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All the zeros of following function f(x)=x4−8x2−9 are 3, -3, i, -i

A number x that reduces the value of a function f to 0 is known as its root in mathematics: f(x) = 0.

Roots are actual objects since polynomials are functions as well.

Every polynomial with complex coefficients has at least one (complex) root, according to the fundamental theorem of algebra.

f(x)=x4−8x2−9

You should set (x4 - 8x2 - 9) to 0.

x4−8x2−9=0

Learn what x's value is.

Put u=x2 in the equation's place.

As a result, applying the quadratic formula will be straightforward.

u2−8u−9=0

Consider the equation x2+bx+c.

Write out the factored form (u-9)(u+1) = 0.

The answer is the set of all numbers that add up to (u9)(u+1)=0.

u=9,−1

If u=x2 has a genuine value, change it to x2=9,  x2= -1

In the case of these equations, x = +3, -3, and  -i, +i .

The whole solution is made of of the solution's positive and negative components.

x4- 8x2- 9 = 0 has a solution.

is x=3,−3, i,−i

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Since the rectangles are similar, that means their sides are proportional.

Since the bigger rectangle has a base of 24cm and the smaller one's base is 20cm, the proportion the sides hold is

This means the sides of the larger rectangle are 1.2 times larger than those of the smaller one.

The area of the small rectangle is 80cm². Since

where b is the lenght of the base and h is the lenght of the height, then

So the height of the small rectangle will be 4cm. But as we previously deduced, the height of the larger rectangle will be 1.2 times larger than that of the smaller one, so it's height will be

And so, its are is

We can confirm this because

which is the proportion the areas of the rectangles hold.

If the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B is negative, the graph of the function reflects over the y-axis.

Let the tangent function be f(z) = tan (Bz)

The period exists [tex]$P=\frac{\pi}{|B|}$[/tex]

The frequency exists [tex]$F=\frac{1}{P}=\frac{|B|}{\pi}$[/tex].

The period exists inversely proportional to B, therefore, as B increases, the period decreases.

Frequency exists inversely proportional to the period, therefore, as the period decreases, the frequency increases.

When B is negative, we get f(z) = tan -Bz = f(-z), therefore, the function exists reflected over the y-axis, as the graph at the end of the answer shows, with f(z) exists red(B positive) and f(-z) exists blue(B negative).

As the value of B increases, the period of the function decreases, and the frequency of the function increases. When the value of B exists negative, the graph of the function reflects over the y-axis.

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Answer:

Explanation:

Given the below system of linear inequality;

The graph of the linear inequality y < 3 will be a graph with a dashed line with a y-intercept of 3 since the inequality is not with an equal sign as seen below;

The graph of the 2nd linear inequality y >= -5 will be a graph with a solid line with a y-intercept of -5 since it has both the inequality sign and an equality sign as seen below;

we have the equation

using a graphing tool

see the attached figure

To be able to determine which among the coupon gives a lower price, let's determine what is 45% of $73 so that we could compare it with the $30 rebate. The highest amount among the two coupons will give you a lower price.

Let's determinte the 45% of 73:

Coupon A gives you $32.85 dollar off of a $73 Jacket.

Coupon A will give you a lower price compared to Coupon B. The price of the jacket will be $2.85 lesser than using Coupon B.

SOLUTION:

Step 1:

In this question, we are given the following:

Step 2:

The details of the solution are as follows:

The equation of a circle is given as :

comparing with the given equation:

we have that:

CONCLUSION:

From the detailed explanation, we can see that the correct answer is:

The length and width of the rectangle are 4.04 and 32.67 respectively for which the area is a maximum.

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

Given that;

The rectangle is bounded by the x - axis and the semicircle y = 49 - x².

Since,

The area of rectangle with sides x and y is,

Area = x × y

A = xy

Since, The equation of the semicircle is;

y = 49 - x².

Substitute the values of y in equation (i), we get;

A = x (49 - x²)

A = 49x - x³

Now, Find the derivative and equate into zero,

A' = 49 - 3x²

A' = 0

49 - 3x² = 0

49 = 3x²

x² = 49/3

x = 7/√3

x = 7/1.73

x = 4.04

Hence, y = 49 - x²

y = 49 - (4.04)²

y = 49 - 16.3

y = 32.67

Since, The area is maximum when we can multiply x by y as;

Maximum area = 4.04 x 32.67

Maximum area = 132

Hence, The length and width of the rectangle are 4.04 and 32.67 respectively for which the area is a maximum.

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We will have the following:

Tim should order approximately 6 pizza.

Division in mathematics is the process of dividing an amount into equal parts. For instance, we may split a group of 20 people into four groups of 5, five groups of 4, and so on. One of the four fundamental arithmetic operations, or how numbers are combined to create new numbers, is division. The other operations are multiplication, addition, and subtraction. Mathematicians use addition, subtraction, multiplication, and division as their four fundamental arithmetic operations. The division is one of these four operations that we employ most frequently in our daily work. It involves dividing a huge group into equally sized smaller units. Divide 25, for instance, by 5.

Given Data

Number of employees = 22

Slice of pizza one should get = 1/4

Dividing 22 by 1/4

[tex]\frac{22}{4}[/tex]

5 and [tex]\frac{1}{2}[/tex]

Tim should order approximately 6 pizza.

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The y-intercept is the value of y when x = 0

To identify y-intercept on a graph, we will check for the the value of y when the line crosses the y axis

From the graph, the line crosses the y axis at y = 6

Hence, the y-intercept is 6

To get the slope, we will pick any two points on the line.

