What number can be divided into 9 equal groups without a remainder?
A. 256
B. 387
C. 424
D. 532

Writing the given trigonometry expression: cos(2 tan inverse (x)) as algebraic expression gives

Data given in the question are as follows:

cos(2 tan inverse (x))

Using trigonometry (double angle formula)

cos 2x = 1 - 2sin² x

when x = tan inverse (x)

cos(2 tan inverse (x))  = 1 - 2sin² tan inverse (x)        (1)

cos² x + sin² x = 1

cos² x = 1 - sin² x

cos x = √(1 - sin x)

tan x = sin x / cos x

[tex]tan x = \frac{sinx }{\sqrt{1-sin^{2}x } }[/tex]

squaring all parts of the trigonometry expression and clearing the fraction

[tex]tan^{2}x = \frac{sin^{2} x }{1-sin^{2}x }[/tex]

[tex](tan^{2}x) (1-sin^2x) = sin^2x[/tex]

[tex]tan^{2}x-tan^{2}xsin^2x = sin^2x[/tex]

[tex]tan^{2}x = sin^2x+tan^{2}xsin^2x[/tex]

[tex]tan^{2}x = sin^2x(1+tan^{2}x)[/tex]

[tex]sin^2x = \frac{tan^{2}x}{(1+tan^{2}x)}[/tex]

since tan (tan inverse) (x) = x

[tex]1 - 2sin^2 tan^{-1} (x) = 1 - 2x^2 / (1 + x^2)[/tex]

[tex]=\frac{ 1 + x^2 -2x^2}{1+x^2}[/tex]

[tex]=\frac{ 1 -x^2}{1+x^2}[/tex]

Therefore trigonometry expression cos(2 tan inverse (x)) gives an algebraic expression in the form (1-x²) / (1+x²)

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Answer:

294 grams

Explanation:

The amount of radioactive material left after t hours given that the half-life is to hours is

Now, in our case t0 = 3, t = 9 and P = 2352 g; therefore, the above equation gives

which is our answer!

Hence, the amount of radioactive copper left after 9 hours is 294 grams.

Answer:

There are 35 episodes in the show

Let x represent the rental cost for each movie.

Let y represent the rental cost for each video game.

We were told that One month Tony rented 5 movies and 3 video games for a total of 532. This means that

5x + 3y = 32

Also, the month, he rented 2 movies and 12 video games for a total of $83. This means that

2x + 12y = 83

Dividing through by 2, we have

x + 6y = 41.5

x = 41.5 - 6y

Substituting x = 41.5 - 6y into 5x + 3y = 532, we have

5(41.5 - 6y) + 3y = 32

207.5 - 30y + 3y = 32

- 30y + 3y = 32 - 207.5

- 27y = - 175.5

y = - 175.5/- 27

y = 6.5

x = 41.5 - 6(6.5) = 41.5 - 39

x = 2.5

Rental cost for each movie = $2.5

Rental cost for each video game = $6.5

The Solution:

Given that a car that cost $10500 was offered as a loan with a down payment of $800.

This means the loan balance will now be:

The loan payment plan is a monthly payment of $187.53 for 60 months.

We are required to find how much was paid in interest.

We shall take the difference between the total payment and the loan balance.

Therefore, the correct answer is $1552

The probability that the sales will will remain steady is; 7/30 or 0.233

We are given the numbers generated by the simulator for the sales as;

0, 1, 0, 2, 0, 0, 0, 1, 0, 3, 2, 0, 0, 0, 0, 2, 1, 2, 3, 1, 2, 0, 2, 0, 3, 0, 0, 2, 1, 0, 1

Now, we are given the following implications of the simulator as;

Now, we want to find the probability that the sales will will remain steady which is the point at which it assigns 1 from the 30 numbers generated. Thus;

P(sales will remain steady) = 7/30 = 0.233

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Answer

The equation in point-slope form is

y - 1 = (-10/3) (x + 2)

We can then simplify this by multiplying through by 3 to obtain

3y - 3 = (-10) (x + 2)

