Rewrite each expression such that the argument x is positive. a. cot(−x)cos(−x) sin(−x)

Answer:

1. AC is perpendicular to BD

1. Given

2. ACB is a right angle

2. Definition of perpendicular lines

3. Triangle ACB is a right triangle

3. Definition of right triangles

4. Angles 1 and 3 are complementary

4. Interior angles of a triangle add up to 180 degrees (Triangle Interior Angle Sum Theorem), and m<ACB = 90 degrees (definition of right angles), so m<1 + m<3 = 90 degrees (subtraction property of equality). By the definition of complementary angles, angles 1 and 3 are complementary.

Rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.

To find the rejected masses:

Therefore, rejected masses x are those that weigh less than 9.02 oz or more than 9.48 oz.

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The correct question is given below:

A company did a quality check on all the packs of trail mix it manufactured. each pack of trail mix is targeted to weigh 9.25 oz. a pack must weigh within 0.23 oz of the target weight to be accepted. what is the range of rejected masses, ×, for the manufactured trail mixes?

Answer:  25 pounds

Step-by-step explanation: 100% - 20% = 80%

20 divided by 80% = 25

From the graph, the equation of f(x) + g(x) is f(x) + g(x) = 2x + 3

The functions are given as:

f(x) = x + 3

g(x) = x

From the above functions, we can see that the function g(x) is the parent function of a linear function.

When the parent function of a linear function is added to another function to form a composite function, the new function would pass through the following points

(x, y)= (0, b) and (-b, -b)

Where b is the y-intercept of the other function

i.e b = 3 from f(x) = x + 3

So, we have the following points

(0, 3) and (-3, -3)

Next, we draw the points and we connect the points

When the equation of f(x) + g(x) is calculated, we have

f(x) + g(x) = 2x + 3

See attachment for the graph of the functions

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Answer:

10724.29

Step-by-step explanation:

mean means average

so to find an average you add everything together then divide it by the amount of variables

m = (10150 + 10211 + 10424 + 10769 + 10884 + 11155 + 11477)/7

m = 75070/7

m = 10724.2857143

m = 10724.29

Flux is zero since asked in [tex]\pi[/tex] is [tex]0\pi[/tex].

Flux is the presence of a pressure field in a detailed physical medium or the glide of electricity through a surface. In electronics, the term applies to any electrostatic field and any magnetic subject. Flux is depicted as "traces" in a plane that contains or intersects electric powered fee poles or magnetic poles.

The definition of flux is a flow of liquid from the body, or a regular movement or exchange. An instance of flux is diarrhea. An example of flux is an ever-converting list of the responsibilities of a particular process. regular or frequent alternate; fluctuation.

Flux is a go-platform computer program that adjusts a show's color temperature in keeping with vicinity and time of day, offering practical respite for the eyes. the program is designed to reduce eye stress at some stage in night-time use, supporting reducing the disruption of sleep patterns.

Our field is IR^3 be,

F= (bz-cy,cx-az,ay-bx)

Now divergence theorem says that Flux can be calculated by

[tex]\int\limits^ {} \, F.n = \int\limits^ {} \,( c.F) dv[/tex]

Now let's calculate the divergence of a vector field

F = (ia/ax + ja/ay + k*a/az)*((bz-cy)i+((x-dz))+(ay-bx)*k)

a/ax(bz-cy)+a/ay(cx-az)+a/az(ay-bx)

= 0+0+0

=0

Flux is zero since asked in [tex]\pi[/tex] is [tex]0\pi[/tex].

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The surface area of the rectangular prism is 2(lw + wh + lh). A rectangular prism has six rectangular faces.

The area of a rectangle with length and width is

Area = length × width

I.e., A = l × w sq. units

A rectangular prism has six rectangular faces and the length 'l', width 'w', and height 'h'.

So, the areas of each face are as follows:

A(R1) = l × w

A(R2) = l × h

A(R3) = w × h

A(R4) = l × w

A(R5) = l × h

A(R6) = w × h

Thus, the area of the prism = sum of areas of all the faces

⇒ Area of the prism = lw + lh + wh + lw + lh + wh

⇒ A = 2lw + 2lh + 2wh

⇒ A = 2(lw + lh + wh)

Therefore, the area of the rectangular prism is A = 2(lw + lh + wh).

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Answer:

1. BD bisects <CBE, AE || BD (Given)

2. <EBD ~= <CBD (Definition of < Bisectors)

3. <AEB ~= <EBD (Alternate Interior Angles Theorem)

4. <CAE ~= <CBD (Corresponding Angles Postulate)

5. <CAE ~= <AEB (Transitive Property of Congruence)

6. AB ~= BE (Converse of Isosceles Triangles Theorem)

Step-by-step explanation:

i)I=PRT/100

I=1800*12*1/100

I=$216

ii) amount to be paid =1800+216

=$2016

iii) monthly installments=2016/12

=$168

b)I=PRT/100

I=

If a trader took a loan of 1,800.00 at an interest of 12 percent per annum

a.  Interest on the loan is $216.

Amount to be paid at the end of the year is $2016

Monthly Installment is $168

b. She took  $2184 to the nearest dollar.

a) i) Interest on the loan:

Interest = Principal × Rate × Time

Interest = $1800 × 0.12 × 1

Interest = $216

ii) Amount to be paid at the end of the year:

Amount = Principal + Interest

Amount = $1800 + $216

Amount = $2016

iii) Monthly installment:

Number of monthly installments = 12

Monthly Installment = Total Amount / Number of Installments

Monthly Installment = $2016 / 12

Monthly Installment ≈ $168

b) Let's X represent the amount she took

Total Payment = Monthly Installment × Number of Months

Total Payment = $200 × 12

Total Payment = $2400

So

Total Payment = X + $216

$2400 = X + $216

Subtract $216 from both sides:

$2400 - $216 = X

$2184 = X

Therefore she took approximately $2184 to the nearest dollar.

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First you have to figure out the side length of the triangle.

sin(60)= X/8

Let's call x the side length.

8 sin(60)=X

X=6.93

The multiply it by 4

The area is 27.72

Answer:

x1 = 5-3squareroot 5/2 x2= -5+3 squareroot 5 / 2

Step-by-step explanation:

Answer: [tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]

Step-by-step explanation:

Given information

[tex](x_1,~y_1)=(6,~-7)[/tex]

[tex](x_2,~y_2)=(4,~3)[/tex]

Given the midpoint formula

[tex]Midpoint=(\dfrac{x_1+x_2}{2} ,~\dfrac{y_1+y_2}{2} )[/tex]

Substitute values into the given formula

[tex]Midpoint=(\dfrac{(6)+(4)}{2} ,~\dfrac{(-7)+(3)}{2} )[/tex]

Simplify values on the numerator

[tex]Midpoint=(\dfrac{10}{2} ,~\dfrac{-4}{2} )[/tex]

Simplify the fractions

[tex]\Large\boxed{Midpoint=(5,~-2 )}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer: x = 4

Step-by-step explanation:

Given equation

4x - 20 = -x

Add x on both sides

4x - 20 + x = -x + x

5x - 20 = 0

Add 20 on both sides

5x - 20 + 20 = 0 + 20

5x = 20

Divide 5 on both sides

5x / 5 = 20 / 5

[tex]\Large\boxed{x=4}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

Multiply both sides of the first equation by 2.

Multiply both sides of the second equation by 3.

Step-by-step explanation:

The y terms are

-3y

2y

The LCM of 2 and 3 is 6.

We need the y terms to add to zero.

Multiply both sides of the first equation by 2 to get -6y.

Multiply both sides of the second equation by 3 to get 6y.

Then -6y + 6y = 0 eliminating the y terms after adding the equations.

Answer:

4368 ways

Step-by-step explanation:

Use nCk for this. 16C5. This is [tex]\frac{n!}{(n-k)!(k!)}[/tex]. This becomes[tex]\frac{16!}{(11!)(5!)}[/tex]. This is [tex]\frac{16*15*14*13*12}{5*4*3*2*1}[/tex] due to 16! and 5! canceling out. This becomes 4368.

Answer:

  (c)  40.5 square units

Step-by-step explanation:

Assuming the kite is oriented so its diagonals are parallel to the sides of the square, each diagonal is 9 units long. The area of the kite is given by an appropriate formula.

