What is the range of the relation in the table below?

Answer:

I will assume that the term "x+2/2" is meant to be "(x + 2)/2)."  Otherwise the equation would read (x/3) = x + 1

Step-by-step explanation:

(x/3) = (x + 2)/2

x = 3*(x+2)/2   [Multiply both sides by 3]

x = (3x + 6)/2

x = (3/2)x + 6/2

x - (3/2)x = 3

-0.5x = 3

x = -6

====================

Check:

Does (x/3) = (x + 2)/2 for x = -6?

(-6/3) = (-6 + 2)/2

-2 = -4/2

-2 = -2  YES

Answer:

Coordinates follow (x,y) so to find a solution to the line you want to find a point in (x,y) form which is on the line.

This means (1,3) is a solution because at x=1 and y=3 it is on the line.

C | (1,3)

Answer:

5. y = 2/3x + 1

8. y = 4/7x - 4

Step-by-step explanation:

5. (-6, -3) and (6, 5)

You can use the slope formula which is (y2-y1)/(x2-x1) to find the slope and plug it back into the slope-intercept form to find the y-intercept

(5-(-3)) / (6-(-6)) = 8 / 12 = 2/3

slope-intercept form: y=mx+b where m is the slope and b is the y-intercept

to find b you can plug in one of the coordinates and the slope

5 = 6(2/3) + b

5 = 4 + b

1 = b

y = 2/3x + 1

8. (-7, -8), (21, 8)

m = (8 -  (-8)) / (21 - (-7)) = 16 / 28 = 4/7

plug in one of the coordinates and the slope to find b or the y-intercept

8 = 21(4/7) + b

8 = 12 + b

-4 = b

y = 4/7x - 4

Answer:

1,530

Step-by-step explanation:

No, the equations -11(x - 2) = 8 and x - 2 = 8 + 11 are not equivalent.

The equivalent is the expressions that are in different forms but are equal to the same value.

Then the equation is given below.

-11(x - 2) = 8

By simplifying, we have

x - 2 = - 8 / 11

No, the equations -11(x - 2) = 8 and x - 2 = 8 + 11 are not equivalent.

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The equation will be a linear equation from (2, 5) to (4, 10) will be y = 2.5x.

Mathematics is replete with functions, which are necessary for the construction of intricate connections.

A 2-column table with 3 rows. Column 1 is labeled x with entries 2, 4, 5. Column 2 is labeled y with entries 5, 10, 12.5.

Use the information in the table to find the constant of proportionality and write the equation.

The equation will be a linear equation from (2, 5) to (4, 10) will be

(y – 5) = [(10 – 5) / (4 – 2)] (x – 2)

 y – 5 = 2.5x – 5

       y = 2.5x

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Answer:

2.5 and y=2.5x

Step-by-step explanation: i got that question on an edguenity assignment

Answer:

(x-6y)(x-4y)

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

8 + h^2

Let h = 3

8 + 3^2

We find the value of 3^2 first using PEMDAS

8 + 9

Then add

17

The result is 17

Solution: 17

Detailed explanation:

[tex]\circ[/tex] Stick in the value of h, which we're provided with (3)

[tex]--\mapsto\boldsymbol{8+(3)^2}[/tex] *

*Be careful here! Here it's very easy to make a mistake, if you aren't familiar with the Order of Operations. The Order of Operations is shown below [tex]\swarrow[/tex]

P=Parentheses

This operation tells us to perform the operations in the parentheses first.

E=Exponents

This one tells us to evaluate all exponents, if any are present.

M=Multiplication | D=Division

These two are completely interchangeable; you can perform Multiplication first and then division, or the other way around.

A=Addition | S=Subtraction

Like the two operations above, A and S are also completely interchangeable.

________________________________________________________

________________________________________________________

Using the information above, let's evaluate (find the value of) the expression [tex]8+h^2[/tex].

We stick in the value of h, 3

[tex]\pmb{8+3^2}[/tex] is what we obtain

Here we see that exponents are  present (3^2) so we'll evaluate that first, as P.E.M.D.A.S. tells us to do.

[tex]\pmb{8+9}[/tex] (3^2=3*3)

And Now we just need to add the numbers

[tex]\boldsymbol{17}[/tex]

Voila! There's our answer!

_____________________

Hope I helped. Best wishes.

Reach far. Aim high. Dream big.

[tex]\cal ReFlEcTioN[/tex]

_____________________

The range of the function f(x) = 3x3 when its domain is {2, 5} is {24, 375}

The domain is the independent value for which a function exists.

Given the function below;

f(x) = 3x^3

If the domain of the function is {2, 5}, the range are;

If x = 2

f(2) = 3(2)^3
f(2) = 3(8)

f(2) = 24

If x = 5

f(5) = 3(5)^3

f(5) = 3(125)

f(5) = 375

Hence the range of the function f(x) = 3x3 when its domain is {2, 5} is {24, 375}

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The number of passwords that would be allowed if users were allowed to reuse the letters and numbers is 30891577600

The given parameters are:

Password length = 8

Letters = 6

Numbers = 2

There are 26 letters and 10 digits.

Since the letters and the numbers can be repeated, then the number of passwords is:

Count = 26^6 * 10^2

Evaluate

Count = 30891577600

Hence, the number of passwords is 30891577600

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Answer:

Step-by-step explanation:

Answer:

(1) 85×9=765 (2) 127×3=381

The value of FY in the triangle will be 30.11

From the information given, the value of BE will be:

= [tex]\sqrt{64.2}[/tex]² - [tex]\sqrt{51.2}[/tex]²

= 38.7

From the triangle, DY will be

= [tex]\sqrt{64.22}[/tex]² - [tex]\sqrt{61.7}[/tex]²

= 17.7

AY will be:

= [tex]\sqrt{61.7}[/tex]² + [tex]\sqrt{17.7}[/tex]²

= 64.2

FY will now be:

= [tex]\sqrt{64.2 - 56.7}[/tex]²

= 30.11

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Answer: f(x) = -2 (x+3) (x-1)

Step-by-step explanation: See Attachment

Answer:

x = 5.81

Step-by-step explanation:

3(12x-7) = 4(5x+18)

36x-21 = 20x +72

16x = 93

x = 5.81

Answer:

1.3 or 1.333333

Step-by-step explanation:

Just do it!

The smallest 4-digit number which is exactly divisible by 72 and 108 is 1080.

The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.

The Least common multiple of both the numbers 72 and 108 is 216. Since 216 is the least common multiple of both the numbers. Therefore, the four-digit number needs to be a multiple of 216 to be divisible by both the numbers. Thus, when 216 is multiplied by 5 the result is 1080, which is divisible by both 72 and 108. Hence, the smallest 4-digit number which is exactly divisible by 72 and 108 is 1080.

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The average rate of change of f(x) = -3x² + 1 over each of the given intervals are; -18, 6 nd 38

We are given the function;

f(x) = -3x² + 1

(a) From 2 to 4;

f(2) = -3(2)² + 1

f(2) = -12 + 1

f(2) = -11  (2, -11)

f(4) = -3(4)² + 1

f(4) = -47  (4, -47)

Slope = (-47 - (-11))/(4 - 2)

Slope = -36/2

Slope = -18

(B) From -2 to 0;

f(-2) = -3(-2)² + 1

f(2) = -12 + 1

f(2) = -11  (-2, -11)

f(4) = -3(0)² + 1

f(4) = 1  (0, 1)

Slope = (1 - (-11))/(0 - (-2))

Slope = 12/2

Slope = 6

(C) From 2 to 5;

f(2) = -3(2)² + 1

f(2) = -12 + 1

f(2) = -11  (2, -11)

f(5) = -3(5)² + 1

f(5) = -74  (0, -74)

Slope = ((-74) - 2)/(0 - 2)

Slope = -76/-2

Slope = 38

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Answer:

the scale factor of a drawing=1:4

Answer:

D

Step-by-step explanation:

The domain are the x values. When you plug those values into the equation, you get 34, 6, 22.

3(-3²) - 2(-3) + 1                     Negative * Negative = Positive

3(9) + 6 + 1

34

3(-1²) - 2(-1) + 1

3 + 2 +1

6

3(3²) -2(3) + 1

3(9) - 6 + 1

22

The constructed bisector of line segment given below in the image.

Process to construct the bisector of a line segment :

Step 1 : Make the compass length ( the distance between the pointed leg and the pencil leg) slightly greater than half the length of the line segment OP. Place the point of the compass on O. Make arcs above and below the line segment OP.

Step 2 : Using the same compass length as same as the previous one, place the point of the compass on P. Make arcs above and below line segment OP. These arcs must intersect the arcs made in previous step.

Step 3 : Connect the points where the arcs intersect. Label the line segment MN and the point where the line intersects OP, Q.

Step 4 : Line segment MN bisects line segment OP at midpoint Q.

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2.

1 day = 24h

1h = 60min

We have 4h 20min

[tex]4h + 20min = 4h+\dfrac{20}{60}h=4h+\dfrac{1}{3}h=4\dfrac{1}{3}h=\dfrac{13}{3}h[/tex]

[tex]\dfrac{\frac{13}{3}}{24}=\dfrac{13}{3}\cdot\dfrac{1}{24}\\\\\huge\boxed{(D)\ \dfrac{13}{72}}[/tex]

3.

6:51PM + 9min → 7:00PM

7:00PM + 27min → 7:27PM

9min + 27min = 36min

[tex]36min=\dfrac{36}{60}h=\dfrac{3}{5}h[/tex]

[tex]\huge\boxed{(C)\ \dfrac{3}{5}}[/tex]

The required slope of the line given by m = -3/4.

The slope of the given y = -3/4x+2 is m, the line passes from (0, 2) and (4, -1)

A line can be defined by a shortest distance between two points is called as a line.

equation of the given line is |

 y =[tex]\frac{-3}{4}[/tex]x + 2

slope of the given line is given by comparing it to standard equation
y = mx + c
by comparing
m= -3/4
Which required slope of the line.
Since we have two points on line begin or end point (0, 2) and (4, -1) respectively. This satisfies the equation while putting it into the equation.

Thus the required slope of line   y =[tex]\frac{-3}{4}[/tex]x + 2is given by  m= -3/4 , This line passes through points  (0, 2) and (4, -1).

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Answer: No

Step-by-step explanation:

A proportional relationship can be represented by y = kx, for some constant k. This means the graph should be a line, which is not shown. Thus, the graph does not represent a proportional relationship.

Answer:

no

Step-by-step explanation:

because it does not represent any propotional relationship.

Answer:

all the options are incorrect

Given - 20 teachers

- 705 students

To find - ratio of teachers to students

20/705

20 : 705 .

Answer:

[tex]\frac{45}{7}[/tex]

Step-by-step explanation:

9 is the same as [tex]\frac{9}{1}[/tex]

∴ 9 ˣ [tex]\frac{5}{7}[/tex]

=  [tex]\frac{9}{1}[/tex] ˣ  [tex]\frac{5}{7}[/tex]

To multiply two fractions, just multiply their numerators together and their denominators together.

9 x 5 = 45

1 x 7 = 7

∴ [tex]\frac{9}{1}[/tex] ˣ  [tex]\frac{5}{7}[/tex]

  = [tex]\frac{45}{7}[/tex]

Answer:

Step-by-step explanation:

6 (x - 5) = 4x + 20

6x - 30 = 4x + 20

6x - 4x = 20 + 30

2x = 50

[tex]x = \frac{50}{2} [/tex]

x = 25

Answer: The value of x = 25 ✅

Step-by-step explanation:

Hii! Do you need to know the solution to the equation [tex]\boldsymbol{6(x-5)=4x+20}[/tex]? No problem! (:

     In any equation, there's a variable that we need to solve for. Here the variable is "x".

So now let's solve for x...

[tex]\twoheadrightarrow\sf 6(x-5)=4x+20[/tex]

[tex]\bullet[/tex] "distribute" 6

[tex]\twoheadrightarrow\sf 6x-30=4x+20[/tex]

[tex]\bullet[/tex] subtract "4x" from both sides

[tex]\twoheadrightarrow\sf 2x-30=20[/tex]

[tex]\bullet[/tex] add "30" to both sides

[tex]\twoheadrightarrow\sf 2x=50[/tex]

[tex]\bullet[/tex] divide both sides by "2"

[tex]\twoheadrightarrow\sf x=25\;\;\;[/tex] ✅

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Hope that this helped! Best wishes.

[tex]\it Reach\;far.\;Aim\;high.\;Dream\;big.[/tex]

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[tex]\bigstar\underbrace[/tex]

The y coordinates doesn't change under a horizontal stretch while the x coordinates do not change under a vertical stretch.

It should be noted that coordinates are vital in determine the position of an object or points.

In this case, the y coordinates doesn't change under a horizontal stretch while the x coordinates do not change under a vertical stretch.

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Answer:

The y-coordinates do not change under a horizontal stretch. The x-coordinates do not change under a vertical stretch.

Step-by-step explanation:

Answer:

[tex]h(1) = 4 \times 2 + 3 \times 1 - 2 \\ = 9[/tex]