Given the following square, solve for x.
(7x+13) °

The product of a, b, and c is 27/8.

What is an expression?

In mathematics, an expression is a combination of numbers, symbols, and operators (such as +, -, ×, ÷, and parentheses) that represents a quantity or a mathematical relationship. Expressions can be simple or complex, depending on the number of terms and the complexity of the operations involved.

The given expression is

                                      [tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2} }[/tex]

To simplify the given expression and write it in the form of ax^by^c, we can start by using the properties of exponents and simplifying the numerator and denominator separately:

Numerator: [tex]6x^2y^(-1) = \frac{6x^2}{y}[/tex]

Denominator: [tex]\sqrt[4]{(16x^5y^2)} = (16x^5y^2)^{(1/4)} = 2x^{(5/4)}y^{(1/2)}[/tex]

Putting the simplified numerator and denominator together, we have:

[tex]\frac{6x^2y^{-1}}{\sqrt[4]{16x^5y^2}} = \frac{6x^2}{y} \cdot \frac{1}{2x^{5/4}y^{1/2}} = \frac{3}{\sqrt{2} \cdot x^{3/4}y^{3/2}}[/tex]

Now we can see that the given expression can be written in the form of ax^by^c, where a = 3, b = -3/4, and c = -3/2. Therefore, the product of a, b, and c is:

a * b * c = 3 * (-3/4) * (-3/2) = 27/8.

Hence, the product of a, b, and c is 27/8.

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Note that in order to solve the above, we had to assume a start date for the construction. Hence, by March 2022​, a total number of liters supplied is 3,380,000 liters.

To solve the problem, we need to know how many weekdays are in March 2022. March 2022 has 23 weekdays (31 days - 4 Saturdays - 4 Sundays).

Since the company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays, we can assume an average of 14 water tankers per weekday. Therefore, the total number of water tankers to be supplied on weekdays in March 2022 would be:

14 water tankers/day x 23 weekdays = 322 water tankers

On Saturdays, the company has to supply a minimum of 4 water tankers. Since there are 4 Saturdays in March 2022, the total number of water tankers to be supplied on Saturdays in March 2022 would be:

4 water tankers/day x 4 Saturdays = 16 water tankers

Therefore, the total number of water tankers to be supplied in March 2022 would be:

322 water tankers (weekdays) + 16 water tankers (Saturdays) = 338 water tankers.

Assuming each water tanker carries a load of 10,000 liters, the total volume of water supplied to the construction site in March 2022 would be:

338 water tankers x 10,000 liters/tanker = 3,380,000 liters

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Full Question:

The company has to supply a minimum of 12 water tankers and a maximum of 16 water tankers to the construction site on weekdays except on Saturdays which is limited to the minimum of 4 water tankers a day. Assuming the start month for the construction was February 2022, Calculate the total number of water loads that were supplied to the project on the constitution site by the water tanker in March 2022​

The following statements are true:

A:The car makes a complete revolution in 10 seconds

B:The maximum height of the Ferris wheel is 65 feet

A full rotation or turning around a focal point is referred to as a revolution. Revolution is the act of rotating around a fixed point or axis . Examples of this include the rotation of a planet around its star or a wheel around its axle.

A. The car makes a complete revolution in 10 seconds:

This can be deduced from the fact that the height of the Ferris wheel car returns to 35 feet after 10 seconds, which means that it has completed one full revolution.

B. The maximum height of the Ferris wheel is 65 feet:

This can be seen from the table, where the height of the Ferris wheel car reaches 65 feet at 2.5 seconds and 12.5 seconds.

C. If the car is loaded at 0 seconds, then the people are loaded at the lowest point of the Ferris wheel: This can be seen from the table, where the height of the Ferris wheel car is 35 feet at 0 seconds.

It is not possible to determine the radius of the Ferris wheel based on the given information alone.

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The pattern for the hypotenuse in the Pythagorean spiral is √(a² + b²)

The Pythagorean spiral is formed by drawing squares whose side lengths are given by the Pythagorean triples, which are sets of three positive integers (a, b, c) that satisfy the equation a² + b² = c².

