Which number produces a rational number when added to 0.25?

Using double angle identity, we are able to prove tan(x)(1 + cos(2x)) = sin(2x).

To prove the identity tan(x)(1 + cos(2x)) = sin(2x), we can start by using trigonometric identities to simplify both sides of the equation.

Starting with the left-hand side (LHS):

tan(x)(1 + cos(2x))

We know that tan(x) = sin(x) / cos(x) and that cos(2x) = cos²(x) - sin²(x). Substituting these values, we get:

LHS = (sin(x) / cos(x))(1 + cos²(x) - sin²(x))

Next, we can simplify the expression by expanding and combining like terms:

LHS = sin(x) / cos(x) + sin(x)cos²(x) / cos(x) - sin³(x) / cos(x)

Simplifying further:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

Now, let's work on the right-hand side (RHS):

sin(2x)

Using the double angle identity for sine, sin(2x) = 2sin(x)cos(x).

Now, let's compare the LHS and RHS expressions:

LHS = sin(x) / cos(x) + sin(x)cos(x) - sin³(x) / cos(x)

RHS = 2sin(x)cos(x)

To prove the identity, we need to show that the LHS expression is equal to the RHS expression. We can combine the terms on the LHS to get a common denominator:

LHS = [sin(x) - sin³(x) + sin(x)cos²(x)] / cos(x)

Now, using the identity sin²(x) = 1 - cos²(x), we can rewrite the numerator:

LHS = [sin(x) - sin³(x) + sin(x)(1 - sin²(x))] / cos(x)

    = [sin(x) - sin³(x) + sin(x) - sin³(x)] / cos(x)

    = 2sin(x) - 2sin³(x) / cos(x)

Now, using the identity 2sin(x) = sin(2x), we can simplify further:

LHS = sin(2x) - 2sin³(x) / cos(x)

Comparing this with the RHS expression, we see that LHS = RHS, proving the identity.

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Answer:

3.75

Step-by-step:

The side length of each piece is given as follows:

\(20\sqrt{2}\) inches.

The Pythagorean Theorem states that for a right triangle, the length of the hypotenuse squared is equals to the sum of the squared lengths of the sides of the triangle.

For this problem, the parameters are given as follows:

Hence the side length of each piece is obtained as follows:

x² + x² = 40²

2x² = 40²

x² = 800

x = sqrt(2 x 400)

\(x = 20\sqrt{2}\)

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Answer:

  D.  13

Step-by-step explanation:

The first step in evaluating a piecewise function at a particular point is to find the piece that includes the point.

For x = 0, the relevant domain specification is x ≤ 0, the one applicable to the third piece. That piece of the function definition tells you ...

  f(0) = 13

Answer:

$8.19

Step-by-step explanation:

1. Add the cost of the items together

5.3 + 1.29 + 0.53 + 0.68 = 7.8

2. Solve for 5% of the cost of the items

5% = 0.05

7.8 · 0.05 = 0.39

3. Add the sales tax to the price of the items

7.8 + 0.39 = 8.19

Explanation:

Add up the prices

5.30 + 1.29 + 0.53 + 0.68 = 7.80

This is the total amount before tax is added. To find the amount after tax, we multiply by 1.05 to get

1.05*7.80 = 8.19

Or a longer way is to find 5% of 7.80 getting 0.05*7.80 = 0.39 in the amount of tax owed, which is added on top of the previous total we got earlier. So we have 7.80 + 0.39 = 8.19

The use of the multiplier 1.05 is handy when you need to apply multiple percentage increases (it also works if you have multiple discounts as well).

Answer:

29/3

Step-by-step explanation:

Multiply and simplify

58/6=29/3

Answer:

29x/3

Step-by-step explanation:

i used math website trust me its right

Step-by-step explanation:

therefore, the correct option should be A.

Answer:

Step-by-step explanation:

Statement                     Reason

PR ≅ TR                        Given

<PQR≅<TSR                 Given

<PRQ≅<TRS                Vertical Angles Theorem

PQR=TSR                      SAS  Theorem   (Side-Angle-Side)

S casts a "shadow" on the x-y plane given by the set

\(S' = \left\{(x,y) ~:~ -1 \le x \le 1 \text{ and } x^2 \le y \le 1\right\}\)

Each cross section is a square whose side length is determined by the vertical distance between y = 1 and y = x², which is |1 - x²|. But since -1 ≤ x ≤ 1, this distance simplifies to 1 - x².

The volume of an infinitesimally thin section is then (1 - x²)² ∆x (where ∆x represents its thickness), and so the volume of S is

\(\displaystyle \int_{-1}^1 (1-x^2)^2 \, dx = \int_{-1}^1 (1 - 2x^2 + x^4) \, dx\)

The integrand is even, so this integral is equal to twice the integral over [0, 1] :

\(\displaystyle \int_{-1}^1 (1-x^2)^2 \, dx = 2 \int_0^1 (1 - 2x^2 + x^4) \, dx = 2 \left(1 - \frac23 + \frac15\right) = \boxed{\frac{16}{15}}\)

The value of x as shown in the right triangle is 6 units.

The value of x as shown in the right triangle is calculated by applying altitude/leg theorem as shown below.

The altitude/leg theorem, also known as the HL congruence theorem, states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

segment / altitude = altitude / segment

4/x = x/9

x² = 4(9)

x² = 36

x = √36

x = 6 units

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Answer:

Where is the figure?

Step-by-step explanation:

Answer:

To calculate Karl Pearson's coefficient of skewness, we need to use the formula:

Skewness = 3 * (Mean - Mode) / Standard Deviation

Given the Mean = 73.19, Mode = 79.56, and Variance = 16, we need to find the Standard Deviation first.

Standard Deviation = √Variance = √16 = 4

Now we can substitute the values into the formula:

Skewness = 3 * (73.19 - 79.56) / 4

Skewness = -6.37 / 4

Skewness = -1.5925

Rounded to four decimal places, the Karl Pearson's coefficient of skewness for the given values is approximately -1.5925.

\(\dfrac{d}{dt} [(4t^2-t)(t^3 -8t^2+12)]\\\\\\=(4t^2-t)\dfrac{d}{dt}(t^3-8t^2 +12) + (t^3 -8t^2 +12) \dfrac{d}{dt} (4t^2 -t)\\\\\\=(4t^2 -t)(3t^2-16t)+(t^3-8t^2+12)(8t-1)\\\\=12t^4-64t^3 -3t^3+16t^2+8t^4-64t^3+96t-t^3+8t^2-12\\\\=20t^4-132t^3+24t^2+96t-12\)

There were 5 1/4 bags of popcorn left after eating 4 bags.

To find out how much popcorn was left after eating 4 bags, we need to subtract the amount eaten from the total amount Brianna made.

Brianna made 9 1/4 bags of popcorn, which can be represented as a mixed number. To perform calculations, let's convert it to an improper fraction:

9 1/4 = (4 * 9 + 1) / 4 = 37/4

Now, let's subtract the 4 bags eaten from the total:

37/4 - 4

To subtract fractions, we need a common denominator. The common denominator of 4 and 1 is 4. Therefore, we can rewrite the expression as:

37/4 - 4/1

Now, let's find a common denominator and subtract the fractions:

37/4 - 16/4 = (37 - 16) / 4 = 21/4

The result is 21/4, which is an improper fraction. Let's convert it back to a mixed number:

21/4 = 5 1/4

Therefore, there were 5 1/4 bags of popcorn left after eating 4 bags.

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The amount you need to sell the job if you want to make 15% net margin, based on the costs, is $7, 857.26

First, find the total cost for the project:
= Equipment + cost of labor + overhead

Cost of labor and equipment:

= 4, 200 + ( 16 x 32 per man- hour)

= $ 4, 712

The total cost is then:
= 4, 712 x ( 1 + 45%)

= $6, 832.40

The amount to sell for is:
= Total cost x ( 1 + net margin)

= 6, 832.40 x ( 1 + 15%)

= $7, 857.26

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Answer:

Step-by-step explanation:

Answer: The value of x in ∆ ABC is

Step-by-step explanation: By AA similarity

x² = 4* 16

x = 8

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Answer:

see below

Step-by-step explanation:  5 23  8 03

the lenght of the longer leg of a right triangle is 9 ft longer than the lenght of the shorter leg x. The hypotenuse is 9 ft shorter than twice the lenght of the shorter leg.

shorter leg    = x

longer leg     = x + 9

hypotenuse  =  2x - 9

Pythagorean theorem  =    a² + b²  = c²

             shorter-leg² + longer-leg² = hypotenuse²

                         x²  +  (x+9)²  = (2x - 9)²                  solve for x

                  x² +  (x+9) (x+9)  =  (2x - 9)(2x - 9)

                 x² +  (x²+18x+81)  =  (4x² - 36x + 81)

                       (2x²+18x+81)  =  (4x² - 36x + 81)

                                          0 =   2x² -54x

                                          0 =  x(2x - 54)  

                           0 = x      and         0 = 2x -54  

                                                       54 = 2x

                                                      27 =  x

shorter leg    = 27        

longer leg     = 36

hypotenuse  =  45

divided all the values by 9 and you get a 3, 4, 5  right triangle, so the answer checks correct  

Answer:

$131250

Step-by-step explanation:

Talia's earnings during one year are equal to her base yearly salary ($65000) added to her commission. Now, to know the commission it is necessary to find the 2.65% of her total sales ($2.5 million)

Step 1. Divide the total sales or 2,500,000 by 100 considering this represents the total or 100%

2,500,000 ÷ 100 = 25000

Step 2. Multiply this number by the specific percentage (2.65)

25000 x 2.65 = 66250

Now add the commission and the yearly salary

65000 + 66250 = 131250

Hence, total earnings of Talia were $131250

Answer:

i think it should be 2.5 or 3

The growth rate function indicates that the number of years The Iron Man's net worth will reach the net worth of T'Challa is about 87 years

The growth rate is the rate of growth of a function with regards to the input variable.

T'Challa's net worth in the Marvel comics = 80 trillion (8 × 10¹³) Dollars

The Iron Man's net worth = 20 billion (2 × 10¹⁰) Dollars

The growth rate per annum of The Iron Man's net worth = 10% per annum

The number of years it will take to reach T'Challa can therefore, be found as follows;;

(2 × 10¹⁰) × (1 + 0.1)ˣ = (8 × 10¹³)

(1 + 0.1)ˣ = (8 × 10¹³)/(2 × 10¹⁰)

x·ln(1 + 0.1) = ln((8 × 10¹³)/(2 × 10¹⁰))

x = (ln((8 × 10¹³)/(2 × 10¹⁰)))/(ln(1 + 0.1)) ≈ 87 years

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The equation of the line that is parallel to x + y = 4 and passes through (2, 3) is expressed as: y = -x + 5.

Two lines are parallel if and only if their slopes are equal. The equation of the line x + y = 4 is in slope-intercept form (y = mx + b), where m is the slope. The slope of this line is m = -1, as the coefficient of x is -1.

An equation of a line that is parallel to the line x + y = 4 and passes through the point (2, 3) can be written in the form y = mx + b, where m = -1.

Substituting the point (2,3) and the slope -1 into the point-slope form of a line gives:

y - 3 = -1(x - 2)

Expanding the right hand side gives:

y - 3 = -x + 2

And rearranging the equation gives the final form of the equation of the line:

y = -x + 5

So, the equation of the line that passes through the point (2, 3) and is parallel to the line x + y = 4 is y = -x + 5.

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Answer:

B) always less than either of the original fractions

Step-by-step explanation:

We can easily Answer this by taking some values.

The question states that the two fractions, each have values between 0 and 1.

Let us say one of the fraction is 1/2 and the other fraction is 1/3 .

The product of the two fractions is 1/2 x 1/3 = 1/6 .

is lesser than both 1/2  and 1/3 .

So, the correct answer is that the product is always less than either of the original fractions.

The two fractions are between 0 and 1 their product will always less than either of the original fractions.

A fraction is number expressed "as quotient, in which the numerator is divided by denominator".

According to the question,

If two fractions are between 0 and 1. In order to check their product be more than 1.

Let us assume one fraction is 1/2 and the other fraction is 1/3. The product of the two fractions:

1/2 x 1/3 = 1/6.

Since the value of fraction 1/2 is 0.5, the value of fraction 1/3 is 0.3333 and the value of fraction 1/6 is 0.166667.

It clearly shows 0.5 > 0.16667 and 0.3333 > 0.16667.

Hence, the two fractions are between 0 and 1 their product will always less than either of the original fractions.

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Answer:

2=240 by the 5th power

Step-by-step explanation:

Answer:

x=2

Step-by-step explanation:

I don’t really have an explanation, it was all mental math

Answer:

Step-by-step explanation:

\(\sf 2(4-x)-3(x+3)=-11\)

Expand:-

Now, add 1 to both sides:-

Divide both sides by -5:-

Therefore, the value of x is 2!

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

Hope this helps!

The angle ABC in the circle is 70 degrees.

The intercepted arc is the arc that is inside the inscribed angle and whose

endpoints are on the angle. The arc angle is half the the inscribed angle.

The intercepted arc that is formed is equal to the inscribed angle,

multiplied by two (intercepted arc measure = inscribed angle × 2).

Therefore, let's find the arc angle ABC as follows:

∠ ABC = 1  /2 (360 - 120 - 100)

∠ ABC = 1  /2 (360 - 220)

∠ ABC = 1  /2 (140)

Therefore,

∠ ABC = 70 degrees

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The values of x and y that maximize the total revenue are approximately 3600 units of A and 3200 units of B.

We are given that;

Function R(x,y)=-5x2-8y2-2xy + 42x+102y

Now,

To maximize the total revenue from x units of A and y units of B, we need to find the values of x and y that maximize the function R(x,y)=-5x2-8y2-2xy + 42x+102y. This is an optimization problem with two variables.

To solve this problem, we need to find the critical points of R(x,y) by taking partial derivatives with respect to x and y and setting them equal to zero.

R_x = -10x - 2y + 42 = 0

R_y = -16y - 2x + 102 = 0

Solving these equations simultaneously gives us:

x = 3.6

y = 3.2

Therefore, by the given function the answer will be 3600 units of A and 3200 units of B.

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Answer:

Some of the graph's coordinates are:

(-2, 1/2)

(-1, 1)

(0, 2)

(1, 4)

Step-by-step explanation: