Find the inequality represented by the graph.

The equation that models the function is P(t) = 20400(1,09)⁺ and the fox population in 2008 is 40648

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

Initial population of fox = 20400

Rate of growth = 9 percent per year

These parameters can be presented as

Initial population of fox, a = 20400

Rate of growth, r = 9%

An exponential function is represented as

P(t) = a(1 + r)⁺

So, we have:

P(t) = 20400(1 + 9%)⁺

Evaluate

P(t) = 20400(1,09)⁺

Recall that

t = 0 in 2000

So, the value of t in 2008 is

t = 2008 - 2000

t = 8

Substitute t = 8 in P(t) = 20400(1,09)⁺

So, we have

P(8) = 20400(1.09)⁸

Evaluate

P(8) = 40648

So, the population is 40648

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The equation that best defines the length of the equal piece is 4x+2¹-12

We should know that an equation is a mathematical model that shows the equality of two sides of an expression

Based on the given condition 12-24=4*x

Applying multiplicative distribution -12=4x

Rearrange the equation 4x=-12

Calculate the product of the quotient x=-3

Now 24feet divided by -3 =-4

Since it deals with length =4

In conclusion the equation that determines the length of each equal piece is  4x+2¹-12

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The inequality is equivalent to 5+y+b0.

A positive number divided by both sides of an inequality results in an equal inequality. And if the inequality symbol is reversed, division on both sides of an inequality with a negative value results in an analogous inequality.

Inequalities that convey the same information are referred to as equivalent inequalities.

In mathematics, larger than symbol (>), less than symbol (), less than or equal to symbol (), and not equal to symbol () are the five inequality symbols.

Algebraic equations with equivalent solutions or roots are called equivalent equations. An analogous equation is one that is created by adding or removing the identical quantity or expression from both sides of a given equation.

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There are four basic properties of numbers: commutative, associative, distributive, and identity.

1.Commutative Property

a. Addition

. When two numbers are added, the sum is the same regardless of the order in which the numbers are added.

3 + 5 = 8       or       5 + 3 = 8

b. Multiplication. When two numbers are multiplied together, the product is the same regardless of the order in which the numbers are multiplied.

3 x 5 = 15       or       5 x 3 = 15

2.Associative Property

a. Addition. When three or more numbers are added, the sum is the same regardless of the way in which the numbers are grouped.

6 + (4 + 3) = 13   or   (6 + 4) + 3 = 13

b. Multiplication. When three or more numbers are multiplied, the product is the same regardless of the way in which the numbers are grouped.

6 x (4 x 3) = 72   or   (6 x 4) x 3 = 72

3.Distributive Property

The sum of two numbers times a third number is equal to the sum of each addend times the third number.

5 x (7 + 2) = 45   or   5 x 7 + 5 x 2 = 45

4.Identity Property

a. Addition. The sum of any number and zero is that number.

12 + 0 = 12

b. Multiplication, The product of any number and one is that number.

18 x 1 = 18

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The various types of inverse function are the inverse of trigonometric functions, rational functions, hyperbolic functions and log functions

If the function is denoted by ‘f’ or ‘F’, then the inverse function is denoted by f⁻¹or F⁻¹.

A function accepts values, performs particular operations on these values and generates an output. The inverse function agrees with the resultant, operates and reaches back to the original function.

The various types of inverse function are:

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Answer:

We can be able to use compatible numbers to estimate the quotient of 925/29 if the whole number that is part of the decimal is less than the divisor, we need to be able to rename the decimal.

Step-by-step explanation:

In Southwest Direction, the left side of the graph of this function point.

What is a function?

A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.

The x-values are input into the function machine. The function machine then performs its operations and outputs the y-values. The function within can be any function.

f(x)= [tex]x^{4}[/tex]-x³+4x-2

it will not pass through the origin, as, f(0)=-2

It is a polynomial of degree four.

The function in question contains two genuine roots and two fictitious roots.

In the third quadrant and a small portion of the fourth quadrant, the left side of the function is located after drawing a line of symmetry. A line of symmetry is at approximately x=0.14.

Hence, In Southwest Direction, the left side of the graph of this function point.

