What are the solutions to the equation (x2-21)2=25?

Answer:

x >-72

Step-by-step explanation:

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The length FE in the circle is 6 units

The arc AE has a measure of 64 degrees

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

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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Admission to the zoo costs $15 per person.

The graph y = 15x correctly represents the total cost for a group to visit the zoo.

Given;

Admission to the zoo costs per person = $15

Let:

The total number of people visiting the zoo = x

The total cost for a group to visit the zoo = y

So,  y ∝ x

y = 15x

Therefore, the graph y = 15x correctly represents the total cost for a group to visit the zoo.

Answer:

A

Step-by-step explanation:

The vertex form of y = 8 · x² + 32 · x + 17 is the quadratic equation y + 15 = 8 · (x + 2)².

In this problem we find a quadratic equation in standard form, that is, an equation of the form y = a · x² + b · x + c, where a, b, c are real coefficients. By algebra properties we need to find its vertex form, whose definition is shown below:

y - k = C · (x - h)²

Where:

First, write the quadratic equation:

y = 8 · x² + 32 · x + 17

Second, use algebra properties until vertex form is found:

y - 17 = 8 · x² + 32 · x

y - 17 = 8 · (x² + 4 · x)

y - 17 + 32 = 8 · (x² + 4 · x + 4)

y + 15 = 8 · (x + 2)²

The quadratic equation y + 15 = 8 · (x + 2)² is the vertex form of y = 8 · x² + 32 · x + 17.

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Answer:

C

Step-by-step explanation:

a1 = 16

a2 = 16/2 + 4= 8 + 4 = 12

only C has 12 for a2 so the answer is C

Answer:

PEMDAS  it sould be correct 5x2+3 is in order

Step-by-step explanation:

1) Polynomial of 4 terms.

2) The rational roots of the function are,

x = - 2, 1

3) The zeroes of the function are,

x = - 2, - 3, 2

4) The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) The correct function which shows the cubic equation is, option 1.

We have to given that;

1) Function is,

⇒ 3x⁵ + 5x⁴ - 7x³ + 15

Clearly, There are 4 terms in function.

Hence, Polynomial of 4 terms.

2) Function is,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

The correct rational roots are satisfy the function,

Hence, We get;

Plug x = 1,

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 1⁴ + 5(1)³ + 7 (1)² - 3(1) - 10 = 0

⇒ 0 = 0

Plug x = - 2;

⇒ x⁴ + 5x³ + 7x² - 3x - 10 = 0

⇒ 2⁴ + 5(2)³ + 7 (2)² - 3(2) - 10 = 0

⇒ 0 = 0

Thus, The zeroes of the function are,

x = - 2, 1

3) Function is,

⇒ y = (x + 3) (x + 2) (x - 2)

Hence, The zeroes of the function are,

x = - 3

x = - 2

x = 2

4) Function is,

⇒ 3x² - 4 = - x⁴

⇒ x⁴ + 3x² - 4 = 0

⇒ x⁴ + 4x² - x² - 4 = 0

⇒ x² (x² + 4) - 1 (x² + 4) = 0

⇒ (x² - 1) (x² + 4) = 0

⇒ x² - 1 = 0

⇒ x² = 1

⇒ x = ±1

⇒ x² + 4 = 0

⇒ x² = - 4

⇒ x = ±2i

Hence, The zeroes of the function are,

x = 1, - 1, 2i, - 2i

5) By given graph the  correct function which shows the cubic equation is, Option 1.

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Answer:

-13

Step-by-step explanation:

The percentage change to the nearest whole percent was 31% lower from January to February.

Therefore,

A. From January to February, there was a 31% decrease.

\(\frac{9.4-6.5}{9.4} \times 100 \% \approx 31 \%\)

B.  May through April;

2%Month          Average Rainfall (inches/month)

January              9.4

February             6.5

March                 6.8

April                    6.6

May                     6.7

June                    6.4.

∴ April to May

\($\frac{6.7-6.6}{6.6} \times 100 \% \approx 2 \%$\)

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Answer:

A

Step-by-step explanation:

Use the above 3 points, base = 1, height = 1, so area is 1/2

Let's put more details in the given figure to better understand the problem:

From the given figure, it appears that the scenario forms a right triangle.

Given were:

Opposite Side = 99 ft

Angle = 59°

And the length of the string appears to be a Hypotenuse of the formed right triangle.

For us to be able to find the length of the string, we will be using the Sine Function:

We get,

Therefore, the length of the string is 155.5 ft.

Answer:

Step-by-step explanation:

Answer:

88.5

Step-by-step explanation:

formula = ab ×(sin∅)/2

= 18×12 × (sin 55)/2

= 88.5

The probability of a defect is 5.7330 x \(10^{-5}\) and the number of defects is 5.73.

To calculate the probability of a defect, we need to find the area under the standard normal curve that lies outside of the process control limits of 9.75 ounces and 10.25 ounces. We can use the standard normal distribution table to find this area.

First, we need to standardize the weight limits as follows -

\(Z_{lower}\) = (9.75 - 10) / 0.25 = -4

\(Z_{upper}\) = (10.25 - 10) / 0.25 = 4

Next, we will find the area under the standard normal curve that lies outside of these limits as follows -

P(Defect) = P(Z < -4) + P(Z > 4)

Using a standard normal distribution table, we can find that P(Z < -4) = 2.8665 x   \(10^{-5}\)  and P(Z > 4) = 2.8665 x  \(10^{-5}\) .

So, the total probability of a defect is -

P(Defect) = 2.8665 x  \(10^{-5}\)  + 2.8665 x  \(10^{-5}\)  = 5.7330 x  \(10^{-5}\)

Finally, we will find the number of defects for a 1,000-unit production run as follows -

The number of defects = 1000 * 5.7330 x  \(10^{-5}\)  = 5.73 (rounded to the nearest whole number).

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Answer:

44 feet per second

Step-by-step explanation:

(already a unit rate, because it is at its lowest form with 1 second in the equation) BIG BRAIN

44 feet per second is written as 44ft/sec when expressed in unit rate.

To rapidly determine the unit rate of quantities, use the unit rate calculator. The calculator, for instance, will simplify the fraction and output the result as a unit rate if two values and their units are entered.

Unit rates include things like km/h, m/sec, cost/litre, etc. The denominator of a unit rate is always 1. Therefore, divide the denominator by the numerator so that the denominator equals one in order to determine the unit rate.

The kilometre per hour (km/hour), price per litre, profit per item, etc. are a few instances of unit rates.

Divide the numerator by the denominator, setting the denominator equal to 1, to determine the unit rate.

The ratio of how many units of the first type of quantity to one unit of the second type of quantity is known as the unit rate. The unit rate is used frequently in daily life.

The unit rate is 40 feet/second which can be written as 40ft/sec this means 40ft has been covered per second.

Hence, 44 feet per second is written as 44ft/sec when expressed in unit rate.

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The angles in the circle is as follows:

m∠1 = 25 degrees

m∠2 = 12.5 degrees

The angle subtended by an arc of a circle at its centre is twice the angle it subtends anywhere on the circle's circumference.

The measure of an arc is the measure of its central angle. Therefore,

m∠1 = 360 - 160 - 175

m∠1 = 200 - 175

m∠1 = 25 degrees

Therefore, let's find the other angle m∠2.

m∠2 = m∠1 / 2

m∠2 = 25 / 2

m∠2 = 12.5 degrees

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Answer: Total expenses if 3 widgets are produced is $11,018.00

Step-by-step explanation: The variable cost per unit is given by the coefficient of q in the expense function. In this case, the variable cost is $6.00 per widget. To find the variable costs to produce 2 widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for 2 widgets = 2 x $6.00 = $12.00 Therefore, the variable costs to produce 2 widgets is $12.00. To find the variable costs to produce q widgets, we simply multiply the variable cost per unit by the number of units produced: Variable costs for q widgets = q x $6.00 = $6q Therefore, the variable costs to produce q widgets is $6q. To find the total expenses if 3 widgets are produced, we can use the expense function and substitute q = 3:E = 6.00 q + 11,000

E = 6.00 (3) + 11,000

E = 18.00 + 11,000

E = 11,018.00 Therefore, the total expenses if 3 widgets are produced is $11,018.00.

Answer:

(1024/3)r^3.

Step-by-step explanation:

Step one: So, we have that x^2 + y^2 = 4^2 × r^2(when z component = 0) . Hence, there is the need to make y^2 the subject of the formula.

Step two: 4y^2 = 16r^2 - x^2. Where 4 ×(16r^2 - x^2) is the the cross sectional area.

Step three: the next thing to do here is to integrate the cross sectional area making 4r and -4r the upper limit and lower limit for the integration.

Step four: the integration will then give a product (16 × 64)/3 A = (1024/3)r^3.

Step-by-step explanation:

a probability is always desired cases over total possible cases.

so, we have actually 8 systems (5 + 3) we can pick from.

therefore, the total possible cases are 8.

the desired case is in this question to pick one of the 3 Wii consoles.

the probability to pick a Wii is therefore

3/8 = 0.375

Answer:

3/8, or 37.5%

Step-by-step explanation:

There are 8 different playing devices there.

