6-5 Practice Operations with radical expressions
1. √540
2. 3√432
3. 3√128
4. - 4√405
5. 3√-5000

1. sin ² x goes in the numerator. 2. sin x (sin x) is the numerator expanded. 3. Separate the two factors sin x / cos x and sin x / cos x. 4. Replace sin x / cos x with tan x. Use the trigonometric identity.

Simply put, trigonometric functions—also referred to as circular functions—are the functions of a triangle's angle. This means that these trig functions provide the connection between the angles and sides of a triangle. The three basic categories of trigonometric functions are sine, cosine, and tangent. In contrast to the fundamental trigonometric functions, the other three functions are essentially employed more frequently. For an explanation of these three main roles, use the diagram below as a guide. The sin-cos-tan triangle is the name for this illustration. Often, the right-angled triangle is used to define trigonometry.

The given trigonometric function is 1 / cos x csc² x.

Now, the csc²x can be written as:

sin²x / cos x. Thus, sin ² x goes in the numerator.

Now, sin x (sin x) is the numerator expanded.

Separate the two factors sin x / cos x and sin x / cos x

Replace sin x / cos x with tan x.

Use the trigonometric identity to complete the proof.

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Answer:

the healthy fruit is 77.07

and the spoiled fruit is 20.19

Step-by-step explanation:

the explanation is a little long but if you want one just ask in the comments and ill edit this

Answer: Alexis is 1.4224 meters tall.

Step-by-step explanation:

If you want your answer rounded, it's 1.4 meters. I hope this helped you! Brainilist is highly appreciated and helpful! <3

When P(opposed | Grade 12) exceeds P(Grade 12 | opposed), the correct response is: P(opposed | Grade 12) P(opposed | Grade 12) (Option C)

An arrangement of things in a particular order is known as a permutation in mathematics. In more detail, an arrangement of a set's members in a certain order is known as a permutation. To give one example, the set 1, 2, 3 contains six permutations: 1, 2, 3, 1, 2, 3, 1, and 3, 2, 1. The formula P(n, r) is frequently used to express permutations, which are the various methods to select r things from a group of n objects and arrange them in a particular order. P(n, r) has the following formula: P(n, r) equals n!/(n-r)!  where the factorial of n is represented by n! (i.e., the product of all positive integers from 1 to n).

given

Using Bayes' theorem, we can contrast P(Grade 12 | opposed) with P(grade 12 | opposed):

Grade 12 opposition formula: P(opposed) = P(Grade 12 opposition) * P(opposed) / P (Grade 12)

The table contains the values we require:

P(grade twelve) = (12+6+11)/(5+3+9+8+12+9+15+16+10+12+6+11) = 0.15 P(opposition) = (3+12+16+6)/(5+3+9+8+12+9+15+16+10+12+6+11) = 0.5 P(opposition | grade twelve) = 6/(12+6+11) = 0.24

Although we do not directly know the value of P(Grade 12 | opposed), we can calculate it using the following formula:

P (12th grade | opposed) = P (12th grade | opposed) * P (12th grade | opposed) / P (12th grade | opposed) = 0.24 * 0.15 / 0.5 = 0.072

As a result, we have:

P (12th grade | opposed) = 0.072 P (12th grade | opposed) = 0.24

When P(opposed | Grade 12) exceeds P(Grade 12 | opposed), the correct response is: P(opposed | Grade 12) P(opposed | Grade 12) (Option C) .

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Answer:

Step-by-step explanation:

cos(x)=1

Choose all answers that apply

A. 0°

B.90°

C.360°

D.540°

E. 720°

F.1080°

Answer:

C or E

Step-by-step explanation:

The answer should be choice.C or E

Step-by-step explanation:

"The difference of twice of a # and 10 is  = to 12

We're gonna do this like statement reason because I don't want to write a paragraph lol

2x-10=12             Given

2x=24                 Simplify (+10 to each side cancels on left, adds on the right)

x=12                    Simplify (divide by 2)

Yay!

Also if you have 2 chances maybe try -1? but I think 12 is right

Yes, the ratio of the hypotenuse to a leg is the same for all isosceles right triangles.

What is hypotenuse ?

In a right triangle, the hypotenuse is the side that is opposite to the right angle. It is also the longest side of the triangle. The hypotenuse is always opposite the right angle and is found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides. In a right triangle with legs of length "a" and "b", the length of the hypotenuse "c" can be found using the formula:

[tex]c^2 = a^2 + b^2[/tex]

Taking the square root of both sides gives us:

[tex]c = \sqrt{a^2 + b^2}[/tex]

The hypotenuse plays an important role in trigonometry, as it is used in the calculation of trigonometric ratios such as sine, cosine, and tangent.

According to the question:
Yes, the ratio of the hypotenuse to a leg is the same for all isosceles right triangles.

In an isosceles right triangle, the two legs are congruent, which means they have the same length. Let's call the length of each leg "a". The hypotenuse of the triangle can be found using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the legs:

[tex]hypotenuse^2 = a^2 + a^2 = 2a^2[/tex]

Taking the square root of both sides, we get:

[tex]hypotenuse = \sqrt{2a^2} = a * \sqrt{2}[/tex]

So, the ratio of the hypotenuse to a leg is:

[tex]hypotenuse / a = (a * \sqrt{2}) / a = \sqrt{2}[/tex]

This shows that the ratio of the hypotenuse to a leg in an isosceles right triangle is always equal to the square root of 2, which is a constant value. Therefore, the ratio is the same for all isosceles right triangles.

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According to given information, the area of kite is 480 m².

What is area of kite?

The area of a kite can be calculated by multiplying the lengths of its two diagonals and dividing the result by 2:

Area of kite = (diagonal 1 x diagonal 2) / 2

The hypotenuse is usually the slanted line in a triangle.

Area of a kite = pq/2 (p and q = diagonal)

Finding the missing side length of triangle₁

37² = 12² + x² (x = unknown side length)

=> 1369 = 144 + x² (x = unknown side length)

=> 1369 - 144 = x² (x = unknown side length)

=> 1225 = x² (x = unknown side length)

=> x = 35 m

Finding the area:

Area of a kite = pq/2 (p and q = diagonal)

=> Area of a kite = (35 + 5)(12 + 12)/2

=> Area of a kite = (40)(24)/2

=> Area of a kite = 40 x 12 = 480 m².

Therefore, the area of kite is 480 m².

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The method that is most appropriate when calculating margin-of-error for population mean is (b) Student's t-distribution.

When calculating the margin of error for the population mean, the most appropriate method depends on the sample size.

If the sample size is large (n > 30) and the population standard deviation is known, then a normal z-distribution can be used to calculate the margin of error.

If the sample size is small (n < 30) or the population standard deviation is unknown, then Student’s t-distribution should be used to calculate the margin of error.

In this case, we are told that the information was obtained from 14 strands of this particular virus. Since n < 30, we should use Student’s t-distribution to calculate the margin of error.

Therefore, the correct option is (b).

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The given question is incomplete, the complete question is

Considering the following scenario, which method would be most appropriate when calculating the margin of error for the population mean?

A research scientist wants to know how many times per hour a certain strand of virus reproduces. she obtains information from 14 strands of this particular virus and finds the mean to be 7.4 . the population is assumed to be normally distributed.

(a) Normal z-distribution

(b) Student's t-distribution

(c) More advanced statistical techniques

Given that AB is a diameter. |BC| = |CD| and AÔD = 64°, The angles  of the quadrilateral ABCD is 90 degrees

Since |BC| = |CD|, we know that triangle BCD is an isosceles triangle.

Since triangle BCD is isosceles, angles BDC and CBD are equal. Let's call each of these angles x.

180 - 64

= 116 degrees

angle BCD = 180 - 116

= opposite angles in a cyclic quadrilateral are supplementary

116 + 64 + 2 OBC = 360

2 obc = 360 - 116 - 64

0bc = 180 / 2

= 90 degrees

Hence the angles  of the quadrilateral ABCD is 90 degrees

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Step-by-step explanation:

The third one is not      all of the others are

Answer: 43.2

Step-by-step explanation:

Do this by ration method:

[tex]\frac{18+36+15+33+48}{18} = \frac{360}{x}[/tex]

x = 43.2

Answer:

2145

Step-by-step explanation:

Given: Sum of three consecutive odd integers = 39

Calculation:Let x, x + 2, x + 4 be the three consecutive odd integers.

Sum of three consecutive odd integers = 39

⇒ x + (x + 2) + (x + 4) = 39

⇒ 3x + 6 = 39

⇒ 3x = 33

⇒ x = 11

∴ The integers are 11, 13 and 15.

∴ Their product = 11 × 13 × 15 = 2145

You're welcome! :)

The cash back you would receive on your purchases of $2,738.21 using this credit card is $33.92.

To calculate the cash back you would receive using the given credit card, we need to multiply the total amount spent in each category by the corresponding cash back percentage, and then add up those amounts.

For gas purchases, you spent $134.92, so the cash back earned on that amount would be:

$134.92 x 3% = $4.05

For grocery store purchases, you spent $384.23, so the cash back earned on that amount would be:

$384.23 x 2% = $7.68

For all other purchases, you spent a total of:

$2,738.21 - $134.92 - $384.23 = $2,219.06

So the cash back earned on that amount would be:

$2,219.06 x 1% = $22.19

Adding up the cash back earned in each category, we get:

$4.05 + $7.68 + $22.19 = $33.92

∴ Cashback = $33.92

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To measure out exactly 1 gallon of water we need exactly six possible number of moves.

To measure out exactly 1 gallon of water using two jugs, one with a 3-gallon capacity and one with an 5-gallon capacity, you can follow some steps

Fill the 5-gallon jug with water completely. Pour the water from the 5-gallon jug into the 3-gallon jug, leaving 2 gallons of water in the 5-gallon jug.

Empty the 3-gallon jug completely. Pour the 2 gallons of water from the 5-gallon jug into the empty 3-gallon jug.

Fill the 5-gallon jug with water again. Pour water from the 5-gallon jug into the 3-gallon jug until it is full, which will leave exactly 1 gallon of water in the 5-gallon jug.

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By answering the presented question, we may conclude that As a result, probability the chance of receiving heads and 4 is 1/12.

Probability is a measure of how likely an event is to occur. It is represented by a number between 0 and 1, with 0 representing a rare event and 1 representing an inescapable event. Switching a fair coin and coin flips has a chance of 0.5 or 50% since there are two equally likely outcomes. (Heads or tails). Probabilistic theory is an area of mathematics that studies random events rather than their attributes. It is applied in many disciplines, including statistics, economics, science, and engineering.

Here is an example space diagram that depicts all of the possible outcomes when Leo flips a coin and rolls a dice:

Each row represents the outcome of rolling the dice, and each column indicates the outcome of flipping the coin. The table entries represent the combined outcome of rolling the dice and flipping the coin. For example, the occurrence of receiving heads on the coin flip and rolling a 1 on the dice is represented by the outcome in the top left corner (H1).

As a result, the chance of receiving heads and 4 is 1/12.

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Nope, and there's an stereotype on medical doctors that their signature is just a garbled or gibberish, which very often is true

these days we also have "digital signatures" you can include in an email, which are just encrypted material verifyable by some encryption keys, it varies but the leading ones are PGP and/or GPG types

so valid is one that's consistent, could be your fingerprint if you wish, and due to its consistency also verifyable.

The percent increase when [tex]$x$[/tex] increases by one unit is approximately 15.8%.

What is exponential function?

An exponential function is a mathematical function of the form:

[tex]f(x) = a^x[/tex]

where a is a constant greater than zero and not equal to 1, and x is the variable that takes on real numbers.

To find the percent increase for the exponential function [tex]$A = 82\times 1.16^x$[/tex], we need to find the ratio of the final value to the initial value, subtract one, and then multiply by 100 to convert to a percentage.

Let's suppose we are interested in finding the percent increase when [tex]$x$[/tex] increases by one unit. We can start by calculating the initial value of [tex]$A$[/tex] when [tex]$x = 0$[/tex]:

[tex]$$A = 82 \times 1.16^0 = 82$$[/tex]

Then we can calculate the final value of [tex]$A$[/tex] when [tex]$x = 1$[/tex]:

[tex]$$A = 82 \times 1.16^1 \approx 95.12$$[/tex]

Now we can find the ratio of the final value to the initial value:

[tex]$\text{ratio} = \frac{\text{final value}}{\text{initial value}} = \frac{95.12}{82} \approx 1.158$$[/tex]

Next, we subtract one and multiply by 100 to get the percent increase:

[tex]$$\text{percent increase} = (\text{ratio} - 1) \times 100 \approx (1.158 - 1) \times 100 \approx 15.8%$$[/tex]

Therefore, the percent increase when [tex]$x$[/tex] increases by one unit is approximately 15.8%.

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The sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 98% confidence level with an error of at most 0.03 is approximately 904

Since the commission wants a 98% confidence level, the z-score associated with that level is 2.33 (which can be found using a standard normal distribution table).

We also know that the commission wants an error of at most 0.03, so we can set up an equation:

0.03 = 2.33 x √(0.23 x 0.77) / √(n)

Solving for n, we get:

n = (2.33 x √(0.23 * 0.77) / 0.03)²

n = 903.78

So, the commission would need a sample size of at least 904 tenth grade students in order to estimate the fraction of students with reading skills at or below the eighth grade level at the 98% confidence level with an error of at most 0.03.

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1/2  will be the probability of getting odd numbers if a dice is

thrown.

What does the math term "probability" mean?

The simple definition of probability is the likelihood that something will occur. We can discuss the probabilities of various outcomes—how likely they are—when we aren't sure how a particular event will turn out.  

                                Statistics describes the examination of events subject to probability. Probability is a measure of how likely or likely-possible something is to happen. For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one way to acquire a head and there are a total of 2 possible outcomes (a head or tail). P(heads) = 12 is the formula.

The total number of possible outcomes n=6.

Sample space = 1,2,3,4,5,6

odd nos. = 1, 3, 5

probability of getting odd nos.= 3/6  = 1/2

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The final triangle has vertices at (3, -1), (3, -4), and (1, -4) on the graph.

In mathematics, a transformation refers to a function that maps points or shapes in one coordinate system to corresponding points or shapes in another coordinate system, while preserving certain properties such as size, shape, orientation, and distance.

Starting with the triangle on a graph with vertices at (-4, 4), (-4, 1), and (-2, 1), we can apply the given transformations as follows:

Go right 1 and down 5: This transformation corresponds to the function T(x, y) = (x + 1, y - 5). Applying this function to each vertex of the triangle, we get:

(-4, 4) -> (-3, -1)

(-4, 1) -> (-3, -4)

(-2, 1) -> (-1, -4)

Reflect on the y-axis: This transformation corresponds to the function R(x, y) = (-x, y). Applying this function to each vertex of the transformed triangle, we get:

(-3, -1) -> (3, -1)

(-3, -4) -> (3, -4)

(-1, -4) -> (1, -4)

Therefore, the final triangle has vertices at (3, -1), (3, -4), and (1, -4) on the graph.

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Answer:

Hope you have understood this sum

Answer:

The coordinates of (-3,0) after a translation of 2 units up is the third one. (-3,2)

the space is A there because A is the one

The length of the model car’s hood is 5√5 inches divided by 6, which is a simplified radical expression.

If the real car’s hood is 20√5 inches long and the model car uses a 1:24 scale, we can find the length of the model car’s hood by dividing the length of the real car’s hood by 24.

Length of model car’s hood = (Length of real car’s hood) / (Scale factor)

Substituting the given values, we get:

Length of model car’s hood = (20√5 inches) / 24

We can simplify this expression by dividing the numerator and denominator by the greatest common factor, which is 4:

Length of model car’s hood = (5√5 inches) / 6

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The exact value of the cosine of angle A + B is equal to - 1239 / 1961.

In this problem we need to determine the exact value of a trigonometric function, this can be done by using definitions of trigonometric functions, Pythagorean theorem and trigonometric formulas:

Trigonometric function

sin θ = y / r

cos θ = x / r

tan θ = y / x

Pythagorean theorem

r² = x² + y²

Trigonometric formula

cos (A + B) = cos A · cos B - sin A · sin B

First, determine the exact values of sines and cosines:

Angle A

r = √(28² + 45²)

r = 53

sin A = 45 / 53

cos A = 28 / 53

Angle B

y = √(37² - 12²)

y = 35

sin B = 35 / 37

Second, calculate the exact value of the trigonometric function by trigonometric formula:

cos (A + B) = (28 / 53) · (12 / 37) - (45 / 53) · (35 / 37)

cos (A + B) = - 1239 / 1961

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The equation of the line from the given graph is y = 3x + 1.

With the aid of the line's slope and a point on the line, the equation of a line may be created. For a better understanding of how a line's equation is created, let's learn more about the line's slope and the necessary point on the line. The slope of a line is the angle that the line makes with the positive x-axis and can be stated as a numerical integer, fraction, or as the tangent of that angle. The term "point" refers to a coordinate system point with the x and y coordinates.

From the given graph we observe the two coordinates of the line are (0, 1) and (3, 10).

The slope of the line is given as:

m = y2 - y1 / x2 - x1

m = (10 - 1) / (3 - 0)

m = 9/3 = 3

The point-slope intercept is given as:

y - y1 = m (x - x1)

Substituting the values:

y - 1 = 3 (x - 0)

y - 1 = 3x

y = 3x + 1

Hence, the equation of the line is y = 3x + 1.

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Answer:

20 : 50

Step-by-step explanation:

sum the parts of the ratio , 2 + 5 = 7 parts

divide 70 by 7 to find the value of one part of the ratio

70 ÷ 7 = 10 ← value of 1 part of the ratio , then

2 parts = 2 × 10 = 20

5 parts = 5 × 10 = 50

then

50 divided in the ratio 2 : 5 is 20 : 50