On which interval are both the sine and cosine functions increasing?

A (3pi/2, 2pi)
B (pi/2, pi)
C (0, pi)
D (pi, 3pi/2)

While an absolute value may be any number, the output from an absolute value expression is always greater than or equal to zero

The absolute value | x | of a real number x is defined as the non-negative value of x without regard to its sign. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero along real number line.

The absolute value of any number is seen to be always greater than or equal to zero. Both a number and its opposite are the same distance from zero on the number line. Since they have the same distance from zero, they have the same absolute value.

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Answer:

3

Step-by-step explanation:

4.5x 2 = 9

\(\sqrt{9}\)= 3

The angle m∠J  in the right angle triangle is 58.1 degrees.

One of the angle of a right tangle triangle is 90 degrees. The sum of

angles in a triangle is 180 degrees.

Therefore, the side length LK can be found using Pythagoras's theorem and the angle can be found using trigonometric ratios.

Hence,

tan ∠J = opposite / adjacent

tan ∠J = 15.1 / 9.4

∠J = tan⁻¹ 1.60638297872

∠J = 58.0909229196

Therefore,

m∠J = 58.1 degrees

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3.1.1 The basic property of operations used is the commutative property of multiplication.

3.1.2 The basic property of operations used is the additive inverse property.

3.1.3 The basic property of operations used is the associative property of addition.

3.1.1 The basic property of operations used in this calculation is the commutative property of multiplication. It states that the order of the factors in a multiplication problem can be rearranged without changing the product. In this case, the numbers 25 and 4 were swapped, resulting in the same product of 100.

3.1.2 The basic property of operations used in this calculation is the additive inverse property. It states that for any number, there exists an additive inverse such that when the number and its additive inverse are added together, the result is zero. In this case, adding 412 and its additive inverse (-412) results in zero.

3.1.3 The basic property of operations used in this calculation is the associative property of addition. It states that the grouping of numbers being added does not affect the sum. In this case, the numbers 25, 37, 20, 5, 30, and 7 were regrouped to facilitate easier mental addition. By grouping 25 and 37, and then grouping 20, 5, 30, and 7, the final sum of 62 is obtained, which is the same as adding all the numbers together in the original order.

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Answer:

y = 5^(x+1)

Step-by-step explanation:

y = 5^(x+1)

x = 1 for the initial step

The total bill after tax is $38.44.

The first step is to determine the total cost of 4 pizzas and 2 orders of breadsticks: (4 x $6.79) + (2 x 2.49) = $32.14

Now, determine the total cost after delivery fee has been added : $3 +  $32.14 =  $35.14

Now determine the total cost after tax : (1.094) x $35.14 = $38.44

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The total bill after tax of 9.4% is $38.44.

It worthy of note that the sales tax of 9.4% is a percentage of the total purchase bills prior to tax computation, it is the tax due on purchases which is an added percentage of the sales price

total cost of 4 pizzas= $6.79 *4

total cost of 4 pizzas=$27.16

total cost of 2 orders of breadsticks=$2.49*2

total cost of 2 orders of breadsticks=$4.98

total cost of purchase prior to adding delivery cost=$27.16+$4.98

total cost of purchase prior to adding delivery cost=$32.14

total cost of purchase after  delivery cost=$32.14+$3

total cost of purchase after  delivery cost=$35.14

total cost inclusive of 9.4% sales tax=$35.14*(1+9.4%)

total cost inclusive of 9.4% sales tax=$35.14*1.094

total cost inclusive of 9.4% sales tax=$38.44

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Answer:

2/35

Step-by-step explanation:

\(\frac{9}{35}-\frac{1}{5}=\frac{9}{35}-\frac{7}{35}=\frac{2}{35}\)

Answer:

one atom of that element

Step-by-step explanation:

For example, F1 means one atom of the element Fluorine

Answer:

They both need to work 3 hours to get the same amount of $14.

Step-by-step explanation:

If you have a graphing calculator handy, just graph the two expressions 3x + 5 and 4x + 2 and look for the point where they intersect. If you don't have a graphing calculator set up the equation 3x + 5 = 4x + 2. Subtract 4x from both sides to get -x + 5 = 2. Then subtract 5 from both sides to get -x = -3. Since x shouldn't be negative, divide both sides by -1. You do this because just like x is 1x, -x is -1x. After dividing, you should get x = 3.

