Find the equation of the line

Answer:

The answer should be 13.928

Step-by-step explanation:

You do A square + B square = C square

The box must be added with 7 cubic feet of sand

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also be defined as the capacity of an object.

It is measured in cubic units.

The volume of a box is length × width × height

represent the original length, width and height by x ,y ,z respectively

This shows that the volume of the original box= x× y× z = 1cubic foot

when the original length, width and height are doubled to give the new dimensions

Therefore the new length,width and height will be 2x, 2y and 2z

the volume of the new formed box = 2x×2y×2z

= 8xyz

XYZ= 1cubic foot

therefore 8xyz = 8cubic feet

since there is 1 cubic foot of sand in the box already,

then( 8-1)cubic feet = 7cubic feet will be added.

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Answer:

B

Step-by-step explanation:

(7x+2)(7x+2)

7x×7x=49

7x×2+2×7x=28x

2x2=4

The probability of the event that the first song played by Alan is a rock song is 0.01.

The probability of an event occurring is the ratio of the number of required outcome divided by the total number of possible outcomes. But the probability of an event say event "a" not occurring is 1 - a.

We shall calculate for the probability of the event that Alan's first song to be played is a rock song as follows:

probability of playing a rock song = 11/229

probability of not playing a Latin American song = 208/229

probability of not playing a gospel song = 183/229

probability of not playing a country song = 199/229

probability of not playing a rap song = 190/229

probability of not playing a classical song = 204/229

probability of not playing a pop song = 172/229

So,

The probability that the first song played is a rock song = (11/229) × (208/229) × (183/229) × (199/229) × (190/229) × (204/229) × (172/229)

The probability that the first song played is a rock song = 0.05 × 0.91 × 0.80 × 0.67 × 0.83 × 0.89 × 0.75

The probability that the first song played is a rock song = 0.01

Therefore the probability of the event that Alan's first song played is calculated to be 0.01 approximated to 2 decimal places.

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Answer: an=4n+5

Step-by-step explanation:

a1 = 9, a2 = 13, a3 = 17, a4 = 21, ...

A formula for the nth term of the arithmetic sequence:

                            [tex]a_n=a_1+d(n-1)[/tex]

where: a₁ - is the first term of the arithmetic sequence

            d - is the difference between the terms of the arithmetic sequence

d=a₂-a₁=a₃-a₂=a₄-a₃= ...

d=13-9=17-13=31-17= ...

d=4

             n - is the number of the arithmetic sequence term

[tex]a_n=9+4(n-1)\\\\a_n=9+4n-4\\\\a_n=4n+5[/tex]

Answer:

x=−5+ 21 ,−5− 21

Step-by-step explanation:

x= 4−20+4= 214−20−4 =21

​

​

Answer:

0

Step-by-step explanation:

subtracting same numbers give you zero

Fraction of her career has she been at her current job is 1/3 or 0.333.

Given:

Mr.Marx has been in the journalism industry for 24 years.

She has worked at her current job 8 of those years.

Fraction = number of year in current job/number of years in journalism industry.

= 8 years/24 years

= 8/24

= 1/3 ≈ 0.333.

Therefore fraction of her career has she been at her current job is 1/3 or 0.333.

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Answer:

The ratio shows that there are 14 girls to 30 students in total

Step-by-step explanation:

14 + 16 = 30 that mean that there are 30 students in total, therefore, the ratio shows 14 girls : 30 students

The value of q after solving the expression, q/3+2/3 = 8q/3-5/3, is 1.

According to the question,

We have the following expression:

q/3+2/3 = 8q/3-5/3

Now, taking 3 as the denominator on both the sides:

(q+2)/3 = (8q-5)/3

Now, 3 in the denominator on the left hand side can be divided by 3 in the denominator on the right hand side:

q+2 = 8q-5

Now, changing the sides of this expression:

8q-5 = q+2

Moving q from the right hand side to the left hand side:

8q-q-5 = 2

7q -5 = 2

Moving 5 from the left hand side to the right hand side:

7q = 2+5

7q = 7

q = 7/7

q = 1

Hence, the value of q after solving the given expression is 1.

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Value of BC is 36  in triangle's similarity .

What is  the triangle's similarity?

ΔABC and ΔPQR are similar .

so all sides are equal in ratio .

let BC is x .

 AB/BC = PQ/QR

 18/x = 2/4

    18 * 4 = 2 * x

       x = 18 * 4/2

        x = 18 * 2

         x = 36

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Answer: 584390

Step-by-step explanation: the r4u819

Cassidy and Calvin have the same amount of money in 11 months.

The amount is $370.

Cassidy has $425 in her savings account, and she has to pay $5 each month to her parents for her cell phone. This will be:

= 425 - 5m

Calvin has $95 and he saves $25 each month from his job walking dogs for his neighbor. This will be:

= 95 + 25m

where m = number of months

The equation will be:

425 - 5m = 95 + 25m

Collect like terms

425 - 95 = 25m + 5m

330 = 30m

Divide

m= 330/30

m = 11

The number of months is 11.