In the Pythagorean spiral, the hypotenuse of each square is the diagonal of the square, which is given by the square root of the sum of the squares of the sides. For a square with side lengths a and b, the hypotenuse (diagonal) is given by:

√(a² + b²)

Since the side lengths of each square in the Pythagorean spiral are given by the Pythagorean triples, the hypotenuse of each square can be calculated using the Pythagorean theorem. Therefore, the pattern for each hypotenuse in the Pythagorean spiral is that it is given by the square root of the sum of the squares of the side lengths, where the side lengths are integers that form a Pythagorean triple.

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Answer:32

Step-by-step explanation: 24 divided by .75=32

Answer:

Step-by-step explanation:

Let me explain step by step:

Determine the common ratio: We see that each term is half the previous term, so the common ratio is 1/2.

Write the formula for the nth term: We can use the formula for an infinite geometric series to find the nth term:

a_n = a_1 * r^(n-1), where a_1 is the first term (60), r is the common ratio (1/2), and n is the term number.

Plug in the values: We want to find the 9th term, so we plug in the values into the formula:

a_9 = 60 * (1/2)^(9-1)

Calculate the expression: We can simplify the expression by using the exponent rule for powers of 1/2:

a_9 = 60 * (1/2)^8

Divide the result by 256: We can simplify the expression further by dividing both sides by 256:

a_9 = 60 * 1/256

a_9 = 60 / 256

Get the final answer: We divide 60 by 256 to get the final answer:

a_9 = 0.234375

So the 9th term of the sequence is approximately 0.234375.

Answer:

[B]. (1,-5)

Step-by-step explanation:

Given:

[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex]

Solve:

[tex]\begin{bmatrix}4x+2y=-6\\ 3x-2y=13\end{bmatrix}[/tex]        Since 2y - 2y = 0 we take that away now we have;

[tex]4x=-6\\3x=13[/tex]        Add 4x + 3x = 7x

[tex]\frac{7x}{7} =\frac{7}{7}[/tex] Divide both sides by 7.

[tex]x=1[/tex]

Now substitute x to find y.

[tex]4(1)+2y=-6[/tex]

[tex]4 + 2y =-6[/tex]  Add 6 to the other side.

[tex]10 = 2y[/tex] Divide both sides by 2.

[tex]\frac{10}{2} =\frac{2y}{2}[/tex]

[tex]y = 5[/tex]

Hence, the answer is [B]. (1,-5)

RevyBreeze

This curve symbolizes the curve of indifference. Those combinations of quantities that the customer considers to be of equal value are connected by a curve on a graph whose axes reflect amounts of two commodities.

It dislikes all product combinations that offer the same level of enjoyment to the consumer. Because each combination provides the same level of enjoyment, the buyer Favours them all equally. The indifference curve therefore gets its name.

An indifference curve is a graphic representation of a collection of products that give consumers comparable levels of satisfaction, leading to their indifference. A consumer or person is indifferent between the two products at every point on the indifference curve because they provide the same kind of benefit.

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To get the cash flows from operating activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.39 billion. Rounding to two decimal places, we get -$1.01 billion).

What is algebraic expression ?

An algebraic expression is a combination of variables, numbers, and mathematical operations, such as addition, subtraction, multiplication, and division. It can be used to represent a mathematical relationship or formula and can be simplified or evaluated using algebraic rules.

The change in total cash of Rectangle is $0.02 billion (3.59 - 0.59 - 4.18 = -0.98, which is rounded to -$1.00 billion, and then added to the beginning cash amount of $0.69 billion to get $0.69 - $1.00 = -$0.31 billion or -$0.31/100 = -$0.02 billion).

The ending cash amount of Circle is $0.72 billion (1.39 - 0.29 - 1.38 = -0.28, which is added to the beginning cash amount of $0.69 billion to get $0.41 billion or $0.41/100 = $0.72 billion).

The amount of cash flows from financing activities of Pentagon is -$0.55 billion (the change in total cash of $0.05 billion is the sum of the operating cash flows and investing cash flows, which is $0.08 billion + $0.62 billion = $0.70 billion. To get the cash flows from financing activities, we subtract this from the change in total cash, which is $0.05 billion, to get -$0.65 billion. Rounding to two decimal places, we get -$0.55 billion).

The amount of cash flows from investing activities of Square is -$0.40 billion (the change in total cash of $0.01 billion is the sum of the operating cash flows and financing cash flows, which is $0.59 billion + $0.41 billion = $1.00 billion. To get the cash flows from investing activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.99 billion. Rounding to two decimal places, we get -$0.40 billion).

The amount of cash flows from operating activities of Hexagon is -$1.01 billion (the change in total cash of $0.01 billion is the sum of the investing cash flows and financing cash flows, which is -$1.40 billion + $1.02 billion = -$0.38 billion.

Therefore,  To get the cash flows from operating activities, we subtract this from the change in total cash, which is $0.01 billion, to get -$0.39 billion. Rounding to two decimal places, we get -$1.01 billion).

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The measure of a from the triangle ATD is 27 units. Therefore, the option B is the correct answer.

Law of Sines In trigonometry, the law of sines, sine law, sine formula, or sine rule is an equation relating the lengths of the sides of any triangle to the sines of its angles.

The formula for sine rule is sinA/a=sinB/b=sinC/c

From the given triangle ADT, ∠A=46°, ∠D=84°, AT=37, AD=t and TD=a.

By angle sum property,

∠A+∠D+∠T=180°

46°+84°+∠T=180°

130°+∠T=180°

∠T=50°

sin46°/a=sin84°/37=sin50°/t

0.7193/a=0.9945/37=0.7660/t

0.7193/a=0.9945/37

0.9945a=0.7193×37

0.9945a=26.6141

a=26.6141/0.9945

a=26.76

≈27

0.9945/37=0.7660/t

0.9945t=0.7660×37

0.9945t=28.342

t=28.342/0.9945

t=28.5

Therefore, the option B is the correct answer.

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Answer:2304.9

Step-by-step explanation:

Answer:

  2304.9 ft

Step-by-step explanation:

You want the distance from point A, which is 1246 ft horizontally from a lighthouse to point B, given the angles of elevation to the light are 14° and 5° from points A and B, respectively.

The tangent relation for sides in a right triangle is ...

  Tan = Opposite/Adjacent

In a model of this geometry, the height (h) of the lighthouse is the side opposite the angle of elevation. This lets us write two equations:

  tan(14°) = h/1246

  tan(5°) = h/(1246 +d) . . . . . where d is the distance from A to B

Solving these equations for d, we have ...

  h = 1246·tan(14°) = (1246+d)·tan(5°)

  d·tan(5°) = 1246·(tan(14°) -tan(5°))

  d = 1246·(tan(14°)/tan(5°) -1) ≈ 2304.9 . . . . feet

The distance from point A to point B is about 2304.9 feet.

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The numeric value of the exponential function at x = 19.5 is given as follows:

f(19.5) = 178.41.

The standard definition of an exponential function is given as follows:

y = ab^x.

In which:

Considering that f(4.5) = 25 and f(14) = 85, the two equations are given as follows:

Hence:

a = 25b^(-4.5).

Then the value of b is obtained as follows:

25b^(-4.5)b^(14) = 85.

b^(9.5) = 85/25

b = (85/25)^(1/9.5)

b = 1.14.

Then the value of a is obtained as follows:

a = 25 x (1.14)^(-4.5)

a = 13.86.

Then the function is defined as follows:

y = 13.86(1.14)^x.

At x = 19.5, the numeric value is given as follows:

y = 13.86(1.14)^19.5

y = 178.41.

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The  total manufacturing costs for each factory are to be the same is M = 3318.52.

Let's denote the number of pairs of jeans produced at the Medney factory as M, and the number of pairs of jeans produced at the Selbourne factory as S.

Total cost of production at the Medney factory = Total cost of production at the Selbourne factory

28000 + 30M = 35200 + 24S

Total number of pairs of jeans produced = 6000

M + S = 6000

We can solve for M and S by using substitution or elimination. Here, we will use substitution:

M + S = 6000 (from equation 2)

M = 6000 - S (subtracting S from both sides)

28000 + 30M = 35200 + 24S (from equation 1)

Substituting M = 6000 - S:

28000 + 30(6000 - S) = 35200 + 24S

180000 - 30S = 35200 + 24S

180000 = 54S + 35200

54S = 144800

S = 2681.48

So the number of pairs of jeans produced at the Selbourne factory is approximately 2681.48. To find the number of pairs of jeans produced at the Medney factory, we can substitute this value of S back into equation 2:

M + S = 6000

M + 2681.48 = 6000

M = 3318.52

So the number of pairs of jeans produced at the Medney factory is approximately 3318.52.

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The difference between 3.25 and 1.75 is done and marked on the number line as below.

What is meant by a number line?

A number line is a representation of a graduated straight line that is used to represent real numbers visually. It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point. This line is used to compare integers on an endless line that extends on both sides, either horizontally or vertically, at equal intervals.

We are asked to plot the difference between 3 [tex]\frac{1}{4}[/tex] and 1 [tex]\frac{3}{4}[/tex] on the number line.

3 [tex]\frac{1}{4}[/tex] = 3 + 1/4 = 3 + 0.25 = 3.25

1 [tex]\frac{3}{4}[/tex] = 1 + 3/4 = 1 + 0.75 = 1.75

Difference = 3.25 - 1.75 = 1.5 = 1 [tex]\frac{1}{2}[/tex]

This can be shown on the number line below.

Each division has the value of 1/4 = 0.25.

We have marked 3[tex]\frac{1}{4}[/tex]  = 3.25 on the number line.

Since we are subtracting 1 [tex]\frac{3}{4}[/tex] = 1.75 from 3.25, we move 7 divisions backward from 3.25 as 7 * 0.25 = 1.75.

So after moving 7 divisions backwards, we land on 1.5, which is the difference we found earlier.

Therefore the difference between 3.25 and 1.75 is done and marked on the number line as below.

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When there are 20 circles and 8 squares, the simplest ratio of squares to circles is equals to the 2/5.

We have some numbers of circles and squares. The number of circles = 20

The number of squares = 8

Ratio is number which expressed that how many times one number is contains other one. The symolically represention of ratio is "/" or " : ". If a and b are two numbers then "a/b or a : b " represents 'a' ratio 'b'. For example, if we consider eight apples and six mangoes in a bowl of fruit, then the ratio of apples to mangoes is equal eight to six, i.e., 8 : 6 or 4:3. Now, we have to determine the ratio of squares to circles. Comparing the square and circles with a and b then the ratio of squares to circles is 8 : 20 or 8/20. But we want simplfy form of ratio so,

simplfy it by dividing the upper and lower parts of ratio with the common factor of 8, 20 that is 4.

=>( 8/4)/(20/4)

=> 2/5

Hence, required ratio is 2/5.

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The slope and y - intercept are -1/3 and - 8 while the equation of line is

y = -1/3x - 8

Taking two points from the graph attached;

A = (-6, -6)

B = (0, -8)

We can find the slope of the line as;

slope (m) = y₂ - y₁ / x₂ - x₁

m = -8 - (-6) / 0 - (-6)

m = -8 + 6 / 6

m = -2 / 6

m = -1/3

Using the slope and any point, we can find the y - intercept of the graph. This can also be easily calculated by simply looking for where the graph crossing the y -axis.

This point is at -8 and the y - intercept is -8

The equation of the line will be written as y = -1/3x - 8

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Answer: Decreased 40%

Step-by-step explanation:

Alright, we know they reduced $10.00 (25-15)

Now all we have to do is find the percentage, 10 is how much of 25?

