a concesquence can be defined as

Answer:

9

Step-by-step explanation:

3(x-5)=12

Use distributive property on with the 3 and parenthesis (3 times x and 3 times -5)

3x-15=12

Add fifteen to both sides (15 on the left side cancels out)

3x=27

Divide both sides by 3 (3 on the left side cancels out)

x=9

The inverse of the function f(x) = 4x is inverse of f(x) = x/4.

A relation between a collection of inputs and outputs is known as a function. A function is a connection between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain.

F(x)= 4x

Let , y=4x

Now we will switch the variables x to y,

x= 4y

Simplify the expression so that y is by itself. And divide each side by 4

x/4= y

or f(x)= x/4.

Therefore, the inverse of the function f(x) = 4x is inverse of f(x) = x/4.

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Answer: 40

Step-by-step explanation:

Answer: 20

Step-by-step explanation:
5x^2

5 ( 2 )^2 (substituting the value of x)

5 ( 2 x 2) (working out the exponents of x)

5 (4) (solving the brackets)

20

Answer:

the height of the goalpost is approximately 10.48 meters.

Step-by-step explanation:

To find the height of the goalpost, Addison needs to use the distance from the mirror to the goalpost, the distance from her eyes to the ground, and the angle formed by the goalpost, the mirror, and her eyes. She can use the law of cosines to solve for the height of the goalpost.

Let "a" be the distance from the goalpost to the mirror, "b" be the distance from the mirror to Addison's eyes, and "c" be the distance from Addison's eyes to the ground.

The law of cosines states that: c^2 = a^2 + b^2 - 2ab * cos(C), where C is the angle formed by the goalpost, the mirror, and Addison's eyes.

In this case, a = 13.25 meters, b = 1.3 meters, and c = 1.55 meters. We can substitute these values into the formula to solve for the angle C:

1.55^2 = 13.25^2 + 1.3^2 - 2 * 13.25 * 1.3 * cos(C)

Solving for cos(C) and using the inverse cosine function (arccos), we find that C = 52.22 degrees.

Now that we know the angle C, we can use the law of sines to solve for the height of the goalpost. The law of sines states that:

sin(C) / a = sin(A) / h, where A is the angle formed by the ground, the mirror, and the goalpost, and h is the height of the goalpost.

In this case, A = 180 - C - 90 = 180 - 52.22 - 90 = 37.78 degrees, and a = 13.25 meters. We can substitute these values into the formula to solve for h:

sin(52.22) / 13.25 = sin(37.78) / h

Solving for h, we find that the height of the goalpost is approximately 10.48 meters.

Therefore, the height of the goalpost is approximately 10.48 meters.

P(tail) = Probability of getting a tail on the coin

P(tail)=1/2

P(4)=Probability of getting the number '4' on the dice.

P(4)=1/6

P(tail and 4)=Probability of getting tail on the coin and number '4' on the dice.

P(tail and 4)=p(tail multiply with 4)

P(tail and 4)= 1/2×1/6

P(trail and 4)=1/12

Hope this helps!

The domain of the function y = √x + 4 is

All of a function's x-values, or inputs, make up the domain, and all of a function's y-values, or outputs, make up the range.

The domain of a function are all possible values that will give output

For the function y = √x + 4

the domain are all positive real numbers which is shown by option C which is 0 ≤ x < ∞

these are numbers from zero to infinity. infinity is denoted by the symbol ∞

Hence the domain is 0 ≤ x < ∞

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As it is given, 1% of left tree is decaying every year.

Number of tree left after 8 years.

A = P{1-R/100}^[tex]^{T}[/tex] = 10M{1-1%/100}^  [tex]^{8}[/tex]

= 10M *(0.99)[tex]^[/tex]^[tex]^{8}[/tex]

= 9227446

If round at hundredth, then,

Number of tree = 9227400.

