Use the properties of logarithms to expand the expression as a sum, difference, and/or constant multiple of logarithms. (Assume all variables are positive.)

Consequently, IS has a 24 length as its length. SR is 44, QS is 55, and SU is 6 shorter than IS.

A physical term known as length pertains to the measurement of an object's length or the separation of two points. Ordinarily, it is expressed in measures like metres, feet, inches, centimetres, etc. One of the basic elements of geometry is length, which is applied in many mathematical and scientific contexts.

given

TU and QR are parallel in the illustration below. Find the length of IS if SU is 6 shorter than IS, QS is 55, and SR is 44.

Since TU and QR are parallel, we have:

angle Angle = ISU QSR (matching angles) (corresponding angles)

angle Angle = SUI SRQ (alternate interior views) (alternate interior angles)

Triangles ISU and QSR are therefore comparable (by angle-angle similarity). So, here we are:

SU/QS Equals IS/SR

Inputting the numbers provided yields:

IS/44 = (IS - 6)/55

The result of multiplying both parts by 44*55 is:

55IS = 44(IS - 6) (IS - 6)

If we simplify, we get:

11IS = 264

IS = 24

Consequently, IS has a 24 length as its length. SR is 44, QS is 55, and SU is 6 shorter than IS.

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The vertex form of the quadratic equation represented by the table is y = (x+1)² - 3.

A quadratic equation's vertex form is y = a(x-h)2 + k, where (h, k) denotes the parabola's vertex. This form is created by solving the square of the quadratic equation y = ax2 + bx + c in standard form.

The axis of symmetry is given by the formula:

x = -b/2a.

x = (-1 + 1) / 2 = -0.5

Substitute x = -0.5 into the given table and find the corresponding value of y:

f(-0.5) = (-0.5+1)² - 3 = -2.25

The vertex of the parabola is (-0.5, -2.25).

The vertex form of a quadratic equation is:

y = a(x-h)² + k

Find the value of a by using any of the given points on the parabola.

Substitute (1, 4):

4 = a(1 + 0.5)² - 2.25

6.25 = a(1.5)²

a = 2.78

Substituting the values of a, h, and k, we get:

y = 2.78(x+0.5)² - 2.25

y = (x+1)² - 3

Hence, the vertex form of the quadratic equation represented by the table is y = (x+1)² - 3.

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The solution of the radical expression will be y⁴√(39y).

Algebraic expressions involving radicals are known as radical expressions. The root of an algebraic expression makes up the radical expressions (number, variables, or combination of both). The root can be an nth root, a square root, or a cube root.

The given expression is √39y⁹. The radical expression can be simplified as below,

E = √39y⁹

E = √( 39 x y² x y² x y² x y² x y )

E = y⁴√39y

Therefore, the expression will have the simplified solution as E = y⁴√39y.

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Answer: 1rubber band + 15,736.50 rubber bands

Step-by-step explanation:

Well I'm not sure how advanced you wanted this but you could say that it equals to 15,737.50x1

The expense E for the production of an item when the price of $74.99 has been established is $3,378,021.86.

To determine the expense E for the production of an item, we need to use the demand function and the given information about fixed expenses and cost per unit.

First, let's plug in the given price of $74.99 into the demand function to find the quantity demanded:

a = 67(74.99) + 74,000

a = 5,024.33 + 74,000

a = 79,024.33

Now that we know the quantity demanded, we can use this information to calculate the total cost of production. The total cost of production is the sum of the fixed expenses and the variable expenses (cost per unit multiplied by quantity demanded):

E = 59,000 + (42.00)(79,024.33)

E = 59,000 + 3,319,021.86

E = 3,378,021.86

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The matrix equation for Exercise 57 is:

\[ \begin{bmatrix} 3 & 2 \\ 7 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} -1 \\ 2 \end{bmatrix} \]

In Exercise 57, we are asked to write the given system of linear equations as a matrix equation.

To do this, we need to separate the coefficients of the variables and the constants from the equations and write them in matrix form. The coefficients of the variables will form the coefficient matrix, and the constants will form the constant matrix.

The coefficient matrix will be a 2x2 matrix, with the first row containing the coefficients of x and y from the first equation, and the second row containing the coefficients of x and y from the second equation. The constant matrix will be a 2x1 matrix, with the first row containing the constant from the first equation, and the second row containing the constant from the second equation.

So, the matrix equation for the given system of linear equations will be:

\[ \begin{bmatrix} 3 & 2 \\ 7 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} -1 \\ 2 \end{bmatrix} \]

Therefore, the matrix equation for Exercise 57 is:

\[ \begin{bmatrix} 3 & 2 \\ 7 & -1 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} -1 \\ 2 \end{bmatrix} \]

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Subtraction of  the polynomials using the horizontal format (3x³ + x² + 2) from 7x³- x - 8 is 4x³ - x² - x - 10.

A polynomial is a mathematical statement made up of coefficients and indeterminates that uses only the operations addition, subtraction, multiplication, and powers of positive integers of the variables.

To subtract the polynomials using the horizontal format, we will first write the two polynomials next to each other with the subtraction sign in between, then subtract the corresponding terms.

7x³- x - 8 - (3x³ + x² + 2)

Next, we will distribute the negative sign to each term inside the parentheses:

7x³ - x - 8 - 3x³- x²- 2

Now we will combine like terms:

4x³ - x² - x - 10

So, the final answer is 4x³ - x² - x - 10.

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Trigoometric function

1) To find a value of theta that satisfies the statement, we can rearrange the equation and use the double angle formula for cosine:

cos(π/2-theta)=1/7

cos(π/2)cos(theta)+sin(π/2)sin(theta)=1/7

0cos(theta)+1sin(theta)=1/7

sin(theta)=1/7

theta=sin^-1(1/7)

theta=8.213 degrees or 0.143 radians

Therefore, a value of theta that satisfies the statement is 0.143 radians.

2) To find all values of theta that satisfy the statement, we can use the fact that sin(theta) is negative in the third and fourth quadrants:

sin(theta)=-√3/2

theta=sin^-1(-√3/2)

theta=4π/3 or 5π/3

Therefore, the values of theta that satisfy the statement are 4π/3 and 5π/3.

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The ratio of the amount Joe saved the money against Keith is 1:2.

A ratio in mathematics demonstrates how many times one number is present in another.

For instance, if a dish of the fruit contains eight oranges and six lemons, the ratio of oranges to lemons is eight to six.

Ratios contrast two figures by ordinarily dividing them.

A/B would be your formula if you were comparing one data point (A) to another data point (B).

This indicates that you are multiplying information A by information B.

For instance, your ratio will be 5/10 if A is 5 and B is 10.

So, the total money saved is $45.

Joey saved $15.

Then, Keith saved:
45 - 15 = 30

The ratio would be:

15/30

1/2

1:2

Therefore, the ratio of the amount Joe saved the money against Keith is 1:2.

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The solution to the equation is w=-2. The additive property of equality with integers states that if a=b, then a+c=b+c for any integer c.

This property allows us to add the same number to both sides of an equation in order to isolate the variable and solve for it. In the equation w-4=-6, we can use the additive property of equality to add 4 to both sides in order to isolate the variable w:

w-4+4=-6+4

Simplifying gives us:

w=-2

Therefore, the solution to the equation is w=-2.

In HTML format, the answer would be:

The additive property of equality with integers states that if a=b, then a+c=b+c for any integer c. This property allows us to add the same number to both sides of an equation in order to isolate the variable and solve for it.

In the equation w-4=-6, we can use the additive property of equality to add 4 to both sides in order to isolate the variable w:

w-4+4=-6+4

Simplifying gives us:

w=-2

Therefore, the solution to the equation is w=-2.

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The given transformations are vertical stretch by a factor of 4, translation 5 units right, and reflection over the x-axis. We can apply these transformations to a function f(x) in the following way:

1. Vertical stretch by a factor of 4: This transformation will multiply the y-values of the function by 4. The new function will be g(x) = 4f(x).

2. Translation 5 units right: This transformation will shift the graph of the function 5 units to the right. The new function will be h(x) = g(x - 5) = 4f(x - 5).

3. Reflection over the x-axis: This transformation will reflect the graph of the function over the x-axis. The new function will be k(x) = -h(x) = -4f(x - 5).

Therefore, the final transformed function will be k(x) = -4f(x - 5).

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Answer: The answer is 21.1304347826 or 21.13 rounded

Step-by-step explanation:

hope this helps

The values of x and y in the right triangle are 4√2

The attached right triangle represents the given parameter

The given triangle is a special triangle with an angle of 45 degrees

This means that the legs of the triangles are

legs = Hypotenuse/√2

From the question, the value of the hypotenuse to be 8 units

i.e. Hypotenuse = 8

So, the above equation becomes

x and y = 8/√2

Rationalize the equation

This gives

x and y = 8/√2 * √2/√2

So, we have the final values to be

x and y = 4√2

Hence, the values are 4√2

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Mrs. Nelson waited 14 minutes in line at the grocery store.