Answer:

The equation would be 2(n+3)-6. So A.

Step-by-step explanation:

It is asking you to subtract first and you cannot do that without  parentheses.

Answer:

First ONE

Step-by-step explanation:

First you are adding 3

n+3

then you mulitply by 2

so, its 2(n+3), you have to put in bracket because you want to do addition first

then you subtract everything by 6

its 2(n+3)-6

Answer:

Step-by-step explanation:

18 * 10 - 8 * 4    (remember pemdas)

180 - 32 =

148 cm²

The vertices of the similar figure that results from the dilation and translation will be A'' = (2a - 1, 2b), B'' = (2c - 1, 2b), C'' = (2c - 1, 2d), and D'' = (2a - 1, 2d).

Assume that the rectangle's four vertices are A, B, C, and D, with the corresponding coordinates being (a, b), (c, b), (c, d), and (a, d).

First, enlarge the rectangle.

We must multiply the coordinates of each vertex by the scale factor of two in order to enlarge the rectangle. We can apply the following formulas because the centre of dilation is at (0, 0):

Old x-coordinate + 2 equals the new x-coordinate

Old y-coordinate + 2 times the new y-coordinate

Therefore, following dilation, the new coordinates for the vertices will be: A' = (2a, 2b)

B' = (2c, 2b)

C' = (2c, 2d)

D' = (2a, 2d)

Translate the Figure in Step 2

The x-coordinate of each vertex must be reduced by one in order to translate the figure one unit to the left. Therefore, following translation, the vertices' new coordinates will be: A' = (2a - 1, 2b)

B'' = (2c - 1, 2b)

C'' = (2c - 1, 2d)

D'' = (2a - 1, 2d)

As a result, A'' = (2a - 1, 2b), B'' = (2c - 1, 2b), C'' = (2c - 1, 2d), and D'' = (2c - 1, 2d) will be the vertices of the similar figure that comes from the dilation and translation. (2a - 1, 2d).

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The following question may be like this:

Suppose he got dilates the rectangle shown below with the center of dilation at 0,0 and a scale factor of 2, and then translates the figure 1 unit to the left. What will be the coordinates of the vertices of the similar figure that results

Here, we want to find the value of x

From the diagram, we have it that the angles 9x, 18 and 90 are on a straight line

Mathematically, the sum of an angles on a straight line is 180

Thus;

Note that the measure of the listed angles is given as follows:

Where the above figure is a regular quadrilateral, the properties are given as follows:

1) Since ∠LKM represents one of the Right Angles, therefore, it is correct to state that m∠KLM is 90°

2) Since ∠LKJ is another Right Angle, and \(\overline{KL}\) ||\(\overline{JM}\),  and  \(\overline{MK}\) is a diagonal cutting across  \(\overline{KL}\) ||\(\overline{JM}\), ∠JKM ≅ ∠LMK

Since ∠JKM = 68°

Thus, ∠LMK = 68°

3) If opposite sides are equal; and

opposite sides are parallel, then the diagonals must bisect each other equally creating triangles that are congruent. Thus, ΔMNL ≅ ΔKNJ.

Given the above, ∠LMK ≅ ∠LJM

since ∠LMK = 68°

m∠LJM = 68°

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Answer: 8/3 or 2 2/3

Answer:

19/100 is in the wrong place. The correct order is

19/100, 0.27, 0.29

Step-by-step explanation:

19/100 = 0.19

0.19 < 0.27 and 0.19 < 0.29

Answer:

\(3\)

Step-by-step explanation:

\(\mathrm{Let\ the\ age\ of\ Sophia\ be\ }x\mathrm{\ and\ age\ of\ Mohal\ be\ }x+2.\\\mathrm{Given,}\\\mathrm{Product\ of\ their\ ages = 15}\\\mathrm{or,\ }x(x+2)=15\\\mathrm{or,\ }x^2+2x=15\\\mathrm{or,\ }x^2+2x-15=0\\\mathrm{or,\ }x^2+5x-3x-15=0\\\mathrm{or,\ }x(x+5)-3(x+5)=0\\\mathrm{or,\ }(x+5)(x-3)=0\\\mathrm{i.e.}\ x=-5\ \mathrm{or}\ 3.\)

\(x=-5\ \mathrm{is\ disgarded\ because\ age\ cannot\ be\ negative.}\\\mathrm{So\ the\ age\ of\ Shopia,\ }x=3\)

The parabola x = √(y - 9) opens upwards.The given parabolic equation is x = √(y - 9). Let's identify the direction of opening of this parabola.The general form of the equation of a parabola is y = a(x - h)² + k.

Comparing this to the given equation, we can see that h = 0 and k = 9. The vertex is therefore (h, k) = (0, 9). Now, let's determine whether the parabola opens upwards or downwards.

If the coefficient of (x - h)² is positive, the parabola opens upwards, and if it's negative, the parabola opens downwards. In this case, since the coefficient of (x - h)² is 1, which is positive, the parabola opens upwards.

Therefore, the parabola x = √(y - 9) opens upwards.

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Answer:

I think it's 6

1) The center of mass of a right-circular cone with a base radius r, height h, and a non-uniform mass density varies as the square of the distance from apex (tip of the cone) is:

ρ(x, y, z) = k × (\(\sqrt{(x^2 + y^2 + z^2)}\))²

where k is a constant of proportionality.

2) The center of gravity of a very thin right-circular conical shell of a base radius R, and height h is: 2h/3

1) Let us assume that m represents the total mass of the right-circular cone.

The center of mass for the x, y, and z-coordinates would be:

x-coordinate:

\(x_{cm}\) = (1/m) × ∫∫∫_V x × ρ(x, y, z) × dV

y-coordinate:

\(y_{cm}\) = (1/m) × ∫∫∫_V y × ρ(x, y, z) × dV

z-coordinate:

\(z_{cm}\) = (1/m) × ∫∫∫_V z × ρ(x, y, z) * dV

where V - the volume of the cone,

ρ(x, y, z) - the mass density function,

Since the mass density varies as the square of the distance from the apex, we have:

ρ(x, y, z) = k × (\(\sqrt{(x^2 + y^2 + z^2)}\))²

where k is a constant of proportionality.

Substituting this into the above equations, we find the center of mass of the cone.

2) Let us assume that x’ be the distance from the vertex of the cone to any point on the axis of the  right-circular conical shell.

Also R be the radius of the base of the  right-circular conical shell and ‘h’ is the height of the  right-circular conical shell.

Let r be the distance of any point on the cone from the axis of the  right-circular conical shell , the distance being measured perpendicular to this axis.

And l is the distance of any point on the  right-circular conical shell directly from the vertex.

r/R = z/h = l / L

Let us assume that σ be the surface density of mass of the cone.

The formule for center of mass of a system is given by,

x=∫z.σ dA / ∫σdA

but dA = 2πr.dl which is an infinitesimal area around the circle.

After solving this expression we get x = 2h/3

Therefore, the center of gravity of a very thin right-circular conical shell of a base radius R, and height h is given by 2h/3

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Answer:

They are collinear if they are on the same line

Answer:

x=pi*n/2+1/2arctan(7/5)

Step-by-step explanation:

5sin(2x)=7cos(2x)

5tan(2x)=7/5

2x=pi*n+arctan(7/5)

x=pi*n/2+1/2arctan(7/5) for n e Z

The mean and standard deviation for each uniform continuous model are (a) 6 and 4 / (2√3) (b) 160 and  (c) 49.5 and  44.5 / (2√3)

For a uniform distribution U(a, b),

Mean (μ) = (a + b) / 2

Standard deviation (σ) = (b - a) / (2√3)

a. U(2, 10)

Mean (μ) = (2 + 10) / 2 = 6

Standard deviation (σ) = (10 - 2) / (2√3) = 4 / (2√3)

b. U(120, 200)

Mean (μ) = (120 + 200) / 2 = 160

Standard deviation (σ) = (200 - 120) / (2√3) = 40 / (2√3)

c. U(5,94)

Mean (μ) = (5 + 94) / 2 = 49.5

Standard deviation (σ) = (94 - 5) / (2√3) = 44.5 / (2√3)

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Answer:

Step-by-step explanation:

sry ion no 11

Answer:

  y = 0

Step-by-step explanation:

You want the horizontal asymptote of y=2x^2/3x^3.

Degree of numerator: 2

Degree of denominator: 3

When the degree of the denominator (3) is greater than the degree of the numerator (2), the horizontal asymptote is ...

  y = 0

__

Additional comment

This reduces to (2/3)(1/x). The value of 1/x approaches zero when the magnitude of x gets large.

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The slope of any line parallel to segment AB is 7/2.

Slope is simply expressed as change in y over the change in x.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ ).

To find the slope of a line parallel to seg,emt AB, we need to use the fact that parallel lines have the same slope.

Segment AB is between point A (3,2) and point B (1,-5),

We find the slope.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ ).

Slope m = ( -5 - 2 )/( 1 - 3 )

Simplify

Slope m = ( -7 )/( -2 )

Slope m = 7/2

Therefore, any line parallel to segment AB will have the same slope of -7/2.

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The rest wavelength of the emission line observed at 2148 nanometers in the galaxy 100 million light-years away is approximately 2103 nanometers.

The rest wavelength of an emission line can be determined by applying the concept of redshift, which is a phenomenon observed in astrophysics where light from distant objects is shifted towards longer wavelengths due to the expansion of the universe.

In this case, the emission line is observed at 2148 nanometers (or 2.148 micrometers) in a galaxy located 100 million light-years away. To calculate the rest wavelength, we need to consider the redshift factor. Redshift, denoted by z, is defined as the observed wavelength divided by the rest wavelength minus 1.

Given that the observed wavelength is 2.148 micrometers and the galaxy is located 100 million light-years away, we need to convert the distance into a redshift factor using the cosmological relationship between redshift and distance. Assuming a standard cosmological model, we can use the Hubble constant to estimate the redshift.

The Hubble constant represents the rate at which the universe is expanding. Taking a typical value of the Hubble constant as 70 kilometers per second per megaparsec, we find that the redshift factor, z, is approximately 0.021.

To determine the rest wavelength, we rearrange the redshift equation as \((observed wavelength) = (1 + z) \times (rest wavelength)\). Substituting the values, we get \((2.148 micrometers) = (1 + 0.021) \times (rest wavelength).\)

Simplifying the equation, we find the rest wavelength to be approximately 2.103 micrometers or 2103 nanometers.

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The  orientation and ratio of the sides of the similar right triangles are  presented as follows;

(a)  ΔZXY ` ΔZYW ~ ΔYXW

(b) ZX/YX =  XY/WX

ZW/ZY =  ZY/ZX

Similar triangles are triangles that have the same shape but may have different  size.

(a) Similar triangles are triangles that have congruent internal angles.

Making use if the angles of the triangle, we get;

∠x ≅ ∠x  (reflexive property of congruency)

∠YZW ≅  ∠YZWX (All 90 degrees angle are congruent)

Therefore; ΔZXY ~ ΔZYW by AA similarity postulate

Similarly; ΔZXY is similar to ΔYXW by AA similarity postulate

The similar triangles are therefore;

(b) The proportion of the corresponding sides of similar triangles are equivalent, and the cosine of an angle in a right  triangle is the ratio of the adjacent side to the hypotenuse side, therefore;

ZX/YX =  XY/WX

The tangent  of an interior angle of a right triangle is the ratio of the opposite side to the adjacent side of the right triangle, therefore;

ZW/ZY =  ZY/ZX

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The solutions of the equation of the graph is -4 and 2.

An placement of values to the uncertainties that establishes the equality in the equation is referred to as a solution. To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself. Particularly but not exclusively for polynomial equations, the solution of an equation is frequently referred to as the equation's root. An equation's solution set is the collection of all possible solutions.

We know that the solution of the equation is determined using the graph by obtaining the point of intersection of the equation.

In the given graph the point of intersection of the two equations are at x = -4 and x = 2.

Hence, the solutions of the equation of the graph is -4 and 2.

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The complete question is:

Answer:

X=5 y=-3

Step-by-step explanation: