Tamika and her friend sold their old toys at a yard sale earning x dollars. Tamika had to pay her parents back the $25 they gave her for making change. She then divided the rest of the money between her and her friend. What algebraic expression can you write for this scenario? Explain what each term means in regards to this scenario.

The value of the integral can be calculated by using the simple rules of definite integral and double integral.

The first integral is a bit tricky, as the limits of integration are not in the standard order (with respect to x and y). However, we can change the order of integration by switching the limits of integration, so that we can use Fubini's theorem.

The double integral can be solved by converting the rectangular region R into polar coordinates.

The double integral is ∫∫R 5xsin(x+y)dA, R=[0,pi/3]×[0,pi/6]. This can be further solved as

= ∫(0,pi/3) ∫(0,pi/6) 5rrsin(rcos(θ)+rsin(θ))dθ dr

= ∫(0,pi/3) ∫(0,pi/6) 5r^2sin(r(cos(θ)+sin(θ)))dθ dr

= ∫(0,pi/3) 5r^2(-cos(r*(cos(θ)+sin(θ))) | (0,pi/6))dr

= ∫(0,pi/3) 5r^2(-cos(r*(√(2)/2)))dr

= -5/2∫(0,pi/3) r^2cos(r*(√(2)/2))dr

The integral above is not in a closed form but can be evaluated using numerical integration techniques.

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Complete Question:

Calculate the iterated integral. integral_0^3 integral_0^1 5xy Square root x^2 + y^2 dy dx = Calculate the double integral. double integral R 5x sin (x + y) dA, R = [0, pi/3] times [0, pi/6] The value of integral is

The value of a is 3√3/2 and value of b is 3/2. The solution has obtained using the trigonometry formulas.

What is trigonometry?

The study of the right-angle triangle's sides, angles, and connection is the main focus of the field of mathematics known as "trigonometry." Therefore, it helps to find the unknown or missing angles or sides of a right triangle using the trigonometric formulas, functions, or trigonometric identities. The angles in trigonometry can either be expressed in degrees or radians. The most used trigonometric angles for computations include 0, 30, 45, 60, and 90 degrees.

In the figure, we are given that one angle measures 30° and the other measures 90° and the hypotenuse is 3.

So, using trigonometry, we know that

Cos theta = adjacent side/hypotenuse

And, Cos 30° is √3/2

So,

⇒√3/2 = a/3

⇒a= 3√3/2

Sin theta = opposite side/hypotenuse

And, Sin 30° is 1/2

So,

⇒1/2 = b/3

⇒b= 3/2

Hence, the value of a is 3√3/2 and value of b is 3/2.

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Answer: 4/7

Step-by-step explanation:

pretty simple, 1/7 and 3/7 both has a denominator of "7", so the seven stays the same. (While writing this I made a chart to see where I put everything)

Write:

 1/7 = (denominator 7)

+ 3/7 = (denominator 7)

Now we start doing the math, what goes into 7? 7x1 so 1 x 3 = 3

know we go up to the numerator, 7x1=7, so 1 x 1 = 1

add 3 + 1 and that adds up to 4

so your answer is 4/7, hope it helps

Answer:

y = 3x - 6

y = -x+2

Step-by-step explanation:

Answer:

for perimeter add 8 17 15 together that probably not helpful lol

The answer is 2¾. You can also buy calculators that do this for you automatically.

Answer:

Step-by-step explanation:

2 3/4

The width of the flower bed is 3m.

A rectangle is a two-dimensional shape where the length and width are different.

The area of a rectangle is given as:

Area = Length x width

We have,

Rectangular lawn = 8m x 4m

The flower bed dimensions are:

Length = (8m + x)

Width = x

The combined area of lawn and flower bed area = 140 m²

(8 + 2x) x (4 + 2x) = 140

32 + 16x + 8x + 4x² = 140

4x² + 24x + 32 - 140 = 0

4x² + 24x - 108 = 0

4 (x² + 6x - 27) = 0

x² + 6x - 27 = 0

x² + (9 - 3) - 27 = 0

x² + 9x - 3x - 27 = 0

x(x + 9) - 3(x + 9) = 0

(x + 9) (x - 3) = 0

x + 9 = 0

x = -9 (rejected)

x - 3 = 0

x = 3

Thus,

The width of the flower is 3m.

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a. Yes, it is possible for a line (y = mx + b) that passes through the origin (0, 0) to pass through no other rational points. An example of such a line is y = sqrt(2)x. This line passes through the origin (0,0), but the y-coordinate will only be a rational number if the x-coordinate is also a rational number and a perfect square.

b. Yes, it is possible for a line to pass through no rational points. An example of such a line is y = sqrt(2)x + sqrt(3). This line will never pass through any rational points because the y-coordinate will only be a rational number if both x and b are rational numbers and perfect squares, which is not possible in this case.

Answer:

18 sattelites

Step-by-step explanation:

Let's make an equation

n is number of sattelites on Saturn

n-2 is number of sattelites on Jupiter

n-16 is number of sattelites on Mars

Equation would be like:

n+(n-2)+(n-16)=36

3n-18=36

3n=54

n=18

It is a scale factor of 2.

You could see that the JKL triangle has only 4 grids on one side and J'K'L' has 8. So 8/4=2, so, therefore, it is a scale factor of 2. Please correct me if I am wrong.

Answer:

the answer is 54 to the question 5 17 18 -2 23

Answer:

I disagree

Step-by-step explanation:

[tex] \frac{ {2a}^{2} {b}^{2} \times ( - 3 {a}^{2} {b}^{2}) }{6ab \times {9a}^{2} {b}^{2} } \\ \frac{ {2a}^{2} {b}^{2} \times {9a}^{4} {b}^{4} }{6ab \times 9 {a}^{2} {b}^{2} } \\ \frac{18 {a}^{2 + 4} {b}^{2 + 4} }{54 {a}^{2 + 1} {b}^{2 + 1} } \\ \frac{18 {a}^{6} {b}^{6} }{54 {a}^{3} {b}^{3} } \\ \frac{1}{3} {a}^{6 - 3} {b}^{6 - 3} \\ \frac{1}{3} {a}^{3} {b}^{3} [/tex]

Hope this helps

The numeric values for the piece-wise function in this problem are given as follows:

A piece-wise function is a function that has different definitions, depending on the intervals of the input x of the function.

From the image given at the end of the answer, the function has four definitions, depending on the range of x, hence for each numeric value, we have to first identify the range of x for which the input belongs, and then apply the rule.

Hence the numeric values are given as follows:

The problem is given by the image presented at the end of the answer.

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If Loretta accidentally recorded a deposit of $47.88 as a debit in her register, her check register will differ from the bank statement by $0.

A deposit amount is debited to the check register as an asset, increasing the amount the account holder has in the bank.

It is the bank's responsibility to credit the deposit since it is a liability to them, not an asset.

Under accounting principles, assets are debited while liabilities are credited.  Loretta's debit entry in her register does not constitute an accounting error under the generally-accepted accounting principles.

Thus, Loretta has not committed an accounting error by recording a deposit of $47.88 as a debit in her register, and her register will not differ from the bank statement for this reason.

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Yes, the statement is a tautology

Tautology is a compound proposition that is always true for all possible truth values of its variable. A tautology has only T in the last column of its truth table.

Truth table for p v ~p

p  ..... ~p  ..... p v ~p

T         F         T

T         F         T

F         T         T

F         T         T

Since the last column of the truth contains only T, the statement is a tautology

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Answer:

  B, C

Step-by-step explanation:

You want to graph the inequalities y≤1/4x+3 and y≥-x+2 and identify points that are solutions to the system.

The graph is attached. It matches selection B of the graphs you are shown. The points that lie in the solution area are B(2, 1) and C(3, 3).

A polygon will map to itself after a rotation of a 60° would be a regular hexagon.

What is a polygon?

A polygon is a closed, two-dimensional geometric shape that is defined by a set of straight lines, called its sides, that are connected end-to-end. The number of sides in a polygon is referred to as its "order" or "degree"

A polygon that maps to itself after a rotation of 60 degrees is called a regular hexagon. A regular hexagon is a polygon with six sides of equal length and six angles of equal measure (120 degrees each).

To sketch a regular hexagon, you can start by drawing a dot in the middle of a piece of paper. From there, use a compass or a straightedge to draw a circle around the dot. Then, use the compass to draw six lines from the center of the circle to the edge of the circle, each line being 60 degrees apart from the other. Finally, connect the endpoints of each line to form a six-sided polygon.

Hence, a polygon will map to itself after a rotation of a 60° would be a regular hexagon.

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The new point that will be formed when the point (-4,5) is rotated 270 degrees counterclockwise is; (5, 4)

There are different types of transformations namely dilation, rotation, reflection e.t.c

Now, when we rotate a point 270 degrees counterclockwise about the origin our point A(x,y) becomes A'(y,-x). This means that we switch x and y and make x negative.

Now, we are told that the point (-4,5) is rotated 270 degrees counterclockwise. Thus, following the transformation rule as described above gives us;

(-4,5) → (5, 4)

Thus, we conclude that the new coordinate we will obtain in this process is (5, 4)

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Part (a)

[tex](CG)(CE)=(CH)(CD)[/tex]

Part (b)

It is possible to find the length of [tex]\overline{DH}[/tex].

[tex](CG)(CG+GE)=(CH)(CH+DH) \\ \\ (3)(3+5)=(2)(2+DH) \\ \\ 24=2(2+DH) \\ \\ 12=2+DH \\ \\ DH=\boxed{10}[/tex]

Answer:

y = 5/6x - 1/12

Step-by-step explanation:

The slope-intercept form is y = mx + b

10x - 12y = 1

We subtracted 10x from both sides

-12y = -10x + 1

Divided by -12 both sides

y = -10/-12x - 1/12

To simplify we can get

y = 5/6x - 1/12

The equation of the line in slope intercept form is y = 1 / 2 x - 3 / 2.

The equation of a line can be represented in slope intercept form as follows:

y = mx + b

where

Let's find the slope of the line using the coordinates.

Therefore, using (-1, -2) and (-5, -4)

Hence, the slope of a line is the change in the dependent variable with respect to the change in the independent variable.

Therefore,

m = -4 + 2 / -5 + 1

m = - 2 / -4

m = 1 / 2

Therefore, let's find the y-intercept using (-1, -2)

y = 1 / 2 x + b

-2 = 1 / 2 (-1) + b

-2 + 1 / 2 = b

- 3 / 2 = b

Therefore, the equation of the line is y = 1 / 2 x - 3 / 2.

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Answer:

[tex]A = 125 \textrm{ yd}^2[/tex]

Step-by-step explanation:

The area of a triangle can be solved for using the formula:

[tex]A_\triangle = \dfrac{1}{2}b h[/tex]

where [tex]b[/tex] is the length of the triangle's base and [tex]h[/tex] is the length of its height (altitude).

Both [tex]b[/tex] and [tex]h[/tex] are given to us for the shown triangle, so all we have to do is plug the given values into the triangle area formula above.

[tex]A = \dfrac{1}{2} \cdot 10 \cdot 25[/tex]

[tex]A = 5 \cdot 25[/tex]

[tex]A = 125 \textrm{ yd}^2[/tex]

Note that the height of the triangle is given on the outline of an auxiliary (dotted) right triangle. This is just to show that the height is in fact an altitude, meaning it is perpendicular to the base, not at the angle of the triangle's other sides.

Answer: Roger should pick Printer B because it prints 2 more pages per minute.

Step-by-step explanation: We are given that printer A prints 33 pages per minute. We have to figure out how many pages printer B prints in a minute.

As shown in the table, in 2 minutes, printer B prints 70 pages, and in 3 minutes it prints 105 pages. We can create a function to model the rate at which printer A prints pages. This is a linear function since for each increase in x, there is a proportional increase in y. This means that if we were to back one minute the printer would print 35 pages since the common difference per minute is 35 pages. The function would therefore be p=35m where m=minutes and p=pages. This means that printer B produces 2 more pages than printer A per minute since 33+2=35.

The statement that complete the proof that quadrilateral EFGH is a square is; A) Line EF, FG, GH, and EH are congruent

The four sides of a square are always congruent to each other which means that they are equal to each other.

Now, we see that;

EF = 3√2

GH = 3√2

FH =3√2

EH = 3√2

Thus, all four sides are equal.

We also see that the slopes that form 90 degrees with each other are perpendicular and as such that is also a requirement for the quadrilateral to be a square.

Thus, we can conclude that all four sides are congruent to each other from the evidence above.

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Answer:

Statement 4 of the proof should be:

segment EH is parallel to segment FG

Step-by-step explanation:

They have the same slope which is -1.

The measure of the tan of the angle T is 3.4286

From the question, we have the following parameters that can be used in our computation:

Opposite = RS

Hypotenuse = 50

Adjacent = 14

The opposite of the angle T can be calculated as

Hypotenuse² = Opposite² + Adjacent²

Substitute the known values in the above equation, so, we have the following representation

50² = RS² + 14²

Evaluate the like terms

RS² = 2304

Take the square root of both sides

RS² = 48

The measure of the tan of the angle T is then calculated as

tan(T) = RS/Adjacent

Substitute the known values in the above equation, so, we have the following representation

tan(T) = 48/14

Evaluate

tan(T) = 3.4286

Hence, the value is 3.4286

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Answer:

2 times the cost

Step-by-step explanation:

1 persona 1 costs

2 persons, double the cost