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Answer:

  (a)  A = W(140 -W)

  (b)  W = 70

  (c)  4900 square yards

Step-by-step explanation:

You want an expression for the rectangular area that can be enclosed by 280 yards of fence, if that area has width W. Further, you want the value of W that maximizes the area, and the size of that maximum area.

The perimeter of the rectangle with length L and width W is ...

  P = 2(L +W)

Then the length can be found from the width as ...

  L = P/2 -W

For P=280, this is ...

  L = 140 -W

The area is the product of length and width:

  A = LW

  A = (140 -W)(W)

The area expression describes a downward-opening parabola with zeros at W=0 and W=140. The vertex (maximum) of the parabola is on the line of symmetry, halfway between these zeros. The value of W there is ...

  W = (0 +140)/2 = 70

The area is largest for W = 70.

For that value of W, the area is ...

  A = (140 -70)(70) = 70² = 4900 . . . . . square yards

__

Additional comment

The generic solution to the area problem when fence is on all sides is that the shape is a square.

If the cost of fence is different for the different sides, the total cost in the east-west direction is equal to the total cost in the north-south direction when cost is minimized.

The relation:

(9, -1) (4,2) (5,3) (8, -1) (3, 0)

Is a function, because each element of the domain appears only once.

A relation maps elements from a set, called the domain, into elements from another set, called the range.

Such that the element x being mapped into the element y is written as:

(x, y).

A relation is a function only if each element in the domain is mapped into only one element of the range.

Here we have the relation:

{  (9, -1) (4,2) (5,3) (8, -1) (3, 0)}

We can see that no element of the domain appears twice, so yes, this is a function.

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Answer:

At least 8 rows

Step-by-step explanation:

45 divided by 9 is 5. That is 5 rows

9x3= 27 and there are 23 adults. So that is 3 rows

5+3=8

8 rows in total.

The area of the larger floor is 64 square units when w = 8 and l = 8. which is the correct answer would be an option (B).

To compare the values, we must first calculate each given situation. The area of any given rectangle is length times width.

If w = 7 and l = 9

A = l × w = 8 × 6 = 48

If w = 8 and l = 8

A = l × w = 8 × 8 = 64

So, the second case would obtain a larger area.

Therefore, the area of the larger floor is 64 square units when w = 8 and l = 8.

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Answer:

4 [tex]\frac{1}{8}[/tex]

Step-by-step explanation:

Using cartesian coordinate system, the points are plotted on the graph below which shows A in the fourth quadrant, B in the third quadrant, C in the first quadrant, D and E in the second quadrant and F on the first quadrant.

A coordinate graph is a graph with two axes which are placed perpendicular to each other. These two axes are called x-axis and y-axis. The vertical line is the y-axis and the horizontal line is the x-axis. It is also called a coordinate plane, a Cartesian plane, and a Cartesian coordinate system.

Kindly check the attached graph below

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Answer: plot point

Step-by-step explanation: plot point, quadrant or axis be smart and learn nivia.

If triangle has 2 congruent sides and 2 congruent angles ,such a triangle is known as Isosceles triangle.

What is congruent triangle?

Congruence of triangles: 2 triangles square {measure} aforesaid to be congruent if all 3 corresponding sides square measure equal and every one the 3 corresponding angles square measure equal in measure. These triangles may be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with one another. The image of congruity is’ ≅’.

Main Body:

A triangle with two congruent sides and congruent base angles is termed as an isosceles triangle.

If two sides of a triangle are congruent, then by isosceles triangle property, the angles opposite to these sides are congruent.

That is, base angles of the triangle are congruent.

Then, such a triangle is known as Isosceles triangle.

Therefore, option B is correct.

The actual question with option is in figure.

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Answer:

The height of the 4th bounce would be 4.7458321; rounded would be 4.8.

Step-by-step explanation:

We can figure this question out by first converting the 83% into a decimal, by bringing back 2 decimal places:

0.83.

And then setting up this equation:

0.83 x 10 = 8.3

Now, this is for 1 bounce. We have to do this 4 more times:

0.83 x 8.3 = 6.889

3rd time:

0.83 x 6.889 = 5.71787

4th time:

0.83 x 5.71787 = 4.7458321.

Now, we can round this answer to:

4.8

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Answer:

160 minutes can be spent on long distance calls each month.

Step-by-step explanation:

first we know that there is standard charge of $17 for basic service, $0.05 cost per minute with a budget of $25.

let's write that into an equation to solve for (a) which will be number of minutes.

17 + a(0.05) = 25

solving:

17 + a(0.05) = 25

carry across the 17 whilst changing the sign, or some people is also thought to minus on both sides to get rid of a certain variable.

a(0.05) = 25 - 17

a(0.05) = 8

carry across the multiplication of 0.05 which will then turn into division, or divide by 0.05 on both sides to remove it.

[tex]a = \frac{8}{0.05} [/tex]

a = 160

therefore 160 minutes can be spent on long distance calls each month.

You can redefine your answer more simply to hours by dividing by 60, which gives 2 hours and 40 minutes

Answer: -23

Step-by-step explanation:

[tex]jk^2 -m=(-5)(2^2)-3=-5(4)-3=-20-3=-23[/tex]

Yes, a cubic graph is an exponential.

What is Cubic Graph?

A cubic graph in the study of graph theory is a graph with all of its vertices having degree three. A cubic graph is a 3-regular graph, to put it another way. Trivalent graphs are another name for cubic graphs. A cubic bipartite graph is known as a bicubic graph.

What is Exponential?

The mathematical expression f(x)=exp or ex denotes the exponential function. Unless otherwise stated, the phrase usually refers to the positive-valued function of a real variable, though it can also be applied to complex numbers or extrapolated to other mathematical objects like matrices or Lie algebras.

Graphs of Exponential Functions if;

When the base is greater than 1, the exponential function has the following characteristics and you can easly understand from this :

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The sphere's radius is 5, and its center is at (0, 3, -4).

A sphere is a geometrical object that resembles a two-dimensional circle in three dimensions.

In three-dimensional space, a sphere is a collection of points that are all located at the same distance from a single point.

The radius of the sphere is denoted by the letter r, and the given point is its center.

List a few typical sphere examples from everyday life.

In everyday objects, sphere shapes can be found in the form of marbles, balls, oranges, yarn, and bubbles.

So, the center and radius of the sphere will be:

We have the sphere's equation, which is given by and has a radius of r.

(x - h)² + (y - k)² + (z - l)² = r² ...(1)

We must convert the following equation in order to determine the center and radius of the provided sphere.

x² + y² + z² - 6y + 8z = 0

By combining the x, y, and z terms and filling in the square, we obtain

x² + (y² - 6y + 9) +(z² + 8z + 16) = 9 + 16

(x - 0)² + (y - 3)² + (z + 4)² = 52

So, the sphere's center is at (0, 3, -4) and its radius is 5.

Therefore, the sphere's radius is 5, and its center is at (0, 3, -4).

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Complete question:

Find the center and radius of the sphere x2 + y2 + z2 - 6y + 8z = 0.

Answer:

expanded: 7+0.08

standard: 7.08

Step-by-step explanation:

The hundredths place is the second digit after the decimal, so 8 hundredths is 0.08.

Answer:

some do but not all

Step-by-step explanation:

some do but there is a right isosceles triangle where there is 45 45 and 90 degrees

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Answer:

add up the exponents of each term and select the highest sum.

The value of x and the unknown angles of the triangle are as follows;

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two remote interior angles of the triangle.

Therefore, let's find the value of x using the exterior angle theorem.

Hence,

37 + 3x + 47 = 5x + 62

3x - 5x + 37 + 47 = 62

-2x = 62 - 37 - 47

-2x = -22

x = -22 / -2

x = 11

Therefore, the angles are as follows:

3x + 47 = 3(11) + 47 = 33 + 47  = 80 degrees

5x + 62 = 5(11) + 62 = 55 + 62 = 117 degrees

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The adult male foot length of 30.8 cm is significantly low.

According to the Range Rule of Thumb, the range is approximately four times the standard deviation. In statistics, another measure of spread is the standard deviation. It explains how your data is grouped around the mean.

