What is the measure of the central size of this rotation?

Answer:

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

Given equation:

Rearrange and factorize it:

According to factors we got, there are two real and two imaginary zeros:

x² = - 16 ⇒ x = ± 4i

The zeros of the equation 12\(x^2\) - 64 = -\(x^4\) are x = 2 and x = -2.

To find all the zeros of the equation 12\(x^2\) - 64 = -\(x^4\) , we can rearrange the equation to set it equal to zero and then solve for x.

First, let's rewrite the equation as \(x^4\) + 12\(x^2\) - 64 = 0.

Now, we can factor the equation.

Factoring a quadratic equation can be quite complex, so let's use a substitution to simplify it.

Let's substitute y = \(x^2\)

Substituting y = \(x^2\), we get \(y^2\) + 12y - 64 = 0.

Now we have a quadratic equation, which is easier to factor.

Factoring the quadratic equation, we have (y - 4)(y + 16) = 0.

Setting each factor equal to zero, we have two possible solutions: y - 4 = 0 and y + 16 = 0.

Solving for y in each equation, we find y = 4 and y = -16.

Now, we substitute back the value of y into our substitution equation y = \(x^2\).

For y = 4, we have \(x^2\) = 4, which gives us two solutions: x = 2 and x = -2.

For y = -16, we have \(x^2\) = -16. Since the square of any real number is always nonnegative, there are no real solutions for this case.

Therefore, the zeros of the equation 12\(x^2\) - 64 = -\(x^4\)  are x = 2 and x = -2.

In summary, the equation has two real zeros: x = 2 and x = -2. The equation does not have any other real zeros.

Learn more about quadratic equation here:

https://brainly.com/question/30098550

#SPJ11

a. the cylindrical coordinates of the point are (4, π/3, 5).

b. the spherical coordinates of the point are (1, π/3, -1).

c. the rectangular coordinates of the point are (√3, √3, 1).

(a) To find the cylindrical coordinates of a point given its rectangular coordinates (-2, -2√3, 5), we use the following formulas:

ρ = √(x^2 + y^2)

θ = arctan(y / x)

z = z

Substituting the values into the formulas:

ρ = √((-2)^2 + (-2√3)^2) = √(4 + 12) = √16 = 4

θ = arctan((-2√3) / (-2)) = arctan(√3) = π/3

z = 5

Therefore, the cylindrical coordinates of the point are (4, π/3, 5).

(b) To find the spherical coordinates of a point given its cylindrical coordinates (1, π/3, -1), we use the following formulas:

ρ = ρ

θ = θ

φ = z

Substituting the values into the formulas:

ρ = 1

θ = π/3

φ = -1

Therefore, the spherical coordinates of the point are (1, π/3, -1).

(c) To find the rectangular coordinates of a point given its spherical coordinates (2, π/4, π/3), we use the following formulas:

x = ρ * sin(φ) * cos(θ)

y = ρ * sin(φ) * sin(θ)

z = ρ * cos(φ)

Substituting the values into the formulas:

x = 2 * sin(π/3) * cos(π/4) = 2 * (√3/2) * (√2/2) = √3

y = 2 * sin(π/3) * sin(π/4) = 2 * (√3/2) * (√2/2) = √3

z = 2 * cos(π/3) = 2 * (1/2) = 1

Therefore, the rectangular coordinates of the point are (√3, √3, 1).

Learn more about coordinates here : brainly.com/question/32836021

#SPJ11

Answer:

300 + 4x

Step-by-step explanation:

200 + 100 = 300

3x + x = 4x

(a plain variable like "x" always has an invisible one in front of it)

there are 33 pleasing ordered triples.

We are given a set {1, 2, 3, 4, 5, 6}. We need to count the number of pleasing ordered triples (a, b, c), where a < b < c, and a, b, c are elements of the set.