Identify the asset's cost. Get the asset's total depreciable value by deducting the projected salvage value from the asset's purchase price. Determine the asset's useful life. The annual depreciation amount is obtained by dividing the sum of steps (2) and (3) by the figure determined in steps (3).

Depreciation is the practice of deducting the cost of a company asset over a number of years as opposed to just one. There are four primary ways to depreciate assets: linear, twofold declining, sum of the years' digits, and manufacturing units.

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The firm's profit margin is 4.17%.

To calculate the firm's profit margin, also known as the return on sales, you need to divide the firm's net income by its total sales. In this case, you are given the firm's return on assets (ROA), which is equal to the firm's net income divided by its total assets.

You can use this information to set up the following equation:

ROA = [tex]\frac{net \ income}{total \ assets}[/tex]

Plugging in the given values, you get:

8%= [tex]\frac{net \ income} {5,960,000}[/tex]

Solving for net income, you find that the firm's net income is

8% × 5,960,000 = 476,800.

Now that you know the firm's net income, you can calculate its profit margin by dividing its net income by its total sales. To do this, you need to know the firm's total sales.

You can use the firm's asset turnover ratio, which is equal to its total sales divided by its total assets, to calculate its total sales. In this case, the asset turnover ratio is 1.9, so you can set up the following equation:

asset turnover ratio = [tex]\frac{total \ sales}{total \ assets}[/tex]

Plugging in the given values, you get:

[tex]1.9 =\frac {total \ sales }{5,960,000}[/tex]

Solving for total sales, you find that the firm's total sales are

1.9 × 5,960,000 = 11,444,000.

Now that you know the firm's total sales, you can calculate its profit margin by dividing its net income by its total sales:

[tex]profit \ margin = \frac{net \ income}{total \ sales}[/tex]

[tex]= \frac{476,800}{11,444,000}= 4.17%[/tex]

Therefore, the firm's profit margin is 4.17%.

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Answer:

16

Step-by-step explanation:

4 / 2

2 / 2

1

4 = 2²

16/2

8/2

4/2

2/2

1

16 = 2^4

lowest common denominator = 2^4 = 16

The equation part of the given word problem is x+y=52 and y=x+16.

a) Let x = number of green eyed dolls

And let y = number of blue-eyed dolls

Now we are told the following:

x+y=52 → eq1

and

y=x+16 → eq2

b) substitute y = x+16 from eq2 into eq1:

x+x+16 = 52 subtract 16 from each side

x+x+16-16 = 52-16 collect like terms

2x = 36 divide each side by 2

x = 18 → number of green-eyed dolls

substitute x = 18 into equation2

y = 18+16 =34 → number of blue-eyed dolls

18+34=52

52=52

and

18+16=34

34=34

THIS PROBLEM CAN ALSO BE SOLVED USING ONE EQUATION AND ONE UNKNOWN:

Let x = Number of green-eyed dolls

Then 52-x = Number of blue-eyed dolls

Now we are told that:

x+16 = 52-x add x to and subtract 16 from each side

x+x+16-16 = 52-16-x+x collect like terms

2x=36 → same as before

x = 18.

Hence, the equation part of the given word problem is x+y=52 and

y=x+16.

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Answer:

A.  The graph that Larry created is a correct representation of his company's charges.

Step-by-step explanation:

The equation for the services charges, y, is made up of the $10 initial service call fee plus $5 times the number of hours, x.

y = 5x + 10

Try any 2 values for x to see if they fits the graph.

x(hr)   y($)

0        10

1         15

4        30

This is the line already drawn on the graph.  Larry did everything correctly, so options B, C, and D are all false/incorrect.

The surface area of the triangular prism is1024.99612 cm².

How do you calculate a triangular prism's surface area?