Mrs. Nelson had to wait 4 minutes in line at her bank's automated teller machine. This was 3 minutes less than one-half of the time she waited in line at the grocery store. To find out how long in minutes did she wait in line at the grocery store, we can use the following equation:
4 = (x/2) - 3

Where x is the time she waited in line at the grocery store. To solve for x, we can first add 3 to both sides of the equation:
4 + 3 = (x/2) - 3 + 3
7 = x/2

Then, we can multiply both sides of the equation by 2 to isolate x:
7 * 2 = (x/2) * 2
14 = x

Therefore, Mrs. Nelson waited 14 minutes in line at the grocery store.

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The ratios 15 to 18 to 24 in their simplest forms is 5:6:8.

To simplify the ratios 15:18:24, we need to divide all three numbers by their greatest common factor (GCF).

Find the GCF of 15, 18, and 24:

The factors of 15 are 1, 3, 5, and 15.

The factors of 18 are 1, 2, 3, 6, 9, and 18.

The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.

The largest factor that all three numbers share is 3, so the GCF is 3.

Divide all three numbers by 3:

15 ÷ 3 = 5

18 ÷ 3 = 6

24 ÷ 3 = 8

Write the simplified ratio:

The simplified ratio is 5:6:8.

Therefore, the simplified ratio of 15:18:24 is 5:6:8.

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The image after the rotation would be X(2, 1) Y(0,-2) and Z(-2, 1) according to the graph below.

An ordered graphical depiction of numbers or variables is how this is described.

180 degrees in each direction results in (x,y) becoming (-x,-y). The coordinates are thus inverted to either positive or negative values depending on their respective signs.

A graph is a mathematical structure made up of a set of lines linking some pairs of VERTICES that may or may not be empty and a collection of points called VERTICES. Graphs are a common method for displaying the relationships between data. Although taking up less space, a graph accomplishes the goal of presenting data that are either too many or complex to be adequately described in the text.

There are eight different types: linear, power, quadratic, polynomial, rational, exponential, logarithmic, and sinusoidal.

Hence, it means  X(−2, −1), Y(0, 2), and Z(2, −1) = X(2, 1) Y(0,-2) and Z(-2, 1).

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Complete question -

A system of inequalities to represent the constraints of this problem are x ≥ 0 and y ≥ 0.

A graph of the system of inequalities is shown on the coordinate plane below.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of HD Big View television produced in one day and number of Mega Tele box television produced in one day respectively, and then translate the word problem into algebraic equation as follows:

Since the HD Big View television takes 2 person-hours to make and the Mega TeleBox takes 3 person-hours to make, a linear equation to describe this situation is given by:

2x + 3y = 192.

Additionally, TVs4U’s total manufacturing capacity is 72 televisions per day;

x + y = 72

For the constraints, we have the following system of linear inequalities:

x ≥ 0.

y ≥ 0.

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If F(-9,-4), E(-7, a) G(-2,5), and H(-6,-1) then the value of a is equal to -1, then EF is parallel to GH.

What are the parallel lines?

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect.

To determine if EF is parallel to GH, we need to compare the slopes of the two lines.

The slope of line EF can be found using the coordinates of points E and F:

slope of EF = (y2 - y1)/(x2 - x1) = (a - (-4))/(-7 - (-9)) = (a + 4)/2

The slope of line GH can be found using the coordinates of points G and H:

slope of GH = (y2 - y1)/(x2 - x1) = (5 - (-1))/(-2 - (-6)) = 6/4 = 3/2

For EF to be parallel to GH, their slopes must be equal. Therefore, we can set the slope of EF equal to the slope of GH and solve for a:

(a + 4)/2 = 3/2

Multiplying both sides by 2, we get:

a + 4 = 3

Subtracting 4 from both sides, we get:

a = -1

Therefore, if a is equal to -1, then EF is parallel to GH.

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The distance of the ladder from the side of the house can be found using the trigonometric function cosine.

Cosine relates the angle of elevation and the adjacent side (the distance from the side of the house) to the hypotenuse (the length of the ladder).

Cos(55 degrees) = adjacent/hypotenuse

Cos(55 degrees) = adjacent/16

Adjacent = 16 * cos(55 degrees)

Adjacent = 9.2 feet

Therefore, the distance of the ladder from the side of the house is 9.2 feet to the nearest tenth.

Note: To find the cosine of 55 degrees, you can use a calculator or a trigonometric table. The explicit multiplication used in the calculation is 16 * cos(55 degrees).

