Pablo bought 5 CDs that were each the same price. Including sales tax, he paid a total of $74.50. Each CD had a tax of $0.80. What was the price of each CD before tax?

Answer:

b

Step-by-step explanation:

The domain and range is ,Range: |x+3|0y|[-2,+] Domain: xR .  

Explanation:

x=R Range: y=(0,+) Domain: y=2

y=x²-4

Range: y'=(x2-4)'=2x x=0,y(0)=02-4=-4 y(-4,+)

y=x²+4x+3

Domain: xR Range: (x2+4x+3)

'=2x+4 ⇒ x=-2,y(-2)=(-2) (-2)

²+4(-2)

+3=4-8+3=-1 \sy∈(-1,+∞)

Domain: x-20x2 x[2,+) Range: y[0,+)

Domain: 4 x 2 0 x 2 4 x 2 2 [-2, +2]

x24y[0,2] range

y=|x+3|-2

Range: |x+3|0y|[-2,+] Domain: xR        

The complete question is,

Determine the graphs' scope and range: y=2x y=x2-4

y=x^2+4x+3

y=sqrt(x-2)

y=sqrt(4-x^2)

y=|x+3|-2 ...?

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The domain and range is ,Range: |x+3|0y|[-2,+] Domain: xR .  

What are the steps to finding an equation's domain and range, We can easily identify the values of the independent variable x and the domain by solving the equation y = f(x). The range may then be found by solving for x. Expressing x as x=g(y) and then determining the domain of g allows us to determine the function's range (y).

The collection of values that can be plugged into a function's domain are called its parameters. The x values for a function like f are contained in this collection (x). The collection of numbers that the function assumes is known as its range.

x=R Range: y=(0,+) Domain: y=2

y=x²-4

Range: y'=(x2-4)'=2x x=0,y(0)=02-4=-4 y(-4,+)

y=x²+4x+3

Domain: xR Range: (x2+4x+3)

'=2x+4 ⇒ x=-2,y(-2)=(-2) (-2)

²+4(-2)

+3=4-8+3=-1 \sy∈(-1,+∞)

Domain: x-20x2 x[2,+) Range: y[0,+)

Domain: 4 x 2 0 x 2 4 x 2 2 [-2, +2]

x24y[0,2] range

y=|x+3|-2

Range: |x+3|0y|[-2,+] Domain: xR        

The complete question is,

Determine the graphs' scope and range: y=2x y=x2-4

y=x^2+4x+3

y=sqrt(x-2)

y=sqrt(4-x^2)

y=|x+3|-2 ...?

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u(x, t) that satisfies this initial-boundary value problem:

u(x,t) = [f(x - at) + f(x + at)]/2

Given the one-dimensional wave equation,

Ut = aʻuzr, where u denotes the position of a vibrating string at the point x at time t > 0.

Assume that the string lies between x = 0 and x = L, we pose the boundary conditions u(0,t) = 0, 4,(L, t) = 0, that is the string is "fixed" at x = 0 and "free" at x = L.

We also assume that the string is set in motion with no initial velocity from the initial position, that is we pose the initial conditions

u(x,0) = f(x), ut(x,0) = 0.

So, the solution of this initial-boundary value problem is,

u(x,t) = [f(x - at) + f(x + at)]/2 + [1/(2a)] ∫(x-at)^(x+at)g(s) ds

Here, g(x) is an arbitrary function that depends on the initial velocity. But here ut(x, 0) = 0. So, g(x) = 0.

Therefore, we get the solution as,u(x,t) = [f(x - at) + f(x + at)]/2

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Given data,We have the following 1-D wave equation Ut = a2uzrWhere, u denotes the position of a vibrating string at the point x at time t > 0.  The string lies between x = 0 and x = L.

And pose ,

the boundary conditions u(0,t) = 0, u(L, t) = 0

initial conditions u(x,0) = f(x),

ut(x,0) = 0.

To find the solution of 1-D wave equation Ut = a2uzr as per the given initial-boundary value problem,We use the method of separation of variables, i.e.,

we assume the solution u(x, t) to be of the form u(x, t) = X(x)T(t).

Let's substitute it in the given equation ,

Ut = a2uzr

=> Xt = a2X''T

=> 1/a2T''/T

= X''/X

= k (say).

By solving above differential equation, we getX(x) = Asin(kx) + Bcos(kx)where A and B are constants.

Let's find the value of k, by applying the boundary conditions at x=0,

X(0) = Asin(0) + Bcos(0) = B = 0

Putting X(L) = Asin(kL) + Bcos(kL) = 0we get, k = nπ/Ln=1,2,3,……..

Let's substitute this value of k in X(x),Xn(x) = Asin(nπx/L)Also, substituting k in

T''/T = k/a2, we get T(t) = C1 cos(ωnt) + C2 sin(ωnt),

where ωn = anπ/L.

Let's substitute these values of Xn(x) and Tn(t) in u(x,t)u(x,t) = Σ [Ancos(anπt/L) + Bnsin(anπt/L)] sin(nπx/L)

where A_n and B_n are constants and can be determined by applying initial conditions.

So, the solution of the 1-D wave equation as per the given initial-boundary value problem is,

u(x,t) = Σ [Ancos(anπt/L) + Bnsin(anπt/L)] sin(nπx/L)where n = 1,2,3,....

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Answer:

The question is asking for the perimeter. There are three ways to answer this depending on the assumptions though so I'll let you choose.

Assumptions are basically the different scenarios

1st scenario being the trim covers the carpet and the tile, they'd need 48m of trim (12+12+4+8+8+4)

2nd scenario in which the trim covers the carpet but not the tiled area, they'd need 44m of trim (12+12+4+8)

3rd scenario where the trim only covers the the tiled area, 4m of trim

(just 4 since the tile only touches 4m of the wall)

Hope this helps!

Step-by-step explanation:

trim is just the perimeter since it covers the base of the wall

Answer:

4.1

Step-by-step explanation:

You would first subtract 55.50 from 71.90 which leaves you with 16.4,

Then you would divide 16.4 by 4 to find how many gigabytes she could use which gives you 4.1

Hope this helped

Answer:

4.1

Step-by-step explanation:

Answer:

x=9.3

Step-by-step explanation:

use SohCahToa

in this case u use cos

cos(41°)=7/x

x=7/cos(41)

x=9.275090953

x=9.3

Answer:

18.75 meters

Step-by-step explanation:

8.75 + 0.25(40) = 18.75

The scale of the diagram as described in the task content is; 1: 8 where k= 8.

It follows from the task content that the original length of the room in discuss is 8cm. It therefore follows that the length of the room in the scale diagram is 1cm. On this note, the scale of the diagram in discuss is; 1 : 8 as 1cm on the diagram corresponds to 8cm actual length.

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Answer:

The answer to your question is in the file.

Answer:

The answer is B

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

let width be x

and because length is 11 times more than the width, therefore length equals to 11x

hence the equation equals to

area = length x width

60 = 11x + x

60 = 12x

x = 60/12

therefore, the width of the rectangle is 5

Answer:

I cannot see the picture

Step-by-step explanation:

The structure of the coordinates associated with specific radian measurements on the unit circle follows a distinct pattern. The x and y coordinates represents the cosine and sine values of the angle, respectively.

The unit circle is a circle with a radius of 1 unit, centered at the origin of a Cartesian coordinate system.

It is commonly used in trigonometry to relate angles to the coordinates on the circle.

When we measure an angle in radians on the unit circle, we can associate specific coordinates with that angle.

The x-coordinate of a point on the unit circle represents the cosine value of the angle, while the y-coordinate represents the sine value of the angle.

These coordinates follow a pattern based on the radian measurement.

For example, when the angle is 0 radians (or 0 degrees), the corresponding point on the unit circle is (1, 0), where the x-coordinate is 1 (cosine of 0) and the y-coordinate is 0 (sine of 0).

As the angle increases, the coordinates change accordingly. For instance, when the angle is π/2 radians (or 90 degrees), the point on the unit circle is (0, 1), where the x-coordinate is 0 (cosine of π/2) and the y-coordinate is 1 (sine of π/2).

This pattern continues as the angle increases or decreases, and the coordinates on the unit circle change accordingly.

By using trigonometric functions, we can determine the cosine and sine values of any given angle and associate them with the appropriate coordinates on the unit circle.

In summary, the structure of the coordinates associated with specific radian measurements on the unit circle follows a pattern where the x-coordinate represents the cosine value of the angle, and the y-coordinate represents the sine value of the angle.

Together, these coordinates create points on the unit circle that correspond to the given radian measurement.

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Answer:

\(x = 2\)

Step-by-step explanation:

Let's solve your equation step-by-step.

−3x−9=−15

Step 1: Add 9 to both sides.

−3x−9+9=−15+9

−3x=−6

Step 2: Divide both sides by -3.

−3x/−3 = −6/−3

x=2

Answer:

$292.74 :)

Step-by-step explenation

i searchd it

Answer:

m∠1 = 106

Step-by-step explanation:

Given: m∠5 = 106

Vertical angles are congruent

The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent.

Therefore: m∠1 = 106

Step-by-step explanation:

1/2 + 3/4

= 2/4 + 3/4

= 5/4

= 1 and 1/4 miles

Answer:

(0, 50) (25, 57.5) (50, 122.5) (75, 195) (100, 275)

Step-by-step explanation:

We know that he earns 30% percent of the money made on sales, plus $50 a week. We know that he starts off with 50, because that's how much he made by working that week. To figure out how much money he made off of each one, we have to calculate 30% of the sale, and add that to the total amount of money he has made up to that point. I hope this helps :)

Answer:

y=50x(.3)+30

Step-by-step explanation:

You get an average of $50 per week and then work 30 hours per week but the outcome is multiplied by .30 from the sales commision so the answer would be y=50x(.3)+30

Pythagoras theorem is used to find the length of sides in geometry. The number of strips of Balsa wood having length of 13cm is  8 approximately.

Pythagoras theorem states that the square of the hypotenuse in a right angled triangle is equal to the sum of the squares of the remaining two sides.

Given that,

The length of each pole = 100cm.

The distance between the pole = 12cm.

The length of each strip of Balsa wood = 13cm.

The diagram for the given question is as follows,

Apply Pythagoras theorem, h² = p² + b² in the given triangle to find the hypotenuse as,

h² = 100² + 12²

=> h² = 10144

=> h = 100.71

Now, the number of strips of balsa wood is equal to hypotenuse divided by 13 which is given as,

100.71 ÷ 13 = 7.74.

Hence, the number of small strips of Balsa wood is 8 approximately.

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Answer:

$9

Step-by-step explanation:

divide 6/4 to get the price per avacado so its $1.5 per avacado.

multiply 1.5 x 6 = 9

To calculate the area formed by the curve y = x^2 - 9, the x-axis, and the ordinates x = -1 and x = 4, we can use definite integration.

The area can be calculated as the definite integral of the function y = x^2 - 9 over the interval [-1, 4].

∫[-1,4] (x^2 - 9) dx

To find the antiderivative of x^2 - 9, we can apply the power rule of integration:

∫ x^2 dx = (1/3) x^3

∫ -9 dx = -9x

Therefore, the definite integral becomes:

(1/3) x^3 - 9x |[-1, 4]

Now we can evaluate the integral at the upper and lower limits:

[(1/3)(4^3) - 9(4)] - [(1/3)(-1^3) - 9(-1)]

Simplifying further:

[(64/3) - 36] - [(-1/3) + 9]

[(64/3) - (108/3)] - [(-1/3) + (27/3)]

(-44/3) - (26/3) = -70/3

The calculated area formed by the curve y = x^2 - 9, the x-axis, and the ordinates x = -1 and x = 4 is -70/3 square units.

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In the given equation, sin2x cosx + cos2x sinx / (cos2x cosx - sin2x sinx) = 1, we can simplify it using trigonometric identities.

