A small town had a population of 12,000 people in 2001. The population has been decreasing at a rate of 3.5% each year. How many people lived in the town in 2016?

The equation y = -5x + 3 is a linear equation.

We know that a linear equation in two variables is nothing but an equation that can be written in the form Ax + By = C,  where A and B are real numbers and A ≠ 0, B ≠ 0.

The above form of equation is called the standard form of a linear equation in two variables.

Here we have been given an equation y = -5x + 3

y = -5x + 3

y + 5x = -5x + 3 + 5x             ........(Add 5x to each side)

y + 5x = (-5x + 5x) + 3           .......(Associative property of addition)

y + 5x = 0 + 3

5x + y = 3                              ........(Commutative property of addition)

Since we can write it in the standard form, Ax + By = C, then we have a linear equation.  

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Answer:

33.56°

Step-by-step explanation:

Base angles of an isosceles triangle are equal.

Base is bisected by a line from top (vertex) of the triangle straight down to form a right angle.  Base, 100 cm, has 2 equal segments, 50 cm each.

Find h, height of the triangle:

h² = 60² - 50²

h = √1100 = 33.17

sin(f) = 33.17/60 = 0.553

m∠f = sin⁻¹(0.553) = 33.56°

Answer:

19r⁵ - r + 8

Step-by-step explanation:

The perimeter of a two-dimensional shape is the distance all the way around the outside.

Therefore, the perimeter of a triangle is the sum of the lengths of its sides.

[tex]\begin{aligned}\textsf{Perimeter}&=(9r^5-7r+8)+(r^5+4r-15)+(9r^5+2r+15)\\&=9r^5-7r+8+r^5+4r-15+9r^5+2r+15\\&=9r^5+9r^5+r^5+4r+2r-7r+8+15-15\\&=19r^5-r+8\end{aligned}[/tex]

Answer:

Perimeter of triangle = 19r⁵ - r + 8

Step-by-step explanation:

Perimeter of triangle formula,

→ A + B + C

→ Sum of all sides

Let's solve for the perimeter,

→ (9r⁵ - 7r + 8) + (9r⁵ + 2r + 15) + (r⁵ + 4r - 15)

→ (9r⁵ + 9r⁵ + r⁵) + (-7r + 2r + 4r) + (8 + 15 - 15)

→ (19r⁵) + (-r) + (8)

→ 19r⁵ - r + 8

Hence, perimeter is 19r⁵ - r + 8.

Answer:

s=17

Step-by-step explanation:

just divide 34 by 2

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{2s = 34}[/tex]

[tex]\textbf{DIVIDE 2 to BOTH SIDES}[/tex]

[tex]\mathsf{\dfrac{2s}{2} = \dfrac{34}{2}}[/tex]

[tex]\textbf{SIMPLIFY it}[/tex]

[tex]\mathsf{s = \dfrac{34}{2}}[/tex]

[tex]\mathsf{s = 17}[/tex]

[tex]\huge\text{Therefore, your answer should be:}[/tex]

[tex]\huge\boxed{\mathsf{x = 17}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

The linear function that relates y to x is given as y = 2x

An equation consists of numbers and variables linked together by mathematical operations to form an expression.

A linear equation is in the form:

y = mx + b

Where m is the rate of change and b is the initial value

From the table, using the points (0, 0) and (1, 2):

y - 0 = [(2 - 0)/(1 - 0)](x - 0)

y = 2x

The linear function that relates y to x is given as y = 2x

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Answer:

40% profit

Step-by-step explanation:

$50 increase, and $50 is 40% of $125

Answer:

40%

Step-by-step explanation:

Sold price =SP = $ 175

Cost price = CP =$ 125

Profit = Sp - CP = 175 - 125 = $ 50

Profit = 40 %

150 years is time required to when the population of north Dakota is equals to the population of South Dakota .

let t is time in years after which the population of both city are equals

so the population of north dakota after t years is given by :

0.3 + 0.017 t ----(i)

Population of South dakota after t years is given by:

0.9 + 0.013 t  ----(ii)

for the population to be equal to each other equation (i) must be equal to equation (ii)

so ,  0.3 + 0.017 t = 0.9 + 0.013 t

=> 0. 004 t = 0.6

=>  0.6/0.004

=> 150

so 150 years is the time required to make population of both city equals.

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The combination of streamers  and balloons can Liana purchase with $15.00 at the Party Palace is 8 and 43.

What is Linear equation ?

Linear equation can be defined as the equation having highest degree is one.

Given ,

Liana needs to purchase AT LEAST 50 party decorations. The Party Palace charges $0.50 per decorative streamer and $0.25 per balloon, including tax.

Let number of decorative streamer be x .

and number of balloons be y .

So, As per the question

The linear equation could be

0.50 x + 0.25 y = 15

Here its equals to the $15 as given that amount.

So,

The equation ,  0.50 x + 0.25 y = 15

So, in the options it is given that,

8 and 43

So lets substitute x = 8 and y = 43 in the equation ,

we get,

LHS = 0.50 * 8 + 43 * 0.25

= 4 + 10.75

14.75

< RHS

So, As LHS is less than RHS , liana can easily purchase with given $15.00 at the party place.

Hence, The combination of streamers  and balloons can Liana purchase with $15.00 at the Party Palace is 8 and 43.

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AxB represents the cross product (also known as the vector product) between two vectors A and B.

AxB is the symbol for the cross product (also known as the vector product) between two vectors A and B. A new vector is produced by a cross-product. The symbol for the mathematical definition of the vector product of two vectors is axb, and it is as follows. Where is the angle between a and b, axb = |a| |b| Sin.

The vector components are joined to create a vector in a vector product of vectors. A vector that is perpendicular to both of the given vectors is the result of adding two vectors together.

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The given statement that "if you plot one point incorrectly while the others correctly, you will achieve partial credit for that object" is false because for both curves and connected points when one point is incorrectly plotted while all others are plotted correctly, the exact object is not achieved and so as you will not get any credit.

This question is asked in the context of the aplia platform, which is an educational technology that provides online interactive learning solutions to engage and prepare students for the courses. Aplia guides students through assignments that drive them from basic knowledge and understanding to application and practice in the real world.

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Answer:

Step-by-step explanation:

A study reveals that young people aged 11 to 14 spend an average of 12.5% ​​of a 24-hour day in front of a screen.

70% of that time is spent in front of the television and the rest is spent in front of a computer.

How many hours and minutes do young people aged 11 to 14 spend on average each day in front of:

(a) a screen? (b) television? (c) a computer?

a screen

The number of earth days that it will take the planet to orbit the star is 500 earth days.

The rate of distance moved in a specific direction to the time taken can be referred to as the speed.

i.e speed = distance/ time taken

In the given question, the total distance covered is the length of the orbit.

So that,

length of the orbit = 2πR

where R is the radius i.e the distance of the star to the planet.

length of the orbit = 2 * 3.142 * 67000000

                              = 421028000 km

speed = distance/ time taken

⇒     time taken = distance/ speed

                          = 421028000 km/ 35,000 km/h

                          = 12029.37 h

But,

1 earth day = 24 hours

x = 12029.37 h

x = 12029.37 h * 1 earth day/ 24 h

  = 501.2238 earth days

The number of earth days it will take the planet to orbit the star is 500 earth days.

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The slope of the new road is zero.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Take points from the Graph (5, 0) and (5, 4).

Slope of a line = m = tanθ

where θ is the angle made by the line with the x−axis.

For a line parallel to y−axis ,θ= π/2.

​

∴m = tan π/2 = undefined

The new road will therefore have 0° of inclination if it is perpendicular to D street because if they are perpendicular and D street is vertical, the new road is level and has 0° of inclination.

An horizontal line now has zero slope.

The new road has a zero slope as a result.

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The equation that has one solution will be 4m + 5 = 25. Then the correct option is B.

The equation that has infinitely many solutions will be 2x + 7 - 2x = 7. Then the correct option is C.

The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.

If the variable and constant get eliminated then the equation has infinitely many solutions. If the variable gets eliminated then the equation has no solution.

7. Let's check option B, then we have

4m + 5 = 25

4m = 20

m = 5

8. Let's check option C, then we have

2x + 7 - 2x = 7

2x - 2x = 7 - 7

The equation that has one solution will be 4m + 5 = 25. Then the correct option is B.

The equation that has infinitely many solutions will be 2x + 7 - 2x = 7. Then the correct option is C.

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The equation of the line of best fit is: y = -1.15x + 102.8 and Using the equation of the line of best fit, the predicted cost is: $62.55

What is the Equation of a Line of Best Fit?

The equation of a line of best fit is represented by the equation, y = mx + b, where m is the slope and b is the initial value.

1. Using two points, (72, 20) and (20, 80):

Slope (m) = change in y / change in x = (80 - 20)/(20 - 72) = 60/-52

Slope (m) = -1.15.

Substitute m = -3 and (a, b) = (72, 20) into y - b = m(x - a)

y - 20 = -1.15(x - 72)

y - 20 = -1.15x + 82.8

y = -1.15x + 82.8 + 20

y = -1.15x + 102.8

The equation of the best line of fit is y = -1.15x + 102.8.

2. Monthly heating cost, y, for a month with an average temperature of 35°F (x) will be calculated by substituting x = 35 into y = -1.15x + 102.8.

y = -1.15(35) + 102.8

y = 62.55

The predicted monthly cost is $62.55.

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Another strategy that one could use to find 20% of the given number is to multiply the number by 1/5.

A percentage simply has to do with the a value or ratio which can be stated as a fraction of 100. It should be noted that when we want to we calculate a percentage of a number, we simply divide it and then multiply the value that is gotten by 100.

In this case, another strategy that one could use to find 20% of the given number is to multiply the number by 1/5. This will be:

= 20% × $400

= 1/5 × $400

= 80

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Hope it helps.

If you have any query, feel free to ask.

Answer: -8

Explanation: Arithmetic operations have some precedence according to each other.

Firstly, begin with the operation inside of the parenthesis:

[tex]9 + 6 = 15[/tex]

The operation becomes:

-3 + (15) ÷ (-3)

Then, you should do the division part because the division has a precedence according to addition:

[tex]15 / (-3) = -5[/tex]

Finally, it becomes:

-3 + (-5) = -8

"-8" is the answer.

The true statements are,

A. Joel's distance is a function of time.

B. Joel's fastest speed occurs in the first hour of the hike.

E. The graph is decreasing at all the times between 3.5 hours and 7 hours.

In mathematics, the graph of a function f is the set of ordered pairs, where {\displaystyle f(x)=y.} In the common case where x and f(x) are real numbers, these pairs are Cartesian coordinates of points in two-dimensional space and thus form a subset of this plane.

here, we have,

from the given graph we get,

The graph represents his journey, and,

the true statements are,

A. Joel's distance is a function of time.

B. Joel's fastest speed occurs in the first hour of the hike.

E. The graph is decreasing at all the times between 3.5 hours and 7 hours.

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Yes, it is possible to draw a triangle.

This will be done by the property: the sum of two sides of a triangle should be more than the third side.

(4.6cm + 5.8cm) =10.3cm

10.4cm = 10.3cm

LHS>RHS

A triangle is possible.

A triangle is a polygon with three edges and 3 vertices. The terminology for categorizing triangles is more than two thousand years vintage, having been defined on the first actual page of Euclid's elements.

In Euclidean geometry, any three factors, while non-collinear, decide a completely unique triangle and simultaneously, a unique plane (i.e. a -dimensional Euclidean space). In different words, there's best one plane that consists of that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is the best one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is not real. this text is ready triangles in Euclidean geometry, and in particular, the Euclidean plane, except wherein otherwise stated.

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On solving the quadratic equation x² + 5x - 14 = 0 by using the quadratic formula , the solution is written as x = 2 , x = -7  .

The formula that is used to find the roots of the quadratic equation is called as quadratic formula and is written as ,

the general quadratic equation is ⇒  ax² + bx + c = 0, the the quadratic formula will be:

⇒ x = [-b ± √(b² - 4(a)(c))]/2a ;

the given equation is ⇒  x² + 5x - 14 = 0 ,

On comparing ,

we get that ; a = 1 , b = 5 and c = -14 ;

substituting  values in quadratic formula ,

we get ;

⇒ x = [-5 ± √(5² - 4(1)(-14))]/2(1) ;

solving further ,

we get ;

⇒ x = (-5 ± √(25+56))/2(1);

⇒ x = (-5 ± √81)/2;

⇒ x = (-5±9)/2 ;

On simplifying the equations separately ,

we have ;

⇒ 2x = -5 + 9    or    2x = -5 - 9   ;

⇒ we get , "x" as 2 or  "x" as -7  .   ;

Therefore , the roots of equations are "x ⇒ 2" or "x ⇒ -7"  .

The given question is incomplete , the complete question is

How do you solve  x² + 5x - 14 = 0  using the quadratic formula ?

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The formula for the sum of all terms is [tex]S_n[/tex]= n(n+1)/2.

Sum most commonly means the whole of two or greater numbers delivered collectively; see addition. A summation additionally known as a sum is the result of arithmetically adding numbers or portions. A summation constantly includes a whole range of terms. There can be as few as two terms, or as many as one hundred, a thousand, or one million. some summations include infinitely many terms.

In arithmetic, the summation is the addition of a chain of any form of numbers, called addends or summands; the result is their sum or general. the combination of two or extra numbers, magnitudes, portions, or details as decided via or as if via the mathematical technique of addition: The sum of 6 and 8 is 14. a selected combination or overall, specifically with regards to money: The fees came to a giant sum.

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Arctan or tan-1 are used to denote the inverse of Tangent.

The ratio of the perpendicular of the triangle and the base of the triangle with respect to the required angle is know as the tangent of the angle. Specifically, tan = (opposite side) / (adjacent side). The inverse tan formula is thus = tan-1[(opposite side) / (adjacent side)] according to the definition of inverse tan.

The reciprocal of the tangent is the cotangent. It is basically just the reciprocal of the tangent, it means that it can be written as the ratio of the base to the perpendicular.

Arccosine is another name for inverse cosine. It is the cos function's opposite. Also known as "arccos," occasionally. When two sides of a right triangle's length are known, it is used to measure the unknown angle.

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Yes, 2x -3y =7 is a Linear equation as the highest power of the variable is linear which is one. Although it has two variables both have one power.

Linear equations are those which have the highest power of variable as one. But it can have n number of different variables. This given equation is called a linear equation with two variables.

Moreover, any expression is called an equation when the expression is equated to some value means the equation is equal to("=") to some other expression, Number, or Zero. And here 2x+3y is being equated to 7 which is a number, So the given expression is an equation.

However if the variables x and y both came together then it will not be linear as x*y will make the power two as one of x and one of y, Which w=makes the highest power of expression two.

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Answer:

Steps in attached photo.

Step-by-step explanation:

Solution is in attached photo, to find f(x), we have to make y as the subject in terms of x, which means putting y on the left hand side of the equation.

The original cost of the tablet is $70.89 in the given algebraic equation.

A mathematical claim containing two equated algebraic expressions is known as an algebraic equation. When P and Q are polynomials, an algebraic equation has the general form P = 0 or P = Q. The term "multivariate equation" refers to an algebraic equation that has more than one variable.

Univariate equations are algebraic equations that only have one variable. Equations in algebra are balanced by definition. Due to this, the right and left sides of the equation will be equal.

Let the original cost be  x

then

15/100 = 24.99.x

x =  166.6

237.49 - 166.6

= $70.89

Thus, the original cost of the tablet is $70.89 in the given algebraic equations.

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Full question?

Lucas bought a tablet that was on sale at a 15% discount on your supra case for $24.99 which is been a total of $237.49. Write an equation to find the original cost of the tablet?

The angle 5 is an acute angle.

The correct answer is an option (a)

We know that the most common types of angles (based on their magnitude) are:

Acute Angle,

Obtuse Angle, (an angle which is less that 180° and greater than 90°)

and Right Angle (an angle that measures 90°)

There are some types of angle based on their rotation:    

Straight Angle, (an angle measuring 180 degrees)

Reflex Angle, (an angle which is greater than 180 degrees but less than 360 degrees )

and Full Rotation

As we know any angle measuring greater than 0° and less than 90° are called as the acute angles.

Here we have been given an angle 5 which is gretaer than 0 and less than 90

so, angle 5 is an acute angle.

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What type of angle is 5?

a) Acute Angles.

b) Obtuse Angles.

c) Right Angles.

d) Straight Angles

According to the given degrees the number of  images are formed when two plane mirrors are placed at 50 is 6

Plane mirror is defined as the flat surface that produces an erect visual image of a real object where front and back are reversed

Here we need to identify the number of images are formed when two plane mirrors are placed at 50.

As we all know that the coordinate is known as the highest power of variables present in an equation.

Here we have given the formula that has been used to calculate the  images are formed is written as,

=> n = (360 / θ) - 1

Here we have the value of θ = 50, then the number of images are formed when two plane mirrors is written as,

=> n = (360 / 50) - 1

=> n = 7.2 - 1

=> n = 6.2

That is approximately is 6 images.

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