X^2=50 where x is a real number

The answer for each of the differentiation are; f'(-6) = 432;  f⁻¹(y) = ∛((y + 5)/4); df⁻¹/dy = 1/432

1) f(x) = 4x³ - 5

We will differentiate it to get;

f'(x) = df/dx = 12x²

f'(-6) = 12(-6)²

f'(-6) = 432

2) We are given the formula;

x = f⁻¹(y)

Thus;

y = 4x³ - 5

4x³ = y + 5

x³ = (y + 5)/4

x = ∛((y + 5)/4)

f⁻¹(y) = ∛((y + 5)/4)

c)  f⁻¹(y) = ∛((y + 5)/4)

df⁻¹/dy = -1/12y²

At f(-6), we have;

df⁻¹/dy = 1/432

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The equation for the red graph is f(x) = -x².

From the information given, g(x) = 4 - x².

The vertex of the point (0, 4) and (0, 0) for g(x) and f(x) respectively. The rule of the translation will be:

(x, y) = (x, y -4).

The equation of the function will be:

f(x) = g(x) - 4

f(x) = (4 - x²) - 4

f(x) = -x²

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Answer: pi/3

Step-by-step explanation:

All of the other answers are asymptotes of the function, which by definition means they are not included in the domain, because they are undefined in the domain at that point. If you graph the function and graph all of those x values, you will see that (pi/3) is the only line that crosses the function.

Also, I took the test and got it right.

Only the value of x , [tex]\frac{\pi }{3}[/tex] is in the domain of the function.

The domain of a function is the set of values that we are allowed to plug into our function which makes the function defined.

The trigonometric functions are also called the angle functions, which relates the angles and the ratios of the sides of a right angle triangle.

According to the given question.

We have a trigonomtery function.

[tex]f(x) = 4cot(2x)+3[/tex]

The above trigonometry function can be written as

[tex]f(x) = 4\frac{cos(2x)}{sin(2x)} + 3[/tex]

For the function to be defined the denominator can't be zero.

[tex]sin(2x) \neq 2n\pi ( n \in0, 1, 2, 3, ..)[/tex]

Therefore, from the given values for the x we can only put [tex]\frac{\pi }{3}[/tex] in the given function because [tex]\frac{\pi }{2}[/tex] makes the denominator o which makes the function undefined. Similarly for the π also.

Hence, only the value of x , [tex]\frac{\pi }{3}[/tex] is in the domain of the function.

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Step-by-step explanation:

[tex] = \frac{2 \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } [/tex]

[tex] = \frac{2 \sqrt{2} - \sqrt{3} }{ \sqrt{2} + \sqrt{3} } \times \frac{ \sqrt{2} - \sqrt{3} }{ \sqrt{2} - \sqrt{3} } [/tex]

[tex] = \frac{ 2( \sqrt{2} - \sqrt{3} )( \sqrt{2} - \sqrt{3} )}{ { \sqrt{2} }^{2} - { \sqrt{3} }^{2} }[/tex]

[tex] = \frac{2(2 - \sqrt{6} - \sqrt{6} - 3) }{2 - 3} [/tex]

[tex] = \frac{2( - 1 - 2 \sqrt{6} )}{ - 1} [/tex]

[tex] = \frac{ - 2(1 + 2 \sqrt{6} )}{ - 1} [/tex]

[tex] = 2(1 + 2 \sqrt{6} )[/tex]

[tex] = 2 + 4 \sqrt{6} [/tex]

An inequality relating 100n and n³ is 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.

An inequality is comparison of  two values, showing if one is less than, greater than, or simply not equal to another value.

Since 100n and n³ for n = 1, 2, 3, . . . 9, 10, 11 are 100, 200, 300, . . . 900, 1000, 1100 and 1, 8, 27, . . . 729, 1000, 1331 respectively.

Therefore, an inequality relating 100n and n³ will be 100n ≥ n³ for n ≤ 10 and 100n ≤ n³ for n ≥ 10.

Induction hypothesis:

Suppose 100n ≤ k³ for some positive integer k ≥ 10.

We need to show that 100( k + 1 ) ≤ ( k + 1 )³ = k³ + 3k² +3k + 1.

Note 100( k + 1 ) = 100k + 100 ≤ k³ + 100

                                                 ≤ k³ + 3k²    (∵ k ≥ 10 )

                                                 ≤ k³ + 3k² + 3k

                                                 ≤ k³ + 3k²+3k + 1

So 100( k + 1 ) ≤ ( k + 1 )³, which is true.

Hence by the principle of mathematical induction, 100n ≤ k³ for every integer  k ≥ 10.

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9.7 to one significant figure is 10

We have:

9.7

To approximate to one significant figure, we have to estimate the number such that it is represented by a non zero digit.

When 9.7 is approximated, we have:

10

Hence, 9.7 to one significant figure is 10

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The polynomial is given by f(x) = 9(4x − 3)² (3x - 1) .

A polynomial is an expression that consists of indeterminate , Coefficients , exponents and mathematical operations.

It is given that

The zero of the function is at 3/4 with multiplicity of 2 = (x - 3/4)²

The zero of the function is at 1/3 with multiplicity of 1 = (x - 1/3)

The polynomial can be written as

f(x) = a (4x − 3)² (3x - 1)

-81 = a (0 − 3)² (0 -1)

a = 9

f(x) = 9(4x − 3)² (3x - 1)

Therefore the polynomial is given by f(x) = 9(4x − 3)² (3x - 1) .

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Answer: x = 130, y = 130

Step-by-step explanation:

By the corresponding angles theorem, x = 130

Thus, by the vertical angles theorem, y = 130

Answer:

8

Step-by-step explanation:

Due to lines r & s being parallel to each other, we can apply the rule of alternate interior angles to solve for y in this problem.

Applying this, we'll be obtaining the equation that of:

[tex]116=15y-4[/tex]

We now simply solve for y.

[tex]120=15y\\y=8[/tex]

Therefore, y is equal to 8.

This can be checked by plugging it into the equation:

[tex]15(8)-4[/tex]

[tex]120-4[/tex]

[tex]116[/tex]

And look at that, we got 116 for our answer, exactly the same as the other angle.

Any questions feel free to ask :)

x² + 12 is equivalent to the polynomial (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i).

Polynomials are defined as algebraic expressions consisting of constants, variables and exponents combined using operations like addition, multiplication, subtraction and division.

The given expression is x² + 12.

We have the identity (a + b) (a - b) = a² - b²

(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (2[tex]\sqrt{3}[/tex]i)²

                                = x² - (2² × √3² × i²)

We know that i² = -1, where i is the imaginary number in complex numbers

(x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) = x² - (4 × 3 × -1)

                                = x² + 12

Hence we get that (x + 2[tex]\sqrt{3}[/tex]i) (x + 2[tex]\sqrt{3}[/tex]i) is equivalent to x² + 12.

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The answer is J. [tex](x+4)(x-2)=x\cdot x[/tex]

The proportion that can be used to represent the given statement is [tex]\frac{3}{1} =\frac{12}{4}[/tex]

Given that there are 3 feet in 1 yard, which is equivalent to 12 feet in 4 yards.

In general, the term "proportion" refers to a part, share, or amount that is compared to a whole. According to the definition of proportion, two ratios are in proportion when they are equal.

We need to determine the proportion that can be used to represent this.

Now, 1 yard = 3 feet implies  4 yards = 12 feet.

The required proportion can be written as [tex]\frac{3}{1} =\frac{12}{4}[/tex].

Therefore, the proportion that can be used to represent the given statement is [tex]\frac{3}{1} =\frac{12}{4}[/tex].

