A population of bacteria is declining at an exponential rate of 5% per day under the impact of a new medical drug. Find the population of bacteria after 20 days if the initial population of bacteria was 3,800,000.

The claim that all isosceles triangles are equivalent to one another is untrue.

There are two equal sides and two equal angles in an isosceles triangle.

The term is derived from the Greek words iso (same) and Skelos (leg).

A scalene triangle is one in which none of its sides are equal, as opposed to an equilateral triangle, which has all of its sides equal.

A right triangle with two equal-length legs is called an isosceles right triangle.

The corresponding angles would also be congruent because the lengths of the two legs of the right triangle are equal.

As a result, the two acute angles and two legs of an isosceles right triangle are congruent.

Therefore, the claim that all isosceles triangles are equivalent to one another is untrue.

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The inverse of the function f(x) = [tex]2x^2 - 4[/tex] is

[tex]f^{-1}(x) = \pm \sqrt{\frac{x + 4}{2}}[/tex]

First option is correct

What is a function?

A function from A to B is a rule that assigns to each element of A a unique element of B. A is called the domain of the function and B is called the codomain of the function.

There are different operations on functions like addition, subtraction, multiplication, division and composition of functions.

Here, f(x) = [tex]2x^2 - 4[/tex]

Let f(x) = y

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

[tex]2x^2 = y + 4\\x^2 = \frac{y + 4}{2}\\x = \pm \sqrt{\frac{y + 4}{2}}[/tex]

[tex]f^{-1}(x) = \pm \sqrt{\frac{x + 4}{2}}[/tex]

First option is correct

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There are 125 of the smallest cubes that will fill the largest cube using the size of their respective volume

The volume of cube is calculated by using a × a × a = a³ where "a" is the edge.

The volume of the smallest cube = 1.5inches × 1.5inches × 1.5inches

The volume of the smallest cube = 3.375inches³

The volume of the largest cube = 7.5inches × 7.5inches × 7.5inches

The volume of the largest cube = 421.875inches³

Thus, the number of the smallest cubes it would take to fill the largest cube is derived by

421.875inches³/3.375inches³ = 125.

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Answer: a polygon is a shape with at least three straight sides and angles, and typically five or more

Step-by-step explanation:

First, 108/9=12

This means that are 12 groups of people.

If there are 8 students in each group, 12 x 8 = 96.

96 should be your answer.

Answer: -1/2

Step-by-step explanation:

Because the degrees given is greater than 360, we must find out what its simplest degree is. The easiest way to do this is to find the remainder of the argument divided by 360.

So let's start by doing 930 / 360. This will give you a remainder of 210 degrees. So now we are finding sin 210 degrees.

Remember that sin is the y-values of the unit circle. From 0 < θ  < 180, sin θ  is positive, so we automatically know it must be a negative answer. Now, 210 is 30 degree below the x-axis, meaning that coordinate pair of (cos 210 degrees, sin 210 degrees) is (-sqrt(3)/2 , -1/2). Tje y-value, -1/2, is your answer.

Answer:

c

Step-by-step explanation:

Isosceles triangle problem can be solved by given steps

what is isosceles triangle ?

An isosceles triangle in geometry is a triangle with two sides that are the same length. Sometimes it is stated as having exactly two sides that are the same length, and other times it is specified as having at least two sides that are the same length, the latter form containing the equilateral triangle as a particular case.

explanation:

In isosceles triangle

1. Two sides of the triangle are congruent

2. The angle opposite those sides are congruent

x + 72 +72 = 180

             x  = 180 -144

             x = 36

Hence the isosceles triangle problem can be solved by above steps and explanation

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B: 1000 + 25 + Water deposit (50) + Phone connection (40) + Elect. connection (60)

1000 + 25 + 200 = 1225

The value of x is in the parallelogram is 10

In a parallelogram, the opposite sides are parallel to each other.

The opposite sides of a parallelogram are equal in length.

The measurement of opposite angles of a parallelogram is equal.

Like all other quadrilaterals, the sum of all the angles of a parallelogram is 360°.

The adjacent or the adjoining angles of a parallelogram add up to 180°.

The adjacent or the adjoining angles of a parallelogram add up to 180°.

9x +8 and 8x + 2 are adjacent angles of the parallelogram

Mathematically, 9x + 8 + 8x + 2 = 180

17x + 10 = 180

17x + = 180 - 10

17x = 170

x = 170/17

x = 10

In conclusion the value of x is 10

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Answer:

B) x + 1

Step-by-step explanation:

Consecutive integers mean continuous integers ( 1, 2 , 3 ,....). We will get the next number by adding 1 to the previous number.

Eg: 5 , 6 , 7 ,.....

6 = 5 + 1

7 = 6 + 1

So, if first number is x, then the next number will be x + 1

The ratio of the length of each transversal will be  [tex]\frac{\overline {CB}}{ \overline {AB}} = \frac{\overline {EF}}{\overline{DE}} =1[/tex]

The ratio of the lines can be compared using Three Parallel Lines Theorem.

What is Three Parallel Lines Theorem?

When two transversals are intersected by three parallel lines, the transversals are proportionally divided.

According to the three parallel lines theorem, the segments created by each transversal and the three parallel lines are proportionate.

The findings are:

Reasons:

The question is a four part question

Let the equations of the parallel lines be as follows;

Line, x; y = x

Line, y; y = x + 1

Line z; y = x + 2

The points at which transversal 1 intersect the lines x, y, and z, are;

A(0.4, 0.4), B(0.6, 1.6), and C(0.8, 2.8)

The length of segment [tex]{\overline {AB}}[/tex]  = √((0.6 - 0.4)² + (1.6 - 0.4)²) = 0.2·√(37)

The length of segment [tex]{\overline {CB}}[/tex] = √((0.8 - 0.6)² + (2.8 - 1.6)²) = 0.2·√(37)

The ratio of the lengths of the segment formed by transversal 1 is therefore;

         [tex]\sqrt{x} \ ratio\ of\ the\ length \ of segments =\frac{\overline {CB}}{ \overline {AB}} = \frac{2.\sqrt{37} }{2.\sqrt{37} } =1[/tex]

The points at which transversal 2 intersect the lines x, y, and z, are;

D(1.1, 3.1), E(1.3, 2.3), and F(1.5, 1.5)

The length of segment  [tex]{\overline {DE}}[/tex]= √((1.3 - 1.1)² + (2.3 - 3.1)²) = 0.2·√(17)

The length of segment [tex]{\overline {EF}}[/tex] = √((1.5 - 1.3)² + (1.5 - 2.3)²) = 0.2·√(17)

The ratio of the lengths of the segment formed by transversal 2 is therefore;

[tex]\sqrt{x} \ ratio\ of\ the\ length \ of segments =\frac{\overline {EF}}{ \overline {DE}} = \frac{0.2.\sqrt{17} }{0.2.\sqrt{17} } =1[/tex]

Therefore;

            [tex]\frac{\overline {CB}}{ \overline {AB}} = \frac{\overline {EF}}{\overline{DE}} =1[/tex]

Which gives;

The the comparison can also be made with the triangle proportionality theorem.

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The quadratic equations and their factors are simplified below

A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0). For writing a quadratic equation in standard form, the x² term is written first, followed by the x term, and finally, the constant term is written. The numeric values of a, b, c are generally not written as fractions or decimals but are written as integral values.

1) (x - 5)(x - 5) = x² - 5x - 5x + 25 = x² -10x + 25

2) (x + 2)(x + 9) = x² + 2x + 9x + 18 = x² + 11x + 18

3) (x + 2)(x + 3) = x² + 2x + 3x + 6 = x² + 5x + 6

4) (x + 1)(x + 2) = x² + x + 2x  + 2 = x² + 3x + 2

5) (x - 3)(x - 3) = x² - 3x - 3x + 9 = x² - 6x + 9

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The value of the variables x and y are,

11) x = 13,  y = 18.4

12) x = 6.9,  y = 8.

What is right angle triangle?

A right triangle is a triangle with one angle at a right angle, meaning that two of its sides are perpendicular. It is also known as a right-angled triangle, an orthogonal triangle, or more commonly as a rectangled triangle. Trigonometry's foundation is the right triangle's relationship between its sides and other angles.

11)Let the given triangle is a right angle triangle.

So we can use trigonometric ratio,

[tex]tan(45) = \frac{x}{13} \\x = 13(tan(45))\\x = 13[/tex]

Using this to find the value of y.

[tex]sin(45) = \frac{x}{y} \\sin(45) = \frac{13}{y} \\y = \frac{13}{sin(45)} \\y = 18.4[/tex]

So, the values of x and y are x = 13 and y = 18.4.

12) The given triangle is a right angle triangle.

So we can use trigonometric ratio,

[tex]tan(30) = \frac{4}{y}\\ y = \frac{4}{tan(30)} \\y = 6.9[/tex]

Now to find the value of x.

[tex]sin(30) = \frac{4}{x} \\x = \frac{4}{sin(30)} \\x = 8[/tex]

Hence, the values of x and y are, x = 6.9 and y = 8.

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There is no fixed range for a square root function.

Range is the set of all the output values that a function can take. In other words, it is simply the set of all values that the dependent variable can take for the function to exist. It is also  known as the co-domain.

