The city of Rock Hill has an approximate population of 70,000. An average of 100 people move in to Rock Hill every month and 150 people move out of Rock Hill each month. The City of Greenville has an approximate population of 61,000. An average of 200 people move into Greenville every month. In how many months will the populations of the 2 cities be the same?

The number that represents Six times a number is at least four less than eight times the number is the expression 6x ≥ 8x - 4.

What is system of equations?

A system of equations, also referred to as a set of simultaneous equations or an equation system, is a finite set of equations for which we searched for the common solutions. Similar to single equations, a system of equations can also be categorised. In everyday life, systems of equations are used to model situations where the unknown values can be represented by variables.

A system of equations is made up of two or more equations with the same variables. A solution to an equation system is the point at which the lines intersect.

According to given question, x represents the number

So, The number would be 6x ≥ 8x - 4

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The equation-CuSO4.5H2O(s)→CuSO4.3H2O(s)+2H2O(g) for blue copper sulfate crytal I two-thirds the ma of the red fluorite crytal.

The following steps are used to make copper sulfate crystals:

Add a few drops of diluted sulfuric acid to a beaker of water.

Water heating. Add the powdered copper sulfate gradually as it begins to boil.

The ma of the blue copper sulfate crystal I two-thirds the ma of the red fluorite crystal

The equation-

CuSO4.5H2O(s)→CuSO4.3H2O(s)+2H2O(g)

the ma (in grams) of the blue copper sulfate crytal

It is 30 divided by 1/3 or 3.

The answer is 10

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The SSA theorem tells us that if two angles and a non-included side of one triangle are congruent to two angles and also the corresponding non-included side of another triangle, then it is claimed that the two triangles supplied are congruent to one another.

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles and squares of any side length are similar objects. To put it another way, if two triangles are similar, then their respective sides are proportionately equal and their corresponding angles are congruent.

The SSA congruence rule is not a reliable standard for determining if two triangles are congruent to one another.

Hence, there is no such SSA similarity from which you can make predictions that whether the two triangles are similar or not.

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Answer:

The GCF of 36 and 69 is 3

Step-by-step explanation:

hope this helps

The percent of decrease from 95 to 19 is 80%

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 by 100. Hence, the percentage means, a part per hundred. The word per cent means per 100.

Given that, what is the percent of decrease from 95 to 19,

Percent of decrease = final value - initial value / initial value x 100

Here, final value = 95

initial value = 19

Therefore,

Percent of decrease = 19-95 / 95 x 100

= -76 / 95 x 100

= -0.8 x 100

= -80%

Here, - sign is representing the decrease,

Hence, the percent of decrease from 95 to 19 is 80%

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Answer: $22.5

Step-by-step explanation:

refer to the image to see the steps and explanation

A horizontal line at y=4 has the following formula: Nothing slopes. The y-intercept is at 4.0.

What are the intercepts and slopes?

The slope or gradient of a line in mathematics is a numerical representation of the steepness and direction of the line.

The slope conveys how quickly the dependent variable shifts in response to changes in the independent variable. Mathematicians and economists frequently use the Greek capital D or D to denote change. The change in the horizontal axis, x, is contrasted with the change in the vertical axis, y.

Negative values are below the origin on the x-axis and to the left of the origin on the y-axis. If the y-coordinate is negative, go downhill; if the x-value is negative, start at the origin and travel to the left.

Line graphs, often referred to as XY graphs, are used to graphically display data (the results of an experiment) to show how multiple aspects, such as time and the severity of the disease, are related.

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Substitute y = 0 and solve for x to find the x-intercept, and do the same for the y-intercept.

Examples on the Y Intercept Using the y-intercept formula, we can find the y-intercept of a function by substituting x = 0 and solving for y; consequently, the given function lacks a y-intercept. 2nd Example: Find the value of "a" if the y-intercept of a function y = a (x - 1) (x - 2) (x - 3) is (0, 12).

We can solve for the y-intercept in the slope-intercept equation y=mx+b by first determining the slope between two points on a line and then writing an equation for that line.

The slope-intercept form is used to write the line's equation, which looks like this: y is equal to mx + b, where m is the slope and b is the y-intercept. We can see that the line has a slope of 6 in our equation, which is y = 6x + 2.

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Using trigonometric identities to decode, the secret message is

2 20-14-25-12 4-19-17 20-14-11-14-25 23-2-21-14-5 23-26-5-7-2-21-14-5! A Nerd who never makes mistakes!

Trigonometric Identities are equality statements involving trigonometry functions that hold true for all values of the input variables in the equation.

The side length and angle of a triangle are both subject to a variety of distinctive trigonometric identities. Only for right-angle triangles do the trigonometric identities hold true.

All trigonometric identities are built upon the foundation of the six trigonometric ratios. It consists of sine, cosine, tangent, cosecant, secant, and cotangent. These right triangle sides—including the adjacent side, opposite side, and hypotenuse side—are used to define all of these trigonometric ratios. The six trigonometric ratios are the starting point from which all fundamental trigonometric identities are derived.

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In summary, the upper and lower bounds for the volume of the box are:

Upper bound: 382.125cm³

Lower bound: 238.375cm³

The volume of the box is calculated by multiplying the length, width, and height together. In this case, the measurements of the box are given as 10cm x 7cm x 4cm, so the volume of the box is:

volume = 10cm x 7cm x 4cm = 280cm³

However, since the measurements are given to the nearest centimeter, there is a slight degree of uncertainty in the exact measurements of the box. To calculate the upper and lower bounds for the volume of the box, we need to consider the possible variations in the measurements.

The upper bound for the volume would be calculated by taking the highest possible measurements for each dimension. So, if the length could be as much as 10.5cm, the width could be as much as 7.5cm and the height could be as much as 4.5cm. Then the upper bound for the volume would be:

Upper bound = 10.5cm x 7.5cm x 4.5cm = 382.125cm³

The lower bound for the volume would be calculated by taking the lowest possible measurements for each dimension. So, if the length could be as little as 9.5cm, the width could be as little as 6.5cm and the height could be as little as 3.5cm. Then the lower bound for the volume would be:

Lower bound = 9.5cm x 6.5cm x 3.5cm = 238.375cm³

In summary, the upper and lower bounds for the volume of the box are:

Upper bound: 382.125cm³

Lower bound: 238.375cm³

And the exact volume is 280cm³

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Answer: A. The y-intercept of a graph is the point at which the graph crosses the y-axis. In the graph provided, the y-intercept appears to be at (0, -500). This means that Tasha's account balance starts at -500 dollars.

B. The y-intercept does not make sense in this situation, as a savings account balance cannot be negative. It is not possible to have negative dollars in a savings account.

C. Tasha's possible error is that she may have misinterpreted the y-axis to represent a negative balance, when in reality it represents zero balance. The y-intercept represents the initial balance of the account, which should be zero or a positive number. This error can be corrected by starting the y-axis from zero and making sure the y-intercept is positioned at a positive value.

Step-by-step explanation:

Answer:

  1/5

Step-by-step explanation:

You want the slope of line AB, given A(-2, 2) and B(3, 3).

The slope is given by the formula ...

  m = (y2 -y1)/(x2 -x1)

  m = (3 -2)/(3 -(-2)) = 1/5

The slope of the line AB is 1/5.

__

Additional comment

You can also find the slope by counting the grid squares. Point B is 1 up and 5 over from point A, so the slope is rise/run = 1/5.

A rectangle is a four-sided geometric shape with opposite sides that are parallel and equal in length. The opposite sides are called the length and width of the rectangle. Area = (30m - 0.5m) x (40m - 0.5m) = 29.5m x 39.5m = [tex]1162.75 m^2[/tex]

a. The maximum area of turf that Toby needs to buy can be found by using the measurements given by James, which are the length and width of the rectangle.

The area of a rectangle is found by multiplying its length and width, so the maximum area of turf needed would be:

Area = length x width = 30m x 40m = [tex]1200 m^2[/tex]

b. The minimum area of turf that Toby needs to buy can also be found by using the measurements given by James, but this time taking into account the margin of error due to the measurements being given to the nearest metre.

If the true length and width of the rectangle are slightly less than the measurements given by James, the mini  mum area of turf needed would be:

Area = (30m - 0.5m) x (40m - 0.5m) = 29.5m x 39.5m = [tex]1162.75 m^2[/tex]

So the minimum area of turf that Toby needs to buy would be [tex]1162.75 m^2[/tex]and the maximum area of turf that Toby needs to buy would be [tex]1200 m^2.[/tex]

In general, the measurements given by James could be off by half a meter in both directions, therefore the minimum area of turf that Toby needs to buy would be the area calculated by taking into account the margin of error, in this case, it's [tex]1162.75 m^2.[/tex]

The maximum area of turf that Toby needs to buy would be the area calculated using the measurements given by James, which is [tex]1200 m^2.[/tex]

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Answer:

14

Step-by-step explanation:

If d is 5

2(5) + 4(5) - 9 - 7

10 + 20 - 9 - 7

30 - 16

= 14

The statue of the cat is 14 meters tall.

If the ladder is 6 meters tall and it casts a shadow that is 3 meters long and the statue of a cat casts a shadow that is 7 meters long, then we can use the concept of similar triangles to determine the height of the statue of the cat.

The ratio of the height of the ladder to the length of its shadow is 6/3 = 2.

We can also assume that the ratio of the height of the statue of the cat to the length of its shadow is also 2.

so, the height of the statue of the cat can be calculated by:

height of statue of the cat = (2 * shadow length of the statue of the cat) = (2 * 7) = 14 meters

Therefore the statue of the cat is 14 meters tall.

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The notation "FG)(x" refers to the composition of two functions, "F" and "G", where the output of "G" is used as the input for "F". The notation for this is usually represented as "F(G(x))", where "x" is the input for both functions.

The rule for this notation is that the innermost function is applied first. In this case, the function "G" is applied to the input "x" first, and then the output of that function is used as the input for the function "F". The composition of the functions F and G is denoted by the notation F(G(x)) and the result of this notation is a new function obtained by applying F to the result of G on x.

The function "F" is applied to the output of the function "G", meaning that the output of the function "G" is used as the input for the function "F".. For example, if the function "F" is applied to the input "x" first, followed by the function "G", the notation would be represented as "G(F(x))", and the resulting function would be different.

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They combine their money to buy as much ice cream as they can afford. If . each pair of socks costs $4.50, what is the maximum number of pairs of socks .

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The factors of the polynomial x^3-9x^2+27x-27 are (x -3), (x - 3) and (x - 3)

The polynomial you provided is x^3-9x^2+27x-27. If you know one of the factors of this polynomial, we can use that to find the remaining factors.

One factor of this polynomial is (x-3) as it gives remainder zero when divided by (x-3)

quotient is  x² - 6x + 9

remainder is zero

So the remaining factors are (x-3) and x² - 6x + 9

Alternatively, we can factor the remaining quadratic polynomial  x² - 6x + 9

by using Factor theorem or by using difference of squares

x² - 6x + 9 = (x - 3)²

So the remaining factors are (x-3) and (x - 3)

So the original polynomial can be factored as (x-3)(x-3)(x-3) = (x-3)³

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The reflection and after that the dilation of triangle ABC is correctly represented by,

⇒ Triangle ABC is reflected across line m and then is dilated to form smaller triangle A double-prime B double-prime C double-prime.

A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

We have to given that;

Triangle ABC was reflected over line m, then dilated by a scale factor between 0 and 1.

Now, After the reflection, the triangle will be inverted and the measure of angle: A should be equal to A", B should be equal to B", and C should be equal to C".

Now, The dilation factor is less than 1 and greater than 0. So, the reflected triangle should shrink its size.

Therefore, The reflection and after that the dilation of triangle ABC is correctly represented by,

⇒ Triangle ABC is reflected across line m and then is dilated to form smaller triangle A double-prime B double-prime C double-prime.

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A circle has a total degree of 360 so 1/6 is a circle is a 60 degree angle turn.

An irregular plane figure is a circle. Every point on the circle is equally distant from the circle's fixed center. It has a radius of 1, making it a 2D shape. The Latin word "circulus," which means "little ring," is the source of the English word "circle.

A total angle of circle is 360 degrees so if a turn is of a 60 degree so then 6 turns are possible to make a whole circle giving us 1/6 part as the total of which the only 60 degree turn is taken.

Angles can be measured using one of two standard units. Degrees are the most widely used unit of measurement. A straight angle is 90° since a circle has 360 equal degrees.

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Answer:

side length of square C is 5 ft

Step-by-step explanation:

A, B andC are the areas of the sides of a right triangle.

C is the square on the hypotenuse of the right triangle.

using Pythagoras' identity in the right triangle.

the square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

C² = A² + B² = 9 + 16 = 25 ft²

the area of a square is  s² , where s is the side length, then

s² = 25 ( take square root of both sides )

s = [tex]\sqrt{25}[/tex] = 5 ft

Polynomials can be simplified by applying the distributive property to multiply the term outside the parentheses by everything inside the parentheses.

The highest degree of terms is written first, followed by the next degree, and so on, to represent a polynomial in standard form. The standard form of the polynomial is f(x) = anxn + an-1xn-1+an-2xn-2+.....+a1x+a0

An expression made up of variables, constants, and exponents that are joined together via mathematical operations is referred to as a polynomial.

A polynomial must be simplified in two ways: Firstly, combine similarities, and secondly, rewrite the terms in descending order of exponent. A polynomial can be written in standard form. To write any polynomial in standard form, consider the degree of each term. Then, from highest to lowest, left to right, you write each term in order of degree.

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The value of third angle is 30 and we can find using angle sum property.

The triangle's angles can be added up to equal 180 degrees, according to the angle sum property of triangles. A triangle has three sides, one at each vertex, and three angles. The total of the interior angles in any triangle, whether acute, obtuse, or right, is 180 degrees.

One of the most commonly employed properties in geometry is the angle sum property of a triangle. Calculating the unknown angles is primarily done using this characteristic. When the values of the other two angles are known, the measure of an unknown interior angle can be determined using the angle sum property.

Given

The two angles are given as 102 and 48

we need to find the third angle

Let the third angle be a then

using the angle sum property we get

102 + 48 + a = 180

a = 30

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The number of images formed by using the angle 120° is 3 or 30° is 11.

Angle in math is defined as the image formed when two rays are joined together at a common point and the common point here is called node or vertex and the two rays are called arms of the angle.

Here we have given that 120 degree and 30 degree object is placed symmetrically with respect to both the mirrors.

As we all know that the formula number of images formed between two mirrors kept at some angles is written as,

=> n = (360 / θ) - 1

Here we have  n is the number of images and θ is the angle between the mirrors.

The value of θ is 120 or 30.

If the angle is 120, then the number of image is calculated as,

=> n = (360 / 120) - 1

=> n = 3 - 1 = 2

Where as the angle is 30, then the number of image is calculated as,

=> n = (360 / 30) - 1

=> n = 12 - 1 = 11

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The equivalent function when the number of bacteria in a lab experiment can be modeled by the function is P(t) = 1161(9)^t

A function illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the situation.

Here, we are given that the number of bacteria in a lab experiment can be modeled by the function given as P(t) = 43(39^(2t + 3)

This will be:

= 43 × 3³ × 3(^2t)

= 1161 × 3²^t.

P(t) = 1161(9)^t

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For the number 10, the prefix used is 10. The correct option is A.

Prefixes derived from numerals or other numbers are known as numeral or number prefixes. They are used to coin numerous series of words in English and many other languages.

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 given number is 10. The prefix used for the number 10 is deci.

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The value of k for which the pair of equations 3xy - 8 = 0 and 6xky - 16 = 0 have infinitely many solutions is 4.

To solve this question, we need to find the value of k for which the two equations are equivalent. Equivalence means that the coefficients of x and y are the same and the constant terms are the same.

From the given equations, we can see that the coefficients of x and y are the same in both equations, which is 6x. The constant terms, however, are different. The first equation has a constant term of -8, while the second equation has a constant term of -16.

To make the equations equivalent, we need to make the constant terms the same. We can do this by dividing the second equation by 2. This gives us 6 ky - 8 = 0. We can see that the constant term is now the same as the first equation. Therefore, the value of k that makes the equations equivalent is k = 4.

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The complete question is:

For what value of k do the pair of equations 3xy - 8 = 0 and 6xky - 16 = 0 has infinitely many solutions?

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The 45-45-90 triangle has two congruent sides and one right angle, with each angle measuring 45°. The sides are perpendicular to each other and the length of the hypotenuse is equal to the square root of 2 times the length of a leg.

The 30-60-90 triangle has one right angle and two sides that are proportional. The shortest side is half the length of the hypotenuse and the middle side is equal to the shortest side times the square root of 3. The two acute angles in the triangle measure 30° and 60°, respectively.

In conclusion, both 45-45-90 and 30-60-90 triangles are special right triangles with distinct relationships between their sides and angles.

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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The expression that represents the height of the cylinder in terms of its radius is 3r - 5.

The cylinder's radius is specified in "r" units.

So, In comparison to its radius, r, a cylinder's height, h, is five units less.

The radius times three will be denoted by the unit "3r."

and

The radius reduced by 5 units will be shown as "3r - 5" units.

The height "h" of the cylinder is equal to 5 units less than 3 times the radius, hence the final equation is,

h = 3r-5

Thus, the expression representing the height of the cylinder in terms of the radius is h = 3r-5

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