The following formula is used to determine a triangular prism's surface area:

A = 2AB+ (a+b+c) h

AB=s(s﹣a)(s﹣b)(s﹣c)

s=a+b+c / 2

Solving for A

Area = ah+ bh+ ch+ 1/2 √ a⁴+2(ab)²+2(ac)²﹣b⁴+2(bc)²﹣c⁴

= 31*14 + 27*14 +6*14+1/2·﹣√31⁴+2·(31·27)²+2·(31·6)²﹣274+2·(27·6)²﹣64

≈ 1024.99612

Hence, the surface area of the triangular prism is1024.99612 cm².

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If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

A quadrilateral is a closed shape that has four sides, four vertices, and four angles. It's made by connecting four non-collinear points. The sum of quadrilateral interior angles is always 360 degrees. A quadrilateral is a four-sided polygon with four edges and four corners in geometry.

A parallelogram is formed when both pairs of opposite sides of a quadrilateral are congruent. A parallelogram is formed when one pair of opposite sides of a quadrilateral are parallel and congruent.

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The x-coordinate of the point i.e. 3/4 of way from R to S is 3/7, using the segment formula.

What is segment formula ?

Segment formula is the easiest way to find x and y coordinate of a point when ratio of distances over end point is given i.e.:

Let the coordinate of point P(x, y) dividing the line segment joining the points A(x1 , y1) and B(x2 , y2) internally in ratio m1:m2 then

x= [tex]\frac{m1x2+m2x1}{m1+m2}[/tex]

y = [tex]\frac{m1y2 + m2y1}{m1+m2}[/tex]

using given information,

Let R is 1st point and S is 2nd point ,

3/4 is the ratio so,

m1 = 3,

m2 = 4

x1 = -3

x2 = 5

y1 = -3

y2 = 2

Putting values in above formula for x,

we get

x = 3/7

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Answer:

-5/4

Step-by-step explanation:

To find the slope, we have to use this formula:

[tex]\frac{y2-y1}{x2-x1}[/tex]

in this case -2 is your first x

5 would be your first y

2 would be your second x

and 0 is your second y

so:

0 - 5

-------    = -5/4

2 - (-2)

Answer:

20

Step-by-step explanation:

AB = DC = 2 - (-4) = 6

AD = BC = 3 - (-1) = 4

Perimeter =  sum of all sides of the rectangle = AB+DC+AD+BC =

6+6+4+4=20

17  is the value of discriminant for quadratic equation.

What in mathematics is a quadratic equation?

A quadratic equation is a second-order polynomial equation in one variable using the formula x = ax2 + bx + c = 0 and a 0.

                               The fundamental theorem of algebra ensures that it has at least one solution because it is a second-order polynomial problem. Real or complex solutions are also possible.

General form of a quadratic equation is

ax² + bx + c = 0

The Discriminant of the quadratic equation is denoted by D and defined as

D = b² - 4ac

The given Quadratic equation is

√2x² - 5x + √2 = 0

Comparing with the general equation of quadratic equation ax² + bx + c = 0 we get

a = √2 , b = - 5 , c = √2

Value of Discriminant

      = b² - 4ac

      = (-5)² - 4 * √2 * √2

       = 25 - 8

       = 17      

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The next step in construction of an equilateral triangle is;

C. Use a straightedge to draw a diameter of the circle.

An equilateral triangle is defined as a triangle that has its' 3 sides equal and three interior angles equal.

Now, the steps to construct an equilateral triangle by hand are;

1. Place your compass point on a paper and draw a circle, O.

2. Use a straightedge, to draw a diameter of the circle, labeling the endpoints P and B.

3. Without changing the span on the compass, place the compass point on P and draw a full circle.

4. Label the points of intersection of the two circle circumferences with A and C.

5. Draw segments from A to B, B to C and C to A, to form the equilateral triangle.

Thus, we see that after drawing the circle, the next point is to Use a straightedge to draw a diameter of the circle.

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Another name for  equilateral quadrilateral is rhombus since equilateral means that all of its sides are equal in length.

Another name for an equiangular quadrilateral, is a rectangle.

Another name for a regular quadrilateral is a  square, one in which all sides are congruent and all angles are congruent.

Due to the equality of its sides, an equilateral triangle is also known as a regular polygon or regular triangle.

Equiangular simply implies "equal angles." 2. A triangle with acute angles is one in which each of the three internal angles is smaller than 90 degrees.

A quadrilateral is a rhombus if each of its diagonals bisects the vertex angles through which it travels.

∴Another name for  equilateral quadrilateral is rhombus since equilateral means that all of its sides are equal in length.

Another name for an equiangular quadrilateral, is a rectangle.

Another name for a regular quadrilateral is a  square, one in which all sides are congruent and all angles are congruent.

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The difference between the two value is 5.6×10^7

The correct option is option B)

What is subtraction?

An arithmetic operation called subtraction simulates the process of removing items from a collection. The minus sign is used to denote subtraction,

We are given two values (1.2 × 10^8) and (6.4 × 10^7)

We are asked to subtract them.

To subtract them we first match their powers of 10

that is we make the powers equal

We convert both the value in terms of 10^7

We get 12×10^7 and 6.4×10^7

Now we perform the subtraction on both values we get

(12-6.4)×10^7

= 5.6×10^7

Hence, The difference between the two value is 5.6×10^7

The correct option is option B)

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Answer:  10

Step-by-step explanation:

As shown below, ∠ABD = ∠DAC = x.

That means tan(x) = 5 by AD and that tan(x) = AD by 20

You can set those two equations equal to each other to find the length of AD:

5 by AD = AD by 20

5 = AD square by 20

100 = AD square

AD = Square root 100 = 10

Answer:

12

Step-by-step explanation:

let a = AB b=AD c=AC

from the pythagorean theorem:

(1)a² + c² = (16+9)² = 625

(2) b² +16² = a²

(3) 81+ b² = c²

by substitution into (1):

(b²+16²) + (81+b²) = 625

2b² = 625-81-256 = 288

b² = 144

b = 12

The expression evaluates because the variable truck weight's true value is present. The correct answer is (C).

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation. An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles. Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.

Given,

In the following expression, the variable truck weight has the value 70000 and the variable weight limit has the value 80000.truck weight < weight limit.

Expression,

Truck weight < Truck limit

The value of expression evaluate,

It is true.

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Answer:  x=12,-4

Step-by-step explanation:

Answer:  -27≥x  OR  x>7

Step-by-step explanation:

[tex]\displaystyle\\a)\ -7\geq \frac{x}{3}+2 \\\\\-7-2\geq \frac{x}{3}+2-2\\\\ -9\geq \frac{x}{3} \\\\[/tex]

Multiply both parts of the equation by 3:

[tex]\displaystyle\\-9(3)\geq \frac{x}{3}(3)\\\\\boxed {-27\geq x}[/tex]

[tex]\displaystyle\\b)\ \frac{3x+1}{2} > 11[/tex]

Multiply both parts of the equation by 2:

[tex]\displaystyle\\\frac{3x+1}{2}(2) > 11(2)\\\\3x+1 > 22\\\\3x+1-1 > 22-1\\\\3x > 21[/tex]

Divide both parts of the equation by 3:

[tex]\boxed{x > 7}[/tex]

The temperature at 6 pm is given as follows:

-40.2 ºF.

To obtain the temperature at 6 pm, we keep looking at the temperature for each interval given in the problem.

At 9 am, the temperature is given as follows:

-10.2ºF.

Between 9am and noon, the temperature rose 1.9°F, hence the temperature at noon is given as follows:

-10.2 + 1.9 = -8.3ºF.

Between noon and 3pm, the temperature dropped 16.4°F, hence the temperature at 3 pm is given as follows:

-8.3 - 16.4 = -24.7ºF.

Between 3pm and 6pm, the temperature dropped 15.5°F, hence the temperature at 6 pm is given as follows:

-24.7 - 15.5 = -40.2 ºF.

