Given f(x) = 5x? + 2 and g(x) = 8 - 3x, find the following.
12. Find g[f(-2)].
11. Find flg(x)).

Answer:

a. 105 and 115 employees

b. 185 employees

c. 20 years

Step-by-step explanation:

The total of employees at any given year is y

x is the number of year

then y = 85 + 10x

a. 2nd year: y = 85 + 10(2) = 85 + 20 = 105

  3rd year: y = 85 + 10(3) = 85 + 30 = 115

b. 10th year: y = 85 + 10(10) = 85 + 100 = 185

c: if y = 285

285 = 85 + 10x

10x = 285 - 85

10x = 200

x = 20

Step-by-step explanation:

gradient = slope. or similar names.

it expresses the "steepness" of the line. how strongly is it going up or down or ... at all ?

it is represented by the ratio

(y coordinate difference / x coordinate difference)

when going from one point on the line to another.

for these 2 points we see (when going from the first to the second)

x changes by +1 (from -1 to 0).

y changes by -6 (from 2 to -4).

so the slope or gradient is

-6/+1 = -6

The right angle is called the hypotenuse and the other two sides are called adjacent and opposite.

A right angled triangle is a triangle that has 3 sides and angles. For a right angled triangle, one of the angles is 90 degrees.

The longest side of the triangle is hypotenuse and the other two sides are known as the adjacent and opposite.

Hence in a right triangle, the longest side opposite the right angle is called the hypotenuse and the other two sides are called adjacent and opposite.

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The measure of the angle x is 22.5 degrees

Circle theorem includes the concept of tangents, sectors, angles, the chord of a circle and proofs.

A circle is the locus of all points in a plane which are equidistant from a fixed point

From the given diagram

arc AC = 180 - 135

arcAC = 45 degrees

Since the angle at the vertex is half the intercepted arc, hence;

x = 1/2(arc AC)

x = 1/2(45)

x = 22.5 degrees

Hence the measure of the angle x is 22.5 degrees

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Answer:

The watermelon's price was $7.02

Step-by-step explanation:

83.2 ounces= 5.2 pound

The watermelon that Jose bought weights 5.2 pounds

If 1 pound= $1.35

5.2= $7.02

The commutative property apply to compositions of f(x) and g(x) when f(g(x)) and g(f(x)) are equal for all values of x.

The commutative property says that  [tex]a*b=b*a[/tex] , for any binary operation [tex]'*'[/tex]. These binary operations can be addition, multiplication, function composition, etc. But subtraction and division does not follow commutative property.

Here the operation is composition of two functions defined as,

               [tex](fog) (x)= f(g(x))[/tex]  ,where f and g are two functions.

Then the function composition has commutative property when

                      [tex]fog = gof[/tex].

That is, when f(g(x)) = g(f(x))

This means that the commutative property apply to the composition of functions, f(x) and g(x) when f(g(x)) and g(f(x) are equal for all values of x.

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Step-by-step explanation:

hey try out the questions urself some tips would be to make the 1/2 and 3/5 have the same denominator as those shown in the diagram denominator means the number below

so1/2 x5 would give u 5/10 and 3/5 would give you 6/10

Answer:

Step-by-step explanation:

The transformed function is g(x) = 20x-6.

The graph of the function y=f(ax) represents a Horizontal Shrink by a factor of "1/a" of the graph y=f(x) .

To find the horizontal shrink by a factor of 1/a we multiply the input by a .

In the given question

f(x)=5x-6 , is horizontally shrink by a factor of 1/4.

So we multiply the inputs by 4 .

On multiplying the inputs by 4 , we get

f(4x)=5(4x)-6        (...as 5*4=20)

Let g(x) represents the horizontal shrink of f(x) by factor 1/4 , So

g(x)=20x-6

Therefore , the horizontal shrink of the graph of f by a factor of 1/4 is g(x)=20x-6.

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The population of town Vic is greater than population of town Val by 52000 .

In the question ,

it is given that

the population of town Val = 8x10³

the population of town Vic = 6x10⁴

Rewriting both the numbers we get

population of town Val = 8x1000 = 8000

population of town Vic = 6x10000 = 60000

It can be clearly seen that 60000 > 8000

So the population of Vic > population of Val

To calculate the difference subtract the population of Val from population of Vic .