Let us take a simple square root function given as-

y = [tex]\sqrt{x}[/tex]

Here, y is the dependent variable. We know that the square root of any number cannot be negative. Thus, y can take only positive values. Therefore, the range of a square root function is [0, ∞)

However, this is not always the case, there are various translations of a square root function for which the range might differ. For example, if we have a function as follows-

y = [tex]-\sqrt{x}[/tex]

Here, because of the minus sign, y will always be negative and thus the range will be (-∞, 0]

Hence, we conclude that there is no fixed range for a square root function.

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The fraction 5 2/3 - 3 3/4 is not equal to 1+ 2/3 + 3/4.

A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.

In this case, 5 2/3 - 3 3/4 will be:

= 5 2/3 - 3 3/4

= 5 8/12 - 3 9/12

= 1 11/12

Therefore 1 + 2/3 + 3/4

= 1 + 2/3 + 3/4

= 1 + 8/12 + 9/12

= 2 5/12

They are not the same.

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The correct answer is the 5 ways to find if two triangles are congruent are SSS, SAS, ASA, AAS and HL.

Two triangles are congruent if and only if they have the same three sides and angles.

SSS (side, side, side): SSS, which stands for "side, side, side," denotes that there are two triangles with identical angles on all three sides. The triangles are congruent if their third sides are the same as those of another triangle.

SAS (side, angle, side): "Side, Angle, Side" stands for two triangles whose two sides and one included angle are known to be equal. The triangles are congruent if two sides and the included angle of one triangle equals the corresponding sides and angle of another triangle.

ASA (angle, side, angle): ASA, which stands for "angle, side, angle," denotes the existence of two triangles whose included side and two known angles are equal. The triangles are congruent if two angles and the included side of one triangle match the corresponding angles and side of another triangle.

AAS (angle, angle, side): AAS, which stands for "angle, angle, side," denotes the equality of the non-included side and two angles in two triangles. The triangles are congruent if two of one triangle's angles and its excluded side are equal to the corresponding angles and sides of another triangle.

HL (hypotenuse, leg): The two triangles are congruent if one right-angled triangle's hypotenuse and one of its legs are equal to its corresponding hypotenuse and leg in another right-angled triangle.

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The equation that best represents the area of the forest each year is A. y = 2,000(0.94)^x.

An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.

Since the certain forest covers an area of 2,000 square kilometers and each year, this area decreases by 6%.

The equation will be:

= 2000(1 - 6%)^x

= 2000(0.94)^x

In conclusion, the correct option is A.

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The rate of change in the given interval would be 1.25 ft/s.

What is the rate of change?

The slope of a graphed function is determined using the average rate of change formula. Divide the change in y-values by the change in x-values to find the average rate of change.

By observation, we can take the points from the graph in between the given interval.

The points would be (3, 2.5) and (5, 4)

Then the rate of change = y2 - y1/ x2 - x1

                                         = 4 - 2.5/5 - 3

                                         = 2.5/2

                                         = 1.25 ft/s.

Hence, the rate of change in the given interval would be 1.25 ft/s.

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A mathematical proof is an inferential justification for a mathematical claim that demonstrates how the premises logically support the conclusion.

Result for an image A proof formula:

There are numerous techniques to demonstrate something; we'll talk about three of them: direct proof, proof by contradiction, and proof by induction. We'll discuss each of these proofs, including what they are and when and how to use them.

Proof: If n is an integer, then. We shall demonstrate the converse statement, "if n is divisible by 4, then n is divisible by 2," in order to demonstrate that "if n is not divisible by 2, then n is not divisible by 4." Let's say n can be divided by 4.

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The area of the polygon EFG with given vertices is, 7.5 units.

What is area of triangle?

The area of a triangle is the area that it completely encloses in a two-dimensional plane. A triangle is a closed shape that, as we all know, has three sides and three vertices. As a result, the total area occupied by a triangle's three sides is known as its area. The general formula for calculating a triangle's area is the product of the triangle's base and height divided by half.

Let the given vertices are,

E(3, 1), F(3, -2), G(-2, -2)

There are three vertices, so the polygon is a triangles.

Since,

Area of triangle = 1/2 x base x height.

If we draw the given vertices on the coordinate plane then the base is FG and the height of the triangle is EF.

Now to find the lengths of side FG and EF.

By using the distance formula,

[tex]d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\EF =\sqrt{(3-3)^2+(-2-1)^2} = \sqrt{9} = 3\\ FG = \sqrt{(-2-3)^2 + (-2-(-2))^2} = \sqrt{25+0} = 5[/tex]

⇒ Area = 1/2 x 5 x 3

             = 1/2 x 15

    Area = 7.5

Hence, the area of the polygon EFG is 7.5 units.