10/25 =0.4

(to get 0.4 to a percentage multiply by 100)

The price was decreased by 40%

Step-by-step explanation:

you have to find your five number summary

An area of a rectangle is 32x¹²y⁹ square inches and the length is 8x⁴y³ therefore the expression which represents the width of the rectangle in inches is 4x⁸y⁶.

This is referred to as a quadrilateral with four right angles.

Area of rectangle = Length × width

Width = Area/ Length

       =   32x¹²y⁹  /  8x⁴y³

        = 4x⁸y⁶

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Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.

What is meant by budget?

Let's assume that Hannah needs to use x gallons of soda and y gallons of fruit drink to make 168 gallons of punch.

We know that the cost of soda is $1.57 per gallon and the cost of fruit drink is $2.41 per gallon, and Hannah's budget requires that the punch cost $1.66 per gallon.

So we can set up the following system of equations:

x + y = 168 (total amount of punch)

1.57x + 2.41y = 1.66(168) (total cost of punch)

Simplifying the second equation:

1.57x + 2.41y = 278.88

Now we can use substitution or elimination method to solve for x and y.

Using substitution:

x = 168 - y

1.57(168 - y) + 2.41y = 278.88

264.36 - 1.57y + 2.41y = 278.88

0.84y = 14.52

y = 17.29

So Hannah needs 17.29 gallons of fruit drink.

Using x + y = 168, we can find that she needs 150.71 gallons of soda.

Therefore, Hannah needs 150.71 gallons of soda and 17.29 gallons of fruit drink to make 168 gallons of punch that costs $1.66 per gallon.

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The required measure of the angle x in the given right triangle is 12.38°.

If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.

Here,
Since the question seems to be incomplete the complete question has been attached after the solution.

We have given a triangle where x° is the angle of the right triangle where the hypotenuse is 54 and one legs is 12. With the help of trig ratios
sin x = 12 / 54
x = sin⁻¹(12/54)
x = 12.38°

Thus, the required measure of the angle x in the given right triangle is 12.38°.

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The estimate of the number 7th grader who play in the school band will be 120.

It is important to note that an expression is simply used to show the relationship between the variables that are provided or the data given regarding an information. In this case, it is vital to note that they have at least two terms which have to be related by through an operator.

Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc. The estimate of the number 7th grader who play in the school band will be:

= 60 / 200 × 400

= 120

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Answer:

The coordinates of the remaining vertices are (1, -1) and (3, 1).

Step-by-step explanation:

A square is a quadrilateral with with four sides of equal length. It has two sets of parallel sides and its interior angles are all right angles.  Therefore, each vertex shares its x-coordinate with one adjacent vertex, and its y-coordinate with the other adjacent vertex.

If AC with vertices A(1, 1) and C(3, -1) is the diagonal of a square, the coordinates of the remaining vertices will be:

Answer:

y = 18 + b

Step-by-step explanation:

Add 18 to both sides

y = 18 + b

Answer: 20% of 160 is 32.

Step-by-step explanation:

The percentage is from the word percent which means one part in a hundred. It is a part of the base or the whole determined by the rate. Usually, the percentage is smaller than the base. However, there are also cases where the percentage is greater than the base. This happens when the percent is greater than 100%.

To find the percentage, you have to multiply the base and the rate. The base is the 100% or original amount or the whole while the rate is the ratio of the percentage to the base and it has the percent sign (%). Remember that you have to convert the rate to a decimal number by moving the decimal point twice to the left.

Let us now find the 20% of 160.

20% = 0.2

percentage = 160 × 0.2

= 32

Answer:

he constant of proportionality is $1.80, since for every 3 lemons the total cost increases by $1.80.

The equation that relates the total cost, y, and the number of lemons, x, is:

y = 1.80 * (x/3) + b

where b is the y-intercept, which represents the cost of 0 lemons. We'll need additional information to determine the value of b.

Here is a table with the values of y and x, assuming b = 0:

x (Number of Lemons) y (Total Cost)

0 0

3 1.80

6 3.60

9 5.40

... ...

Step-by-step explanation: