2(t-3)² - 72 = 0. extracting square roots. with solution please​

Answer:

\((x+2)(x+3)\)

Step-by-step explanation:

⭐What does factorisation mean?

⭐What are factors?

Thus, we have to write \(x^2+5x+6\) in terms of its factors.

I have a picture attached to this response to show you how factorisation works, but I will also explain it here.

How to factorise:

The picture of factorisation is attached to this response.

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The value of the trigonometric function sin a is given by a and has a domain of -1 to 1. The value of a is calculated by sin⁻¹(a), and the output is given in radians.

The letter "a" represents the value of the trigonometric function (sin a), and the letter "t" represents the angle in radians in the equation t = sin⁻¹(a).

The inverse sine function is known as the arcsine function. It is a mathematical function that allows you to calculate the angle measure of a right triangle based on the ratio of the side lengths. The ratio of the length of the side opposite to the angle to the length of the hypotenuse is a, the value of the sine function.

In mathematical terms, this is stated as sin a = opposite / hypotenuse.

The output of the arcsine function is an angle value that ranges from -π/2 to π/2.

The value of the trigonometric function sin a is given by a and has a domain of -1 to 1. The value of a is calculated by sin⁻¹(a), and the output is given in radians.

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Step-by-step explanation:

......

Answer:

fourth option

Step-by-step explanation:

Given

3x³ + 3x² - 18x ← factor out 3x from each term

= 3x(x² + x - 6) ← factor the quadratic

Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)

The factors are + 3 and - 2, since

3 × - 2 = - 6 and 3 - 2 = + 1, thus

x² + x - 6 = (x + 3)(x - 2) and

3x³ + 3x² - 18x = 3x(x + 3)(x - 2) ← in factored form

Answer:

x = 25

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Sum the 3 angles and equate to 180

2x + 3x + 55 = 180, that is

5x + 55 = 180 ( subtract 55 from both sides )

5x = 125 ( divide both sides by 5 )

x = 25

The values of the composite function are (f o g)(x) = √2x² - 8 and (f o g)(x) = 2x - 8, while their domains are x > 2 and 0 < x < oo, respectively

Lastly, the value of (g o f)(3) is -2

Composite function 1

The functions are given as

f(x) = √x

g(x) = 2x² - 8

The composite function definition is given as

(f o g)(x)

This composite function is calculated using the following composite function formula

(f o g)(x) = f(g(x))

Substitute the known values in the above equation

(f o g)(x) = √g(x)

This gives

(f o g)(x) = √2x² - 8

For the domain, we have

2x² - 8 > 0

This gives

x > 2

Composite function 2

The functions are given as

f(x) = √x

g(x) = 2x² - 8

The composite function definition is given as

(g o f)(x)

This composite function is calculated using the following composite function formula

(g o f)(x) = g(f(x))

Substitute the known values in the above equation

(g o f)(x) = 2f(x)² - 8

This gives

(g o f)(x) = 2(√x)² - 8

Evaluate

(g o f)(x) = 2x - 8

The function is a linear function

So the domain is the set of all real values

Substitute 3 for x in (g o f)(x) = 2x - 8

(g o f)(3) = 2(3) - 8

Evaluate

(g o f)(3) = -2

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The value of k for which the constant function x(t) = k is a solution of the differential equation 4t^3(dx/dt) - 6x - 6 = 0 is k = -1.

To find the value of k for which the constant function x(t) = k is a solution of the given differential equation, we substitute x(t) = k into the equation and solve for the value of k that satisfies the equation.

The given differential equation is:

4t^3(dx/dt) - 6x - 6 = 0

Substituting x(t) = k, we have:

4t^3(dk/dt) - 6k - 6 = 0

Since x(t) = k is a constant function, the derivative dx/dt is zero, so dk/dt is also zero. Therefore, we can simplify the equation further:

-6k - 6 = 0

To solve for k, we isolate it on one side of the equation:

-6k = 6

Dividing both sides by -6, we get:

k = -1

Therefore, the value of k for which the constant function x(t) = k is a solution of the differential equation 4t^3(dx/dt) - 6x - 6 = 0 is k = -1.

In summary, by substituting the constant function x(t) = k into the given differential equation and solving for k, we find that the value of k is -1. This means that when x(t) is a constant function equal to -1, it satisfies the differential equation.

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The absolute value of x=5 is 5.

The absolute value of a number is its positive equivalent of the number

For instance, the absolute value of -5 is 5 and the absolute value of 5 is also 5.

Generally, it is denoted by the symbol |x|.

So, we have

The absolute value of x=5

This gives

x = |5|

Evaluate

x = 5

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Answer:

63 degrees

Step-by-step explanation:

Side by side angles, I believe are called supplementary. So, they are equal to 180 when added together. 180-117 is 63.

~theLocoCoco

The Answer is:

63°

Step-by-step explanation:

The angle 117° is the key information. Across the line, the angle 117° is part of the 180° across the line. Angle RMN is equal to 180° - 117° =  63°

The area of the triangular yard is 7000 ft².

The entire area enclosed by three sides of a triangle is the area of it.

Given,

The base of the triangle is 200 feet and the height of the triangle is 70 feet.

Therefore, the area of the triangle

= (1/2) × base of the triangle × height of the triangle =  (1/2) × 200 × 70 ft² = 7000 ft².

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Emma is asking an empirical question so that she she can test her hypothesis

What is a Empirical hypothesis?

Something empirical is something based on real evidence .

Evidence that is verifiable by observation as opposed to something that is true in theory or by some kind of reckoning or logic

A hypothesis is a theory that is put forward for further examination to see if it is correct. It is not a call but it is an explanation that fits the available evidence so , An empirical hypothesis is a theory that is based on real evidence and experience but that has not been proven yet

So, According to the question

Emma wants to know if long distance relationship in college have a greater likelihood of ending than a relationship that are not long distance and for that she creates a questionnaire and the crowds 100 student from our school to complete the questionnaire so she can test her hypothesis

Here, Emma is asking an empirical questions ( question about experience) and will conclude the test based on these 100 students experience and thoughts.

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Answer:

8

Step-by-step explanation:

just take the numerator and thats how many

Option D, which refers to how much you need or get, equals the amount of money paid on July 8 and is $ 1600.

aggregate attempting to calculate the time required, total number or quantity.  The quantity at hand or under consideration is incredibly energetic.  the overall result, importance, or import. Principal, interest, and a third accounting. amounts, amounting, and amounted are word forms. flexible noun The quantity of something is how much there is, how much you have, how much you require, or how much you obtain. He requires that sum of money to get by.

given

Cash paid on July 8 equals ($1,800 - $200)* (1 - 0.02)

$1,568 (Purchase value - value of products returned)* (1 - Discount percentage) ( option c , option d )

Cash paid in August equals Purchase value minus Value of Returned Goods ($1,800 minus $200 = $ 1600). ( Option D )

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Answer: 119 minutes

Step-by-step explanation:

$13608

Amount saved by Bao per month = $179

Amount saved by Bao per month = Ada's savings - 179

Amount saved by Ada = $179 + $145

Amount saved by Ada per month = $324

time = three and a half years

We convert years to months:

12 months = 1 year

time = 3(12) + 1/2(12) = 36 + 6

time = 42 months

Amount Ada saved = $324 × number of months

Amount Ada saved = $324 × 42

Amount Ada saved = $13608

Answer:

• \(x\) = 42°

• \(y\) = 74°  

• \(z\) = 114°

Step-by-step explanation:

To solve these problems, we have to use the triangle sum theorem, which states that "the sum of all the interior angles of a triangle is 180°".

A)

\(x\) + 90° + 48° = 180°

⇒ \(x\)  + 138° = 180°

⇒ \(x\) + 138° - 138° = 180° - 138°      [Subtracting 138° from both sides]

⇒ \(x\) = 42°

B)

The triangle in this question is an isosceles triangle, therefore the two angles at the base of the triangle are equal and have measures of \(y\).

\(y\) + \(y\) + 32° = 180°

⇒ 2\(y\) + 32° = 180°

⇒ 2\(y\) = 180° - 32°

⇒ 2\(y\) = 148°

⇒ \(\frac{2}{2} y\) = \(\frac{148^{\circ}}{2}\)             [Dividing both sides by 2]

⇒ \(y\) = 74°                    

C)

\(z\) + 28° + 38° = 180°

⇒ \(z\) + 66 = 180°

⇒ \(z\)  = 180° - 66°

⇒ \(z\) = 114°

answer:

d). Restaurant 2, because the range of Restaurant 2 is greater

Answer:

m = 6

Step-by-step explanation:

We have the proportion:

12/m = 18/9

To solve for m, we can cross-multiply the terms in the proportion:

12 × 9 = 18 × m

Simplifying both sides of the equation, we get:

108 = 18m

Dividing both sides by 18, we get:m = 6

Therefore, the solution to the proportion 12/m = 18/9 is m = 6.

Answer: m = 6

Step-by-step explanation:

First, we will rewrite this proportion:

     \(\displaystyle \frac{12}{m} =\frac{18}{9}\)

Next, we will cross-multiply:

     12 * 9 = 18 * m

     108 = 18m

Lastly, we will divide both sides of the equation by 18:

     m = 6

We can also solve this proportion another way.

     We know that 18/9 = 2, so 12/m must equal 2 as well.

     12/6 = 2, so m = 6.

Answer:

B (-3 -2)

Step-by-step explanation:

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Answer:4.62x10^13

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Step-by-step explanation:

\(59.094 - 59.09 = 0.004\)

The point (-2, -10) does not lie on the line y = 3x - 3.

The formula for equation of line is expressed as;

y = mx + b

Where m is slope and b is y-intercept.

Given the equation of line in the question:

y = 3x - 3

To check if the point (-2, -10) lies on the line y = 3x - 3, we need to substitute the values of x and y into the equation and see if it is true.

y = 3x - 3

Plug in x = -2 and y = -10

-10 = 3(-2) - 3

Simplify

-10 = -6 - 3

-10 = -9

But we know that -10 ≠ -9, hence, this is not a true statement.

Therefore, the point does not lie on the line.

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Answer:

(1,3)

Step-by-step explanation:

You are at (-3,5).  Ordered pairs are written (x,y)  The x tells you how far right or left you are from the origin (0,0) and the y tells you how high above or below You are from the origin (0,0).

(-3+ 4,5 -2)  We are 3 unit to the right of (0,0) to begin with and the directions tell us to go 4 more units right.  We will now be 1 units to the right of zero.  We started at 5 units above zero, the directions tells us to move two units down.  That would be at 3.

So, our new order pair will be (1.3)

The hands of a clock are perpendicular to each other twice in every 12-hour cycle, once at 3:00 and once at 9:00. Therefore, the petrography contest will be stopped at either 3:00 or 9:00.

To understand why this is the case, we need to consider the angles between the hands of the clock. In a standard clock, the minute hand completes a full revolution (360 degrees) in 60 minutes, while the hour hand completes a full revolution in 12 hours (720 minutes). This means that the minute hand moves 6 degrees every minute (360/60) and the hour hand moves 0.5 degrees every minute (360/720).

When the hands of the clock are perpendicular, the angle between them is 90 degrees. Let x be the number of minutes past some starting time when the hands are perpendicular. At time x, the minute hand will be at x*6 degrees and the hour hand will be at (x/12)*360 + 90 degrees. We want to find the values of x that satisfy the equation (x/12)*360 + 90 - x*6 = 90, which simplifies to x/2 - x/60 = 1. Solving for x, we get x = 30 or x = 360/11, which is approximately 32.73. Since the contest started at 5:00, the two times when the hands are perpendicular to each other fall at 3:00 and 9:00.

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Answer:

18c

= 18(36)

=648

Hope this helps you

Answer:

Part H

How many holes need to be drilled for 36 parts? Show your work.

Step-by-step explanation:

18c

= 18(36)

= 648

Answer:

Your answer is A

Step-By-Step

did it on edge