Consider the function below.

f(x)=8/x−6
What would be the output if the input is 8?


8/14

8/6

2 1/3

4

Answer:

\(x=\pm1 \:\textsf{or}\:x=\pm3\)

Step-by-step explanation:

\(x^4-10x^2+9=0\)

\(\textsf{let}\:x^2=y\)

\(\implies y^2-10y+9=0\)

To factor a quadratic in the form \(ax^2+bx+c\), find 2 two numbers that multiply to \(ac\) and sum to \(b\).

⇒ two numbers that multiply to 9 and sum to -10:  -9 and -1

Rewrite \(b\) as the sum of these 2 numbers:

\(\implies y^2-y-9y+9=0\)

Factorize the first two terms and the last two terms separately:

\(\implies y(y-1)-9(y-1)=0\)

Factor out the common term \((y-1)\):

\(\implies (y-9)(y-1)=0\)

\(\implies (y-9)=0 \implies y=9\)

\(\implies (y-1)=0 \implies y=1\)

Change \(y\) back to \(x^2\):

\(\implies x^2=9\implies x=\pm3\)

\(\implies x^2=1\implies x=\pm 1\)

\(\textsf{So}\: x=\pm1 \:\textsf{or}\:x=\pm3\)

Answer:

\($x=\pm1\;\textrm{or}\;x=\pm3$\)

Step-by-step explanation:

Substitute \(u = x^2\) into the equation. This will make the quadratic formula easy to use.

\(\implies u^2 - 10u + 9 = 0\)

Consider the form \(x^2 + bx + c = 0\). Find a pair of integers whose product is \(c\) and whose sum is \(c\). In this case, whose product is \(9\)and whose sum is \(10\). And write the factored form using the integers.

\(\implies (u - 9)(u - 1) = 0\)

If any individual factor on the left side of the equation is equal to \(0\), the entire expression will be equal to \(0\).

\(\implies \begin{cases}u - 9 = 0 \\ \\ u - 1 = 0\end{cases}\)

Set \(u - 9\) equal to \(0\) and solve for \(u\). Similarly, Set \(u - 1\) equal to \(0\) and solve for \(u\).

\(\implies \begin{cases}u = 9 \\ \\ u = 1\end{cases}\)

Substitute the real value of \(u = x^2\) back into the solved equation.

\(\implies \begin{cases}x^2 = 9 \\ \\ x^2 = 1\end{cases}\)

Take the square root of both sides of the equations to eliminate the exponent on the left side.

\(\implies \begin{cases}x = \sqrt{9} \\ \\ x = \sqrt{1}\end{cases}\)

Solve both the equations for the value of \(x\).

\(\implies \begin{cases}x = \pm3 \\ \\ x = \pm1\end{cases}\)

Hence, this is our required solution for this question.

\(\rule{300}{1}\)

Additional information:

There are three ways to solve a quadratic equation:

Factoring uses the logic that the product of any number and zero is zero. Complete the square method uses square root, and the quadratic formula is the simpler method of it.

Quadratic Formula \(x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}\)

The degree of a polynomial is the highest exponent of the variable in the polynomial.

In this case, the degree of the polynomial y = -3x^5 + 4x^4 + 2 + x^2 is 5, because the highest exponent of x is 5 (in the term -3x^5). Therefore, the answer is 5.

The factored expression of 4x³ - 2x² + 8x - 4 is (2x² + 4)(2x - 1) by grouping

From the question, we have the following parameters that can be used in our computation:

4x³ - 2x² + 8x - 4

Group the expression in 2's

So, we have

(4x³ - 2x²) + (8x - 4)

Factorize each group

2x²(2x - 1) + 4(2x - 1)

So, we have

(2x² + 4)(2x - 1)

Hence, the factored expression is (2x² + 4)(2x - 1)

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The calculated period of the function is 12

From the question, we have the following parameters that can be used in our computation:

The graph

By definition, the period of the function is calculated as

Period = Difference between cycles or the length of one complete cycle

Using the above as a guide, we have the following:

Period = 13 - 1

Evaluate

Period = 12

Hence, the period of the function is 12

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Answer:

c

Step-by-step explanation:

just took the quiz

Answer:

The answer is C) factor by grouping

Step-by-step explanation:

Edge 2020

The measure of the complement of a 1-degree angle is 89 degrees.

The complement of an angle is defined as the angle that, when added to the given angle, results in a sum of 90 degrees. To find the measure of the complement of a 1-degree angle, we need to determine the angle that, when added to 1 degree, equals 90 degrees.

Let's denote the measure of the complement as x degrees. According to the definition, we can set up the equation:

1 degree + x degrees = 90 degrees.

To solve for x, we need to isolate it on one side of the equation. By subtracting 1 degree from both sides, we have:

x degrees = 90 degrees - 1 degree.

Simplifying the right side, we get:

x degrees = 89 degrees.

In summary, when an angle measures 1 degree, its complement measures 89 degrees. Complementary angles are pairs of angles that add up to 90 degrees. In this case, since the given angle measures only 1 degree, its complement is significantly larger, nearly forming a right angle. The concept of complementary angles is fundamental in geometry and can be applied to various problems involving angles and their relationships.

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Answer:

y+14x=74

Step-by-step explanation:

By transforming the following equation of a line y − 4 = −14 (x − 5) to its general form, we obtain:

The given equation of line is :

y − 4 = −14 (x − 5)

Firstly we solve RHS of the equation.

y − 4 = -14x+70

Taking variable on LHS and constants on RHS.

y+14x=70+4

y+14x=74

Hence, the general equation is y+14x=74.

Answer: 222cm

Step-by-step explanation:

To find the area of this composite shape you will have to split them into 2 shapes; a rectangle and a triangle.

To work out the area of the rectangle you have to do 15×12= 180

Then, to work out the area of the triangle, you use the formula base times height divided by 2.

7×12=84

84÷2=42

Then to work out the total area of both the rectangle and the triangle, you have to add the area of both.

180+42=222cm

Hope this helps :)

If the function h(t) = tan(5t +4 )  using chain rule  we found values h'(1)=  6.02 and h"(1) = -27.24

Chain rule for differentiation states that the differentiation of the composition of two functions f, g

(fоg)' = f'(g(x))* g'(x)  , where '  represents first derivative  with respect to independent variable x .

For three functions : x, y, t

(x(y(z(t))))' = x'(y(z(t)))*(y'(z(t)))*z'(t)

Given h(x) = tan(5t+4)

Let  f(t) = tan t and g(t) = 5t+4

f'(t) = sec² t and g'(t) = 5

Then h(t) = fоg(t)

Using chain rule of differentiation:

h'(t) = (fоg(t))' = f'(g(t))* g'(t) = sec²(5t+4) *(5) = 5 sec²(5t+4)

let x(t) = 5t², y(t) = sec(t), z(t) = 5t+4

x'(t) = 10t , y'(t) = sect tan t  , z'(t) =5

(x(y(z(t))))' = x'(y(z(t)))*(y'(z(t)))*z'(t)

h"(t) =(x(y(z(t))))'= 10 sec(5x+4) * sec(5t+4)tan(5t+4)*5

h"(t) = 50sec²(5t+4)tan(5t+4)

The value of h'(t)  at t =1

h'(1 ) = 5 sec²(5(1)+4)= 5 sec²(9) =6.02

h"(1) = 50sec²(5(1)+4)tan(5(1)+4) = 50sec²(9)tan(9) = -27.24

Therefore, the values h'(1 ) = 6.02 and  h"(1)  = -27.24

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Cοmparing the medians fοund using the given bοx plοt, we fοund that the median οf eighth graders is greater than the median οf the seventh graders.

A bοx and whisker plοt, οften knοwn as a bοx plοt, shοws a data set's five-number summary. The minimum, first quartile, median, third quartile, and maximum make up the five-number summary.

A bοx is drawn frοm the first quartile tο the third quartile in a bοx plοt.

At the median, a vertical line passes thrοugh the bοx. It is generally used tο shοw whether a distributiοn is skewed οr nοt and whether there are any pοtential οutliers, οr οdd οbservatiοns, in the data set.

When cοmparing οr invοlving numerοus data sets, bοxplοts are alsο highly helpful. Graphs can be used tο determine hοw widely the data values vary οr are spread οut.

Frοm the bοx plοt given, we can summarize the fοllοwing,

Fοr seventh graders,

The first quartile Q1 = 3

The third quartile Q3 = 4

Interquartile range = Q3 - Q1 = 4-3 = 1

The median = 3.5

Fοr eighth graders,

The first quartile Q1 = 3.5

The third quartile Q3 = 4.5

Interquartile range = Q3 - Q1 = 4.5 -3.5 = 1

The median = 4

Therefοre cοmparing the medians fοund using the given bοx plοt, we fοund that the median οf eighth graders is greater than the median οf the seventh graders.

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Answer:

Step-by-step explanation:

This is clearly a linear relationship.  If Alex rented the movie for 0 days, he'd owe nothing.  If he paid $6 for a 3-day rental, the slope of this line would be m = rise / run = $6/(3 days) = $2/day, which is positive.

Then the equation for this graph is C(x) = ($2/day)x, where x is the number of days for which the movie is rented.

Using this formula, we find three particular points on the graph:

(1, $2), (2, $4), (3, ($6)

Answer:

D

Step-by-step explanation:

i just took the test ur welcome:)

Answer:

second one

Step-by-step explanation:

f(3)=g(3)=6

Answer:

The probability that one marble drawn at random is not blue is 70%

Answer:

If two chords intersect in a circle, then the product of the segments of one chord equals the product of the segments of the other chord.

6(3x) = 4(4x + 1)

18x = 16x + 4

2x = 4

x = 2

Answer:

3/4 written as a percent would be 75%

Answer:

x intercept: (-8,0)

y intercept: (0,2)

Answer:

If the radius of a circle is 5 inches, the diameter is 10.

Step-by-step explanation:

This is because to find the diameter of a circle sing the radius is to multiply it by two. 5x2=10

So the diameter is 10. If you want to find the radius just reciprocate the process, divide the diameter by 2 and yo will get the radius.

I really hope this helped you out. Make sure to give my answer brainliest. Have a radiant day or night ! :D

The correct expression is (a) n = 100; (x + 10)^2

The expression is given as:

x^2 + 20x + n

Take the coefficient of x

k = 20

Divide by 2

k/2= 10

Square both sides

(k/2)^2 = 100

The above value represents the value of n

i.e.

n = 100

So, we have:

x^2 + 20x + 100

Expand

x^2 + 10x + 10x + 100

Factorize

x(x + 10) + 10(x + 10)

Factor out x + 10

(x + 10)^2

Hence, the correct expression is (a) n = 100; (x + 10)^2

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Consider the following diagram,

Consider the side 212 feet side makes an angle as denoted in the figure.

Consider that both the triangle have the same base length,

Solve the expression further,

Now, the height of the statue is calculated as,

Thus, the height of the statue is approximately 154.744 feet.

A construction of the box-and-whisker plot for the data is shown below.

In Mathematics and Statistics, a box plot is sometimes referred to as box-and-whisker plot and it can be defined as a type of chart that can be used to graphically or visually represent the five-number summary of a data set with respect to locality, skewness, and spread.

Based on the information provided about the given box-and-whisker plot, the five-number summary for the given data set include the following:

In conclusion, we can reasonably infer and logically deduce that the maximum number is 38 while the minimum number is 6, and the median is equal to 23.

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The dimensions of the rectangular box are given as follows:

All the dimensions.

The volume of a rectangular prism, with dimensions length, width and height, is given by the multiplication of these dimensions, according to the equation presented as follows:

Volume = length x width x height.

The box's volume is obtained as follows:

54 x 1³ = 128 x (3/4)³ = 54 cubic inches. (the volume of a cube is the side length cubed)

Hence all the options can be the dimensions of the box, as all the options have a multiplication resulting in 54.

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Answer:

Option B.)

Step-by-step explanation:

Just took the test and got 100% :]

The system of logarithmic equation is graphed and the point of intersection of the equation is log₃ ( 5x ) = log₅ ( 2x + 8 ) is A ( 1.0 , 1.4 )

Graphs behave differently at various x-intercepts. Sometimes the graph will cross over the x-axis at an intercept. Other times the graph will touch the x-axis and bounce off.

Identify the even and odd multiplicities of the polynomial functions' zeros.

Using end behavior, turning points, intercepts, and the Intermediate Value Theorem, plot the graph of a polynomial function.

The graphs cross or are tangent to the x-axis at these x-values for zeros with even multiplicities. The graphs cross or intersect the x-axis at these x-values for zeros with odd multiplicities

Given data ,

Let the solution to the logarithmic equation be represented as A

Now , the value of A is

log₃ ( 5x ) = log₅ ( 2x + 8 )

On simplifying , we get

log₃ ( 5x ) = log₁₀ ( 5x ) / log₁₀ ( 3 )

log₅ ( 2x + 8 ) = log₁₀ ( 2x + 8 ) / log₁₀ ( 5 )

Substituting the logarithmic quantities , we get

log₁₀ ( 5x ) / log₁₀ ( 3 ) = log₁₀ ( 2x + 8 ) / log₁₀ ( 5 )

On cross multiplying , we get

log₁₀ ( 5x ) / log₁₀ ( 2x + 8 ) = log₁₀ ( 3 ) / log₁₀ ( 5 )

( 5x ) / ( 2x + 8 ) = 3/5

On cross multiplying , we get

25x = 6x + 24

Subtracting 6x on both sides , we get

19x = 24

Divide by 19 on both sides , we get

x = 1.26

Therefore , the approximate values of the function on graphing is A ( 1.0 , 1.4 )

Hence , the solution of function from graphing is A ( 1.0 , 1.4 )

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Using corresponding and alternating angle theorem. The values of the angles in the figure are m∠1 = 47, m∠2 = 133, m∠3 = 139, m∠4 = 41, m∠5 = 139 degrees respectively.

The corresponding angle postulate states that the corresponding angles are congruent if the transversal intersects two parallel lines. In other words, if a transversal intersects two parallel lines, the corresponding angles will be always equal.

Alternate angle theorem states that when two parallel lines are cut by a transversal, then the resulting alternate interior angles or alternate exterior angles are congruent.

a. m∠1 = m∠7

Reason : Corresponding angles are equal

m∠1 = 47°

b. m∠2 = 180 - m∠1

Reason: Angles on a straight line

m∠2 = 180 - 47

m∠2 = 133°

c. m∠3 = m∠16

Reason : alternating angles are equal

m∠ = 139°

d. m∠4 = 180 - m∠3

Reason : Angles on a straight line

m∠4 = 41°

e. m∠5 = 180 - m∠4

Reason: Angles on a straight line

m∠5 = 139°

n. m∠17 = 180 - m∠6

m∠17 = 41°

f. m∠ 6 = m∠15

m∠15 = m∠17

Reason : Opposite angles are equal

m∠ 6 = m∠ 17

Reason : Alternating angles are equal

m∠ 6 = 41°

g. m∠8 = m∠1

m∠ 8 = 47°

h. m∠ 9 = m∠2

m∠9 = 133°

m. m∠15 = m∠ 17

m ∠ 15 = 41°

o. m∠ 18 = 360 - (m∠15 + m∠16  m∠ 17)

m∠18 = 360 - (41 + 139 + 41)

m∠18 = 139°

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\(\dfrac{7!4!}{5!3!}=6\cdot7\cdot4=168\)

