Solve the system of equations. y=4x+5y=x2+12x+20

The double-angle trigonometric identities for cosines and sines indicates that the values of cos(2·θ) and sin(2·θ) are;

The double-angle trigonometric identities for cosines and sines are;

cos(2·θ) = cos²θ - sin²θ

sin(2·θ) = 2·sin(θ)·cos(θ)

1. cos(θ) = 11/15

sin(θ) = √((1 - (11/15)²) = (2/15)·√(26)

The angle 2·θ will be in the 2 × 270° = 540° in the third quadrant, therefore;

cos(2·θ), will have a negative value

|cos(2·θ)| = (11/15)² - ((2/15)·√(26))² = 17/225

cos(2·θ) = -17/225

2. cos(2·θ) = cos²θ - sin²θ

sin(θ) = √((1 - (11/61)²) = 60/61

cos(2·θ) = (11/61)² - (60/61)² = -3479/3721

3. sin(2·θ) = 2·sin(θ)·cos(θ)

cos(θ) = √((1 - (7/12)²) = (1/12)·√(95)

sin(2·θ) = 2 × (7/12) × (1/12)·√(95) = (7/72)·√(95)

4. cos(2·θ) = cos²θ - sin²θ

sin(θ) = √((1 - (-3/5)²) = 4/5

cos(2·θ) = (-3/5)² - (4/5)² = -7/25

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Step-by-step explanation:

The usual thing to do is to try to get rid of one variable first. So to get rid of x, we multiply the first equation by 5.

5(x + y) = 2(5)

-5x - 5y = -10

---> 5x + 5y = 10

-5x - 5y = -10

---> 0 = 0

As you can see, everything cancels out. If the statement is true, then it is infinitely many solutions.

Answer:

- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries

After answering the presented question, we can conclude that equation Therefore, the solution to the given system of equations is (x, y) = (2, 2).

An equation is a mathematical statement that proves the equality of two expressions connected by the equal symbol '='. 2x - 5 Equals 13, for example. Expressions include 2x-5 and 13. The character '=' joins the two expressions. A mathematical formula with two algebraic expressions on either side of an equal sign (=) is known as an equation. It demonstrates the relationship of equivalence between the left and right formulas. In every formula, LHS = RHS (left side = right side).

\(4x + y = 10 ...(1)\\y = 2x - 2 ...(2)\\y = 2x - 2 ...(2)\\y + 2 = 2x ...(2)\\x = (y+2)/2 ...(3)\\4x + y = 10 ...(1)\\4[(y+2)/2] + y = 10 \\\)

\(2(y+2) + y = 10 \\3y + 4 = 10\\3y = 6\\y = 2 \\y = 2x - 2 ...(2)\\2 = 2x - 2 \\4 = 2x \\x = 2 \\\)

Therefore, the solution to the given system of equations is (x, y) = (2, 2).

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Check the picture below.

Answer:

∠ U = 12°

Step-by-step explanation:

the inscribed angle RST is half the measure of its intercepted arc RT , then

arc RT = 2 × ∠ RST = 2 × 30° = 60°

the secant- tangent angle U is equal to half the difference of its intercepted arcs, that is

∠ U = \(\frac{1}{2}\) ( RS - RT ) = \(\frac{1}{2}\) × (84 - 60)° = \(\frac{1}{2}\) × 24° = 12°

Answer:

353 kg

Step-by-step explanation:

So you want to find the number of kg by finding the answer through the density formula. To do this you take the formula of Density, which is  \(D=\frac{m}{v}\). Now you substitute D for the density of 0.1765,  and v for the volume, which is 2000, to then get  \(0.1765=\frac{m}{2000}\). Now you solve for m. To do this you multiply each side by 2000. This brings you with \(353=m\) after multiplying 0.1765 and 2000. Hope this helps!

The mass of the helium that the balloon contain will be 353 kilograms.

Density is defined as the mass per unit volume. It is an important parameter in order to understand the fluid and its properties. Its unit is kg/m³.

The mass and density relation is given as

Mass = density × volume

A weather balloon holds 2,000 cubic meters of helium.

The density of helium is 0.1765 kilograms per cubic meter.

The mass of the helium that the balloon contain will be

Mass = 0.1765 × 2000

Mass = 353 kilograms

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Answer: 59 cars per month

Step-by-step explanation:

The domain of the given function would be -

- 5 ≤ x < 3.

An function in mathematics defines a relationship between one variable (the independent variable {x})  and another variable (the dependent variable {y}). Example → y = f{x} = ax + b.

Given is the graph of the linear equation as shown in the image.

Domain represents the set of values along the {x} - axis.

So, we can write -

- 5 ≤ x < 3

Therefore, the domain of the given function would be -

- 5 ≤ x < 3.