3y - 3 = 10x - 20

3y = 10x - 20 + 3

3y = 10x - 17

Explanation

The general form of the equation in point-slope form is

y - y₁ = m (x - x₁)

where

y = y-coordinate of a point on the line.

y₁ = This refers to the y-coordinate of a given point on the line

m = slope of the line.

x = x-coordinate of the point on the line whose y-coordinate is y.

x₁ = x-coordinate of the given point on the line

We can calculate the slope of the line and then use any of the two points given to serve as the point (x₁, y₁) in the equation

For a straight line, the slope of the line can be obtained when the coordinates of two points on the line are known. If the coordinates are (x₁, y₁) and (x₂, y₂), the slope is given as

For this question,

(x₁, y₁) and (x₂, y₂) are (-5, 11) and (-2, 1)

x₁ = -5

y₁ = 11

x₂ = -2

y₂ = 1

Slope = m = (-10/3)

Using the point (-2, 1) as (x₁, y₁), we can write the equation of the line

y - y₁ = m (x - x₁)

y - 1 = (-10/3) (x - (-2))

y - 1 = (-10/3) (x + 2)

We can then simplify this by multiplying through by 3 to obtain

3y - 3 = (-10) (x + 2)

3y - 3 = 10x - 20

3y = 10x - 20 + 3

3y = 10x - 17

Hope this Helps!!!

1) Since the equation of the circle is given by:

And we've been told the Center (1,-5) and one point located at the circumference, (2,1). So let's find the radius, i.e. the distance from the center to any point to the circumference.

2) Let's use the Formula for the distance between (1,-5) and (2,1), derived from the Pythagorean Theorem:

3) So d = radius, and now we can plug those pieces of information into the formula of the circle:

So we now have the formula for that circle.

Answer:

Radius (R) is equal to the distance between the points (-2,1) and (3,1)

R² = (1 - 5)² + (1 - 1)² = (-24)² + 0 = 579

R =  23.16

Answer:

I think it is y

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

the function calculates the number of pages left to print. that means for every minute it subtracts a number of pages from the total of pages (that total being 152 pages).

the colored print only manages 30 pages per minute, while the pure black ink printing manages 33 pages per minute.

The given inequality has the following solution set

9.52 ≤ x ≤ 22.22

If we express this as an interval, we get [9.52, 22.22].

Here is the inequality which is Kali's earning potential

200 ≤ 15.75x + 50 ≤ 400

To solve the inequality, we must isolate the variable in the center; if we remove 50 from each of the three sides, we get:

200 - 50 ≤ 15.75x + 50 - 50 ≤ 400 - 50

150 ≤ 15.75x ≤ 350

Now we must divide both totals by 15.75, yielding:

150/15.75 ≤ 15.75x/15.75 ≤ 350/15.75

9.52 ≤ x ≤ 22.22

This is the inequality's solution; the solution set expressed as an interval will be [9.52, 22] or 9.52 ≤ x ≤ 22.22

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The expected number of the real number in any sample size is 150.

What is sample size?

In statistics, the sample size refers to the group of people whose data is analyzed during calculation. Depending upon the constraints, the data is analyzed for the measurement. The analysis of samples is perform with the help of Binomial distribution.

According to the question, the given random sample can be solved with the help of Binomial distribution:

The sample size of teachers: n = 50

Percentage of ghost workers: 30%

Percentage of real workers: 70%

For ghost workers: n = 50 and p = 0.31 and q = 1 - p = 1 - 0.31 = 0.69

Now, to calculate the expected number of the real workers as per given samples:

For real workers: n = 50 and p = 0.70 and q = 1 - p = 1 - 0.70 = 0.30

Expected number is: (n)(q) = (50)(0.30) = 150

Hence, the expected number of the real number in any sample size is 150.

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The minimum result (to 2 dp) of a / b is 38.66

Given:

a=460 rounded to the nearest 10

b=11.9

Now, substitute the values of a and b in a/b,

a/b = 460/11.9

Multiply the same integer(10) by both the numerator and denominator,

a/b = 4600/119

Round the number obtained

a/b ≅ 38.66

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The Standard form of the equation will be;

⇒ x - 5y = -21

What is Standard form of equation?

The standard form of the equation is defined as;

Ax + By = C

Where, A, B and C are integers.

Given that;

The equation in slope - intercept form as;

⇒ y - 3 = 1/5 (x + 6)

Now,

We convert the equation in standard form as;

Since, The equation in slope - intercept form as;

⇒ y - 3 = 1/5 (x + 6)

Change into standard form as;

⇒ y - 3 = 1/5 (x + 6)

Multiply by 5 both side, we get;

⇒ 5( y - 3) = (x + 6)

⇒ 5y - 15 = x + 6

Add 15 both side, we get;

⇒ 5y - 15 + 15 = x + 6 + 15

⇒ 5y = x + 21

Subtract 21 both side, we get;

⇒ 5y - 21 = x + 21 - 21

⇒ 5y - 21 = x

Subtract 5y both side, we get;

⇒ 5y - 21 - 5y = x - 5y

⇒ - 21 = x - 5y

⇒ x - 5y = -21

Therefore,

The Standard form of the equation will be;

⇒ x - 5y = -21

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Since the scaling factor of the dilation (0.5) is fewer than 1, it shrinks (make smaller) the triangle around the origin (zero). Intuitively, the dilation is getting the points of the triangle closer to zero (in a way that preserves the shape of the triangle).

Formally, to know the coordinates of a point of the triangle after the dilation, we just need to multiply the original coordinates of the point by the scaling factor (this works for the dilation is around zero).

The original coordinates of D are

Multiplying them by the scale factor, we get

The coordinates of D after the given dilation is

Answer:

The total surface area is;

Explanation:

Given the square pyramid as show in the attached image.

The total surface area is the sum of the area of the base square and the area of the four triangles.

Given;

substituting the given values;

Therefore, the total surface area is;

Whereas working with laws of exponents, when splitting the exponential equations with the same base, the exponents ought to be subtracted.

Basically, the Quotient of Powers rules is used to decrease the number of terms when parts like terms with exponents. In order to get the solution, just remove the exponents while dividing the terms with the same base, it is applicable to exponents with the same bases. when powers are multiplied,  for two whole numbers of the same bases the exponents are added, whereas when powers are divided for two whole numbers of the same bases,  exponents are subtracted. The zero exponent rule basically states that when any number is raised to the power of zero it results in 1.

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SOLUTION

Given the question, the following are the solution steps to answer the question.

STEP 1: Write the given equation

STEP 2: Substitute 3 for b in the equation

STEP 3: Simplify the equation to solve for a

Hence, the value of a is 15

Answer: 22.8 miles or 22 4/5

Step-by-step explanation:

To find the unit rate you do

28.5 ÷ 1.25 = 22.8

After 2.14 hours the trains are exactly 300 miles apart.  

Two trains leave the same station at the same time, one traveling west at a constant speed of 60 miles per hour, the other traveling south at a constant speed of 80 miles per hour.

The time both of them will travel 300 miles can be calculated as follows:

Therefore,

speed = distance / time

distance = speed × time

The train that travel west:

let

t = time of the train that travel west

distance = 60t

The train that travel south:

distance = 80t

Therefore,

total distance = 60t + 80t

300 = 140t

t = 300 / 140

t = 2.14285714286

t = 2.14 hours

Therefore,

time taken  = 2.14 hours

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Answer:

For A and B, we have (10, 6)

For C and D, we have (12, 8)

For E and F, we have (12, 8)

Explanation:

To determine the missing numbers along each side of the triangle, we have to

*Add the two numbers at the vertex

*Subtract it from 32

*Divide it by 2

*Add 2 to it to have the 1st number

*Subtract 2 from it to have the 2nd number

So to find the pair of numbers that can be used for A and B, we'll have;

Therefore the missing numbers for A and B are 10 and 6.

So to find the pair of numbers that can be used for C and D, we'll have;

Therefore the missing numbers for C and D are 12 and 8.

So to find the pair of numbers that can be used for E and F, we'll have;

So to avoid repetition of any of the numbers between 4 and 12, we have to add and subtract 1 instead of 2.

The vertex form is y= (x+ 6)²+1.

The vertex form of a quadratic equation is y = a (x- h)² + k as opposed to the regular quadratic form, which is an x² + bx + c = y. In both cases, the variables that indicate whether the parabola is facing up (+ a) or down ( a) are y, the y-coordinate, x, and a.

a=1

b=12

c=37

Consider the vertex form of a parabola.

a(x+ d)²+e

Now, d= b/2a

d=12/ 2

d=6

and, e= c-b²-4a

e= 37 - (12)²/4x1

e= 37 - 36

e= 1

Then, the vertex form is

y = a(x+ d)²+e

y= 1(x+ 6)²+1

y= (x+ 6)²+1

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The largest of three consecutive odd integers whose sum is 111 is 39

Positive, negative, and zero are all examples of integers. The Latin word "integer" signifies "whole" or "intact." As a result, fractions and decimals are not included in integers.

Odd integers that follow each other grow (or shrink) by a factor of 2. Consider the numbers 1, 3, and 5. Add two to the preceding number to move from one to the following. You don't know where to begin, and that is the issue here. In actuality, you are searching for the least of the three integers, therefore this is your unknown.

x + (x + 2) + (x + 4) = 111

x + x + 2 + x + 4 = 111

3x + 6 = 111

3x = 105

x =[tex]\frac{105}{3}[/tex]

x = 35

35 ,37,39

The largest of three consecutive odd integers whose sum is 111 is 39

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The greatest common factors of 2^5 · 5· 11 and 2^3· 5^2 · 7 is equivalent to 2^3 * 5

The largest positive integer that divides each of two or more non-zero integers is known as the greatest common divisor.

This factor must be able to divide all the terms of the expression withour remainder.

Given the numbers 2^5 · 5· 11 and 2^3· 5^2 · 7. Find the factors;

2^5 · 5· 11 = 2^3 * 2^2 * 5 * 11

2^3· 5^2 · 7= 2^3 * 5 * 5 * 7

Since the number 2^3 * 5 is common to both factors, hence the GCF of these numbers 2^5 · 5· 11 and 2^3· 5^2 · 7 is 2^3 * 5

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Answer:

33by 11

Step-by-step explanation:

in 41 3 games firstly we find 1 point it is 3by41

Answer:

let's say you need to find the absolute value of -5 the answer would be 5.

Step-by-step explanation:

Since the distance between -5 and 0 in a number line is 5. This would also be applied If you you were trying to find the absolute value of 5. it would also be 5.

When in math, I figured out negative number's absolute value will always be positive. absolute value numbers of positive numbers will stay the same.

Step 1:

The ratio for 5ml to 120ml

Step 2:

The symbol of ratio is :

Therefore,

Step 3

Final answer

1 : 24

What is the product of



In the multiplication of fractions, you multiply the numerators with each other and the denominators with each other

( - 3/5) *(-7/8)

= -3*-7 / (5*8) = (positive)

= 21/40

_____________________

Answer

= 21/40

_____________________

Do you have any questions regarding the solution?

​

The value of of angle x of the circumscribing circle is x° = 140°

In the above question, the following figure is given, where

The angle inside the circle made by the intersection of two line segments is = 40°

We need to find the angle x made by the angle made by the tangents outside the circle

A line that touches a curve or a circle at one point is said to be tangent.

The point of tangency is the intersection of the tangent line and the curve.

We'll find the value of of angle x using the theorems of the circumscribing   circle.

The sum of opposite angles of a circumscribing quadrilateral is always 180°

Using this property we can write,

40° + x° = 180°

x° = 180° - 40°

x° = 140°

Hence, the value of of angle x using the theorems of the circumscribing   circle is x° = 140°

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