Condition (b) requires that both b and c be greater than a. Since a can take any value from 1 to 4, the number of possibilities for (a, b, c) is:

For a = 1, there are 4 choices for b (2, 3, 4, 5) and 5 choices for c (3, 4, 5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 4 × 4 - 1 = 15 pleasing triples with a = 1.

For a = 2, there are 3 choices for b (3, 4, 5) and 4 choices for c (4, 5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 3 × 4 - 1 = 11 pleasing triples with a = 2.

For a = 3, there are 2 choices for b (4, 5) and 3 choices for c (5, 6, 5). However, we must exclude the case where b = c = 5, since both b and c must be greater than a. Therefore, there are 2 × 3 - 1 = 5 pleasing triples with a = 3.

For a = 4, there is only 1 choice for b (5) and 2 choices for c (6, 5). Therefore, there is only 1 × 2 = 2 pleasing triples with a = 4.

The total number of pleasing ordered triples is:

15 + 11 + 5 + 2 = 33

To learn more about elements visit:

brainly.com/question/13794764

#SPJ11

The type of sample that was taken in this example is:

stratified random sample.

A stratified random sample is a type of probability sampling technique in which the population is divided into different subgroups (strata) based on certain characteristics and a sample is taken from each of the strata.

In this example, the population is divided into ten groups based on departments and a sample of 50 randomly selected employees is taken from each group. This ensures that the sample is representative of the entire population, as it is drawn from all of the different departments.

A stratified random sample is beneficial in that it allows researchers to ensure that their sample is representative of the whole population.

By taking a sample from each of the different strata, the researcher is able to account for any differences between the strata, and make sure that the sample accurately reflects the population as a whole.

This type of sampling technique is often used when it is important to ensure that the sample is representative of the population, as is the case with the example provided.

To learn more about stratified random sample, use the link:

brainly.com/question/20692763

#SPJ4

We can conclude that -

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that the regular price on a pair of jeans is $54. The store advertises a back-to-school sale at 40% off the regular price of the jeans. Two weeks later, the store advertises a sale at an additional off the sale price of these jeans at 5%.

Original price -

$54

Cost after 40% discount -

54 - {40% of 54}

54 - {40/100 x 54}

54 - {2/5 x 54}

54 - 21.6

$32.4

Cost after 5% discount -

32.4 - {5% of 32.4}

32.4 - {5/100 x 32.4}

32.4 - 1.62

$30.78

{ 3 } -

Calculating 60% of new price -

60% of 30.78

(60/100) x 30.78

18.5

Calculating 40% of new price -

40% of 30.78

(40/100) x 30.78

12.4

So, 60% of new price is greater than calculating 40%.

So, Manny is correct.

Therefore, we can conclude that -

To solve more questions on functions & expressions, visit the link below

brainly.com/question/17613163

#SPJ9

Answer:

100/360 * 2\(\pi\)5

1000\(\pi\)/360 = 25\(\pi\)/9 = 8.722

Step-by-step explanation:

Step-by-step explanation:

35% of 50 dollars is 17.50.

The item would cost 32.50 and you saved 17.50 on it.

The confidence associated with an interval estimate is called the confidence level.

When making an interval estimate, such as estimating a population parameter based on a sample, it is important to provide an indication of the level of confidence we have in the estimate. The confidence level represents the probability or level of certainty that the true population parameter falls within the calculated interval.

For example, if we calculate a 95% confidence interval for the mean height of a population, it means that we are 95% confident that the true population mean height lies within that interval. This implies that if we were to repeat the sampling and interval estimation process multiple times, approximately 95% of the intervals would contain the true population parameter.

The confidence level is typically expressed as a percentage, such as 90%, 95%, or 99%. A higher confidence level indicates a greater level of certainty in the interval estimate but also results in a wider interval.

In summary, the confidence level associated with an interval estimate represents the level of confidence or probability that the interval contains the true population parameter.

To know more about confidence level click here :

https://brainly.com/question/22851322

#SPJ4

Answer:

4

Step-by-step explanation:

negative divided by a negative is a positive

Answer:
Option c

Step-by-step explanation:

Since tangent = op/adj, in this case the tan37 would be x/1000.

Then, set it up as an algebra problem.

tan37 = x/1000

Multiply both sides by 1000, so 1000tan37=x

that simplifies to x = 753.6

Answer:

zero point six hundred and four

Step-by-step explanation:

The 3 inside angles of a triangle need to equal 180.

X = 180 - 70 - 20 = 90

x = 90 degrees

Answer: 15

Step-by-step explanation:

As a result, the measurements of angles KAG and JAF are both 90, and the measure of arc KG is 2 * 90 = 180. Angle HAE and angle HAF are both 90 degrees.

An angle is a figure in Euclidean geometry created by two rays, called the sides of the angle, that share a common termination, called the vertex of the angle. Angles created by two rays are located in the plane containing the rays. Angles are also generated when two planes intersect. These are known as dihedral angles.

Here,

In the diagram, since KG, JF, AE, and AH intersect at point A, we know that angle KAG = angle JAF (both are inscribed angles and intercept the same arc), and angle HAE = angle HAF (both are alternate interior angles and are equal in measure).

To find the value of x, we need to use the angle relationships. Since angle KAG = angle JAF, and they are both inscribed angles, they are equal to half the measure of the intercepted arc KG. We also know that angle HAE = angle HAF, so we can use them to find the measure of KG.

Let's call the measure of KG = 2x. Then, angle KAG = angle JAF = x, and angle HAE = angle HAF = x.

Adding the measures of angle KAG and angle HAE, we get x + x = 2x = 180. Solving for x, we get x = 90.

So, the measures of angle KAG and angle JAF are 90, and the measure of arc KG is 2 * 90 = 180. The measures of angle HAE and angle HAF are also 90.

To know more about angle,

https://brainly.com/question/14569348

#SPJ1

Answer:

Step-by-step explanation:

3 +- \/5 over 2

Answer:

Respectful ??

Step-by-step explanation:

Answer:

ldlelskekkskek

Step-by-step explanation:

zkmelslelslsps

Answer:

Explanation:

given f(x) = 3x - 1

for f(x) = 2

3x - 1 = 2

3x = 2 + 1

3x = 3

x = 3/3

x = 1

Answer:

Step-by-step explanation:

5+8+11+...+116x(n)=a+d(n-1)   a=first term, d=common difference, n=term116=5+3(n-1)116=5+3n-3116=2+3n116-2=3n114=3nn=114/3n=38 terms S(n)=(n/2)(2a+[n-1]d)S(38)=(38/2)(10+37*3)S(38)=19(10+111)S(38)=19(121)S(38)=2299

The conclusion that can be drawn using the simulation results depends on comparing the actual proportion to the distribution of proportions obtained from the simulation and assessing the statistical significance of the survey result.

For more such questions on simulation

https://brainly.com/question/15892457

#SPJ8

Answer:

m = - 1/4

Step-by-step explanation:

When two line is perpendicular to each other the product of them is - 1

So let the other line be B

Gradient of B = t

Gradient of A = 4

\(t \times 4 = - 1 \\ t = - \frac{1}{4} \)

therefore m = - 1/4

Step-by-step explanation:

Let x be the diagonal distance,

by pythagoras' theorem,

\( {c}^{2} = {a}^{2} + {b}^{2} \)

where c is the diagonal

a and b are the 2nd and 3rd longest side, interchangeable.

given a = 50m, b = 25m,

\( {c}^{2} = {50}^{2} + {25}^{2} \\ {c}^{2} = 2500 + 625 \\ {c}^{2} = 3125 \\ c = \sqrt{3125} \\ = 55.9m \: (nearest \: tenth)\)

kk where my brainliest

Step-by-step explanation:

Explanation: You can find the diagonal of a rectangle if you have the width and the height. The diagonal equals the square root of the width squared plus the height squared.

Answer:

25

explanation:

\(\hookrightarrow \sf 1-3+3^3\)

using PEDMAS order of operations

we should know the following: * \(\bold{ \sf 3^3 = 3 * 3 * 3 = 27}\) *

\(\hookrightarrow \sf 1-3+27\)

\(\hookrightarrow \sf 25\)

Hey there!

1 - 3 + 3^3

= 1 - 3 + 3 * 3 * 3

= 1 - 3 + 9 * 3

= 1 - 3 + 27

= -2 + 27

= 25

Therefore, your answer is: 25

Good luck on your assignment & enjoy your day!

~Amphitrite1040:)

Answer:

y =  -2x + 10

Step-by-step explanation:

The equation in point slope form is expressed using the equation

y - y1 = m(x - x1) where;

m is the slope = -2

(x1, y1) is the point on the line = (4,2)

Substitute into the formula:

y - 2 = -2(x - 4)

y -2 = -2x + 8

y = -2x +8 +2

y = -2x + 10

Hence the required equation of the line is y =  -2x + 10

From the given graph , we see that it passes through the point (0,-1) .

→ y intercept = -1

For finding slope , take another point as (1,3) . Now using the points (1,3) and (0,-1) we can find out the slope as ,

→ m = y2 - y1 / x2 - x1

Substituting the respective values,

→ m = 3 -(-1)/1-0

→ m = 3+1/1

→ m = 4/1

→ m = 4

Hence the slope of the line is 4 and its y intercept is -1 .

15 meter distance separates Hillary and Eugene when they finish.

The definition of π is Circumference/diameter, so C = πd

In this case, that is C = 80π meters

Hillary runs at 300 m/min for 50 minutes.  

That's (300 m/min)*(50 min) = 15000 m

or 59.7 times around the track.

Eugene runs 240 m/min in the opposite direction for 50 minutes.

That's (240 m/min)*(50 min) = 12000 m

or 47.7 times around the track in the opposite direction.

So Eugene's distance from Hillary (along the track) is:

(0.3+0.3)*C = 0.6*C

0.6*(80π) meters = 4.8π meters = 15.0 meters

Therefore, 15 meters distance separates Hillary and Eugene when they finish.

Learn more about distance here;

https://brainly.com/question/20847624

#SPJ4

The total amount Austin to pay if she were to buy 7 snacks for everybody to share is $119.

What is a numerical expression?

Mathematical operations like addition, subtraction, multiplication, and division can be used to mix integers and numbers to create a numerical expression.

Here, we have

Given,

Austin is going to see a movie and is taking his 5 kids.

Each movie ticket costs $14 and there is an assortment of snacks available to purchase for $5 each.

The total amount Austin to pay if he were to buy 7 snacks for everybody to share is,

= (14×7) + (3×7)

= 98 + 21

= $119

Hence, the total amount Austin to pay if she were to buy 7 snacks for everybody to share is $119.

To learn more about the numerical expression from the given link

https://brainly.com/question/4344214

#SPJ1

No, these two events cannot be disjoint. Disjoint events, also known as mutually exclusive events, are events that cannot occur simultaneously.

In other words, if events A and B are disjoint, it means that the occurrence of one event excludes the possibility of the other event occurring.

However, in this case, we are given that P(A) > 0 and P(B) > 0. This means that both events A and B have non-zero probabilities of occurring. Since both events have a positive probability, they cannot be disjoint because there is a possibility of their intersection, where both events occur simultaneously.

Disjoint events would have the property that P(A ∩ B) = 0, indicating that their intersection is an empty set. But given that P(A) > 0 and P(B) > 0, it implies that there is some non-zero probability for the events A and B to occur together, making them not disjoint.

for such more question on Disjoint events

https://brainly.com/question/7331447

#SPJ8