Solve the system, using the method of your choice. For systems that do not have one unique solution, also state the number of solutions and whether the system is inconsistent or the equations are dependent. Express answers as integers or simplified fractions if necessary.
-8x+8y=-80
8x-4y=68

Answer: y= 2x - 5

Step-by-step explanation: lmk if u need explanation to solve

Answer:

let width=x

length = x + 2ft

Area = 82ft^2

Area= length×width

=(x+2)x

=x^2 +2x=82

x^2+2x-82=0

Use Quadratic Equation to get x.

x = -10.1(reject, length cannot be minus value or 8.11)

x = 8.11

width = 8.11ft

length = 10.11ft

Answer:

97.5/100

Step-by-step explanation:

To write 97.5% as a fraction in simplest form, we first convert the percentage to a decimal by dividing it by 100: 97.5% / 100 = 0.975. We can then express this decimal as a fraction by using the fact that any number can be represented as a fraction with the number as the numerator and a power of 10 as the denominator: 0.975 = 0.975/1. Finally, we simplify the fraction by dividing the numerator and denominator by the greatest common factor, which in this case is 1: 0.975/1 = 97.5/100. Therefore, 97.5% can be written as the fraction 97.5/100 in simplest form.

Answer:

39/40

Step-by-step explanation:

97.5/100

   Step 1: Write down the percent divided by 100;

   Step 2: If the percent is not a whole number, then multiply both top and bottom by 10 until you get an integer at the numerator.

   Step 3: Simplify (or reduce) the fraction if it is not in the simplest form.

The value of x when both the function give the same value is 10

Solution:

Given f(x) = 0.2x , g(x) = 0.5(x-6)

let x = 0 , f(x) = 0 , g(x) = -3

let  x = 1 , f(x) = 0.2 , g(x) = -2.5

let  x = 2 , f(x) = 0.4 , g(x) = -2

let  x = 3 , f(x) = 0.6 , g(x) = -2.5

let  x = 4 , f(x) = 0.8 , g(x) = -2 and so on till x=10

let x=10, f(x) = 2, g(x) = 2

∴ The value of x when both the values of the function are same is x = 10

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The value of x when both the function give the same value is 10

What are functions?

Function, in mathematics is an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Solution:

Given f(x) = 0.2x , g(x) = 0.5(x-6)

let x = 0 , f(x) = 0 , g(x) = -3

let  x = 1 , f(x) = 0.2 , g(x) = -2.5

let  x = 2 , f(x) = 0.4 , g(x) = -2

let  x = 3 , f(x) = 0.6 , g(x) = -2.5

let  x = 4 , f(x) = 0.8 , g(x) = -2 and so on till x=10

let x=10, f(x) = 2, g(x) = 2

∴ The value of x when both the values of the function are same is x = 10

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Answer:

a)  A' = (2, 4)

b)  A'' = (1, -2)

Step-by-step explanation:

When reflecting a shape in a vertical line, each vertex of the shape will be the same distance from the vertical line but in the opposite direction.  

Therefore, the x-values change but the y-values remain the same.

To reflect point A in x = -1, determine the number of horizontal units the point is from x = -1.  Count the same number of units on the other side of the vertical line (remembering that the y-value remains unchanged).

The x-value of point A is x = -4.  This is 3 units to the left of x = -1.

Therefore, the x-value of point A' is 3 units to the right of x = -1.

The y-value of point A is y = 4, so the y-value of point A' is also y = 4.

Therefore, the coordinates of the point A' are:

To translate point A' by the given vector, translate the point:

Therefore, the coordinates of the point A'' are:

Answer:

-5

-9+5

Step-by-step explanation:

Answer:

please download the attached file and let me know if you need any further information about addmition in roots international and if so how to make food with clay

Step-by-step explanation:

ok inshallah and a have of safe Earth’s warm and and

[tex]85(94 + 611) < 64(85 - 54)[/tex]

it same like before the end

Answer: 2/5 days

Step-by-step explanation:

4 / 5 = 2d

4 / 10 = d

2 / 5 = d

Using fractions and mathematical operations, the number of students in the class are 53, the number of juniors are 21 and 16 seniors did not attend the field trip

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely numerator and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.