Answer:

can you write it in a clearer way

Step-by-step explanation:

Therefore, the expression (7-3i) + (x - 2i)² - (4i + 2x²) in the simplest a + bi form is: -2x² - 1 - (4x + 7i)

Linear Equation                   General Form                    Example

Slope intercept form             y = mx + b                            y + 2x = 3

Point–slope form                   y – y1 = m(x – x1 )              y – 3 = 6(x – 2)

General Form                            Ax + By + C = 0               2x + 3y – 6 = 0

Intercept form                        x/a + y/b = 1                 x/2 + y/3 = 1

As a Function f(x) instead of y      f(x) = x + C                         f(x) = x + 3

The Identity Function                      f(x) = x                     f(x) = 3x

Constant Functions                      f(x) = C                       f(x) = 6

Let's start by expanding the square term (x - 2i)² using the formula for (a + b)²:

(x - 2i)² = x² - 4xi + 4i²

Note that i² = -1, so we can simplify this expression to:

(x - 2i)² = x² - 4xi - 4

Substituting this expression and the given values into the original expression, we get:

(7 - 3i) + (x² - 4xi - 4) - (4i + 2x²)

Grouping the real and imaginary terms, we get:

(7 - 4 - 2x²) + (-3i - 4i - 4x) + (x²)

Simplifying the real part, we get:

-2x² - 1

Simplifying the imaginary part, we get:

-7i - 4x

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Answer:

The equation is    x+3<12  

The answer is       x<9

Step-by-step explanation:

(The sum of a number = x) (and = +) (three is less than twelve = 3<12)

This means the equation is x+3<12, so then you subtract 3 from both sides and end up with x<9

Hope this helps :)

Answer:

Step-by-step explanation:

a. To calculate the incremental income after taxes, we need to determine the incremental costs and revenues associated with extending credit to the new customers. The additional credit sales will generate $180,000 in revenue, but we need to subtract the expected uncollectible amount of 12% * $180,000 = $21,600. The net additional credit sales will be $180,000 - $21,600 = $158,400.

The production and marketing costs will be 72% * $180,000 = $129,600. The total incremental costs will be $129,600 + $16,200 (collection expense) = $145,800.

The incremental income before taxes will be $158,400 - $145,800 = $12,600. The income tax will be 34% * $12,600 = $4,284. The incremental income after taxes will be $12,600 - $4,284 = $8,316.

To calculate the return on incremental investment, we need to determine the incremental investment required to extend credit to the new customers. Since no additional investment in assets is required, the incremental investment will be equal to the incremental costs of $145,800. The return on incremental investment will be $8,316 / $145,800 = 5.7%.

Based on the return on incremental investment of 5.7%, the company should not extend credit to the new customers, as it is below the desired return of 10%.

b. If an additional investment in inventory is required to extend credit to the new customers, we will need to recalculate the incremental income after taking into account the additional investment. If the additional investment in inventory is $x, the incremental investment will be $145,800 + $x. The incremental income before taxes will be $158,400 - ($129,600 + $16,200 + $x) = $12,600 - $x. The income tax will be 34% * ($12,600 - $x) = $4,284 - $x * 0.34. The incremental income after taxes will be ($12,600 - $x) - ($4,284 - $x * 0.34) = $8,316 - $x * 0.34.

To determine whether credit should be extended, we need to compare the return on incremental investment to the desired return of 10%. The return on incremental investment will be ($8,316 - $x * 0.34) / ($145,800 + $x). Setting this equal to the desired return of 10% and solving for x, we find that the additional investment in inventory cannot exceed $24,764 for the company to meet its desired return. If the additional investment in inventory is less than or equal to $24,764, the company should extend credit to the new customers. If it is greater than $24,764, the company should not extend credit to the new customers.