A kite is a parallelogram with two pairs of adjacent congruent sides. Its diagonals meet at right angles. One diagonal bisects the other.

The formula for the area of a kite is ...

   A = 1/2(d1)(d2) . . . . . where d1 and d2 are the lengths of the diagonals

In this problem, the inscribed kite has congruent diagonals, both of length 9 units.

The area of the kite is ...

  A = 1/2(9)(9) = 81/2 = 40.5 . . . . square units

The arrow hits the top of a 3 meters tall wigwam at 0.054 seconds

The complete question is added as an attachment

The function is given as:

[tex]h(t) = -9.8t^2 + 28t + 1.5[/tex]

Set the height to 3

[tex]-9.8t^2 + 28t + 1.5 = 3[/tex]

Subtract 3 from both sides

[tex]-9.8t^2 + 28t - 1.5 = 0[/tex]

Apply the following quadratic formula

[tex]t = \frac{-b \pm \sqrt{b^2- 4ac}}{2a}[/tex]

So, we have:

[tex]t = \frac{-28 \pm \sqrt{28^2- 4*-9.8*-1.5}}{2*-9.8}[/tex]

This gives

[tex]t = \frac{-28 \pm \sqrt{725.2}}{-19.6}[/tex]

This gives

[tex]t = \frac{-28 \pm 26.93}{-19.6}[/tex]

Expand

[tex]t = \frac{-28 + 26.93}{-19.6}[/tex] and [tex]t = \frac{-28 - 26.93}{-19.6}[/tex]

This gives

t = 0.054 and t = 2.80

0.054 is less than 2.80

This means that the arrow hits the top of a 3 meter tall wigwam at 0.054 seconds

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The correct option is D.

An equation to determine the area, a, of the patio that will be painted :

a = (x + 25)(x + 15) - 30

Geometric shapes are the mathematical figures that show how ordinary objects in our world are shaped. Shapes in geometry are the configurations of things with boundary lines, angles, and surfaces.

Length of the rectangular patio is (x+25).

Width of the rectangular patio is (x+15).

Length of bench is 5.

Width of the bench is 1.

Area of a rectangle is:

A = Length x Width

Area of rectangular patio is:

A[tex]_1[/tex] = (x + 25)(x + 15)

Area of bench is:

A[tex]_2[/tex] = 10 x 3

   = 30

The painting area is:

A = A[tex]_1[/tex] - A[tex]_2[/tex]

A = (x + 25)(x + 15) - 30

Therefore, the correct option is D.

An equation to determine the area, a, of the patio that will be painted :

a = (x + 25)(x + 15) - 30

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Answer: b. the two triangles are similar by SAS

Step-by-step explanation:

       These two triangles (ABC and ADE) both share angle A. This means that one angle is congruent.

       Next, we will look at the sides. Triangle ADE has side lengths of 6, 9, and x. Triangle ABC has side lengths of 8+6, 12+9, y. Let us see how these side lengths compare.

[tex]\frac{8+6}{12+9} =\frac{14}{21} =0.6666[/tex]

[tex]\frac{6}{9} = 0.6666[/tex]

       THey are similar. This means the triangles can be prooven similar with SAS.

Step-by-step explanation:

f(a):

   So for this you simply plug in "a" as x, and this doesn't really do anything beside replace all values with x, so you just have the equation:

  [tex]f(a) = 5a+4[/tex]

2 f(a):

   So for this one, you want to represent f(a) using the equation it's equal to (5a + 4), and substitute it in for f(a). In doing so, you get the expression:

   2*f(a) -> 2(5a + 4) -> 10a + 8

f(2a):

   So this is very similar to the first question, although you will have to do some multiplication. So just plug in 2a as "x" to get the equation:

   [tex]f(2a) = 5(2a) + 4 = 10a+4[/tex]

f(a+2):

   Basically the same process, you plug in (a+2) as "x" and simplify:

   [tex]f(a+2) = 5(a+2) + 4\\f(a+2) = 10a+10+4\\f(a+2) = 10a+14[/tex]

f(a) + f(2):

  This is similar to the second question, and you simply want to replace the f(a) with the equation that represents it (5a + 4) and same thing for f(2) = 5(2) + 4

   [tex]f(a) + f(2) = (5a+4)+(5(2)+4) \\f(a) + f(2) = (5a+4)+(10+4)\\f(a)+f(2) = (5a+4) + (14)\\f(a) + f(2) = 5a+18[/tex]

The attached graph represents the graph of the linear equation y = 1000x - 5000 on a scale of 1 to 1000 units on both axes

Linear equations are equations that have constant average rates of change, slope or gradient

The equation of the linear function is given as:

y = 1000x - 5000

The x values are given as:

x = -3 to 8

This means that the domain of the function is [-3, 8] or -3 <= x <= 8

So, we set x = -3 and x = 8, and we calculate the y values.

So, we have:

y = 1000 * -3 - 5000 = -8000

y = 1000 * 8 - 5000 = 3000

So, we draw two points at (-3, -8000) and (8, 3000) and connect the dots

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Answer:

120.

Step-by-step explanation:

That would be factorial 5, written 5!.

That  is 5*4*3*2*1

= 120.

Answer:

120

Step-by-step explanation:

We have 5 digits that can be used to create different 5 digit numbers. We are also not allowed to repeat any numbers. Let's say we have 5 boxes to put the 5 numbers in.

Box 1

Box 2

Box 3

Box 4

Box 5

In the first box, we have 5 different choices. Since we aren't allowed to repeat any digits, the second box only has 4 different choices. And so on...

Box 1 --> 5 choices

Box 2 --> 4 choices

Box 3 --> 3 choices

Box 4 --> 2 choices

Box 5 --> 1 choice

Therefore the amount of 5 digit numbers that can be created is:

[tex]5\times4\times3\times2\times1[/tex] or 5 factorial (a factorial is all the product of all the positive integers equal to and less than the number), which is equivalent to:

120 5-digit numbers

The piecewise function graphed below is given as follows:

A piecewise function is a function that has different definitions, depending on the input.

For x between -4 and -2, inclusive, the function is constant at 3, hence the definition is:

[tex]f(x) = 3, -4 \leq x \leq -2[/tex]

For x greater than -2 until 3, the function is a line with slope 1 and y-intercept 2, hence the definiton is:

[tex]f(x) = x + 2, -2 < x \leq 3[/tex]

For x greater than 3 until 5, the function is constant at -1, hence the definition is:

[tex]f(x) = -1, 3 < x \leq 5[/tex]

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35miles Rick have to run to burn one pound of adipose tissue.

According to the given question.

Rick runs 5miles to burn 500 calories.

⇒ 1 mile burns the amount of calories = 500/5 = 100 calories.

As we know that

1 pound = 3,500 calories.

So the number of miles Rick needed to run to burn 1 pound of adipose tissue = 3500/100 = 35miles

Hence, 35miles Rick have to run to burn one pound of adipose tissue.

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The values of the function if the function f(x) is reflected over y-axis is  g(x) = 10/21x

Reflection is a transformation technique that changes the position of an object on an xy-plane.

If the function f(x) is reflected over y-axis, the resulting function is y = f(-x). Given the following function;

f(x) = -2/7(5/3)x

This can also be written as;

f(x) = -10/21 x

Replace x as -x

f(-x) = -10/21(-x)

f(-x) = g(x) = 10/21x

Hence the values of the function if the function f(x) is reflected over y-axis is  g(x) = 10/21x

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Answer:5.50 a hour

Step-by-step explanation:

Step-by-step explanation:

Transcribed image text: Choosing a Photo Francesca wants to give one of her photographs to a friend as a gift. Help her choose the photograph and determine the style and size of the mat she can afford 1. Describe the design and original dimensions of the photo you chose for Francesca to give as a gift. 2 points: 1 point for describing the photo and 1 point for including the dimensions) Photo description: The photo Shous Francasca and has Friend huagina. Dimensions (including units): The still Photo is a Xg meaning its width is indas and Langth is gind Finding the Total Area of the Photo and Mat 2. Francesca wants to glue her photo on top of a mat that will increase the length of each side. The mat border has a width of x, so the length of each side would increase by 2x inches. Represent the length and width of the mat with an expression. (2 points) Length: Width: 3. The area of the mat is the product of the length and width. Write an expression for area as the product of two binomials. Do not multiply.(1 point)