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Rewriting the equation of the given line in slope-intercept form,

[tex]8x-7y=87\\\\-7y=-8x+87\\\\7y=8x-87\\\\y=\frac{8}{7}x-\frac{87}{7}[/tex]

The slope of the given line is thus 8/7, and since parallel lines have the same slope, the slope of the line we want to find is also 8/7.

Substituting into point-slope form,

[tex]y+17=\frac{8}{7}(x-3)\\\\y+17=\frac{8}{7}x-\frac{24}[7}\\\\\boxed{y=\frac{8}{7}x-\frac{143}{7}}[/tex]

Answer:

B

Step-by-step explanation:

(f + g)(x)

= f(x) + g(x)

= x + 8 - 4x - 3 ← collect like terms

= - 3x + 5

Answer:

[tex]\huge\boxed{\sf (f + g)(x) = -3x + 5}[/tex]

Step-by-step explanation:

Add both functions

(f + g)(x) = x + 8 + (-4x - 3)

(f + g)(x) = x + 8 - 4x - 3

(f + g)(x) = x - 4x + 8 - 3

(f + g)(x) = -3x + 5

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

Step-by-step explanation:

the answer is (c)

because 0 is 3 in number,

1 is 4 in number,

2 is 3in number

3 is 2 in number,

4 is 2 in number,

no 5,6,7

8 is 1 in number

and no 9

The dot plot ( C )is solved and each dot represents one student's response

A dot plot, also known as a dot chart or dot graph, is a type of data visualization that displays the frequency of values in a dataset. It is a simple graphing technique that uses dots to represent data points on a horizontal or vertical axis.

Each data point in the dataset is represented by a dot placed above the corresponding value on the axis. If there are multiple data points with the same value, the dots are stacked vertically above that value. The resulting plot shows the distribution of data points along the axis, with the height of the stack of dots representing the frequency of each value.

Given data ,

Let the data of the number of pets owned by student be represented as A

Now , the value of A = { 0, 0, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 8 }

The frequency of 0 = 3

The frequency of 1 = 4

The frequency of 2 = 3

The frequency of 3 = 2

The frequency of 4 = 2

The frequency of 8 = 1

In this dot plot, each dot represents one student's response. The number on the left indicates how many pets the students reported owning, and the dots are arranged vertically above that number.

For example, three students reported owning 2 pets, so there are three dots arranged above the number 2. This type of plot is useful for displaying the frequency of different values in a dataset.

Hence , the dot plot is solved

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Using subtraction of perfect squares, it is found that the factored expression is:

9t² - 4 = (3t - 2)(3t + 2).

It is given as follows:

a^2 - b^2 = (a - b)(a + b)

In this problem, the binomial is given as follows:

9t² - 4.

Hence:

Hence the factored expression is:

9t² - 4 = (3t - 2)(3t + 2).

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2x + 9 = 5x - 12

2x - 5x = - 1- 9

- 3x = - 21

x = 21/3

x = 7

Y = 60°

If the factors of quadratic function f are (x – 7) and (x + 3). The solution of the quadratic function f will be the negative 3 and 7.

It is a method for dividing a polynomial into pieces that will be multiplied together. At this moment, the polynomial's value will be zero.

If the factors of quadratic function f are (x – 7) and (x + 3).

Then the zeroes of function f will be

(x – 7)(x + 3) = 0

                x = 7, -3

Then the solution of the quadratic function f will be the negative 3 and 7.

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Answer:

212520 different committees

Step-by-step explanation:

Candidates

For a President: 23

For a Vice President: 22

For a Secretary: 21

For a Treasurer: 20

Number of ways: (23)(22)(21)(20) = 212520

Hope this helps

Answer:

To whom it may concern the answer to this problem would be 212,520.

Step-by-step explanation:

Many people think this problem to be a combination problem, but it is actually a permutation. Since there must be some specific semblance to the order of the equation. Now, to begin with, the work for this problem is...