There are only 3 Nintendo Wii consoles.

So, the probability is 3/8

The mean from a Histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

Out of the given options, the display of data for which it is not possible to find the mean is the stem-and-leaf plot.

A histogram displays data in the form of bars, where the height of each bar represents the frequency of data within a specific range. From a histogram, it is possible to calculate the mean by summing up the products of each value with its corresponding frequency and dividing it by the total number of data points.

A table presents data in a structured format, typically with rows and columns, allowing for easy calculation of the mean. By adding up all the values and dividing by the total number of values, the mean can be obtained from a table.

A stem-and-leaf plot organizes data by splitting each value into a stem (the first digit or digits) and a leaf (the last digit). While a stem-and-leaf plot provides a visual representation of the data, it does not directly provide the frequency or count of each value. Hence, it is not possible to determine the mean directly from a stem-and-leaf plot without additional information.

A dot plot represents data using dots along a number line, with each dot representing an occurrence of a value. Similar to a histogram and table, a dot plot allows for the calculation of the mean by summing up the values and dividing by the total number of data points.

In summary, while it is possible to find the mean from a histogram, table, and dot plot, it is not possible to determine the mean directly from a stem-and-leaf plot.

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Answer:

Step-by-step explanation:

-4

Answer:

2

Step-by-step explanation:

If Chee has 12 dimes and 7 quarters, she has Total = $2.95 and If she has x dimes and y quarters, she has Total = 0.10x + 0.25y

what is quarters ?

Quarters refer to a unit of currency in the United States and Canada, equal to 25 cents. It is also used as a term to refer to a coin worth 25 cents.

In the given question,

If Chee has 12 dimes and 7 quarters, she has:

12 × $0.10 = $1.20 from the dimes

7 × $0.25 = $1.75 from the quarters

Total = $1.20 + $1.75 = $2.95

If she has x dimes and y quarters, she has:

x × $0.10 = $0.10x from the dimes

y × $0.25 = $0.25y from the quarters

Total = $0.10x + $0.25y

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Answer:

from what i know c

Step-by-step explanation:

Answer:

(X'U'Y) + (XUY')

Step-by-step explanation:

Starting with [Xn(X'nY)]', we can use De Morgan's laws to simplify the expression:

[Xn(X'nY)]' = (Xn)' + (X'nY)'

Recall that Xn represents the logical operator "and", while X' represents "not X". Using these definitions, we can expand the expression:

(Xn)' + (X'nY)' = (X'U'Y) + (XUY')

where U represents the logical operator "or".

Therefore, [Xn(X'nY)]' simplifies to (X'U'Y) + (XUY').

You need to multiply by 5 instead of 6 because each pair of opposite faces on a cuboid has the same area, so by considering one face from each pair, you ensure that you don't count any face twice.

When calculating the total surface area of a cuboid, you need to understand the concept of face pairs.

A cuboid has six faces, but each face has a pair that is identical in size and shape.

Let's break down the reasoning behind multiplying by 5 instead of 6 in the given scenario.

To find the surface area of a cuboid, you can add up the areas of all its faces.

However, each pair of opposite faces has the same area, so you avoid double-counting by only considering one face from each pair. In this case, you have five pairs of faces:

(1) top and bottom, (2) front and back, (3) left and right, (4) left and back, and (5) right and front.

By multiplying the average area of a pair of faces by 5, you account for all the distinct face pairs.

Essentially, you are considering one face from each pair and then summing their areas.

Since all the pairs have the same area, multiplying the average area by 5 gives you the total surface area.

When dividing 150 by 4 (to find the average area of a pair of faces), you are essentially finding the area of a single face.

Then, by multiplying this average area by 5, you ensure that you account for all five pairs of faces, providing the total surface area of the cuboid.

Thus, multiplying by 5 is necessary to correctly calculate the total surface area of the cuboid by accounting for the face pairs while avoiding double-counting.

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Answer:

$13.75

Step-by-step explanation:

If you have 12 cans of soup for $33 you need to find the unit price for the cans ,by dividing the 33 and 12 to get $2.75 this is how much it costs for 1 can of soup so if you want to see how much 5 cans of soup costs you multiply by 5 so then you get $13.75

Answer:

C=20

Step-by-step explanation:

1. 25÷5=5

2. 5×4=20

I hope this helped☺

Answer:

10

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

The answer is 10 because:

1) Absolute value makes all negative or positive numbers positive (unless there is a negative sign outside the absolute value sign).

2) Therefore, the absolute value of 10 is positive 10.

Hope this helps! :D