Solve the equation

This is a question from a mock exam I could not answer

An expression is defined as a set of numbers, variables, and mathematical operations. The value of g(f(x)) is (x²-10x+13) / (x²-10+29).

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The complete questions is,

Write g(f(x)) as an expression in terms of x

f(x) = x-5

[tex]g(x) = \dfrac{x^2-12}{x^2+4}[/tex]

The value of g(f(x)) as an expression in terms of x can be written as,

[tex]g(f(x)) = \dfrac{(x-5)^2-12}{(x-5)^2+4}\\\\\\g(f(x)) = \dfrac{x^2+25-10x-12}{x^2+25-10x+4}\\\\\\g(f(x)) = \dfrac{x^2-10x+13}{x^2-10+29}[/tex]

Hence, the value of g(f(x)) is (x²-10x+13) / (x²-10+29).

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Answer:

See below

Step-by-step explanation:

If you can't tell just by looking at them, you will need to convert them all to fractions of a common denominator .....in this case (the smallest) common denominator would be 18

1/2 = 9/18  

1/3 = 6/18

1/6 = 3/18

4/9 = 8/ 18             so now you can see least to greatest is

                                    1/6    1/3    1/2   4/9

Answer:

Answer:

9

Step-by-step explanation:

The surface, in this case, describes the number of squares that are painted. On the left hand side, we have a cube, so we know we're going to have 6 faces. And each face on the cube has 9 little squares, they can be counted on the diagram. So, the total number of squares that are painted on the left cube = [tex]9 * 6 = 54[/tex]

The star means multiplication.

We are told in the question that it takes 9 litres of paint to cover the surface of the left hand cube, meaning it takes 9 litres of paint to cover 54 squares.

This can be written in the ratio = [tex]9:54[/tex]

If we divide both sides of the ratio by 9, we can figure out the amount of squares that 1 litre of paint covers, [tex]1:6[/tex].

The ratio tells us that 1 litre of paint covers 6 squares.

Let's look at the shape on the right. It is still a cube, however, some segments have been removed. Some faces still remain the same as in the shape on the left, such as the bottom face, the back face and the face to the left. Those faces may not be so apparent on the diagram, however, they exist. So we have to count them.

The number of small squares on these faces = [tex]9 * 3=27[/tex]

If you look on the inside of the cube, which can be seen on the diagram, we can see three faces, each having four squares. So, the total number of squares here = [tex]3*4=12[/tex]

Also, we have some squares on the top, and if you count these, there are 5.

This also applies for the front and the right hand side if you count, so we add 10 squares to the total as there are another two lots of five.

So, the total number of squares on the right cube = [tex]27 + 12 + 5 + 5 + 5 = 54[/tex]

Let's bring back the ratio of litres of paint to the number of squares covered: [tex]1:6[/tex]

In the ratio, there are 6 squares per litre. We know that 6 × 9 = 54 (our total). So, we multiply left hand side of the ratio by 9 as well, bringing the total amount of paint required to 9 litres.

I hope this helps.

The surface area of cuboid = [tex]$400 \mathrm{~cm}^{2}$[/tex].

If the left cube takes 9 liters of paint to cover the surface. Then, also right cube takes 9 liters of paint to cover the surface.

Cuboid dimension [tex]$\frac{10 \mathrm{~cm}}{(l)} \times \frac{10 \mathrm{~cm}}{(b)} \times\frac{5 \mathrm{~cm}}{(h)}$[/tex]

Surface area = 2(lb + lh + bh)

= 2((10 [tex]\times[/tex] 10)+(10 [tex]\times[/tex] 5)+(10 [tex]\times[/tex] 5))

= 2(100+50+50)

= [tex]400 \mathrm{~cm}^{2}[/tex]

Therefore, surface area of cuboid = [tex]$400 \mathrm{~cm}^{2}$[/tex].

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Answer:

radius = 8

Step-by-step explanation:

the equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

x² + y² = 64 ← is in this form

with r = [tex]\sqrt{64}[/tex] = 8

The middle number is 16.95

The collection of numbers is called the number system. These numbers are of different types such as natural numbers, whole numbers, integers, rational numbers and irrational numbers.

Given:

Numbers are 12.7 and 21.2

Difference between number

= 21.2-12.7

=8.5

middle number

= 12.7+ 8.5/2

= 12.7+ 4.25

= 16.95

Hence, the middle number is 16.95.

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Answer:

[tex]\frac{3}{11}[/tex]

Step-by-step explanation:

assuming the recurring digits are 0.272727.... , then

we require 2 equations with the repeating digits placed after the decimal point.

let x = 0.2727.... (1) ← multiply both sides by 100

100x = 27.2727... (2)

subtract (1) from (2) thus eliminating the repeating digits

99x = 27 ( divide both sides by 99 )

x = [tex]\frac{27}{99}[/tex] = [tex]\frac{3}{11}[/tex] ← in simplest form

Answer:

Jimrgrant1 has already answered this correctly, 3/11.

Step-by-step explanation:

I took 1.0 and divided it by 0.272727 to give 3.666666 . . .

I looked for value that would convert this into a whole number when multiplied.  3 times 3.666666 . . . is equal to 11.  

That would mean a fraction equal to 0.272727 . . . would be 3/11

Answer:

where is  the question  Skidoo

this is just a statement

Answer:

6

Explanation:

[tex]\textsf {The range of a data representation refers to difference of the smallest and }\\\textsf {greatest possible values. }[/tex]

[tex]\textsf {Here :}[/tex]

[tex]\textsf {smallest value = 5}\\\textsf {greatest value = 11}[/tex]

[tex]\textsf {Then the range will be :}\\\implies \textsf {greatest value - smallest value}\\\implies \mathsf {11 - 5}\\\implies \mathsf {6}[/tex]

a) 26 teenagers are in the group.   21+3+2=26

b) 21 like to drink coffee or tea only.    (3 like both and 2 like neither, so 21 enjoy one or the other)

Answer:

They will always intersect at one point

Step-by-step explanation:

^^

Answer: 4²

Step-by-step explanation:

There is some rule but just remember:

1. parenthesis

2. exponents

3. division/multiplication

4. subtraction/addition

Answer: six ways

Step-by-step explanation: The pairs when the cube is rolled that are less than five would be; (1,1), (1,2), (1,3), (2,1), (2,2), (3,1) since each cube is out of six.

Answer:

3.75

Step-by-step explanation:

17.15-13.40=3.75

Answer:

3.75

Step-by-step explanation:

17.15- 13.40=3.75

The vale of x is 54°.

The tangent is defined as a line touching circles or an ellipse at only one point.

We have,

As, the tangent is perpendicular to the radius of the circle.

So, using Angle sum property in a triangle

x+90+36= 180

x+126 = 180

x= 54°

Hence, the value of x is 54°

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The volume of the cone is V = 381.15 cu.cm

The curved surface area of the cone is given by

A = πrl

The slant height given in the question is

l = 10.5 cm

A = 115.5 sq.cm

radius = ?

Height = ?

Volume = ?

Using the Curved Surface Area Formula

115.5 = π * r * 10.5

taking π = 22/7

r = 3.5 cm

The slant height is given by

[tex]\rm l = \sqrt{ r^2 + h^2}[/tex]

Therefore the height is

[tex]\rm h = \sqrt{ 10.5^2 -3.5^2}[/tex]

h = 9.9 cm

The volume of the cone is

V = π r²h

V = (22/7) * 3.5 * 3.5 * 9.9

V = 381.15 cu.cm

The volume of the cone is V = 381.15 cu.cm

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Answer:33.65

Step-by-step explanation:

6.73 x 5= 33.65

The vertex is the lowest/highest point, depending on if the parabola opens upwards or downwards.

So because the vertex opens upwards, we are looking for the lowest point which is at (2,-3).

Answer:

a

Step-by-step explanation:

2^3 = 8; 4^3 = 64; 8/64 = 1/8

(g^5)^3 = g^15

(h^2)^3 = h^6

g^15/8h^6

Answer:

-3

Step-by-step explanation:

both are negatives, so think of it as addition

at the very end make sure you add the negative symbol :)

-1 1/3 - 1 2/3

The time needed by Lola to sign all the 96 invitations is 508.8 second

Product is the number obtained when two numbers are multiplied with each other

It is given that

Total Invitations that Lola needs to sign = 96

Time taken to sign full name = 5.3 seconds

Total time needed by Lola to sign invitations is  

96 * 5.3

= 508.8 seconds

Therefore the time needed by Lola to sign all the 96 invitations is 508.8 second

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Answer:

B, D

Explanation:

8(-10x+3.5y-7)

= -80x + 28y - 56

4 (-20x + 7y - 14)

= 8(-10x+3.5y-7)

= -80x + 28y - 56

Answer:

B) -80x + 28y - 56

D) 4 (-20x + 7y - 14)

Original Expression:

⇒ 8(-10x+3.5y-7)

⇒ -80x + 28y - 56

Now confirmed that option B is correct when the expression is simplified which makes option A and C not applicable.

For option D:

⇒ 4 (-20x + 7y - 14)

⇒ -80x + 28y - 56

Option E is not correct as:

⇒ -4 (-20x + 7y - 14)

⇒ 80x - 28y + 56

The equation of the graph is y ² = 16x.

A parabola is a U shaped curve ,all the point of which is equidistant from a point called as focus and a line called as Directrix .

In the given question , the graph is a horizontal parabola as the directrix is x = -4 , and as the focus lies on the right side , it is opening towards the right.

The equation for the horizontal parabola is given b y

(y-k)² = 4p(x-h)

h , k is the mid point of focus and the directrix , i.e. the vertex and is given by

h = ([tex]\rm x_f[/tex] +a )/2 , k = [tex]\rm y_f[/tex]

h = (4 -4)/2 , k = 0

h=0 , k = 0

The vertex is 0 , 0

p = (|[tex]\rm x_f[/tex] - a|)/2 = 8/2 = 4

Therefore the equation of the graph is

y ² = 4 * 4 *x

y ² = 16x

The equation of the graph is y ² = 16x.

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Answer:

y=3 (1/3)x

Step-by-step explanation:

On a graph, the closest graph you pictured is this answer

Answer:

y =  [tex]3 (\frac{1}{3} )^{x}[/tex]

Step-by-step explanation:

Step 1:

Check the y-intercept; in the graph, when x = 0, y = 3. Which equation satisfies this?

y = [tex]\frac{1}{3}[/tex] [tex](3)^{x}[/tex] = [tex]\frac{1}{3}[/tex] [tex](3)^{0}[/tex] =        [tex]\frac{1}{3}[/tex]      ❌

y = [tex]3 (\frac{1}{3} )^{x}[/tex]  = [tex]3 (\frac{1}{3} )^{0}[/tex]  = 3          ✅

y =  [tex](\frac{1}{2} )^{x}[/tex] + 2  = [tex](\frac{1}{2} )^{0}[/tex] + 2 = 3  ✅

So the last two equations are possible.

Step 2:

Now check the y-value on the graph for any other x-value, whose corresponding y-value can be easily estimated from the graph.

For example, when x = 2, the y-value is between 0 and 1.

• 2nd equation: y = [tex]3 (\frac{1}{3} )^{x}[/tex]  =  [tex]3 (\frac{1}{3} )^{2}[/tex] = 0.333               ✅

• 3rd equation:  y =  [tex](\frac{1}{2} )^{x}[/tex] + 2 = y =  [tex](\frac{1}{2} )^{2}[/tex] + 2 = 2. 25  ❌

∴ 2nd equation (y = [tex]3 (\frac{1}{3} )^{x}[/tex] ) is the one being represented by the graph.

Answer:

V = 4*8

V= 32

(x+x) * (x+x) = 2x * 2x = 4x^2

Answer:

(3,-4)

Step-by-step explanation:

The percentage of employees with 8 or more years at the company reported that email is their preferred method of communication  is 20.48%

The two-way frequency table below shows the preferred communication method of employees at a company, based on years of employment with the company.

See attachment

What percentage of employees with 8 or more years at the company reported that email is their preferred method of communication?

A. 44.79% B. 20.48% C. 48.84% D. 67.19%

From the attached image, we have:

Email 8 or more  =  43

The total number of employees in the company is

Total = 210

So, the percentage that prefers email is

Percentage = 43/210 * 100%

Evaluate

Percentage = 20.48%

Hence, the percentage of employees is 20.48%

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