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Answer:

\(\sqrt{7}\)

Step-by-step explanation:

Law of cosines

c^2 = a^2 + b^2 - 2abcosC

c^2 = 2^2 + 3^2 - 2(2)(3)cos60

c^2 = 4 + 9 - 12 * 0.5

c^2 = 7

c = \(\sqrt{7}\)

Answer:

x = 4

Step-by-step explanation:

(4 + 10)
14 x 5 = 70





~ LadyBrainiac

Step-by-step explanation:

-coefficent=1

-collect like terms /variables

-add numbbers (1+2)=3p

Answer:

1

Step-by-step explanation:

(p+q)(p-q)/(p+q)(p-q)=1

[It is an identity : a²-b²= (a+b)(a-b)]

Hope this will help:)

Answer:

79.45 is a rational number, but not a whole number.

Step-by-step explanation:

A rational number is obtained by dividing one integer by another one to get an integer result. For example, 2/3 equals the rational 78/100 or 842-32=814 that are both integers, which means that they are both valid representation of it. Non-integers are called irrational numbers. Irrationals are also obtained through division sometimes but they do not always end up being an integer at the end even though they still have a finite decimal value for their denominator or numerator (i). Euler's Constant, for instance has the decimal expansion 2.719926... repeated indefinitely and so cannot be represented as an integral.

Answer:

c = 10.6

Step-by-step explanation:

c² = a² + b²

c² = 7² + 8²

c² = 49 + 64

c² = 113

Take the square root of both sides

c = 10.6301458127

Rounded

c = 10.6

Answer:

1.029 is greater than 1.0275

Step-by-step explanation:

Answer:

1.029

Step-by-step explanation:

What is greater 1.0275 or 1.029

.027 < .029

So, 1.029 is greater.

\(\huge\text{Hey there!}\)

\(\large\text{We cannot do much of nothing because we don’t have all the information}\\\large\text{to solve.. so we can just simply do process of elimination until we fully find}\\\large\text{the ANSWER you are trying to look for.}\)

\(\large\text{Given equation: 25b - 14b}\\\large\text{COMBINE your LIKE TERMS}\\\large\text{\underline{25b - 14b} = 11b}\\\large\text{So, we are looking for an equation that gives us \bf{11b}}\)

\(\large\text{Option A.}\downarrow\\\large\text{b(25 - 14)}\\\large\text{DISTRIBUTE: b(25) + b(-14)}\\\bullet\large\text{ Reverts to: 25b - 14b (our ORIGINAL EQUATION) so this can be}\\\large\text{equal to 11b}\\\\\large\text{Option A. could POSSIBLY be your ANSWER}\)

\(\large\text{Option B. }\downarrow\\\large\text{b(25 + 14)}\\\large\text{Distribute}\\\large\text{25(b) + 14(b)}\\\large\text{It DOES NOT revert to the original equation. It gives us: 25b + 14b}\\\large\text{If we COMBINE your LIKE TERMS in that equation. We would get: 39b}\\\large\bf{39b \neq 11b}\\\\\large\text{Option B is NOT your ANSWER}\)

\(\large\text{Options C and D CANNOT be your answers because Option C. is}\\\large\text{-11b and Option D. is -39b}\)

\(\boxed{\boxed{\large\text{To sum it all up, your ANSWER is: \bf{Option A. b(25 - 14)}}}}\huge\checkmark\)

\(\text{Good luck on your assignment and enjoy your day!}\)

~\(\frak{Amphitrite1040:)}\)

Answer:

  4 and 5

Step-by-step explanation:

For answering questions like this, it can be useful to remember a few of the powers of small integers:

  2^4 = 16

  2^5 = 32

A logarithm can be considered to be an exponent of the base.

  \(\log_b(x) = a \ \Longleftrightarrow\ b^a=x\)

The ordering of powers of 2 relative to the number of interest (17) is ...

  16 < 17 < 32

  2⁴ < 17 < 2⁵ . . . . . . . . . . . . . . . . . . . expressed as powers of 2

  log₂(2⁴) < log₂(17) < log₂(2⁵) . . . . . log₂ of the above inequality

  4 < log₂(17) < 5 . . . . . . . . . . . . . . . . showing the values of the logs

Log₂(17) lies between 4 and 5.

__

Additional comment

Using the "change of base" formula, you can use a calculator to find the value of log₂(17). It shows you the value is between 4 and 5.

  log₂(17) = log(17)/log(2) . . . . . . using logs to the same base

Answer:

b. Hо : μ ≥ 40.1; Ha : μ > 40.1

Step-by-step explanation:

Note: The complete options to the question is attached as picture below

The alternative hypothesis is focusing on "the recession has led to a reduction in the average work week".

So, it will be less than the past average. i.e, 40.1.. so, we will use a less than (<) sign to write the alternative hypothesis.

The hypotheses are as below:

Hо : μ ≥ 40.1 (Null hypothesis)

Ha : μ > 40.1 (Alternative hypothesis)

Area of rectangular prism: Base x Height.

so 3x1/3x2/5=0.4 0r 2/5

Answer:

38.46 (Rounded: 38.5)

Step-by-step explanation:

67.32-2(14.43)=38.46

Step-by-step explanation:

firstly firstly we have to suppose f(X) as y and then solve it by interchanging X and y.

hope this is helpful

Answer:

B

Step-by-step explanation:

To find inverse you switch f(x) and x use y for f(x) then solve for y.

1. x = 2y - 8

2. x + 8 = 2y

3. (x + 8) / 2 = y

4. 1/2x + 4 = y

Answer:

4x (x²+2)

Hope that helps

Answer:

4x(x+2x)

Step-by-step explanation:

There is no further explanations on it

Step-by-step explanation:

x = first angle

second angle = 2x

third angle = x + 2x - 30

x + 2x + x + 2x - 30 = 180

6x - 30 = 180

6x = 210

x = 210/6 = 35

the first angle = 35°

the second angle = 2×35 = 70°

the third angle = 35 + 70 - 30 = 75°

Answer:

  f(x) = -2/3(x +11) +5

Step-by-step explanation:

The point-slope form of the equation of a line will give you the desired linear function:

  y = m(x -h) +k . . . . . for slope m through point (h, k)

You are give point (x, f(x)) = (-11, 5) = (h, k), and you are given slope m = -2/3. Putting these values into the function form gives ...

  f(x) = -2/3(x +11) +5

Answer:

\((a)\ \cos(180 - x)\) --- Never true

\((b)\ \cos(90 -x)\) --- Always true

\((c)\ \cos(x)\) ---- Sometimes true

\((d)\ \cos(2x)\) ---- Sometimes true

Step-by-step explanation:

Given

\(\sin(x )\)

Required

Determine if the following expression is always, sometimes of never true

\((a)\ \cos(180 - x)\)

Expand using cosine rule

\(\cos(180 - x) = \cos(180)\cos(x) + \sin(180)\sin(x)\)

\(\cos(180) = -1\ \ \sin(180) =0\)

So, we have:

\(\cos(180 - x) = -1*\cos(x) + 0*\sin(x)\)

\(\cos(180 - x) = -\cos(x) + 0\)

\(\cos(180 - x) = -\cos(x)\)

\(-\cos(x) \ne \sin(x)\)

Hence: (a) is never true

\((b)\ \cos(90 -x)\)

Expand using cosine rule

\(\cos(90 -x) = \cos(90)\cos(x) + \sin(90)\sin(x)\)

\(\cos(90) = 0\ \ \sin(90) =1\)

So, we have:

\(\cos(90 -x) = 0*\cos(x) + 1*\sin(x)\)

\(\cos(90 -x) = 0+ \sin(x)\)

\(\cos(90 -x) = \sin(x)\)

Hence: (b) is always true

\((c)\ \cos(x)\)

If

\(\sin(x) = \cos(x)\)

Then:

\(x + x = 90\)

\(2x = 90\)

Divide both sides by 2

\(x = 45\)

(c) is only true for \(x = 45\)

Hence: (c) is sometimes true

\((d)\ \cos(2x)\)

If

\(\sin(x) = \cos(2x)\)

Then:

\(x + 2x = 90\)

\(3x = 90\)

Divide both sides by 2

\(x = 30\)

(d) is only true for \(x = 30\)

Hence: (d) is sometimes true

Answer:

67.25

Step-by-step explanation:

Since they can each get 1/2 the jelly beans but need to eat it over 4 days they will be eating 1/2*1/4 jelly beans per day. This is equal to 1/8x where x is the total jelly beans. We know the total so we can plug 538 in for x and divide 538 by 8 to get 67.25

People at the concession stand as input Cost of their order's output.

(1) The relation in question is a function.

(II) This function is not constant. (Each category of concession has a different order cost.)

Not a 1-1 function (iii). (Several persons arrived seeking the same sort of concession. So they all pay the same price for their order.)

A function describes the relationship between patrons' inputs at the concession stand and the cost of their order as an output. A function is a relationship between a set of possible inputs and outputs, where each input is associated to exactly one output.

The quantity of patrons at the concession stand serves as the input in this scenario, while the cost of their order serves as the output.

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Answer:

55,000

Step-by-step explanation:

Look at 40 on the x-axis and the y-axis. The line is inbetween 50 and 60 so the best answer would be 55,000