Can function notations be simplified?
I was working on this equation: f(x) = -6/9x + 300
I was wondering if I can convert the fraction ‘-6/9’ into ‘-2/3’?

Answer:

Step-by-step explanation:

3(-3) - 2 = -9 - 2 = -11

3(1) - 2 = 3 - 2 = 1

3(5) - 1 = 15 - 1 = 14

Answer:

g(x)=(x-7)/3

Step-by-step explanation:

Answer:

The answer would be  [tex]f^{-1} (x)=\frac{x}{3} -\frac{7}{3}[/tex] finding the inverse

Step-by-step explanation:

Answer:

Transformation: (x,y) → (x - 26, y + 17) or

[tex]T _{-26,17}[/tex](x,y) [translation]

A, since the transformation of a translation simply changes the location of a certain figure because all the points of the figure are moved the exact same way. This is because a translation is a rigid transformation.

Explanation:

Let the preimage of points A and P be A(x1,y1), and P(x2,y2). And the image of points A and P be A'(x3,y3) and P'(x4,y4).

Given points A and P are A(-2,20) and (10,-13). And points A' and P' are A'(-28,37), and P'(-16,4). The translation is found by calculating the difference between these points for the figure. (x,y) → (( x + ((x3-x1) + (x4-x2))/2), (y + ((y3-y1) + (y4-y2))/2 )). If this does not match all the points in the transformation of the figure, than it is not a rigid transformation, and so it cannot be a translation.

The simple formula for the uniform translation of a figure is : (x,y) → ((x + (x2-x1), (y + (y2-y1)) . Where x2, and y2 are part of the image, while x1, and y1 are part of the preimage. This will get you from the preimage(1) to image(2) following a translation.

Given all the points, the more complicated work is shown here:

(x,y) → ((x + ((-28--2) + (-16-10))/2), (y + ((37-20) + (4--13))/2)) = (x,y) → ((x + (-26 + -26)/2),(y + (17 + 17)/2) = (x,y) → ((x - 26),(y + 17)) = (x,y) → (x - 26, y + 17).

When writing a transformation like a translation in a function, it will look like this: [tex]T _{∆x,∆y}[/tex](x,y). ∆x,∆y are just placeholders for the change in these variables that get you from the preimage to image.

Answer:

The correct calculation is 180 - 56

Step-by-step explanation:

From the question, we have DCG and DCF

looking at the diagram, we can see that both lie on a straight line and are a linear pair

So the addition of both will give 180

But DCG is 56

So;

DCF + 56 = 180

So;

DCF = 180 - 56

Answer:

170

Step-by-step explanation:

you have to set up a proportion and cross multiply.

[tex] \frac{408 \: miles}{6 \: hours} = \frac{x \: miles}{2.5 \: hours} [/tex]

that would cross multiply to

[tex]408 \: miles \: \times 2.5 \: hours \: = 6 \: hours \: \times x \: miles[/tex]

which would simplify to

[tex]1020 = 6x[/tex]

then, you isolate x by dividing 6 from both sides to get the final answer of

[tex]170 \: miles = x[/tex]

Answer:

22

Step-by-step explanation:

You can just put it in your calculator

Answer:

22

Step-by-step explanation:

Answer:

Slope= 1/2

Step-by-step explanation:

The slope of the given line is 0.5.

The slope of a line is defined as the angle of the line. It is denoted by m

Slope m = (y₂ - y₁)/(x₂ -x₁ )

The points on the table lie on a line, as follows;

x: (-2), 0, 2, 4

y: 3,4,5,6

To determine the slope of a line, you can use the formula:

(change in y)/(change in x)

As per the points in the table,

the change in x is (4-(-2)) = 6, and the change in y is (6-3) = 3.

Slope =  (3)/(6)

Slope = 1/2

Apply the division operation, and we get

Slope = 0.5

Therefore, the slope of the line is 0.5.

Learn more about the Slope of the Line here:

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Answer:

once again, the pattern is multiply by 3

Answer:

972

Step-by-step explanation:

the pattern is multiplied by 3

Answer: $0.14 per fluid ounce.

Step-by-step explanation: $4.48 divided by 32 = $0.14

Answer:

.

Step-by-step explanation:

Answer:

1.07x

Step-by-step explanation:

Since they both have a x, you can simply add .05 + 1.02 to get 1.07x.

Answer:

It is 1.07x (✿◠‿◠)

Answer:

The answer is 22.4.

Answer:

22.4

Step-by-step explanation:

you multiply 6 and -2.4 by 9

that gives you 54 and -21.6

then you add -10 to -21.6 giving you -31.6

lastly subtract -31.6 out of 54

which gives you 22.4

Quadrilateral ABCD is rotated 90 degrees clockwise, to get A'(0, 1), B'(-1, 0), C'(-3, 2) and D'(-2, 3).

Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.

If a point A(x, y) is rotated clockwise by 90 degrees, the new point is at A'(y, -x)

Quadrilateral ABCD is at A(-1, 0), B(0, -1), C(-2, -3) and D(-3, -2). If ABCD is rotated 90 degrees clockwise, the new point is at A'(0, 1), B'(-1, 0), C'(-3, 2) and D'(-2, 3).

Find out more on transformation at: https://brainly.com/question/1548871

Answer:

B)

Step-by-step explanation:

edge

Answer:

x = 2

Step-by-step explanation:

10x - 7 = 7x - 1

10x = 7x + 6

3x = 6

x = 2

Answer:

x = 2

Step-by-step explanation:

Add seven to both sides to move it over to the right, then subtract 7x from both sides to move that over to the left.

You should be left with 10x - 7x = 7 - 1.

10x - 7x = 3x

7 - 1 = 6

3x = 6

Divide both sides by three to get your answer of x = 2.

Answer:

1.94

Step-by-step explanation:

Let the number be x

So when three times a number which is positive which means when a number is x so three times a number must be 3x is subtracted from the square of that number ,

now the number 3x is subtracted from its own square i guess it should look like this

[tex](3x)^2-3x[/tex]

and the answer is 28 so the final form of the problem should be

[tex](3x)^2-3x=28[/tex]

[tex]9x^{2} -3x-28=0[/tex]

now we solve the quadratic equation by using the quadratic formula and we two values for x

one is a positive value and the other is negative value we take the positive value as said in the question itself  "when three times a number which is positive" so that value of x is 1.94

Answer:

Option: D is the correct answer.

D) 20.455 <= X <= 20.545

Step-by-step explanation:

We are given The ideal length of a particular metal rod is 20.5 cm.

It is given that:

The measured length may vary from the ideal length by at most 0.045 cm.

By atmost we mean either less than or equal to that amount but not more than that.

It means that:

|X-20.5|≤ 0.045

⇒  -0.045  ≤ X-20.5 ≤ 0.045

⇒    -0.045+20.5 ≤ X ≤ 20+0.045

⇒   20.455 ≤ X ≤ 20.545.

Hope this helped! <3

If a triangle is equilateral, then each of its angles measures 60°. Therefore, option D is the correct answer.

An Equilateral triangle is a triangle in which all three sides are equal and angles are also equal. The value of each angle of an equilateral triangle is 60° therefore, it is also known as an equiangular triangle.

The given statements are

(1) If a triangle is equilateral, then it has three congruent sides.

(2) If all the sides of a triangle are congruent, then each of its

Here, if a triangle is equilateral, then each of its angles measures 60°.

Therefore, option D is the correct answer.

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Let the digit in one's place be y and digit at ten's place be x.

Sum of the digits = 11

⟶ x + y = 11

⟶ x = 11 - y -- equation (1).

And,

The number formed by reversing the digits is 27 more than the original number.

⟶ Reversed number = Original number + 27

reversed number = 10y + x.

⟶ 10y + x = 10x + y + 27

⟶ 10y + x - 10x - y = 27

⟶ 9y - 9x = 27

Substitute the value x from equation (1).

⟶ 9y - 9(11 - y) = 27

⟶ 9y - 99 + 9y = 27

⟶ 18y = 27 + 99

⟶ 18y = 126

⟶ y = 126/18

⟶ y = 7

Substitute the value of y in equation (1).

⟶ x = 11 - 7

⟶ x = 4

The number = 10(4) + 7 = 40 + 7 = 47.

∴ The required two digit number is 47.

I hope it will help you.

Regards.

Answer:

146

Step-by-step explanation:

Since we know that this is a rhombus, we know that opposite angles must be equal to each other. This means that angle QTS is equal to angle QRS. Therefore angle QTS also equals 34.

Now, we also know that all the interior angles in a quadrilateral add up to 360. We can subtract 360-34-34=292.

Now we know that the remaining two angles S and Q need to add up to 292. We also know that they are equal because they are opposite angles. Therefore, we can solve the equation 292÷2=146. Each of these angles is 146. So the measure of angle S is 146.

The measure angle of S is 146 .

A rhombus is a special case of the parallelogram and is a quadrilateral with four equal sides. In a rhombus, the opposite sides are parallel and the opposite angles are equal. Also, all the sides of the rhombus are equal in length and the diagonals bisect each other at right angles. The rhombus is also known as a diamond.

By symmetry ;

This means that m∠QTS is equal to m∠QRS. Therefore ∠QTS is also equals 34.

We also know that The common property for all the above four-sided shapes is the sum of interior angles is always equal to 360 degrees. For a regular quadrilateral such as square, each interior angle will be equal to: 360/4 = 90 degrees.

Now we know that the remaining two angles S and Q need to add up to 292.

= 360 -34 -34= 292

We also know that they are equal because they are opposite angles.

Therefore, we can solve the equation,

[tex]\frac{sum of two opposite angle}{2}[/tex] = [tex]\frac{292}{2}[/tex] = 146

Each of these angles is 146.

So the measure of angle S is 146.

For the more information about properties of rhombus click the link given below.

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Answer:

Subtract

43

from

10

.

−

33

−

|

7

p

+

12

|

Step-by-step explanation:

The positive value of p from the equation is; p = 3

This is about absolute values.

10 = 43 - |7p + 12|

10 - 43 = - |7p + 12|

-33 = - |7p + 12|

divide both sides by -1 to get;

33 = |7p + 12|

Answer:

(d/f)-1=x

Step-by-step explanation:

d=f+fx

d-f=fx

(d-f)/f=x

(d/f)-1=x

Answer:

2.68

Step-by-step explanation:

Answer:

5/7

Step-by-step explanation:

You can convert them to fractions to answer:

7/5=1.4

5/7=0.714

7/5 is 0.4 away from 1, while 5/7 is 0.3 away.

Answer:

5/7 is closer

Step-by-step explanation:

7/5= 49/35=1 14/35

5/7= 25/35

7/5 is 14/35 away from one whereas 5/7 is 10/35 away.

Answer:

The differences between a physical change and a chemical change are as follows :

Hope I helped!

Best regards ! :D

~[tex] \text{TheAnimeGirl}[/tex]

Answer:

It is 3/13

Step-by-step explanation:

it is because there are 13 total marbles and 3 yellow ones

Answer:

I think that's it :)

Step-by-step explanation:

cause 2.5 x 2 = 5

and then 3 x 2 = 6