Find the domain and range of the function. f(x)=|2x|-sin x

Answer:

4

Step-by-step explanation:

The value of Side DC is 4.

Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.

We have three similar triangles because each has a right angle and shares an angle.   Let's write the angles in order: opposite to the short leg, long leg, and the hypotenuse.

CAB ≡ BAD ≡ CBD

Or as ratios,

CA:AB:CB = BA:AD:BD = CB:BD:CD

We also know

AC = AD + CD

(AD+CD):AB:CB = BA:AD:BD = CB:BD:CD

(AD+CD)/CB=CB/CD

Let CD = x

(5 +x )/6 = 6/x

(5+x)*x = 6*6

5x + x² = 36

x² + 5x - 36 = 0

x² + 9x -4x -36 = 0

x(x+9 ) -4 (x +9 ) = 0

(x-4)(x+9) = 0

x= 4, -9

We reject the negative root and conclude x=4

Therefore, Side DC is 4.

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Answer:

[tex]\boxed{\text{16 ft}}[/tex]

Step-by-step explanation:

h(x) = -2x² + 4x + 16

At the time the ball is thrown,

x = 0

h(0) = -2 × 0² + 4 × 0 + 16 = [tex]\boxed{ \textbf{16 ft}}[/tex]

Answer:

The height of the ball at the time it is thrown is 16 meters.

Step-by-step explanation:

To find the height of the ball at the time it is thrown, we have that we set the time accordingly. So the height of the ball at the time it is thrown is given by h(0) since the ball was thrown at second 0.

Now that we know the time, which is our x, we set all of our x's to 0.

[tex]h(0)=-2(0)^{2} +4(0)+16[/tex]

Next we solve,

      [tex]=0+0+16[/tex]

      [tex]=16[/tex]

In conclusion, the height of the ball at the time it is thrown is 16 meters.

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[tex] \sqrt{ - 75} = \sqrt{ - 1 \times 75} = \sqrt{ {i}^{2} \times 75 } = 5i \sqrt{3} \\(therefore \: {i}^{2} = - 1)[/tex]

Answer:

[tex]\large\boxed{\sqrt{-75}=5\sqrt3\ i}[/tex]

Step-by-step explanation:

[tex]i=\sqrt{-1}\\\\\sqrt{-75}=\sqrt{(25)(3)(-1)}\qquad\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{25}\cdot\sqrt3\cdot\sqrt{-1}=5\cdot\sqrt3\cdot i=5\sqrt3\ i[/tex]

Hence, the probability that the two coins are of different denomination is:

                            2/3

Let N denote nickel, D denotes dime and Q denotes Quarter.

Now when two coins are drawn one after the other with replacement then the outcomes is given by:

         (N,N)     (N,D)      (N,Q)

         (D,N)     (D,D)      (D,Q)

         (Q,N)     (Q,D)      (Q,Q)  

This means that there are a total of  9 outcomes.

The outcomes such that both the denominations are different i.e. the number of favorable outcomes are:  6

{ (N,D) (N,Q) (D,N) (D,Q) (Q,N) (Q,D) }

The probability that the two coins are of different denomination is:

                             6/9=2/3

Answer:

[tex](1-\sqrt{2})a^2[/tex]

Step-by-step explanation:

Consider irght triangle PRS. By the Pythagorean theorem,

[tex]PS^2=PR^2+RS^2\\ \\PS^2=a^2+a^2\\ \\PS^2=2a^2\\ \\PS=\sqrt{2}a[/tex]

Thus,

[tex]MS=PS-PM=\sqrt{2}a-a=(\sqrt{2}-1)a[/tex]

Consider isosceles triangle MSC. In this triangle

[tex]MS=MC=(\sqrt{2}-1)a.[/tex]

The area of this triangle is

[tex]A_{MSC}=\dfrac{1}{2}MS\cdot MC=\dfrac{1}{2}\cdot (\sqrt{2}-1)a\cdot (\sqrt{2}-1)a=\dfrac{(\sqrt{2}-1)^2a^2}{2}=\dfrac{(3-2\sqrt{2})a^2}{2}[/tex]

Consider right triangle PTS. The area of this triangle is

[tex]A_{PTS}=\dfrac{1}{2}PT\cdot TS=\dfrac{1}{2}a\cdot a=\dfrac{a^2}{2}[/tex]

The area of the quadrilateral PMCT is the difference in area of triangles PTS and MSC:

[tex]A_{PMCT}=\dfrac{(3-2\sqrt{2})a^2}{2}-\dfrac{a^2}{2}=\dfrac{(2-2\sqrt{2})a^2}{2}=(1-\sqrt{2})a^2[/tex]

Answer:

  $4140

Step-by-step explanation:

For each of the amounts, the final balance is ...

  A = P(1 +rt)

Filling in the given numbers, we can add the final balances:

  900(1 + 0.06·4) + 900(1 + 0.06·3) + 900(1 + 0.06·2) + 900(1 + 0.06·1)

  = 900(4 + 0.06(4 +3 +2 +1)) = 900·4.60

  = 4140

The amount withdrawn is $4140.

Final answer:

The practical domain of the function f(x), representing the height of a model rocket after launch, is [0,4], including the launch at time x=0, reaching the maximum height at x=2 seconds, and landing at x=4 seconds.

Explanation:

The practical domain for the function f(x), which represents the height of a model rocket x seconds after launch, refers to the interval of time during which the rocket is in flight. Since the rocket is launched at time x=0, reaches its maximum height at x=2 seconds, and hits the ground at x=4 seconds, the practical domain of f(x) is [0,4].

This domain includes all times from the launch to when the rocket lands, as the function's values will only be meaningful or defined within this interval.

12 is the diameter. We need the circumference which you get by multiplying 12x2 sides which = 24 which is the circumference

Answer:

196

Step-by-step explanation:

Answer:

-2

Step-by-step explanation:

Since it would be immensely helpful to know the equation of this parabola, we need to figure it out before we can continue.  We have the work form of a positive upwards-opening parabola as

[tex]y=a(x-h)^2+k[/tex]

where a is the leading coefficient that determines the steepness of lack thereof of the parabola, x and y are coordinates of a point on the graph, and h and k are the coordinates of the vertex.  We know the vertex: V(-3, -3), and it looks like the graph goes through the point P(-2, -1).  Now we will fill in the work form equation and solve for a:

[tex]-1=a(-2-(-3))^2-3[/tex]

which simplifies a bit to

[tex]-1=a(1)^2-3[/tex]

and

-1 = a(1) - 3.  Therefore, a = 2 and our parabola is

[tex]y=2(x+3)^2-3[/tex]

Now that know the equation, we can find the value of y when x = -3 (which is already given in the vertex) and the value of y when x = -4.  Do this by subbing in the values of x one at a time to find y.  When x = -3, y = -3 so the coordinate of that point (aka the vertex) is (-3, -3).  When x = -4, y = -1 so the coordinate of that point is (-4, -1).  The average rate of change between those 2 points is also the slope of the line between those 2 points, so we will use the slope formula to find it:

[tex]m=\frac{-1-(-3)}{-4-(-3)} =\frac{2}{-1}=-2[/tex]

And there you have it!  I'm very surprised that this question sat unanswered for so very long!  I'm sorry I didn't see it earlier!

Answer: it’s 200ft

Step-by-step explanation:

    A)

No solution--

No solution is obtained when there is a condition such that the equation gives a absurd condition.

Hence we write our equation as:

        2x+9+3x+x=6x+1

 Hence, we have:

          6x+9=6x+1

i.e. we have:   9=1

which is a contradiction.

Hence, we get no solution.

B)

         One solution--

One solution or unique solution is obtained when we obtain a unique value for our given variable.

i.e. if we write our equation as:

             2x+9+3x+x=5x+1

i.e. 6x+9=5x+1

i.e. x= -8

Hence, we get a unique value for x.

C)

            Infinite many solution--

The infinite many solution is where we get a condition such that we could not get a unique value for x but the equation is true.

Hence, we have:

                     2x+9+3x+x=6x+9

i.e.   6x+9=6x+9

as left hand side of equation is equal to right hand side of the equation for every ''x'' Hence, we get infinite many solution.

Answer:

1. 6x+1

2. 5x+1

3. 6x+9

Answer:

D.

Step-by-step explanation:

Lines EG and CD are cut by transversal CF.

By construction, ∠FEG=∠FCD. These two angles are corresponding angles.

Since two corresponding angles are congruent, then lines EG and CD are parallel (by  converse of the corresponding angles postulate).

Converse of the Corresponding Angles Postulate: If the corresponding angles formed by two lines and a transversal are congruent, then lines are parallel.

ANSWER

x+y=1

EXPLANATION

We want to find the equation of line CD which passes through (0, 1) and is parallel to x + y = 3.

In slope intercept form, the given line is

y=-x+3

The slope of this line is m=-1

Line CD also has the same slope

The equation is given by:

y=mx+b

The given point (0,1) means the y-intercept;is b=1

Hence the equation is

y=-x+1

In standard form the equation is:

x+y=1

Answer:

The answer is x + y = 1

Step-by-step explanation:

Given: Line CD passes through (0, 1) and is parallel to x + y = 3.

We know that if two line are parallel then they have equal slopes.

Thus, the slope of line = slope of line x + y = 3

 x + y = 3  when we compare this to the standard linear equation

= 3 - x

y = m x + c  .we get m = -1 .

The slope of CD (m)= -1

Now, the equation of line CD passing through (0,1) is given by :-

( y - 1 ) = m ( x - 0 )

⇒ ( y - 1 ) = ( -1 ) x

⇒ x + y = 1

The equation of line CD = x + y = 1

If you know that [tex]\sin\dfrac\pi3=\dfrac12[/tex], then you know right away

[tex]\tan\left(\sin^{-1}\dfrac12\right)=\tan\dfrac\pi3=\dfrac1{\sqrt}3=\dfrac{\sqrt3}3[/tex]

###

Otherwise, you can derive the same result. Let [tex]\theta=\sin^{-1}\dfrac12[/tex], so that [tex]\sin\theta=\dfrac12[/tex]. [tex]\sin^{-1}[/tex] is bounded, so we know [tex]-\dfrac\pi2\le\theta\le\dfrac\pi2[/tex]. For these values of [tex]\theta[/tex], we always have [tex]\cos\theta\ge0[/tex].

So, recalling the Pythagorean theorem, we find

[tex]\cos^2\theta+\sin^2\theta=1\implies\cos\theta=\sqrt{1-\sin^2\theta}=\sqrt{1-\left(\dfrac12\right)^2}=\dfrac{\sqrt3}2[/tex]

Then

[tex]\tan\theta=\tan\left(\sin^{-1}\dfrac12\right)=\dfrac{\sin\theta}{\cos\theta}=\dfrac{\frac12}{\frac{\sqrt3}2}=\dfrac1{\sqrt3}=\dfrac{\sqrt3}3[/tex]

as expected.

Answer:

c. square root 3/3

Step-by-step explanation:

just did it on edg

Answer:

1. Not Independent

2. Independent

3. Not Independent

4. Independent

Step-by-step explanation:

Independent: An event is independent if the outcome of one event doesn't effect the outcome of the other event.

Not independent : An event is Not independent if the outcome of one event effect the outcome of other event.

1. A jar contains twenty coins. Two coins are picked randomly without replacement.

Not Independent because if coins are not replaced the outcome of next event will be effected.

2. A coin is flipped three times.

Independent because when a coin is flipped once its outcome doesn't effect the outcome of the coin flipped again

3. A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement.

Not Independent because if balls are not replaced the outcome of next event will be effected.

4. A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice.

Independent because when the spinner is spuned once its outcome doesn't effect the outcome of the spinner spun again

The correctcorrect probabilityprobability conditiony for each of the given situation as regards independent or not are;

A) Not Independent

B) Dependent

C) Not Independent

D) Dependent

An independent event is one that doesn't depend on the probability of another one happening while a dependent event is one that depends on the probability of another one happening.

A) A jar contains twenty coins. Two coins are picked randomly without replacement; This is not independent because when we do not replace a selected coin, it affects the outcome of the next choice.

B) A coin is flipped three times; This is dependent because a flip doesn't depend on another flip.

C) A bag contains 5 red balls and 3 green balls. A red ball is chosen followed by a green ball without replacement; This is not independent because when we do not replace a selected ball, it affects the outcome of the next choice.

D) A spinner contains 3 equal sectors labeled A, B and C. The spinner is spun twice; This is independent because spinning doesn't affect the outcome of the next spin.

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Answer:

Option B: y = -2x + 17.

Step-by-step explanation:

Lets calculate values for option B:

x = 2 , y = -4+17 = 13   ( B gives the value 12)

x = 4, y = -8+17 = 9   (10)

x = 5, y = -10+17 = 7  (6)

x = 6, y = -12+17 = 5 (6)

x = 8, y = -16+17 =- 1  (1)

Sum of the differences =  1 + 1 + 1 + 1 = 4.

These values are close to the ones given in the question.

Option A  y = 6, 10, 12, 14, 18 -  some of the values of y are  a lot different than the given values.

Option C:

Working them out we get y =  14, 10, 8, 6, 2. which are not quite as good as Option B values The total difference is 5 compared with 4 for option B.

