The number of butterflies in an exhibit is decreasing at an exponential rate of decay. The number of butterflies is decreasing by 5% every year. There are 500 butterflies in the exhibit right now. How many butterflies will be in the exhibit in 7 years? Round your answer to a whole number.

The intersection of the two lines represent the solution of the system of equations.

Hence the intersection of the two lines in this problem has the coordinates given as follows:

(2,1).

The definition of the system of equations in this problem is given as follows:

Replacing the second equation into the first, the variable x is obtained as follows:

x + 2(2x - 3) = 4

x + 4x - 6 = 4

5x = 10

x = 2.

Then, replacing x = 2 into the second equation, the variable y is given as follows:

y = 2(2) - 3 = 1.

The solution means that the linear functions x + 2y = 4 and y = 2x - 3 intersect at the coordinates (2,1).

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A hole in a graph asymptote is a point where the curve of the graph does not go through, but instead veers away from the point and goes towards an infinite value.

A hole in a graph asymptote is a point at which the curve of the graph does not go through, but instead veers away from the point and goes towards an infinite value. This can occur when the graph is a function of two or more variables, and the asymptote is the line at which the graph tends towards infinity. As the graph approaches the asymptote, it will either increase or decrease in value. The hole in the asymptote is the point where the graph does not pass through and instead deviates from the asymptote and goes towards infinity. This is often seen when the graph is a graph of a rational function, where the asymptote is formed by the denominator of the function. A hole in the graph asymptote can also be caused by the fact that the graph is not continuous, or by the presence of multiple asymptotes. In this case, the hole is formed by the intersection of the two asymptotes.

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90 degrees or a straight angle is always one angle. The hypotenuse is the side that has an angle of 90° on it. Always, the hypotenuse is the longest side. The remaining two inner angles add up to a total of 90°.

Right angles are created when two straight lines cross at a 90° angle or are perpendicular to one another at the intersection.

An angle having a value of 90° is considered to be a right angle. Right angles are created when two rays cross one other and angle 90 degrees at the intersection. The screen of a mobile phone, the borders of a cabinet, and other places are only a few examples of where we might see it.

90 degrees or a straight angle is always one angle. The hypotenuse is the side that has an angle of 90° on it. Always, the hypotenuse is the longest side. The remaining two inner angles add up to a total of 90°.

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Let us take f(x)=x^2 to define the domain and range of a function.

The set of all values that the function might return when the domain is provided as input is the definition of range.

In real life, range is employed to perform mathematical computations. Range can be used to determine how much time has elapsed, just like when determining your age. You were born in 2005, which makes the current year 2020. What age are you?

The collection of all potential inputs for a function is its domain. For instance, the domain of f(x)=x^2 and g(x)=1/x are all real integers with the exception of x=0.

The collection of potential output values for a function is known as its range. For instance, the range is the non-negative real numbers for the function f(x)=x^2 on the domain of all real numbers (x∈R), which may be represented as f(x)0 (or [0,∞] using interval notation).

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Answer:

[tex]x^3+x^2-5x+5-\frac{30}{x+5}[/tex]

Step-by-step explanation:

[tex]\frac{x^4 + 6x^3 -20x-5}{x+5} \\ \\ =\frac{x^3(x+5)+x^3-20x-5}{x+5} \\ \\ =\frac{x^3(x+5)+x^2(x+5)-5x^2-20x-5}{x+5} \\ \\ =\frac{x^3(x+5)+x^2(x+5)-5x(x+5)+5x-5}{x+5} \\ \\ =\frac{x^3(x+5)+x^2(x+5)-5x(x+5)+5(x+5)-30}{x+5} \\ \\ =x^3+x^2-5x+5-\frac{30}{x+5}[/tex]

Step-by-step explanation:

the domain of a function is the interval or set of all valid x (input) values.

the range of a function is the interval or set of all valid y (function result) values.

we see in the graph that we get for y all continuous values between 0 (max) and -9 (min).

both end points are filled, so we need to include them into the interval of valid values (via the <= or >= signs).

so the range is

-9 <= y <= 0

The slope of the line is -7 and the y-intercept is negative 3. The line is drawn below.

The collection includes all locations on the surface of the shape (x, f(x)) that make up a function of f's graph. We may alternatively say that the graph of f is the curve of y = f. (x). As a result, the diagram of an equation is a particular instance of the graphs of functions.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

The equation is given below.

y = -7x - 3

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Answer:

SAS proves congruence.

Step-by-step explanation:

⭐What is SAS?

⭐How do we determine if 2 triangles are congruent by SAS?