(subtracting the decline from the previous temperature, as we did for previous intervals).

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The perimeter of the isosceles  triangle with side lengths 3·x, (4·x - 7), and (1/2·x + 9) is 51[tex]\frac{1}{14}[/tex]

An isosceles triangle is a triangle that has a pair of congruent sides and according to the triangle inequality theorem, a pair of congruent angles.

The lengths of the sides of the isosceles triangle are;

3·x, 4·x - 7, and 1/2·x + 9

Let the sides, 3·x and 4·x - 7 represent the congruent sides of the triangle, we get;

3·x = 4·x - 7

4·x - 3·x = x = 7

x = 7

The length of the sides of the triangle, found by plugging in x = 7 in the specified expressions for the lengths of the sides of the triangle are therefore;

Length of the first side; 3·x = 3 × 7 = 21

The length of the second specified side; 4·x - 7 = 4 × 7 - 7 = 21

Length of the third specified side; (1/2×x) + 9 = (1/(2 × 7)) + 9 = 1/14 + 9

The perimeter of the triangle is the sum of the lengths of the sides of the triangle, therefore;

The perimeter of the triangle is; 21 + 21 + 1/14 + 9 = 51 [tex]\frac{1}{14}[/tex]

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The expression for the exact number of inches in 1 centimeter is 1/2.54.    Using a calculator to evaluate the expression gives 0.39370074. There may be a slight difference when converting due approximation of figures

Given the conversion facts:

1 inch = 2.54 centimeters and 1 centimeter = 0.39 inch

a. The expression for the exact number of inches in 1 centimeter will be:

1 centimeter  = 1/2.54           (Since 1 inch = 2.54 centimeters)

b. Using a calculator to evaluate the expression in (a) will give:

1 centimeter  = 1/2.54  = 0.39370074

The measurement conversion may be slightly different when converting between metric units and U.S. custumary units because of the approximation of figures when converting from one unit to the other

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The Insurance policy's anticipated value in this case is -20.

What is Insurance?

Insurance is a tool for risk management. You purchase protection against unforeseen financial losses when you purchase insurance. If something unpleasant happens to you, the insurance company pays you or someone else of your choosing.

Given,

Man pays -118 for one year

coverage = 140000

probability = 0.9993

The method used to calculate the insurance policy's expected value is:

= Chance that he won't live to see the end of the year * Coverage value - The cost of the insurance

= (1 - 0.9993)*140,000 - 118

= -20.

In this situation, the man's insurance coverage is expected to be worth -20.

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The distribution of the given function is a uniform distribution.

A strictly increasing function is the one which increases continuously in a given interval. If f-1(u) is a strictly increasing function of u, then the distribution of f-1(u) is the same as that of u. This is because a strictly increasing function preserves the rank ordering of its input, so if u-1 and u-2 are two random variables with a uniform distribution on the interval (0,1), then the rank order of f-1(u-1) and f-1(u-2) will be the same as the rank order of u-1 and u-2. Since the uniform distribution is defined by the rank order of its values, this means that the distribution of f-1(u) is also uniform on the interval (0,1).

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The equation to find how much money they will save after 3 weeks is y = 68x, and they will save $518, so yes they have enough money to buy the gift.

An assertion that two mathematical expressions have equal values is known as an equation. An equation simply states that two things are equal. The equal to sign, or "=," is used to indicate it.

Given:

Total money Jason and his 3 brothers have = $314,

Each of them will save $17 a week until they have at least $515,

At the end of three weeks, the money saved by Jason and his brothers,

Money saved = 17 × number of person × number of weeks

Assume the number of weeks is x and the money saved is y then,

y = 17x × 4

y = 68x

Money saved, y = 68 × 3

Money saved = $204

Total money after the end of three weeks = $314 + $204

Total money after the end of three weeks = $518

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