Option D.

y =  12.4,  9.8, 8.5, 7.2, 4.6 where some of  the differences are large.

Answer:

C) weak negative association

Step-by-step explanation:

As X increases, Y generally decreases.  So this is a negative association.  Because the points are widely scattered, it is also a weak association.  So the answer is C.

the answer is c because the graph is going down

Answer:

Second option

g(x), and the maximum is 5.’

Step-by-step explanation:

In the graph it can easily be seen that the maximum value reached by the function f(x) is y = 3.

Then, the function g (x) is:

[tex]g(x) = 3cos(\frac{1}{4}(x + \frac{1}{3}x)) + 2[/tex]

By definition the function

[tex]y = cos(x)[/tex] reaches its maximum value when x = 0,  [tex]2\pi[/tex],  [tex]4\pi[/tex], ..., [tex]2k\pi[/tex]

So

When [tex](\frac{1}{4}(x + \frac{1}{3}x)) = 0[/tex]  entonces [tex]cos((\frac{1}{4}(x + \frac{1}{3}x)) = 1[/tex].

Thus:

[tex]g(0) = 3(1) + 2\\\\g(0) = 5[/tex].

Therefore the function that has the greatest maximum is g(x) when [tex]g(x) = 5[/tex]

The answer is the second option

Check the picture below.

let's notice that the angle -150° has a reference angle of 30°, so any trigonometric function for either angle will be the same value, however, let's recall that the sine or y-coordinate is negative on the III Quadrant, so sin(-150°) is the same as sin(30°) BUT negative, -sin(30°).

Answer:

C. -sin(30°)

Step-by-step explanation:

180-150=30

-sin(30) = -.5 on calculator j like sin(-150) is

Answer:

6 hazelnut

4 almond

Step-by-step explanation:

Answer:

Samantha should make six hazelnut chocolate boxes and four almond chocolate boxes in order to maximize the number of chocolates she gives to her friends.

Step-by-step explanation: This is the right answer

The probability of rolling a sum of 2 with two dice is 1/36. This is calculated by determining the independent probabilities of rolling 1 on each die and multiplying these probabilities together.

Explanation:

The subject of this question is probability in mathematics, specifically involving the numbers on two rolled dice. The only way two dice (number cubes) can add up to 2 is if both rolled dice shows 1. Each die has 6 sides, so the probability for each dies rolling 1 is 1/6.

The probability of two independent events both occurring is founding by multiplying the probability of each event. As the two dice is rolled independently, the probability of both are showing 1 (and hence their sum is being 2) is (1/6) x (1/6), which simplifies to 1/36. Therefore, the probability that the sum of the numbers rolled on two dice is 2 1/36.

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Answer:

The price of one pound of coffee is 32 pesos

The price of one pound of sugar is 7 pesos

Step-by-step explanation:

The question in English is

6 pounds of coffee and 5 pounds of sugar cost 227 pesos and 5 pounds of coffee and 4 pounds of sugar (at the same prices) cost 188 pesos Find the price of one pound of coffee and one pound of sugar.

Let

x-----> the price of one pound of coffee

y-----> the price of one pound of sugar

we know that

6x+5y=227 -----> equation A

5x+4y=188 ----> equation B

Solve the system of equations by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (32,7)

see the attached figure

therefore

The price of one pound of coffee is 32 pesos

The price of one pound of sugar is 7 pesos

Answer:

The function is f(n) = 10n - 13 ⇒ answer A

Step-by-step explanation:

* Lets revise the arithmetic sequence

- There is a constant difference between each two consecutive

  numbers

- Ex:

# 2  ,  5  ,  8  ,  11  ,  ……………………….

# 5  ,  10  ,  15  ,  20  ,  …………………………

# 12  ,  10  ,  8  ,  6  ,  ……………………………

* General term (nth term) of an Arithmetic sequence:

# U1 = a  ,  U2  = a + d  ,  U3  = a + 2d  ,  U4 = a + 3d  ,  U5 = a + 4d

# Un = a + (n – 1)d, where a is the first term , d is the difference

  between each two consecutive terms, n is the position of the

  term in the sequence

* Now lets solve the problem

- The sequence is -3 , 7 , 17 , 27 , .........

∵ 7 - (-3) = 7 + 3 = 10

∵ 17 - 7 = 10

∵ 27 - 17 = 10

∴ The sequence is arithmetic with constant difference 10

∴ f(n) = a + (n - 1)d

∵ a = -3

∵ d = 10

∴ f(n) = -3 + (n - 1)(10) ⇒ lets simplify it

∴ f(n) = -3 + n(10) + (-1)(10) = -3 + 10n - 10 ⇒ add like terms

∴ f(n) = 10n - 13

* The function is f(n) = 10n - 13

Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.

To determine which function could be used to define and continue the given sequence (-3, 7, 17, 27...), we need to analyze the pattern of differences between consecutive terms and see which option best represents this pattern. The sequence increases by 10 each time, as can be seen from the differences (7 - (-3) = 10, 17 - 7 = 10, 27 - 17 = 10).

Looking at the functions provided:

Therefore, Option A is the correct function to define the sequence. It starts at -3 when n=1 and increases by 10 as n increases, consistently matching the given sequence.

Answer:

Option d.

Amplitude: None

Period: π

Step-by-step explanation:

To quickly solve this problem, we can use a graphing tool or a calculator to plot the equation.

Please see the attached image below, to find more information about the graph

The equation is:

f(t) = 2.5 tan (t)

We can see from the graph that the amplitude goes up to infinity, and the period is equal to π.

Option d.

Amplitude: None

Period: π

The amplitude of the function f(t)=2.5 tan t is 2.5, as it's the coefficient of the tangent function. The period is π, as it's obtained by dividing π by the number multiplying 't', which in this case, is 1.

The function given, f(t)=2.5 tan t, is a trigonometric function, which represents a wave. In the context of a wave represented by a trigonometric function such as this, there are several key components. The two most important for this question are:

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Answer: try A I took the same test earlier

Step-by-step explanation:

Answer:

2nd table

Step-by-step explanation:

Because it’s split into 3 equal sections so each region is one third

Answer:  d) 4/9, 4/9, 1/9

Step-by-step explanation:

Let's look at all of the possible combinations of 1st spin & 2nd spin:

AA        BA         CA

AB        BB         CB

AC        BC         CC

P (X=0): how many times is A not in the combination? 4 out of 9

P (X=1): how many times is A in the combination once? 4 out of 9

P (X=2): how many times is A in the combination twice? 1 out of 9

Answer: OPTION C

Step-by-step explanation:

 Given the equation [tex]\frac{\sqrt{3-2x} }{\sqrt{4x} } =2[/tex], you need to solve for  the variable "x".

First, you need to multiply both sides of the equation by [tex]\sqrt{4x}[/tex]:

[tex](\frac{\sqrt{3-2x}}{\sqrt{4x}})(\sqrt{4x} })=2(\sqrt{4x} })\\\\\sqrt{3-2x}=2\sqrt{4x}[/tex]

Now you need to square both sides of the equation:

[tex](\sqrt{3-2x})^2=(2\sqrt{4x})^2\\\\3-2x=4(4x)\\\\3-2x=16x[/tex]

Subtrac 3 and 16x from both sides:

[tex]3-2x-(3)-(16x)=16x-(3)-(16x)\\\\-18x=-3\\[/tex]

Divide both sides by -18:

[tex]\frac{-18x}{-18}=\frac{-3}{-18}\\\\x=\frac{1}{6}[/tex]

Answer 81x^2 - 4y^2     Note this is the difference of 2 perfect squares

a^2 - b^2 = (a + b)(a - b)

so here we have a = 9x and b = 2y

and our factors are

(9x + 2y)(9x - 2y)

the dimensions are 9x + 2y and 9x - 2y

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Show Work

81x^2 - 4y^2     Note this is the difference of 2 perfect squares

a^2 - b^2 = (a + b)(a - b)

so here we have a = 9x and b = 2y

and our factors are

(9x + 2y)(9x - 2y)

The dimensions of the rectangle with an area of (81x² - 4y²) square units are (9x + 2y) and (9x - 2y) units, as the area expression is a difference of squares that has been factored accordingly.

The area of a rectangle is given by the expression (81x² − 4y²) square units. To determine the dimensions of the rectangle, we need to factor this expression completely.

Therefore, the dimensions of the rectangle can be 9x + 2y and 9x - 2y units.

Answer:

12 pack for $15.00

Step-by-step explanation:

4 pack for $7.00:  7 ÷4  = 1.75

6 pack for $10.25:  10.25 ÷6 ≈ 1.71

10 pack for $13.00:  13 ÷10  = 1.30

12 pack for $15.00:  15.00 ÷12 = 1.25

25 pack for $32.50:  32.50 ÷25 = 1.30