The amount will be:

= 425 - 5m

= 425 - 5(11)

= 425 - 55.

= 370

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The correct option regarding the price is C. no; The packs of socks are marked up to $7 and then discounted to $4.20.

In this situation, a shoe store buys packs of socks wholesale for $5 each and marks them up by 40%. The price will be:

= Original price + Markup

= 5 + (40% × 5)

= 5 + 2

= $7

Then, the store decides to discount the packs of socks by 40%. This will give a price of:

= 7 - (40% × 7)

= 7 - 2.8

= $4.2

The price isn't discounted to $5.

In conclusion, the correct option is C.

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The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle.

The ratio is the division of the two numbers.

Proportion is the relation of a variable with another. It could be direct or inverse.

The area of a circle with radius "r" is given as,

A = πr²

Since,π = constant.

Removing constant by proportionality.

A ∝ r²

Hence "The area of any circle is directly proportional to the square of the radius thus there are proportional relationships between the area of a circle and to the radius of the circle".

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The table has been shown using the function rule y = 5x - 2. (Refer to the table attached below).

So, the rule is y = 5x - 2:

Now calculate values as follows:

(A) When x = 0:

(B) When x = 1:

(C) When x = 2:

(D) When x = 3:

Therefore, the table has been shown using the function rule y = 5x - 2. (Refer to the table attached below)

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The percentage decrease in population is 17%

A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate percent of a number, divide the number by the whole and multiply it by 100. percentage . The word per cent means per 100. It is represented by the symbol “%”.

percentage decrease in population= (0riginal population- new population)÷ original population × 100

%decrease in population = (181000 - 150230) ÷ 181000× 100

=( 307770×100)/181000

= 17%

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17%

Step-by-step explanation:

i tried it it worked

Answer:

  (x, y) ≈ (3.4, 1.8)

Step-by-step explanation:

You want the point of intersection of the lines through (0, 1), (4.3, 2) and (2.1, 3), (5.4, 0).

The first attachment shows a graph of the lines and the coordinates of the point of intersection. The solution is ...

  (x, y) ≈ (3.42, 1.8)

  (x, y) = (3.4, 1.8) . . . . accurate to 1 decimal place

__

Additional comment

For each pair of points, the equation of the line can be written as ...

  (y2 -y1)(x -x1) -(x2 -x1)(y -y1) = 0

  (2 -1)(x -0) -(4.3 -0)(y -1) = 0   ⇒   x -4.3y +4.3 = 0

and

  (0 -3)(x -2.1) -(5.4 -2.1)(y -3) = 0   ⇒   -3x -3.3y +16.2 = 0

The calculator result in the second attachment shows the exact solution to be ...

  (x, y) = (3 229/540, 1 43/54) ≈ (3.42407, 1.79630)

Answer:

x = 3

y = -1

Step-by-step explanation:

4x + 10y = 2        Eq. 1

 x  - 10y = 13       Eq. 2

The result of the sum of Eq. 1 and Eq. 2 is:

4x + x = 5x

10y - 10y = 0y = 0

2 + 13 = 15

Then the result is:

5x = 15

x = 15/5

x = 3

From Eq. 2:

x - 10y = 13

3 - 10y = 13

-10y = 13 - 3

-10y = 10

y = 10/-10

y = -1

Check:

From Eq. 1:

4x + 10y = 2

4*3 + 10*-1 = 2

12 - 10 = 2

The solution of the equation is that the value of x = 3 and y = -1.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The equation will be solved as,

4x + 10y = 2        Eq. 1

x  - 10y = 13       Eq. 2

The result of the sum of Eq. 1 and Eq. 2 is:

4x + x = 5x

10y - 10y = 0y = 0

2 + 13 = 15

Then the result is:

5x = 15

x = 15/5

x = 3

From Eq. 2:

x - 10y = 13

3 - 10y = 13

-10y = 13 - 3

-10y = 10

y = 10/-10

y = -1

Therefore, the solution of the equation is that the value of x = 3 and y = -1.

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The minimum temperature in Salt Lake City in December is 5 degrees Fahrenheit.

The average December temperature in Salt Lake City, Utah, is 10 degrees Fahrenheit. The actual December temperature can vary in Salt Lake City by 5 degrees Fahrenheit either above or below the average.

We need to find out the minimum temperature in Salt Lake City in December. Let the temperature be denoted by the variable "M". The minimum temperature is the difference between the average temperature and the variation in the temperature.

M = 10 - 5

M = 5

Hence, the minimum temperature in Salt Lake City in December is 5 degrees Fahrenheit.

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By using a trigonometric relation we will see that FD = 32, the correct option is C.

We can see a right triangle, such that FD is the hypotenuse.

We also know one angle of this triangle, and the adjacent cathetus to that angle.