Substituting the values of population we get ,

difference = 60000 - 8000

= 52000

Therefore , the population of town Vic is greater than population of town Val by 52000 .

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Solving the fraction negative four and one fifth ÷ two and one fourth gives; negative one and 39 over 45

We want to divide the fraction negative four and one fifth ÷ two and one fourth. This can be expressed as;

-4¹/₅ ÷ 2¹/₄

Converting to improper fraction gives;

-21/5 ÷ 9/4

= -21/5 * 4/9

= -84/45

3 is a common factor that both numerator and denominator can be divided by to get; -28/15

Expressing the answer as a mixed fraction is; -1 ³⁹/₄₅

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The coordinate of B is (13, -3).

What is Midpoint of line?

Measure of Distance between the two points and then divide by two is known as midpoint of line.

Given that;

The midpoint of the line AB is M (-5, 0).

The coordinate of A is (-3, 3).

Now, Let the coordinate of the point B is (x, y )

Then, By definition of midpoint of two point,

(-3 + x / 2 , 3 + y / 2 ) = (-5, 0)

By compare we get;

-3+ x / 2 = -5

- 3 + x = 2 * 5

- 3 + x = 10

x = 10 + 3

x = 13

And, 3 + y / 2 = 0

3 + y = 0

y = -3

Hence, The coordinate of B (x, y) = (13, -3).

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Answer:  (−7,−3)

Step-by-step explanation: I had the question

Answer: x=-3.25

y=7/12

Step-by-step explanation:

2x + 6y = -3

12y = 4x + 20

6y = -3-2x

6y=20-(-3)+4x-(-2x)

6y=20+3+4x+2x

6y=23+6x

23+6x=-3-2x

23=-3-8x

-8x=26

x=-13/4

x=-3.25

12y = 4(-3.25) + 20

12y=-13+20

12y=7

y=7/12

Supplementary angles are two angles whose measures add up to 180°. If An angle is 134.2 then other angles are 22.9.

Supplementary angles are two angles whose measures add up to 180°

Supplementary angles are those that add up to 180.

supplementary angle: x

an angle: x+134.2

and together they must measure 180:

x+x+134.2 = 180

2x+134.2=180

2x=180-134.2

2x=45.8

x=22.9

This is the supplementary angle the other angle is 22.9+134.2 = 157.1

Thus the the angle of each is 22.9.

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The exponential functions to the nearest cent :

y = (500)(1.06)^3 is $595.51

y = (20,000)(0.088)^3 is 13,629,44

y = (15,000)(1.05)^5 = 19,144.22

Cent is hundredth value of the dollar. The hundredth term is the second digit to the right of the decimal point. For example, the cent in this amount, $100.11 is 0.01.

In order to round off to the nearest cent, look at the thousandth term, if the number is equal to 5 or greater than 5, add 1 to the hundredth term and the thousandth term becomes 0. For example, $100.527 to the nearest cent is $100.53

In order to round off to the nearest cent, look at the thousandth term, if the number is less than 5, the hundredth term does not change and thousandth term becomes 0. For example, $20. 124 becomes $20.12 to the nearest cent.

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Using the average rate of change, it is found that snow was falling at a rate of 0.1 inch an hour during the first period.

This problem is incomplete, but researching it on a search engine, it asks the rate at which snow was falling during the first period.

The average rate of change of a function is given by the change in the output divided by the change in the input. Hence, over an interval [a,b], the rate is given as follows:

[tex]r = \frac{f(b) - f(a)}{b - a}[/tex]

From the graph, the first period is until the 10th hour, hence:

The rate is:

r = (2 - 1)/(10 - 0) = 0.1.

Hence snow was falling at a rate of 0.1 inch an hour during the first period.

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This density in kilograms per pint is 0.946.

Important conversions:

1 gram = 0.001 kilogram

1 ml = 0.001 litres

1 pint = 0.473 litres

1 litre = 2.113 pints

Step 1 : Convert 2 grams per millilitre of volume (2 g/ml) into kilograms per litre (kg/l)

=> (2  x 1000)/ (0.001) = 2 kg / l

Therefore, we get the density in kilograms per litre (kg/l) as 2 kg/l.

Step 2 : Convert the density in kilogram per litre (kg/l) into kilograms per pint (kg/pint)

=> 2 x 0.473 = 0.946 kg/l

Therefore, by converting 2 grams per millilitre of volume into kilograms per pint, we get the density as 0.946 kg/pint.

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The sum of two odd integers is an even integer. Therefore, the set S is not closed under addition.

The following subsets of Z (with ordinary addition and multiplication) satisfy all but one of the

axioms for a ring. In each case, which axiom fails?

(a) The set S of odd integers.

• The sum of two odd integers is an even integer. Therefore, the set S is not closed under addition.

Hence, Axiom 1 is violated.

(b) The set of nonnegative integers.

• If a is a positive integer, then there is no solution of a + x = 0 that is also positive. Hence, Axiom

5 is violated.

In general, to show that a subset S of a ring R, is a subring of R, it is sufficient to show that

(i) S is closed under addition in R

(ii) S is closed under multiplication in R;

(iii) 0R ∈ S;

(iv) when a ∈ S, the equation a + x = 0R has a solution in S.

Let a, b, c ∈ S ⊂ Z with a = rk, b = sk, c = tk.

(i) a + b = rk + sk = (r + s)k ∈ S

(ii) ab = (rk)(sk) = (rsk)k ∈ S

(iii) 0Z = 0 = 0 · k ∈ S

(iv) a = rs ∈ S ⇒ x = −rs ∈ S is a solution ofa + x = 0S

Thus, S is a subring of Z.

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Based on the solution below, we have:

A. a + 2b =5 corresponds to 5. a = 5 - 2b;

B. 5a = 2b  corresponds to 1. a = 2b/5;

C. a + 5 = 2b corresponds to 4. a = 2b - 5;

D. 5(a + 2b) = 0 corresponds to 3. a = -2b; and

E. 5a + 2b=0 corresponds to 2. a = -2b/5.

For clarity purposes, the equations in the question are restated as follows:

A. a + 2b = 5                1. a = 2b/5

B. 5a = 2b                   2. a = -2b/5

C. a + 5 = 2b               3. a = -2b

D. 5(a + 2b) = 0          4. a = 2b-5

E. 5a + 2b =0              5. a = 5-2b

A. From the equation a + 2b = 5, a can be solved as follows:

a + 2b = 5

a = 5 - 2b

B. From the equation 5a = 2b, a can be solved as follows:

5a = 2b

a = 2b/5

C. From the equation a + 5 = 2b, a can be solved as follows:

a + 5 = 2b

a = 2b - 5

D. From the equation 5(a + 2b) = 0, a can be solved as follows:

5(a + 2b) = 0

5a + 10b = 0

5a = -10b

a = -10b/5

a = -2b

E. From the equation 5a + 2b =0, a can be solved as follows:

5a + 2b =0

5a = -2b

a = -2b/5

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Answer:

(a)20π

(b)74π

Step-by-step explanation:

(a) 2π(5) + (2π(10) × 1/2) = 2π(5) + 2π(5)

= 2π(10)

= 20π

(b) π(5)^2 + (π(10)^2 × 1/2) = 25π + 50π

=75π

Answer: P=20 cm    S=75 cm²

Step-by-step explanation:

We have 2 semicircles with diameter d=10 cm and 1 semicircle with diameter D=20 cm

[tex]\displaystyle\\The\ length \ of \ the\ circle\ is\ \pi D\\The\ length\ of \ the\ semicircle \ is\ \frac{\pi D}{2}[/tex]

[tex]\displaystyle\\a)\\P=2*\frac{\pi d }{2} +\frac{\pi D}{2} \\\\P=\pi d+\frac{\pi D}{2} \\\\P=\pi *(d+\frac{D}{2} )\\P=\pi *(10+\frac{20}{3} )\\\\P=\pi *(10+10)\\\\P=20\pi \ cm\\\\[/tex]

[tex]b)\\\displaystyle\\The\ area \ of \ the\ circle\ is\ \frac{\pi D^2}{4} \\The\ area\ of \ the\ semicircle \ is\ \frac{\pi D^2}{8}\\\\S=2*\frac{\pi d^2}{8} +\frac{\pi D^2}{8} \\\\S=\frac{2*\pi *10^2}8} +\frac{\pi *20^2}{8} \\\\S=\frac{2*\pi*100 }{8} +\frac{\pi *400}{8} \\\\S=\frac{200\pi }{8}+\frac{400\pi }{8} \\\\S=\frac{600\pi }{8} \\\\S=75\pi \ cm^2[/tex]

The value of x in the given parallelogram is: x = 90°.

A parallelogram is a quadrilateral with four interior angles and four sides, whose opposite angles are equal to each other.

In the image given:

Angle A = 120°

Since ABCD is a parallelogram, therefore, the angle that is opposite to angle A would also be 120°. Therefore:

Angle C = 120°

Angle D = 180 - 120 = 60°.

Angle DCO = 1/2(angle C) = 1/2(120) = 60°

Angle CDO = 1/2(angle D) = 1/2(60) = 30°

x = 180 - m<DCO - m<CDO [triangle sum theorem]

Substitute

x = 180 - 60 - 30

x = 90°

Therefore, the value of x in the given parallelogram is: 90°.

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Answer:

2yds 33 in

Step-by-step explanation:

Convert everything to the lowest unit(inches) perform the operation and convert back

1 yard = 3 feet
1 foot = 12 in
1 yard = 3feet x 12in = 36 in

19yd, 28in = 19 x 36 + 28 = 684 + 28 = 712 in

16yd, 31 in= 16 x 36 + 31 = 576 + 31 = 607 inches

19yd, 28in - 16yd, 31 in = 712 - 607 = 105 inches

Divide by 36 to get the whole number of yards as quotient
105/36  with remainder of 33

∴ 19yd, 28in - 16yd, 31 in = 105 inches = 2yds 33 inches

We can verify this by converting 2yds 11inches to inches and seeing the values agree

2 yds 33 in = 2 x 36 + 33 = 105

The number of weeks it would take the workers to build 15 more floors is 5 weeks.

The number of weeks it would take to build 15 more floors can be determined by dividing the number of additional floors by the number of floors the workers can build in one week.

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations. The result of the division process is known as the quotient.

Number of weeks = additional floors ÷ number of floors that can be built in a week

15 ÷ 3 = 5 weeks

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The correct option is D,  -√15 < -2.75 < -2 3/8 < 15/2.

A number line is just that – a straight, horizontal line with numbers placed at even increments along the length. It’s not a ruler, so the space between each number doesn’t matter, but the numbers included on the line determine how it’s meant to be used.

The value of the given numbers in the decimal form can be written as,

-√15 = -3.873

√15 = 3.873

15/2 = 7.5

-15/2 = -7.5

2 3/8 = 2.375

-2 3/8 = -2.375

Now, let's check in which options are the numbers arranged correctly.

A.) -√15 < -2 3/8 < -2.75 < 15/2

Since -2 3/8 > -2.75. Therefore, this is wrong.

B.) 15/2 < -2 3/8 < -2.75 < -√15

Since -2 3/8 > -2.75. Therefore, this is wrong.

C.) 15/2 < -2.75 < -2 3/8 < -√15

Since 15/2 > -2.75. Therefore, this is wrong.

D.) -√15 < -2.75 < -2 3/8 < 15/2

This is correctly arranged.

Hence, the correct option is D.

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The additional information required to prove the SSS Triangle Congruence Postulate is TR = JL

The congruence postulate is given as:

SSS Triangle Congruence Postulate

The above means that the three sides of the triangles are congruent.

From the figure, the following side lengths are said to be congruent

ST and KL

SR and KJ

For the congruence postulate of the triangle to be SSS Triangle Congruence Postulate, then the third corresponding sides must be congruent

This is represented as:

TR = JL

Hence, the additional information required to prove the SSS Triangle Congruence Postulate is TR = JL

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When 5 is divided by 1/3, we get 15.

Multiplication is an operation that represents the basic idea of repeated addition of the same number.

Given is 5 divided by 1/3.

Assume the result after 5 is divided by 1/3 is equal to [x]. Then, we can write -

x = 5/(1/3) = 15

Therefore, when 5 is divided by 1/3, we get 15.

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