[tex]_{n}_P_{r}=\frac{n!}{(n-r)!} \\_{23} _P_{4}=\frac{23!}{(23-4)!} \\_{23}_P_{4}=\frac{23!}{19!} \\_{23}_P_{4}=\frac{23*22*21*20*19!}{19!} \\_{23}_P_{4}=\frac{212,520}{1} \\_{23}_P_{4}=212,520[/tex]

Remember that the 19! cancel each other out. Hope this helps!

Smaller angle = 50
Larger angle = 130

Let smaller angle be x degree

=> larger angle= [tex]3x - 20[/tex]

Since these angles are supplementary , So

[tex]= > x + 3x - 20 = 180\\= > 4x = 200\\= > x = 50\\= > 3x - 20\\ = > 150 - 20 = 130[/tex]

So smaller angle would be 50 deg & larger angle would be  130 deg.

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Answer:

Step-by-step explanation:

[tex]3x+6-2 = 6x-( \frac{7}{2} \times \frac{9}{0} ) \\ \\ 3x + 4 = 6x - \frac{63}{0} \\ \\ 3x + 4 = 6x - 0 \\ \\ 4 + 0 = 6x - 3x \\ \\ 3x = 4 \\ \\ x = \frac{4}{3} .[/tex]

The value of x is 4/3 .

Answer: No Solution

Why?

Any number divided by 0 is not defined, but we are given 9/0 in the question. Hence we cannot solve the equation for the value of ‘x’.

A straight line passing through the point (-2,1) and having a gradient of -3 yields the equation y = -3x - 5.

We know that a straight line is an infinitely long line with no curves on it. A straight line's equation is

y = mx + c...(1), where m is the gradient of the straight line and c is a constant.

Given that the gradient of the given straight line = m = -3.

Putting this value in (1), we get

y = -3x + c ...(2)

Again, the given straight line passes through the point (-2,1). So, we can put x = -2 and y = 1 to get the value of the constant c.

So, 1 = (-3)(-2) + c

i.e. 6 + c = 1

i.e. c = 1 - 6 = -5

(2) can be written as

y = -3x - 5

Therefore the equation of the given straight line is

y = -3x - 5

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Answer: 2 3/4 > 2.68 is correct (only)

Step-by-step explanation: 2 3/4 = 2.75, and 2.75 is greater than 2.68

The rest are incorrect. 7.895 * 10^2 (100) = 789.5, and 5.43 * 10^3 (1000) = 5430. So 789.5 > 5430 is false.

Sqrt(63) = 7.93, and 7.93 > 8.11 is false.

Absolute values ( | | ) mean that no matter if it is negative or positive, it will become positive (unless the negative sign is outside the absolute value). 1.5 > 3.2 is false, and even without the absolute value, -1.5 is still less than 3.2

The probability that exactly 4 are cured from 7 dolphins is 0.0128

Probability is the likeliness of an event to occur and it has a range of 0 to 1, where 0 means unlikely and 1 indicates certainty of the event to happen.

It is given that the 92% of all the dolphins are cured of an ear infection ,When treated with an antibiotic

If there are total dolphins given as 7

On the basis of given data

The dolphin that cannot be cured is given by

1 - p = 1 - (92/100) = 0.08 = 8/100

q = (8/100)
n= 7

r = 4

Therefore by Binomial Distribution

[tex]P = ^nC_r p^r q^{n-r}[/tex]

Putting the values

[tex]P = ^7C_4 (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]

[tex]P = \dfrac{7!}{4! \;3!} (\dfrac{92}{100})^4 (\dfrac{8}{100})^{7-4}[/tex]

P =  0.0128

Therefore the probability is 0.0128.

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y=2x+3

to find inverse swap x and y

x=2y+3

x-3=2y

y=(x-3)/2

y=(x/2)-(3/2)

The inverse is f^-1(x)=(x/2)-(3/2)

Hope it helps!