Algebra 2 - Composition Functions

#4-6: let f(x)= 5x^3-2x and g(x)= 3x^3. Perform the indicated operation.

The first difference between Tn and Tn-1 where Tn= 688 is 88 if the quadratic sequence is defined as:2;12;28;50

It is defined as the systematic way of representing the data that follows a certain rule of arithmetic.

The quadratic sequence:

2, 12, 28, 50

a + b + c = 2

10, 16, 22 (first difference)

3a + b = 10

6, 6 (second difference)

2a = 6

a = 3

b = 1

c = -2

Tterm:

T(n) = 3n² + n - 2  = 688 (given)

After solving the quadratic equation:

n = 15, n = -46/3(n cannot be nagatve)

n = 15

n - 1 = 14

T(14) = 600

T(n) - T(n-1) = 688 - 600 = 88

Thus, the first difference between Tn and Tn-1 where Tn= 688 is 88 if the quadratic sequence is defined as:2;12;28;50

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Answer:

Step-by-step explanation:

The function that represents a geometric sequence is given by:

C. [tex]A(n) = P(1 + i)^{n-1}[/tex], where n is a positive integer.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

Following this pattern, a function that is also a geometric sequence is:

C. [tex]A(n) = P(1 + i)^{n-1}[/tex], where n is a positive integer.

For the function, we have that:

[tex]a_1 = P, q = 1 + i[/tex].

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Answer

He needs to buy 27 Cows

Step-by-step explanation:

if the ratio from horses to cows is 5-3 then you multiply 5 by the number to get 45 and also multiply it by 3

5 x 9 = 45

3 x 9 = 27

T

Step 1 and 2: Draw an isosceles right triangle

See attachment (figure 1) for this triangle

The legs of this triangle have a length of 1 inch

Step 3: The hypotenuse

This is calculated using the following Pythagoras theorem

[tex]h^2 = 1^2 + 1^2[/tex]

This gives

[tex]h = \sqrt 2[/tex]

Step 4: Draw another isosceles right triangle

Add 1 inch to one of the legs

See attachment (figure 2) for this triangle

The legs of this triangle have lengths of 1 inch and 2 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

[tex]h^2 = 2^2 + 1^2[/tex]

This gives

[tex]h = \sqrt 5[/tex]

Step 5: Draw another isosceles right triangle

Add 1 inch to one of the legs

See attachment (figure 3) for this triangle

The legs of this triangle have lengths of 1 inch and 3 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

[tex]h^2 = 3^2 + 1^2[/tex]

This gives

[tex]h = \sqrt {10[/tex]

Step 6: Draw another isosceles right triangle

Add 1 inch to one of the legs

See attachment (figure 4) for this triangle

The legs of this triangle have lengths of 1 inch and 4 inches, respectively

This hypotenuse is calculated using the following Pythagoras theorem

[tex]h^2 = 4^2 + 1^2[/tex]

This gives

[tex]h = \sqrt{[17[/tex]

See that the hypotenuse is the square root of 17

Hence, the right triangle whose legs are 1 inch and 4 inches has an hypotenuse of √17

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The expression equivalent to -21.8 - (-18.3) would be option A; -21.8+18.3.

Those expressions that might look different but their simplified forms are the same expressions are called equivalent expressions.

To derive equivalent expressions of some expression, we can either make it look more complex or simple.

The given expression is

-21.8 - (-18.3)

So, open the bracket and distribute the negative;

-21.8  (+18.3)

Thus, the expression equivalent to -21.8 - (-18.3) would be option A; -21.8+18.3.

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Answer: A

Step-by-step explanation: –21.8 – (–18.3) = -3.5 and –21.8 + 18.3 = -3.5

Answer:

[tex]\huge\boxed{\sf \$ \ 8.79\ per\ hour}[/tex]

Step-by-step explanation:

Work hours = 2:00 pm - 11:00 pm

So,

9 hours = $79.11

Using unitary method

9 hours = $79.11

Divide both sides by 9

1 hour = $79.11/9

1 hour = $8.79

So, Kenya is being paid $8.79 per hour.

[tex]\rule[225]{225}{2}[/tex]

The ratio of sin X and cos X are as follows;

sin X = √119 / 12

cos X = 5 / 12

Right angle triangle has one of its angle as 90 degrees. The side and angles can be found using trigonometric ratios.

Therefore,

sin X = opposite / hypotenuse

sin X = √119 / 12

Therefore,

cos X = adjacent / hypotenuse

cos X = 5 / 12

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Answer:graph a  

Step-by-step explanation:

bc if you subtract 3

from 2 you find the one you line your numbers up with

The graph that best describes the new function is shown in the image attached below.

The equation for a linear function with a slope of m and y-intercept of b is represented as y = mx + b.

Given a linear function graph passes the points (-0.5, 0) and (0, 1):

Y-intercept (b) = 1 (value of y when x = 0)

Slope (m) = change in y/change in x = (1 - 0)/(0 - (-0.5)) = 2

If the slope (1) is multiplied by 2, the new slope would be: 2

If the y-intercept (2) is increased by 3 units, the new y-intercept would be: 5

The equation of the new function would be: y = 2x + 5

The graph that best represents the function is shown in the image attached below.

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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad \tt \rightarrow \: \{ 0,4 \}[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

[tex]\qquad \tt \rightarrow \: - {a}^{2} + 4a = 0[/tex]

[tex]\qquad \tt \rightarrow \: - ( {a}^{2} - 4a) = 0[/tex]

[tex]\qquad \tt \rightarrow \: {a}^{2} - 4a = 0[/tex]

[tex]\qquad \tt \rightarrow \:a(a - 4) = 0[/tex]

The two cases are :

or

We can conclude :

[tex]\qquad \tt \rightarrow \:solution \: (a) = \{ 0,4\}[/tex]

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

[tex] \quad \quad \quad \quad\huge \tt \pink ❆ AnSweR \pink ❆[/tex]

[tex]\quad\quad \tt-a^2+4a= 0[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex] \quad\quad\tt⇢-1(a^2 - 4a) = 0[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\quad\quad\tt⇢-1(a-4)a = 0[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\quad\quad\tt⇢a-4=0[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: [/tex]

[tex]\quad\quad\tt⇢a = 0[/tex]

-----------------------------------------------------------

[tex] \boxed{ \tt \blue{a = 0}}[/tex]

[tex]\boxed{ \tt\blue{a = 4}}[/tex]

Answer:

x = 10

Step-by-step explanation:

Proof: If a line is parallel to one side of the triangle, then it divides the other two sides proportionally.

6/9 = x/15

9x = 90

x = 10

Answer:

16 ounce can sells for 85 cents

Step-by-step explanation:

29cents / 6 ounce = 4.833cents/ounce

65cents / 16 ounce = 4.0625cents/ounce

4.0625 < 4.833

then:

the better deal is:

16 ounces per 65 cents

$14.90 spent with the amount left for an extra pencil or notebook being $0.30 or $1.50 short respectively indicates that a notebook costs $1.8 more than a pencil.

Let x represent the cost of a notebook and let y represent the cost of a pencil. The following equations can be obtained;

4•x + 3•y = 14.9...(1)

Let a represent the total money Tina has, which gives;

4•x + 4•y = a - 0.3...(2)

5•x + 3•y = a + 1.5...(3)

Subtracting equation (2) from equation (3) gives;

5•x - 4•x + 3•y - 4•y = a - a + 1.5 - (-0.3) = 1.8

Which gives;

Multiplying equation (4) by 4 and subtracting the result to equation (1) gives;

4 × (x - y) = 4 × 1.8 = 7.2

4•x - 4•y = 7.2

4•x - 4•x + 3•y - (-4•y) = 14.9 - 7.2 = 7.7

7•y = 7.7

x - y = 1.8

x = 1.8 + 1.1 = 2.9

The difference between the cost of a notebook and the cost of a pencil is therefore;

x - y = $2.9 - $1.1 = $1.8

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Answer:

55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49

Step-by-step explanation:

To simplify this equation, follow these steps:

(7.5x² +5.4x +3.7) (7.4x² -2.1x +7.7)

Multiply 7.5x² by all the terms in the right parenthesis.

7.5x² (7.4x² -2.1x +7.7)=55.5[tex]x^{4}[/tex] - 15.75x³+ 57.75x²

Then multiply 5.4x by all the terms in the right parenthesis.

5.4x(7.4x²-2.1x+7.7)=39.96x³-11.34x²+41.58x

Now multiply 3.7 by all the terms in the right parenthesis.

3.7(7.4x²-2.1x+7.7)=27.38x²-7.77x+28.49

Add all of those answers together.

55.5[tex]x^{4}[/tex] - 15.75x³+ 57.75x²+39.96x³-11.34x²+41.58x+27.38x²-7.77x+28.49=

=55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49

The answer is 55.5[tex]x^{4}[/tex]+24.21x³+73.79x²+33.81x+28.49

Hope this helps!

If not, I am sorry.

Answer:

F=9/5c+32

Step-by-step explanation:

Simplified value of  subtraction of 7x+27x+2 from -5x^2-2x−5x 2 −2x. is [tex]-10x^{2} -38x-2[/tex].

Given Expressions  7x+27x+2 and  -5x^2-2x−5x 2 −2x.

Expressions refers to the combination of numbers, variables and symbols. It represents the relationship between variables. They are solved for finding out the value of variables. It is mainly not in equal to form. Subtraction is possible when subtracting the coefficients of same variable.

We have to subtract 7x+27x+2 from -5x^2-2x−5x 2 −2x. and to do this we need to first solve the expressions itself.

7x+27x+2=34x+2------------------1

[tex]-5x^{2} -2x-5x^{2} -2x[/tex]=[tex]-10x^{2} -7x-2x[/tex]--------------------2

Now subtract 1 from 2

=[tex]-10x^{2} -7x-2x[/tex]-34x+2

=[tex]-10x^{2} -38x-2[/tex].

Hence the simplified value of subtraction is [tex]-10x^{2} -38x-2[/tex].

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The solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.

The interval notations are used to represent numbers between two numbers excluding or including the numbers as per the use. We use the following four interval notations:

[a, b] ⇒ All numbers between a and b including both a and b.

(a, b) ⇒ All numbers between a and b excluding both a and b.

(a, b] ⇒ All numbers between a and b excluding a but including b.

[a, b) ⇒ All numbers between a and b including a but excluding b.

We are asked to write the solution for x ≥ 0 and x ≥ -5 in the interval notation.

We first write each inequality in interval notation:

x ≥ 0 ⇒ x are all numbers greater than 0 including 0. This can be written in the interval notation as [0, ∞). We don't include ∞ as it is indeterminant.

x ≥ -5 ⇒ x are all numbers greater than -5 including -5. This can be written in the interval notation as [-5, ∞). We don't include ∞ as it is indeterminant.

Now, we are asked to solve for x ≥ 0 or x ≥ -5. Since it is 'or', we take unions of the two sets, that is the solution is:

[0, ∞) ∪ [-5, ∞) = [5, ∞).

Therefore, the solution for x ≥ 0 and x ≥ -5 is [-5, ∞), in the interval notation.

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(1,18)

Let's verify

Verified

Answer:

12.56637ft

Step-by-step explanation:

Formula: c=2π*r

c=2π*2 = 12.56637ft

The simplified expression are as follows;

6mn³ - mn² +  3mn³ + 15mn² =  9mn³ + 14mn²

a⁴b³ + 8a⁴b³  = 9a⁴b³

A simplified expression is express to its lowest term.

Therefore,

6mn³ - mn² +  3mn³ + 15mn²

combine like terms

6mn³  +  3mn³ - mn² + 15mn²

9mn³ + 14mn²

a⁴b³ + 8a⁴b³  = 9a⁴b³

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Answer:

y=x^2+7x+4

Step-by-step explanation:

because the sign before x^2 is positive, the graph would concave up, if there's only one intercept, it has to be the vertex. the vertex is the critical point.

solve every make the derivative of each function equals zero, you get the x where the vertex shall be, then get this"x" into y=x-5 see if the y in y=x-5 is equal to y=x^2+6x+9 or other options.

let me give u an example.

for y=x^2+x-4, the critical point shall be 2x+1=0,x=-1/2, and the y is -4.25,

if you plug x=-1/2 into y=x-5, it's -5.5, -5.5 doesn't equal to -4.25

Answer:

D

Step-by-step explanation:

y = x2 + 7x + 4

The answer is [tex]11c^3[/tex].

Answer:

11:37

Step-by-step explanation:

11 thin-crust pizzas

11+24=37 total pizzas

=>11:37

Answer:

49/100

Step-by-step explanation:

So you can find the area of shaded area by finding the area of the circle inside the entire circle that has a diameter of 3 cm and 4 cm and then find the area of the most inner circle which only has a diameter of 4 cm and then subtract these 2. After that you want to find the area of the entire circle and then divide the area of the shaded area by the entire circle. The formula for the area of a circle is given as: [tex]\pi r^2[/tex]

Area of the two "inner" circles of a diameter of 4 and 3 cm. This gives you an entire diameter of 7 cm with a radius of 3.5. The area of this circle is [tex]\pi(3.5)^2[/tex] which is [tex]12.25\pi[/tex].

The area of the most inner circle only has a diameter only 4 cm. The radius is 2, thus the area of this circle is [tex]\pi (2)^2[/tex] which is [tex]4\pi[/tex]. Now subtract this from the 12.25 pi to find the area of the shaded area. This gives you the equation: [tex]12.25\pi-4\pi[/tex] which equals [tex]8.25\pi[/tex].

Now to find the area of the entire circle you add up all the "diameters" which gives you 4 cm + 3 cm + 3 cm = 10 cm. So the radius is 5. This gives you the equation: [tex]\pi(5)^2[/tex] which is equal to [tex]25\pi[/tex].

Now to find the fraction of circle that is shaded we divide the area of the shaded area and the area of the entire circle. This gives you the equation: [tex]\frac{12.25\pi}{25\pi}[/tex] but since it wants it as a fraction, I'm assuming it wants integers in the decimal and numerator place. So we can represent 12.25 as 12 + 1/4. And then convert the 12 into 1/4ths by multiplying by 4 and then adding that to the numerator. This makes the fraction [tex]\frac{49}{4}=12.25[/tex]. So now all we have to is divide the two values: [tex]\frac{\frac{49}{4}}{\frac{25}{1}}[/tex]. If you're wondering where the pi's when you can just cancel them out since they're both in the numerator and denominator. Now all we have to do is keep the 49/4, change the operator to multiplication, and flip the 25/1 to 1/25. This gives you the equation: [tex]\frac{49}{4} * \frac{1}{25}[/tex] which becomes [tex]\frac{49}{100}[/tex] which is the answer

Answer:

C

Step-by-step explanation:

12 /13   is definitely less than 36/30   because 36/30 =  1  1/5

The sum of the expression (–x² + x) and (x² – 3x – 1) will be –2x – 1. Then the correct option is D.

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

The expression can be written as

(–x² + x) and (x² – 3x – 1)

Then the sum of the expression (–x² + x) and (x² – 3x – 1) will be

(–x² + x) + (x² – 3x – 1) = –2x – 1

Then the correct option is D.

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To calculate the average speed of the horse in miles per hour, holding the all-time record for running a 2-kilometer race in 1 min and 59.4 sec, we do the necessary conversions over distance from kilometers to miles and over time from minutes and seconds to hours.

The average speed thus calculated is 393.2722 miles per hour.

The average speed of any object is the ratio of the total distance the object travels, and the total time taken by the object to cover that distance.

Thus, Average speed = Total Distance/Time taken.

In the question, we are informed that a horse holds the all-time record for running a 2-kilometer race in 1 min and 59.4 sec.

We are asked for the necessary conversions required to calculate the average speed of the horse for the race in miles per hour.

The necessary conversions that will be required will be:

Distance: 2 kilometers to miles.

Time: 1 minute 59.4 secs to hours.

To convert from kilometers to miles, we follow the conversion rate:

1 kilometer = 0.621371 miles.

Thus, distance = 2 kilometers = 2 * 0.621371 miles = 1.24274 miles.

For the time, we first convert seconds to time, using the conversion rate:

1 second = 1/60 minutes,

Therefore, 59.4 seconds = 59.4/60 minutes = 0.99 minutes.

Thus, the total time = 1.99 minutes.

To convert from minutes to hours, we follow the conversion rate:

1 minutes= 1/60 hours.

Thus, time = 1.99 minutes = 1.99/60 hours = 0.03316 hours.

Thus, the average speed of the horse = Distance/Time = 1.24274/0.003316 miles per hour = 393.2722 miles per hour.

Thus, to calculate the average speed of the horse in miles per hour, holding the all-time record for running a 2-kilometer race in 1 min and 59.4 sec, we do the necessary conversions over distance from kilometers to miles and over time from minutes and seconds to hours.

The average speed thus calculated is 393.2722 miles per hour.

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By the inscribed angle theorem, [tex]m\angle AEB=30^{\circ}[/tex] and [tex]m\angle ACB=30^{\circ}[/tex].