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Answer:

Step-by-step explanation:

SLOPE OF THE GIVEN LINE

6x + 18y = 36

x + 3y = 6

3y = -x + 6

3/3 y = -1/3 x + 6/3

y = -1/3 x + 2

Slope = -1/3

slope of a perpendicular line  = 3

POINT SLOPE FORM

y-4 = 3(x-(-5)

y - 4 = 3(x+5)

SLOPE INTERCEPT FORM

y-4 = 3x + 15

y = 3x + 15 + 4

y = 3x + 19

STANDARD FORM

3x - y + 15 + 4 = 0

3x - y + 19 = 0

Equation of line in point slope form is y-4= 3 (x+5), y=3x+19 is equation in slope intercept form and equation in standard form is 3x-y+19=0.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

6x+18y=36

18y=-6x+36

Divide both sides by 18

y=-6/18x+36/18

y=-1/3x+2

Slope of given line is -1/3, so slope of perpendicular line is 3.

The equation of line in point slope form with slope 3 and goes through the point (-5,4) is given below

y-4= 3 (x+5)

To find the equation in slope intercept form we need to find y intercept

4=3(-5)+b

4=-15+b

19=b

y=3x+19 is equation in slope intercept form.

The equation in standard form is 3x-y+19=0

Hence,  equation of line in point slope form is y-4= 3 (x+5), y=3x+19 is equation in slope intercept form and equation in standard form is 3x-y+19=0.

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The population increases by 4.3% each year

From the question, we have the following parameters that can be used in our computation:

Population of a city next year = Multiply its current population by 1.043

This means that

Growth factor =1.043

The percentage population increment is then calculated as

Percentage population increment = Growth factor - 1

Substitute the known values in the above equation, so, we have the following representation

Percentage population increment = 1.043 - 1

Evaluate

Percentage population increment = 0.043

Express as percentage

Percentage population increment = 4.3%

Hence, the percentage is 4.3%

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Answer: [tex](-\infty, \infty)[/tex]

Step-by-step explanation:

Absolute value is always non-negative.

a. The number of ways that this is done, if the order of the choices is relevant is 12 ways.

b. The number of ways that this be done, if the order of the choices is irrelevant is 6 ways

Combinations are also referred to as selections. Combinations implies the selection of things from a given set of things. In this case, we intend to select the objects.

Combination formula

= n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time.

When the orders are relevant, this will be:

= 4! / (4 - 2!)

= 4! / 2!

= 12

When orders are irrelevant, this will be:

= 4! / (4 - 2!)2!

= 6 ways

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Answer:

c=13.4

Step-by-step explanation:

Answer:3; the ride costs $3 per mile

Step-by-step explanation:

Rate of Change of the function is 3. then the ride costs $3 per mile.

The average Rate of Change of the function f(x) can be calculated as;

[tex]f(x) = \dfrac{f(b) - f(a)}{b-a}[/tex]

We are given  the total cost of a ride-sharing trip, y, is a function of the distance traveled,

Distance (mi), Total Cost ($). y

2                       0

5                       1  

8                        2

11                       3

14                       4

Therefore,

Rate of Change of the function

(5 - 2) / (1- 0)

= 3 / 1

Hence, we can conclude that the ride costs $3 per mile.

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By using the law of exponents, it has been proved that

[tex]a^{-n} = \frac{1}{a^n}[/tex]

What are exponent?

Exponent tells us how many times a number is multiplied by itself.

For example : In [tex]2^4 = 2 \times 2 \times .... \times 2[/tex]

Here, 2 is multiplied by itself 4 times.

If [tex]a^m = a \times a \times a \times ..... \times a[/tex] (m times),

a is the base and m is the index.

The laws of exponents are

[tex]a^m \times a^n = a^{m+n}\\\\a^ m \div a^n = a^{m - n}\\\\a^ 0 =1\\\\a^{-m} = \frac{1}{a^m}\\\\(ab)^m = a^m \times b^m\\\\(\frac{a}{b})^m = \frac{a^m}{b^m}\\\\(a^m)^n = a^{mn}[/tex]

We know this law

[tex]a^p \times a^q = a^{p + q}[/tex]

Putting  p = n and q = -n

[tex]a^n \times a^{-n} = a^{n + (-n)} = a^{n - n} = a^0 = 1[/tex]

So,

[tex]a^n \times a^{-n} = 1\\a^{-n} = \frac{1}{a^n}\\a^{-n} = \frac{1^n}{a^n}\\a^{-n} = (\frac{1}{a})^n[/tex]

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The lowest form of 6/42 is 1/7 and,

the lowest form of 14/28 is 1/2.

What is the lowest form of fraction?

When there is no common factor between the fraction's numerator (top) and denominator (bottom), the fraction is said to be in its simplest form. This is also known as its Lowest form.

In fraction 6/42, both denominator and numerator have common factor as 6, So we divide the denominator and numerator by 6.

Hence, we get 1/7.

Similarly, In fraction 14/28, both denominator and numerator have common factor as 14, So we divide the denominator and numerator by 14.

Hence, we get 1/2.

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