A)

From the information given, 3/5 of the students are seniors

However, we know that he has 32 seniors currently

Let's use the concept of percentage here

3/5 = 0.6. Expressing this in percentage = 60%

This we can say 60% of the students are seniors

60/100 = 32/ x

x = total number of students

x = 32 / 0.6

x = 160/3 = 53 students

We have 53 students in the class

B) The number of juniors in the class are

53 - 32 = 21

C) The number of seniors that did not go will be

3/5 * 40 =  24

40 - 24 =  16

16 seniors did not go

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Answer:

step By step

First   multiply 5 by 3 and  multiply 12 by 3

Which is 15,36

Add to x endpoint to determine y endpoint which is (15,36)

Explain:

This multiplication is used to find full distance from the endpoints of XY

The linear equation each graph is y = (1/5)x +3, y = 2x,  y = -3x+5 and y = (1/3)x +5 respectively

The equation of a line is of the form y = mx+c

Where m is the slope and c is the y-intercept

Graph 1

c = 3

m = 1/5 = 0.2

y = mx+c

Thus, the linear equation is y = (1/5)x + 3 or y = 0.2x + 3

Graph 2

c = 0

m = 2/1 = 2

y = mx+c

Thus, the linear equation is y = 2x+0 or y = 2x

Graph 3

c = 5

m = -3/1 = -3

y = mx+c

Thus, the linear equation is y = -3x+5

Graph 4

c = 5

m = 1/3 = 1/3

y = mx+c

Thus, the linear equation is y = (1/3)x+5 or y = 0.33x+5

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Answer:

2.51 x 10^5

Step-by-step explanation:

Scientific notation gives you a number between 1 and 10 multiplied by a power of ten. In this case, you'll want to use the significant digits, 251, and divide or multiply by a power of ten to get a number between 1 and 10.

251,000 can become 2.51 (which is between 1 and 10) multiplied by 10 to a certain exponent. All you need to do is calculate the exponent.

2.51 x 10^(?) = 251,000

For each power of 10, the decimal moves a space. Since you want the decimal to move 5 spaces, you'll want to multiply 2.51 by 10^5.

2.51 x 10 = 25.1

2.51 x 10^2 = 251

2.51 x 10^3 = 2510

2.51 x 10^4 = 25,100

2.51 x 10^5 = 251,000

Using difference of squares, [tex]81x^6-25y^{10}=\boxed{(9x^3-5y^5)(9x^3 + 5y^5)}[/tex].

12/√3 is  the direction of the vector v .

What does a basic math vector mean?

A thing with both magnitude and direction is called a vector.

                               A vector can be visualized geometrically as a directed line segment, where the direction is indicated by an arrow and the length of the segment equals the magnitude of the vector.

Normalize (make length 1) the vector v = <1, 1, -1>.

||v|| = √(1^2 + 1^2 + (-1)^2) = √3.  

So, the unit vector u is given by u = v/||v|| = <1, 1, -1>/√3.  

To find the rate of change of the potential in the direction of the vector v, you should calculate the   ∇f(6, 6, 5) and multiply by u.

=<df/dx, df/dy, df/dz>*u

= <4x-3y+yz, -3x+xz, xy> {at (6, 6, 5)} * u

= <36, 12, 36> · <1, 1, -1>/√3

= 12/√3.

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The complete question is -

Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 2x2 − 3xy + xyz (a) Find the rate of change of the potential at P(6, 6, 5) in the direction of the vector v = i + j − k.

The total distance ran during these days, written as a mixed number, is (38 + 3/4)mi

We know that the student ran a distance of (3 + 1/2) miles each day for 5 days, so the amount that the student ran in these 5 days is given by the product:

5*(3 + 1/2) mi = (15 + 5/2) mi

Now, on the next 5 days, the student ran a distance of (4 + 1/4) miles, so the total distance that the student ran in these days is:

5*(4 + 1/4) mi = (20 + 5/4)mi

Now to get the total distance that the student ran on the 10 days we need to add the two distances above, we will get:

(15 + 5/2) mi +  (20 + 5/4)mi

So we have a sum of mixed numbers, we can rewrite this as:

(15 + 5/2) mi +  (20 + 5/4)mi = (15 + 20)mi + (5/2 + 5/4)mi

(15 + 20)mi + (5/2 + 5/4)mi = 35mi + (10/4 + 5/4) mi

35mi + (10/4 + 5/4) mi = 35mi + 15/4mi

35mi + 15/4mi = 35mi + 12/4 mi + 3/4 mi

35mi + 12/4 mi + 3/4 mi  = (38 + 3/4)mi

That is the total distance that the student ran on the 10 days.

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The f(x) = -ax²+18 function equation for his parabolic path. x=√8  is he reached, to the nearest tenth of a foot.

A function is an equation that has just one answer for y for every possible value of x. When utilizing a function, each input of a certain type receives exactly one output.

f(x) = -ax² + 18

f(2)= -a(2)²+18 = 12

-4a = 12-18

-4a = -6

  a = -6/-4

  a = 3/2

f(x) = (-3/2) x² + 12

f(0) = (-3/2) x² + 12

(3/2) x² = 12

x² = 8

x = √8

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Answer: x≥48

Step-by-step explanation:

The inverse of y is [tex]\sqrt{4-x} ,-\sqrt{4-x}[/tex].

What is the inverse of a function?

A function whose inverse returns the initial value for the specified output is called an inverse function of the function. The inverse function of y, or[tex]f^{-1}[/tex] (y), will return the value x if f (x) produces an output of y.

Given equation is [tex]y=-x^{2} +4[/tex]

We find the inverse function f(x) by substituting x and y.

We compute the resulting equation for x. We change the variable to:

[tex]x=4-y^{2}[/tex]

Now, solve the equation [tex]x=4-y^{2}[/tex] for y

We get, y = [tex]\sqrt{4-x} ,-\sqrt{4-x}[/tex]

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The total commission Fred was paid for that month is $2570.5.

Given that, Fred sells new and used kayaks.

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

Let the number of kayaks be x and the total amount of money Fred get paid per week be y.

A) An equation for the way Fred is paid.

So, equation is y =395.50 +12.5% of x

⇒ y=395.50 +0.125x

B) Last month, the total value of the kayaks he sold was $17400.

Here, x=17400

So, y=395.50 +0.125×17400

= $2570.5

Therefore, the total commission Fred was paid for that month is $2570.5.

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The end behavior of the functions is obtained considering the limits of the functions as the input variable x goes to infinity.

For limits when x goes to infinity, only the term with the highest exponent of each of the numerator and of the denominator is considered, hence the functions are written as follows:

Applying the exponent properties, the equivalent expressions are given as the base x elevated to the subtraction of the exponents 2 and 3, hence:

Which is how the functions behave as x goes to infinity.

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Answer:

Step-by-step explanation:

SORRY CANT HELP YOU I AM ONLY IN 4 GRADE SO SORRY

1.  m∠5 + m∠6 = 180° - Pair of linear angles

2. ∠ 2+ ∠ 3 = ∠ 6 - Exterior Angle Theorem.

3. m∠2 + m∠3 + m∠5 = 180° - Sum of angles of Triangle

The angles that are created outside of a triangle are its external angles. In other terms, the angle created between one of a triangle's sides and its neighboring extended side is the triangle's exterior angle.

Each exterior angle of the triangle and its corresponding interior angle will form a pair of linear angles i.e the Sum of an Exterior angle and its corresponding interior angle is 180°.

A triangle's exterior angle is equal to the sum of its two opposite interior angles. This property of the triangle is known as Exterior Angle Theorem.

Here we have

∠2, ∠3, and ∠5 are the interior angles of a triangle

∠1, ∠4, and ∠6 are exterior angles of the same triangle

Let's assume that the given triangle is ΔABC

Can be represented as given in the picture  

As we know the sum of angles in a triangle = 180°

=> m∠2 + m∠3 + m∠5 = 180°  will be true

If we observe the given picture,

From line BC, m∠5 + m∠6 = 180°   [ Pair of linear angles ]

From Exterior angle Property

=> ∠ 2+ ∠ 3 = ∠ 6.

Therefore,

The correct statements are

1.  m∠5 + m∠6 = 180° - Pair of linear angles

2. ∠ 2+ ∠ 3 = ∠ 6 - Exterior Angle Theorem.

3. m∠2 + m∠3 + m∠5 = 180° - Sum of angles of Triangle.  

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(a) The depreciation for the first year is $99,732.40.  (b) If the Machine was sold at the end of the fifth year, the gain or loss is $498,662

We know that in accounting, depreciation is the loss on a fixed asset over the accounting period that benefited from it.

Using straight line method of depreciation,

Depreciation = [tex]\frac{Cost os asset-Residual value}{Estimated number of years}[/tex]

Applying the figures we have

Depreciation = [tex]\frac{637362-138700}{5}[/tex]

Depreciation= [tex]\frac{498662}{5}[/tex]

Depreciation= $99,732.40

(b) If the machine is sold at the end of the fith year, the loss is accumulated depreciation for 5 years

Loss= $(99,372.4*9) = $498,662

(c)    The journal appears as follows

                                           Journal

                                            $                                                        $

Coat of machine           637,362.00     Depreciation             498,662

                                                               Balance                     138,700

Totals                             637,362.00                                        637,362.

In conclusion, the depreciation for the first year and loss after the fifth year are $99,732 and $498,662 respectively.

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Answer: x=±2/3

Step-by-step explanation:

The first thing we want to do is isolate the variable, x² in this case.

We can divide both sides by 9 which yields the equation x²=[tex]\frac{4}{9}[/tex].

Then we can take the square root of both sides, x=2/3.

Note: When the exponent is an even number both positive and negative x values will yield the same positive answer, so x=±2/3

Answer:

17. VN ll OP

18. VN perp. TR

19. Yes because the both a straight line (m 180) and are not crossing at any point.

20. Yes because there crossing at an right angle.

Hope this helps!

Step-by-step explanation:

we need to find the value of x for which C(x) = 2200.

2200 = 270ln(x + 1) + 1900

300 = 270ln(x + 1)

300/270 = ln(x + 1)

10/9 = ln(x + 1)

e^(10/9) = x + 1

x = e^(10/9) - 1 = 2.037731778... ≈ 2.0 acres

for an average intake of 2200 calories per day the number of acres of land owned is approximately 2.0.

The monthly payment will be 1,228.18.

What is principle amount?

The amount you owe at any one moment is the primary amount. When you first took out the loan, it is exactly your loan amount. The principle amount drops as you make EMI payments, and when it hits zero, your loan is closed.

The total price of the home is $241,000.

The down payment will be 15% among the total price.

Rest amount will be paid by taking loan for 30 years.

The down payment amount is

15% of $241,000 = $ 241,000×15/100 = $36,150.

Hence the loan amount is going to be the rest amount, that is,

$(241,000-36,150) =$204,850.

So the principle amount, P= $204,850.

Interest rate= 5% implies

interest, R= 5/100 = 1/20 = 1/12×1/20 (monthly) = 1/240.

Number of years, N= 30 years = 30×12 months = 360 months.

Hence the monthly payment will be

[  P × R × (1+R)N ] / [ (1+R)N - 1 ] = $1,099.68.

So the principle amount, P= $204,850.

Interest rate= 6% implies

interest, R= 6/100 = 1/12×6/100 (monthly) = 1/200.

Number of years, N= 30 years = 30×12 months = 360 months.

Hence the monthly payment will be

[  P × R × (1+R)N ] / [ (1+R)N - 1 ] = 1,228.18

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Answer:

m = -4

b =1

y = -4x+1

Step-by-step explanation:

We want to find the slope and y intercept

Given the two points ( -1,5) and ( 1,-3), we can use the slope formula

m = ( y2-y1)/(x2-x1)

    = ( -3 -5)/( 1 - -1)

   = -8/( 1+1)

   = -8/2

   = -4

The y intercept is where it crosses the y axis

It crosses at 1

The slope intercept form of the line is

y = mx+b

y = -4x+1

The standard equation for the position s of a body moving with a constant acceleration a along a coordinate line is proved below.

In statistics, the term equation refers the combination of variable and numbers.

Here we have to prove the the standard equation for the position s of a body moving with a constant acceleration a along a coordinate line.

While we looking into the given question, we have given the function

Here we are given that dt²/d²s ​= a (a constant), and when t=0, 

dt/ds ​= v₀ 

and s = s₀​.

And we need to show that s=a/2t²+v₀t+s₀​.

While we differentiate the equation , then we get,

=>  dt²/d²s ​= a 

=> ds/dt = ∫a dt

=> ds/dt = at + c

Since ds / dt = v₀  when t = 0, we have

=> a(0) + C=  C

Again we have to take the differentiation on the term, then we get,

=> s = ∫(at+v0​)dt = a/2t²+v₀t+s₀​.

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The automobile needs 26.5 gallons of gas to reach 890 miles.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, An automobile uses 17 gallons of fuel to go 570 mi.

∴ The automobile requires (17/570) gallons of gas to reach 1 mile.

∴ To reach 890 miles the automobile needs (17/570)×890.

= 26.5 gallons of gas.

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