Using points (0, 6) and (4, 0)

Applying the slope formula:

NOTE: the slope is negative because it is going from up to down (moving downwards)

The equation of slope in intercept form: y = mx + b

m = slope = -3/2

b = y-intercept = 6

The equation in y-intercept becomes:

The ratio of the volume of cube B to the volume of cube A is 1/64

The volume of cube A is 8^3 = 512 cubic inches

The volume if cube B is 2^3 = 8 cubic inches

The ratio of the volume of cube B to the volume of cube A is:

8/512 = 1/64

The alternate interior angles theorem states that, when two parallel lines are cut by a transversal, the resulting alternate inferior angles are congruent.

In this case:

Given:

The expression for g(f(x)) is,

Substitute x=-9 in the above expression.

Thus, the final value of the expression is -72.

ANSWER

1,440

EXPLANATION

We have that 4 boys are competing and also 5 girls are competing. 3 medals are given to the boys and 3 medals are given to the girls.

For the boys, the gold medal can be awarded to one of 4 boys, then the silver medal can be awarded to 3 boys because 1 of them already got the gold medal. Finally, the bronze medal can be awarded to one of 2 boys, since the gold and silver medals are already taken. The number of ways the medals can be given to the boys is,

This situation is similar for the girls, but in this case, there are 5 girls in total,

The total ways the six medals can be given is,

Hence, there are 1,440 ways to give the six medals to the 4 boys and 5 girls.

to find the distribution of

rewrite 32 as an addition

rewrite the product

distribute the 9

We have that the scale factor is 5, then, the dilation is an enlargement.

Then, the new lengths are:

therefore, A'C' =25.

Finally, the dilations don't affect the angles, therefore, angle A remains with the measure of 37°

Solution:

For this case we know that the width is given by:

w = 6x +8

The lenght is given by:

l= 12x +16

And the perimeter would be given by:

P= 2l +2w = 2(12x+16)+ 2(6x+8)= 24x+32 +12x+16=36x + 48

And then the ratio would be:

Answer:

x = 21

Explanation:

Figure A is a scaled version of figure B. This means that the ratio between any two sides must be the same for both figures.

It follows then

which just means that the ratio f sides 27 with 45 must be the same as the ratio between side x and 35. Why? Because these two sides are the same across the two figures and therefore their size with respect to each other must not change.

Now to find the value of x, we simply need to solve for x.

We do this by multipying both sides by 35:

n = number of nickels

d = number of dimes

1 nickel = 5 cents

1 dime = 10 cents

total number of 21 coins:

n + d = 21

Total value = $1.70

5n + 10 d = 170

Divide by 100

0.05n + 0.10 d = 1.70

Answer:

n + d = 21

0.05n + 0.10 d = 1.70

Hello!

First, let's analyze the figure and write each side:

Analyzing it, we don't have enough information yet to calculate the tangent (because we don't know the measurement of P).

So, let's calculate the opposite side (by Pithagoras):

As we know the opposite side, we can calculate the tangent of P, look:

Curiosity: using the trigonometric table, this value corresponds to approximately 13º.

The tangent of P is 0.225.

Answer:

15 Hours

Step-by-step explanation:

259miles = 7 hours

555miles = x

Cross Multiply

259x = 555×7

259x = 3885

Divide Both sides by 259

x = 3885 ÷ 259

x = 15 hours

It would take the driver 15 hours to get to Atlanta

The given points are (5, 1) and (-3, 17).

First, we have to find the slope using the following formula.

Where,

Let's use the coordinates above to find the slope.

The slope is -2.

Now, we use the point-slope formula to find the equation.

Let's use the same coordinates x_1 and y_1, and the slope m = -2.

Now, we solve for y to express the equation in slope-intercept form.

The calculation of the coefficient of determination, or R² rounded to three decimal places is 0.080.

The coefficient of determination, R², is a statistical measurement that determines the proportion of variance in the dependent variable that the independent variable can explain.

In other words, R² shows how well the actual data is approximated by the regression line.

R-Squared (R²) is widely used to predict future outcomes and for hypothesis testing because it provides information about the goodness of fit of the statistical model.

x         y

61      48

95     76

97     82

101    95

115    118

The total sum of squares (SST) = 2640.8

The sum of squares of regression (SSR) = 2429.8

R² = 1 - SSR/SST

R² = 1 - 2429.8/2640.8

R² = 1 - 0.92

R² = 0.080

R² = 8%

Thus, with R² = 8%, we can conclude that the y values are only accountable for 8% of the variation in x.

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In order to graph g(x) with the graph of f(x), first we need a translation of 3 units to the right, because of the term f(x - 3)

Then, we need a translation of 4 units down, because of the term -4.

So the movements are: translations of 3 units right and 4 units down.

The budget is 20000 times greater.

Mathematics' fundamentals are arithmetic operations. Addition, subtraction, multiplication, and division are the main operations that make up this concept. The phrase "mathematical operations" also refers to these.

The math operation of subtracting two integers reveals the difference between them. The '-' sign is used to indicate it. In math, subtraction is the process of taking one number away from another to determine what is left over after something has been taken away. Rational number operations are equivalent to those performed on whole numbers. The main distinction is that rational numbers take the form p/q, where p and q are integers and q is not equal to 0. It is necessary to take the LCM of the numerators when adding or subtracting two rational integers.

Here we are discussing the four basic rules of arithmetic operations for all real numbers.

Company A = $2 × [tex]10^{4}[/tex]e

Company B = $ 5 × [tex]10^{8}[/tex]

The difference = $2 × [tex]10^{4}[/tex]

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we are given a table of inputs and ouputs of a function. We notice that each output is obtained by multiplying the input by -4:

Therefore, the right answer is A.