 / 6

x = 75

The number book she did not sell = 120 - 75 = 45

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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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