According to the range rule, the standard deviation of a sample is approximately equal to one-fourth of the data range. To put it another way, s = (Maximum - Minimum)/4. This is a simple formula to use, but it should only be used as a rough estimate of the standard deviation.

The value will then be:

= (30.8 - 27.27) / 4.

= 3.53 / 4

= 0.8825

The number is less than the standard deviation of 1.46.

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Answer:

d

Step-by-step explanation:

This is an example of the distributive property, a(b-c) = a(b) - a(c)

a=t, b=14, c=5

t(14-5) = t(14) - t(5)

Applying the definition of an Isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.

In geometry, an isosceles triangle is a triangle that has at least two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case. Examples of isosceles triangles include the isosceles right triangle, the golden triangle, and the faces of bipyramids and certain Catalan solids.

The two equal sides are called the legs and the third side is called the base of the triangle. The other dimensions of the triangle, such as its height, area, and perimeter, can be calculated by simple formulas from the lengths of the legs and base. Every isosceles triangle has an axis of symmetry along the perpendicular bisector of its base. The two angles opposite the legs are equal and are always acute, so the classification of the triangle as acute, right, or obtuse depends only on the angle between its two legs.

An Isosceles triangle has a vertex angle and two equal base angles.

Given that triangle TIC is an isosceles triangle:

angle I is the vertex angle = 90 degrees

angle T is a base angle

angle C is also a base angle

Thus:

angle C and angle T are congruent or equal to each other.

Therefore,

    Angle T = (180 - 90)/2

⇒ Angle T = 90/2

⇒ Angle T = 45 degrees.

applying the definition of an isosceles triangle, given that isosceles triangle TIC has a vertex angle I of 90 degrees, the measure of angle T is 45 degrees.

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Using trigonometric ratio the distance to the control tower is 750.7ft

In trigonometry, there are six trigonometric ratios, namely, sine, cosine, tangent, secant, cosecant, and cotangent. These ratios are written as sin, cos, tan, sec, cosec(or csc), and cot in short.

The values of these trigonometric ratios can be calculated using the measure of an acute angle, θ in the right-angled triangle given below. This implies that the value of the ratio of any two sides of the triangle here depends on angle C.

Using trigonometric ratio, the distance is

tan θ = opposite / adjacent

tan 47 = x / 700

x = 700 tan 47

x = 750.7 ft

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The diagonal measure of a canvas whose sides are 12 inches and 16 inches in length is  20 inches.

The Pythagorean theorem  can be used in the solving of the question since  the square of the diagonal can be regarded as the sum of the squares of the sides:

Pythagorean theorem can as well be regarded as one that have fundamental relation in Euclidean geometry between the three sides of a right triangle.

The sides are be given as : 12 inches and 16 inches in length

Then this can be expressed as ;

 d^2 = (16^2 +12^2 )

= 256 +144 = 400

 d = √400 = 20

Therefore the diagonal measure is 20 inches.

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The lowest common multiple (LCM) of x and y is 2⁴ × 3 × 7³ × 11 × 13.

The least common multiple (LCM) of two or more numbers is the smallest number which is a multiple of all of the numbers and this is found by expressing the numbers as products of its prime factors and multiplying each factors with the highest index.

for x = 2⁴ × 7 × 11 × 13

y = 2³ × 3 × 7³ × 13

2⁴, 7³ and 13 are common with their highest index

thus;

LCM = 2⁴ × 3 × 7³ × 11 × 13.

Therefore, the lowest common multiple of x = 2⁴ × 7 × 11 × 13 and y = 2³ × 3 × 7³ × 13 is 2⁴ × 3 × 7³ × 11 × 13 in index form.

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(A) The formula for nth bounce is [tex]a_n = 20 (7/9)^{n}[/tex].

(B) 4.43 feet is the maximum height of the ball on the 6th bounce.

An algebraic expression is consists of variables, numbers with various mathematical operations,

Given that,

The height from where the ball is dropped = 20 feet.

Also, the ball bounces and returns to 7/9 to its original height.

(A)

The representation of the maximum height of the ball on the nth bounce can be given as

[tex]a_n = 20 (7/9)^{n}[/tex]

(B)

The maximum height of the ball on the 6th bounce = 20 (7/9)⁶ =  4.43 feet

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