Now remember the relation:

cos(a) = (adjacent cathetus)/(hypotenuse)

Replacing the values we know we get:

cos(30°) = 28/hypotenuse

Solving the equation for the hypotenuse we get:

hypotenuse = 28/cos(30°) = 32.3

Rounding to the next whole number we get FD = 32

The correct option is C.

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The final solution is all the values that make (x+5) (x+2) (x−2)=0 true.

x = −5,−2,2

What is factorization?

Factorization, also known as factoring, is the process of breaking down an object (such as a number, a matrix, or a polynomial) into a product of another object, or factors, which when multiplied together yield the original object (such as the number or matrix) in question.

What is inequality?

A relationship between two expressions or values that are not equal to each other is called an inequality.

Here, we have

Factor out the greatest common factor from each group

x²(x+5) - 4(x+5) = 0

Factor the polynomial by factoring out the greatest common factor, (x+5)

(x+5)(x²-4) = 0

Rewrite 4 as 2².

(x+5)(x²-2²) = 0

(x+5)(x+2)(x-2) = 0

Now,

x+5 = 0

x-2 = 0

x+2 = 0

set x+5 =0 then we get

x = -5

set x+2 =0 then we get

x = -2

set x-2 =0 then we get

x = 2

Hence, the final solution is all the values that make (x+5) (x+2) (x−2)=0 true.

x = −5,−2,2

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Answer:

Charlie gets paid more then Derek. Charlie gets paid per hour $52.25

The money spent by Mr. Dunston is $ 35.

Given that:-

Money spent by Mr. Dunston and Mr. Dolland = $ 45

Money spent by Mr. Dunston and Ms. Campbell = $ 65

Ms. Campbell spent 3 times as much as Mr. Dolland.

We have to find the money spent by Mr. Dunston.

Let the money spent by Mr. Dunston be $ x,

Let the money spent by Mr. Dolland be $ y and,

Let the money spent by Ms. Campbell be $ 3y

Hence, from the data given in the question, we can write,

x + y = 45  ...(1)

x + 3y = 65 ... (2)

By elimination method, we can write,

(2) - (1)

2y = 20

y = 10

x + 10 = 45

x = 45 - 10 = 35

x = 35

Hence, the money spent by Mr. Dunston is $ 35.

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The classification and the output rule for each function in this problem is given as follows:

1. Output rule: y = 5x + 11. Classification: Linear.

2. Output rule: y = 2^x. Classification: Exponential.

3. Output rule: y = 3 if |x| is even, y = 1 if |x| is odd. Classification: Neither.

A linear function is defined when the increase of 1 in x result in the addition of a constant to y, hence the rule is:

y = mx + b.

In which:

Hence, for the first table, as 5 is added to x when x increases by one, the rule is:

y = f(x) = 5x + 16.

An exponential function is defined when the increase of 1 in x result in the multiplication of a constant to y, hence the rule is:

y = a(b)^x.

In which:

Hence, for the second table, the rule is:

y = 2^x.

For the third table, none of the definitions for linear and for exponential functions are true, hence the function is neither, as it is a piece-wise function that assumes one value for odd numbers and another for even numbers.

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The depreciation expense under the straight-line method for 2022, for Monty Corp., is $5,450.

Under the straight-line depreciation method, one of the cost-recovery methods, the depreciable amount of an asset is divided by its estimated useful life.

The quotient is the depreciation expense for each year.  However, if the asset is not used for a full year, the depreciation expense is prorated according to the number of months or days that the asset is in use.

Note that the depreciable amount is the difference between the cost of the asset and its salvage value.

Cost of new machine = $124,000

Purchase date = October 1, 2022

Estimated salvage value = $15,000

Depreciable amount = $109,000 ($124,000 - $15,000)

Estimated useful life = 5 years

Estimated working hours = 10,000 hours

Depreciation method = Straight-line

Annual Depreciation Expense = $21,800 ($109,000/5)

October 1, 2022, to December 31, 2022, = 3 months

Depreciation expense for 2022 = $5,450 ($21,800 x 3/12)

Thus, using the straight-line method, Monty Corp. will record a depreciation expense of $5,450 for the new machine it purchased on October 1, 2022.

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Answer:

23

Step-by-step explanation:

the numbers from -10 to 10 cancel out, so all that is left is 11+12=23

The sum form of the trigonometric function 2 · sin 2x · sin 2x by product-to-sum formula is 1 - cos 4x.

Herein we find the definition of a trigonometric function defined as a product of trigonometric function, this can be transformed into a sum of trigonometric functions by means of the following product-to-sum formula:

sin α · sin β = [cos (α - β) - cos (α + β)] / 2

First, write the trigonometric function defined in the statement:

2 · sin 2x · sin 2x

Second, use the product-to-sum formula by considering α = β = 2 · x:

2 · [[cos (2x - 2x) - cos (2x + 2x)] / 2]

cos 0 - cos 4x

1 - cos 4x

Third, write the resulting expression:

2 · sin 2x · sin 2x = 1 - cos 4x

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