Let's rewrite the equation using the double-angle identities:

\(2sinxcosxcosx + (cos^2x - sin^2x)sinx / (cos^2x cosx - sin^2x sinx) = 1\)

Next, simplify further using the Pythagorean identity:

\(2sinxcosxcosx + cos^2x sinx - sin^3x / (cos^3x - sin^3x) = 1\)

Now, let's factor out sinx from the second term in the numerator:

\(sinx(2cosxcosx + cos^2x - sin^2x) / (cos^3x - sin^3x) = 1\)

Since we're looking for solutions in the interval [0°, 90°], we know that sinx cannot be zero. Therefore, we can divide both sides of the equation by sinx:

\(2cosxcosx + cos^2x - sin^2x / (cos^3x - sin^3x) = 1 / sinx\)

Further simplifying the equation:

\(2cosxcosx + cos^2x - sin^2x = (cos^3x - sin^3x) / sinx\)

Now, we can use the identity \(cos^2x = 1 - sin^2x\) to replace \(cos^2\)x in the equation

\(2cosxcosx + (1 - cos^2x) - sin^2x = (cos^3x - sin^3x) / sinx\)

Simplifying the numerator on the right side:

\(2cosxcosx + 1 - cos^2x - sin^2x = (cos^3x - sin^3x) / sinx\\ cos^2x + sin^2x = 1, \\2cosxcosx + 1 - 1 = (cos^3x - sin^3x) / sinx\\2cosxcosx = (cos^3x - sin^3x) / sinx\)

Next, we can use the identity \(cos^3x - sin^3x = (cosx - sinx)(1 + cosxsinx)\)to simplify the right side of the equation:

\(2cosxcosx = (cosx - sinx)(1 + cosxsinx) / sinx\)

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The number 169 can replace the given symbols.

What is a Quadratic Function?

The quadratic function can represent a quadratic equation in the Standard form: ax²+bx+c=0 where: a, b and c are your respective coefficients. In the quadratic function, the coefficient "a" must be different than zero (a≠0) and the degree of the function must be equal to 2.

For solving a quadratic function you should find the discriminant: Δ=b²-4ac . And after that, you should apply the discriminant in the formula:  \(x=\frac{-b\pm\sqrt{\Delta} }{2a}\).

The question gives the equation 2x²+7x-15=0, and it shows the step by step for finding x.  The symbols ??? represents the discriminant, then you should find the result. See below.

???= (7)²-4*(2)*(-15)

???= 49-8*(-15)

???= 49+120

???= 169

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Answer:

(3,-2)

Step-by-step explanation:

(0,-2)

you move 3 right

you change the x-axis

(3,-2)

Answer:

(3, -2)

There you go!! rlly hope this helps!!

Answer:

It should be (3, 6)

Step-by-step explanation:

(x-3)(x+3)/(x-3) --> (x-3) cancels out because the numerator and the denominator both have it --> the hole would be at x = 3

plug 3 back into the equation --> delete the (x-3) from the equation which will result to (x+3)/0 --> y would be 6 since 3+3=6

The restaurant is using a method called "acceptance sampling" to ensure the quality of the white napkins provided by the laundry.

Acceptance sampling is a statistical quality control technique used to determine whether a batch of products meets a specified quality standard or not. In this case, the restaurant is sampling 10 napkins from each bundle of 100 napkins to check for cleanliness and defects.

By inspecting a sample instead of examining every single napkin, the restaurant can make an informed decision about the quality of the entire bundle without having to inspect every individual napkin. This method allows for efficient quality control while maintaining a reasonable level of confidence in the cleanliness and condition of the napkins.

If the sampled 10 napkins meet the restaurant's quality standard, the entire bundle of 100 napkins is accepted. If any of the sampled napkins are found to be defective, further actions can be taken, such as rejecting the entire bundle or requesting a replacement from the laundry.

Overall, acceptance sampling provides a practical and cost-effective way for the restaurant to ensure the quality of the white napkins received from the laundry.

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