⭐Example (figures not drawn to scale):

Answer:

distribute

2 and r  ; 2 and + 3

2 * r = 2r

2 * 3 = 6

combine:

2r + 6

Step-by-step explanation:

Step-by-step explanation:

2 (r+3)

You are asked to multiply 2 by (r + 3).

To remove the ()'s, you must multiply 2 by both terms within the ()'s:

2(r + 3)

= 2 * r + 2 * 3

= 2r + 6

Please comment below if you have further questions for this problem.

The angle of elevation of the sun if a building of 135 feet tall cast a shadow  is 42°.

The angle of elevation is an angle that is formed between the horizontal line and the line of sight.

To calculate the angle of elevation, we use the formula below.

Formula:

Where:

From the question,

Given:

Substitute these values into equation 1

Hence, the angle of elevation of the sun is 42°.

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The angle pair that forms alternate interior angles are: C. ∠4 and ∠6.

Alternate interior angles are angles that lie on alternate sides of a transversal but on different parallel lines. They are also congruent angles.

In the figure given, lines x and y are parallel to each other, and are crossed by the transversal a.

Angle 4 and 6 lie on each of the parallel lines but on alternate sides of the transversal a.

Also, angle 3 and angle 5 lie on lines x and y that are parallel which is intersected by line a.

Angles 3 and 5, and angles 4 and 6 are both pairs of alternate interior angles.

Therefore, the answer is: C. ∠4 and ∠6.

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The equation does not include the value of 6, we can also express the solution as –[infinity], 6), which excludes the value of 6

The equation 5x - 10 ≤ 20 can be solved by isolating the x variable and rearranging the equation to solve for x. First, we need to add 10 to both sides of the equation in order to get all the terms on one side of the equation. This gives us 5x ≤ 30. Then, we need to divide both sides of the equation by 5 in order to isolate the x variable. This results in x ≤ 6. The solution for this equation can be written as the set of all real numbers less than or equal to 6, which can be represented as –[infinity], 6]. Since this equation does not include the value of 6, we can also express the solution as –[infinity], 6), which excludes the value of 6.

In more detail, when solving a linear inequality, the objective is to isolate the variable on one side of the inequality sign. The first step is to move all terms not containing the variable to the other side of the inequality sign by performing the opposite operation of the given equation. In this case, the equation 5x - 10 ≤ 20 has a subtraction on the left-hand side, so the opposite operation is to add 10 to both sides of the equation. This results in 5x ≤ 30.

Next, we need to divide both sides of the equation by 5 to isolate the x variable. This yields x ≤ 6. The solution for this equation is the set of all real numbers that are less than or equal to 6, which can be written as –[infinity], 6]. Since the equation does not include the value of 6, we can also express the solution as –[infinity], 6), which excludes the value of 6.

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You may get back payment for limited capability for work.

In the event that you receive Universal Credit, the decision-maker will affix a letter indicating whether you passed the assessment to your journal. Whether or not you pass, you can still receive Universal Credit. If you don't succeed, though, you might have to start seeking employment.

If you did well on the test, the letter will state which group you were assigned to. In most cases, you will get additional funds for your Universal Credit claim if you have been assigned to the Limited Capability for Work Related Activity (LCWRA) category. Additionally, you might get some back pay.

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There are 37 elves are helping Santa by solving both the equations x + y=58 and 4x+2y=158 the concept of equations.

Equations are mathematical expressions that have two algebraic expressions on either side of an equals (=) sign. This relationship is illustrated by the left and right expressions being equal to one another. L.H.S = R.H.S is the first term in every mathematical equation.

According to the question we assume the number of reindeer are x and number of elves are y.

Total 37 elves are helping Santa. There are a total of 58 reindeer and elves helping Santa get ready for Christmas hence the equation of given condition is as follows:

x + y=58

Each reindeer has 4 legs and each elf has 2 legs counted 158 legs when all the reindeer and elves were in Santa’s workshop helping Santa. Hence the equation of given condition is as follows:

4x+2y=158

By solving both the above equation multiplying first equation by 2

2x+2y=116

Subtract both the above equation

2x=42

x=21

Hence the number of reindeer are x=21

Inserting value of x in first equation gives y=37

The number of elves is y=37

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Yes, two is the zero of the given polynomial  x³+ 4x²- 3x - 18 is the true statement.

As given in the question,

Given polynomial is equal to :

x³+ 4x²- 3x - 18

Check whether two is the zero of the given polynomial  x³+ 4x²- 3x - 18 we have,

let f(x) =  x³+ 4x²- 3x - 18

If f(2) = 0 then 2 is the zero of the given polynomial.

Substitute the value of x = 2 in f(x) we get,

f(2) = 2³ + 4(2)² -3(2) -18

⇒ f(2) = 8 + 16 - 6 -18

⇒ f(2) = 24 - 6 - 18

⇒ f(2) = 18 - 18

⇒f(2) = 0

Therefore, the two is the zero of the given polynomial  x³+ 4x²- 3x - 18 is the true statement.

The above question is incomplete , the complete question is:

Is 2 a zero of the polynomial x³+ 4x²- 3x - 18 ?

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Answer:

m<1+m<2+m<3=180°

90°+26°+m<3=180°

116°+m<3=180°

m<3=180°-116°

m<3=64°

m<3=64

The algebraic expression for 10 more than a number is x + 10 or 10 + x.

The x in the expression is called a variable, which can be represented by any letter in the alphabet.

An algebraic expression is a mathematical expression that consists of numbers, variables and operators, and its value can change.

Some basic mathematical operators are +, -, x and /.

The given phrase states that a result can be obtained by adding 10 more to the variable.

The variable x can be replaced by any number.

If x equals 2, then the expression x + 10 has a value of 12.

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The roots of the quadratic equation are real and distinct

What is Quadratic Equation?

A quadratic equation is a second-order polynomial equation in a single variable x , ax² + bx + c=0. with a ≠ 0. Because it is a second-order polynomial equation, the fundamental theorem of algebra guarantees that it has at least one solution. The solution may be real or complex.

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

where ( b² - 4ac ) is the discriminant

when ( b² - 4ac ) is positive, we get two real solutions

when discriminant is zero we get just one real solution (both answers are the same)

when discriminant is negative we get a pair of complex solutions

Given data ,

Let the quadratic equation be represented as A

Now , the value of A is

2x² + 4x - 7 = 0   be equation (1)

On simplifying the equation , we get

The roots of the quadratic equations are

x = [ -b ± √ ( b² - 4ac ) ] / ( 2a )

Substituting the values in the equation , we get

x = [ -4 ± √ ( ( 4 )² - 4 ( 2 ) ( -7 ) ) ] / 2 ( 2 )

On simplifying the equation , we get

x = [ -4 ± √ ( 16 + 56 ) ] / 4

x = [ -4 ± 6√2 ] / 4

x = ( -2 + 3√2 ) / 2

And ,

x = ( -2 + 3 ) / √2

Therefore , the roots are x = ( -2 + 3√2 ) / 2 and x = ( -2 + 3 ) / √2

Hence , the roots of the equations are real and distinct

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By observing the concave nature of the polynomial graph , We can tell the leading coefficient is positive or negative .

Sums of terms with the form  kxⁿ, where K is any number and N is a positive integer, are known as polynomials.

The term with the greatest x power is the leading term in a polynomial function. The leading coefficient is the coefficient of the leading phrase.

If the polynomial graph is concave downwards, The leading coefficient is negative.

If the polynomial graph is concave upwards, The leading coefficient is positive.

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Answer: [tex]\frac{-7}{8}[/tex]

Step-by-step explanation:

    First, we will need to find the slope of line r.

[tex]\displaystyle \frac{y_{2} -y_{1} }{x_{2} -x_{1}} =\frac{9-1}{8-1}=\frac{8}{7}[/tex]

    Next, we know that perpendicular slopes are negative reciprocals of one another. To find the slope of line s, we will find the negative reciprocal of line r's slope.

[tex]\displaystyle \frac{8}{7} \rightarrow \frac{-7}{8}[/tex]

In 1 gallon contains 768 ounces.

In the given, 1 cup = 8 ounce

4 cups = 1 quart

4 quart = 1 gallon

We can see that, 1 gallon is 4 quarts,

So, 6 gallon = 6×4= 24 quarts

Also 1 quart is 4 cups

So, 24 quarts =24×4=96 cups

1 cup is 8 ounce

So, 96 cups = 96×8=768 ounces

Therefore, 768 ounce in 1 gallon.

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There will be 128 ounce in 1 gallon.

given values in the question:

 1 gallon = 4 quarts

 1 quarts = 4 cups  

 so we have 16 cups in 1 gallon .

next we are given in the question that:

  1  cup = 8 ounce

and in 1 gallon we have 16 cups .

and we have to find number of ounce 1 gallon have , number of ounce have direct relation with number of cups.

so in 1 gallon , we have 16* value of 1 cup in ounce

hence value of 1 gallon = 16 * 8 ounce

=> 1 gallon = 128 ounce

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Answer:

x = 6

y = 2

(6,2)

Step-by-step explanation:

THE SOLUTION WORK IS ATTACHED

2x² 7x 0 is not a quadratic equation.

A quadratic equation is an equation of the second degree, meaning it contains at least one term that is squared. The standard form of quadratic equation is ax^2+bx+c

Standard Form: y = a x 2 + b x + c y=ax^2+bx+c y=ax2+bx+c.

Factored Form: y = a ( x − r 1 ) ( x − r 2 ) y=a(x-r_1)(x-r_2) y=a(x−r1)(x−r2)

Vertex Form: y = a ( x − h ) 2 + k y=a(x-h)^2+k y=a(x−h)2+k.

Comparing given  equation 2x² 7x 0 with standard form of quadratic equation is , we are not able to find values of a,b,c.

Hence,2x² 7x 0 is not a quadratic equation.

2x² 7x 0 is not a quadratic equation.

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The group of things from which data are taken for a statistical research is referred to as a population in statistics. A data pool for study might consist of numerous things, many individuals, etc.

large-scale numerical data collection and analysis, especially with the aim of extrapolating proportions in the total from those in a representative sample.

The study and development of techniques for gathering, processing, interpreting, and presenting empirical data are the focus of the science of statistics. It could be a collection of things, a gathering of people, etc. It serves as the study's data set.

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Therefore, the solution to this given problem is the standard deviation comes out to be 139.41 .

A measure of how far measurements for a group deviate from the mean is called standard deviation (mean or expected value). A low standard deviation indicates that most of the numbers are within a few standard deviations of the average, whereas a large standard deviation indicates that the numbers are more dispersed.

Here,

Given:

sample size(n) =100

SE =13.941

Since we are aware, the standard error of the mean

=> SE = [tex]\frac{\alpha }{\sqrt{n} }[/tex]

So α = SE * [tex]\sqrt{n}[/tex] = 13.941 * 10 = 139.41

Therefore, the standard deviation comes out to be 139.41 .

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with the Application of Analytical geometry a dotted line is used to mark x=3  inequalities on a number line

what is Analytical geometry ?

Combining algebra and geometry is called analytical geometry. Analytical geometry aims to present geometric figures through algebraic equations in either a two-dimensional or three-dimensional domain.

solution:

The graph below shows the inequality 3.

All points that lie in the shaded area satisfy the equation x<3.

In other words, x can take any value less than 3.

x≠3 or any number that is greater than 3.

Since there is strict inequality,

i.e., x<3, the points that lie on the line

x=3 will not satisfy the equation.

Therefore, a dotted line is used to mark x=3.

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Answer:

AO = 14

Step-by-step explanation:

The figure we are given shows the intersection of the medians of this triangle. In fact, the point of intersection of the medians is called the centroid. In this problem, O is the centroid.

The intersection of the medians of a triangle has some properties:

(1) The distance from a vertex of the triangle to the centroid is 2/3 of the distance from said vertex to the opposite side of the vertex

(2) The distance from the centroid to a side opposite of a vertex is 1/3 of the distance from said vertex to the opposite side of said vertex

(3) The longer part of the median partitioned by the centroid is twice the distance of the shorter part of said median partitioned by the centroid

We can use the first property stated to find the distance of AO.

[tex]AO = \frac{2}{3} AM[/tex]

We are given that AM = 21

[tex]AO = \frac{2}{3}(21)[/tex]

[tex]AO = \frac{42}{3}[/tex]

[tex]AO = 14[/tex]

Answer:

  x = -3

Step-by-step explanation:

You want the x-coordinate of the relative maximum of f(x) = x³ +4x² -3x +1.

The x-coordinates of the relative extrema of the function will be those values of x where the derivative of the function is zero.

  f'(x) = 3x² +8x -3 = (x +3)(3x -1)

The derivative is zero where its factors are zero, at x = -3 and x = 1/3.

The leading coefficient of this cubic is positive, so the function values generally increase from left to right. That means the relative maximum will have the lowest x-coordinate: x = -3

The x-coordinate of the relative maximum is -3.

Answer:

60

Step-by-step explanation:

One way to do this is to take your total volume ([tex]120cm^{3}[/tex]) and divide that by the volume of each cube ([tex]2cm^{}[/tex]).

120 ÷ 2 = 60

The chef can make 60 cubes.

Let's check our work.

To check our work, we can take the volume of each cube, and multiply that by the number of cubes.

2 × 60 = 120

Therefore, the chef can produce 60 cubed watermelons.