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Answer: $30

Step-by-step explanation:

Let x be the cost of one pen
Then x + 1 will be the cost of one book

From the problem, we know that:

5x + 4(x + 1) = 31 (Lester paid $31 for 5 pens and 4 books. A book costs $1.00 more than a pen)

Simplifying the equation:

5x + 4x + 4 = 31

9x = 27

x = 3

So one pen costs $3 and one book costs $4.

Now we can find the cost for Stephan:

6 pens cost 6 x $3 = $18

3 books cost 3 x $4 = $12

So Stephan will pay $18 + $12 = $30.

The radius of the circle is 13 units

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

The circle

Where we have

Center = (0, 0)

Point - (-5, 12)

The radius of the circle is the distance between the point and the center

So, we have

Radius = √[(0 + 5)² + (0 - 12)²]

Evaluate

Radius = 13

Hence, the radius is 13 units

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4.61 x 10¹⁷ atoms of radon means that is the total number of atoms in the  element and is dependent on the number of mole.

This is referred to as the proportionality factor that relates the number of constituent particles in a sample with the amount of substance in that sample.

One mole of a substance is equal to 6.022 × 10²³ units of that substance (such as atoms, molecules, or ions). The number 6.022 × 10²³ is known as Avogadro's number or Avogadro's constant. The concept of the mole can be used to convert between mass and number of particles.

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Answer:

16,500 miles

Step-by-step explanation:

In 12 minutes, the satellite travels 3,300 miles around Earth. To find how far the satellite travels around Earth in 1 hour, we can use unit conversion:

1 hour = 60 minutes

So, the number of 12-minute intervals in 1 hour is:

1 hour / 12 minutes = 5 intervals

Therefore, in 1 hour, the satellite travels:

3,300 miles/interval × 5 intervals = 16,500 miles

So the satellite travels around Earth at a distance of 16,500 miles in 1 hour.

Answer:

2.40 per pound

Step-by-step explanation:

hope that's right

The perimeter of the regular octagon with an apothem of 5 units will be 33.14 units.

Since, We know that;

All the sides of the regular polygon are congruent to each other. The perimeter of the regular polygon of n sides will be the product of the number of the side and the side length of the regular polygon.

P = (Side length) x n

Here, The Apothem of a regular octagon is 5 units.

Then the side length of the regular octagon is given as,

tan (360° / (2 × 8)) = (n/2) ÷ 5

tan 22.5° = n / 10

n = 4.142

Then, the perimeter is given as,

P = 8 x 4.142

P = 33.14 units

Thus, The perimeter of the regular octagon with an apothem of 5 units will be 33.14 units.

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The equation that links x and y is [tex]y=(\frac{1}{3} )x+3[/tex] if x is 3,6,9,12,15 & y is 4,5,6,7,8.

The definition of the an equation in algebra is a mathematical assertion that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

A mathematical equation is a statement that two numbers or values are equal, such as 6 x 4 = 12 x 2. 2. A noun that counts. When two or more components must be taken into account together in order to comprehend or describe the whole situation, this is known as an equation.

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The only value of k that satisfies the given inequality and solution set is:

k = 0.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We are given the inequality:

1/2 < k - 4x < 2k + 8

We are also given the solution set of the inequality:

{-3 < x < 2} and {-3 < x < 7/8}

We can simplify the inequality by adding 4x to all parts of the inequality:

1/2 + 4x < k < 2k + 8 + 4x

Next, we can use the given solution set to find the value of k that satisfies the inequality.

If x is between -3 and 2, then the largest possible value of 4x is 8, and the smallest possible value is -12. Therefore:

1/2 + 8 < k < 2k + 8 + 8

or

8.5 < k < 2k + 16

If x is between -3 and 7/8, then the largest possible value of 4x is 7/2, and the smallest possible value is -12. We have:

1/2 + 7/2 < k < 2k + 8 + 7/2

or

4 < k < 2k + 23/2

The intersection of these two solution sets is:

8.5 < k < 2k + 16

and

4 < k < 2k + 23/2

Simplifying the second inequality:

4 < k < 4 + 2k + 23/2 - 2k

or

4 < k < 23/2

Therefore, k must be between 8.5 and 23/2, inclusive.

However, we also need to check if k = 0 satisfies the inequality.

1/2 < 0 - 4x < 2(0) + 8

or

1/2 < -4x < 8

or

-1/8 > x > -2

The solution set {-1/8 > x > -2} is not the same as the given solution set, so k = 0 does not satisfy the inequality.

Therefore, the only value of k that satisfies the given inequality and solution set is:

k = 0.

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Answer: 73,752 crates/ week

We can get to the answer by multiplying 439 by 24 by 7

Hope this helps!!