for k(x)=4÷5x-6,determine k^-1(8)

The difference between logarithmic and exponential functions can be determined by looking at the form of the equation and by performing a calculation.

A logarithmic equation is written as log_b(x) = y, where b is the base and x and y are variables. An exponential equation is written as b^x = y, where b is the base and x and y are variables.

To determine if an equation is logarithmic or exponential, begin by comparing the form of the equation to the two equations above. If the equation is written in the form of log_b(x) = y, then it is a logarithmic equation. If the equation is written in the form of b^x = y, then it is exponential.

To perform a calculation, plug in a known value for x and then solve for y. For example, if the equation is log_2(x) = 4, then plug in x = 8. The calculation would then be:

log_2(8) = 4

This is a logarithmic equation, as the form of the equation matches log_b(x) = y.

If the equation is b^x = 16, then plug in x = 4. The calculation would then be:

2^4 = 16

This is an exponential equation, as the form of the equation matches b^x = y.

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Answer:

x=0 and y=36

Step-by-step explanation:

30 + 6 equals 36 but it is negative so you would add 30 to negative thirty to get to zero and go into the positive numbers. So if you add 6 more you would have positive 6. so it it 36 y is 36

The classification of the transformations based on the properties are presented as follows;

[tex]\begin{array}{|c|c|c|} & \mathbf{Preserves \ length} & \mathbf{Does \ not \ preserve \ lengths} \\\mathbf{Preserves \ angle \ measure} & Reflection\ Rotation &Translation \ followed \ by \ dilation \\&&Dilation \ with \ K > 1\\\mathbf{Does \ not \ preserve \ angle \ meas} & & \\\end{matrix}[/tex]

The transformations that preserves the lengths of the original figure or pre-image and also preserves the angle measure is a rigid transformation.

Rigid transformations includes; Reflections, rotations, and translations

Transformations that preserves the angle of measure but in which the lengths of the preimage is not preserved are non-rigid transformations

Non rigid transformations includes; Dilation with a scale factor

Transformations that does not preserve the angle measure includes; Shear transformation

A translation and a dilation transformation does not preserve the lengths of the original figure.

The classification of the transformations based on their properties are therefore presented as follows;

[tex]{}[/tex]                               Preserves lengths      Does not preserve lengths

Preserves               Reflection              [tex]{}[/tex]    Translation followed by dilation

angle measure       Rotation                   [tex]{}[/tex]  with k > 1

                                                          [tex]{}[/tex]        Dilation with k > 1

Does not              

Preserve angle

measure

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Answer:

Since she already has $565, her goal is $665.

5 × 20 = 100

w = 20 weeks

Answer: The width of the room is 36 feet and the length of the room is 48 feet.

Step-by-step explanation:

To solve this problem using elimination, you can set up a system of equations to represent the information given in the problem.

Let w be the width of the room, and let l be the length of the room. We are told that the length of the room is 12 feet longer than its width, so we can set up the equation:

l = w + 12

We are also told that half the perimeter of the rectangular floor is 72 feet. The perimeter of a rectangle is given by the formula:

Perimeter = 2 * (length + width)

Since half the perimeter is 72 feet, the full perimeter is 2 * 72 = 144 feet. Substituting the equation for the length of the room, we get:

144 = 2 * (w + 12 + w)

Combining like terms and solving for w, we get:

w = 36

Substituting this value back into the equation for the length of the room, we get:

l = 36 + 12 = 48

Therefore, the width of the room is 36 feet and the length of the room is 48 feet.

To solve this problem using substitution, we could start by solving for the width of the room in one of the equations, and then substituting that value into the other equation to solve for the length of the room.

For example, we could solve the equation l = w + 12 for w to get:

w = l - 12

Substituting this expression for w into the equation for the perimeter, we get:

144 = 2 * (l - 12 + l)

Combining like terms and solving for l, we get:

l = 48

Substituting this value back into the equation for the width of the room, we get:

w = 48 - 12 = 36

Therefore, the width of the room is 36 feet and the length of the room is 48 feet.

For example, if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5, 6}, then x=6>5=y, but if S={1, 2, 3, 4, 5, 6, 7} and T={1, 2, 3, 4, 5, 7}, then x=6=y. not sufficient.

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Complete question is: If the ranges of values = 40 and the number of sets = 10 , then what will be the length of set ?

The ordered pairs are a linear equation if the graph plotted is the straight line.

A linear equation can be represented by a graph in the Cartesian coordinate system as a straight line. If the equation is in the form of "y = mx + b" where m and b are constants, it is a linear equation. The ordered pairs of a linear equation will always satisfy this equation, and when plotted on a graph, will fall on a straight line. To check if a set of ordered pairs is a linear equation, you can plot them on a graph and see if they form a straight line or can substitute the x- and y-values of the ordered pairs into the equation "y = mx + b" and see if they make the equation true.

So, if the graph plotted is the straight line, then the ordered pairs are of a linear equation.

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The closest number to the circumference of the circle is 157 feet.

What is circumference?

The circumference of a circle or ellipse in geometry is its perimeter. That is, if the circle were opened up and straightened out to a line segment, the circumference would be the length of the arc. The curve length around any closed figure is more generally referred to as the perimeter.

Given:

Kate bought a circular swimming pool with a diameter of 50 feet.

We have to find the closest number to the circumference of the circle.

Since,

Circumference = 2πr

where r is the radius of circle.

Here diameter of circle = 50 feet.

⇒ Radius of circle = 25 feet.

⇒ Circumference = 2*π*25 = 157.08

Hence, the closest number to the circumference of the circle is

157 feet.

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The volume of the triangular prism is 120 cm cube.

A triangular prism  is a three-sided prism.  The volume of a triangular prism can be represented as follows:

volume of a triangular prism = 1 / 2 bhl

where

Therefore,

b = 10 cm

h = 12 cm

l = 6 cm

Therefore,

volume of a triangular prism = 1 / 2 × 10 × 12 × 6

volume of a triangular prism = 1 / 2 × 120 × 6

volume of a triangular prism = 60 × 6

volume of a triangular prism = 120 cm³

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Answer:

c

Step-by-step explanation:

The circumference should equal c = 2π × 8 cm = 50.265 cm . The area should equal A = π × (8 cm)² = 201.06 cm² . To check your results, input the 8 cm diameter in the calculator. The results should also be 50.265 cm and 201.06 cm². which is closest to c

From the equation (2-3 x 2⁹ = 2n), the value of n is -767.

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized.

The word equation and its cognates in various languages may have slightly different meanings. In mathematics, an equation is a formula that uses the equals sign to denote the equality of two expressions.

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Given data :

2-3 x 2⁹ = 2n

= 2n = 2 - 3 .

= 3 .   = 1536

= 2n = 2 - 1536

= 2n = -1534

Divide both sides by 2

= 2n/2

= -1534/2

n = -767

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Answer: 18

Step-by-step explanation:

18*1=18

18*2=36

The unit rate of change of the proportional relationship is given as follows:

2.25.

The graph of the proportional relationship is given by the image presented at the end of the answer.

A proportional relationship is a linear function with an intercept of zero modeled as follows:

y = kx.

In which k is the constant of proportionality.

The input and output variables for this problem are given as follows:

The constant k, representing the unit rate, is obtained by the division of the output of the input from the table, hence:

k = 4.5/2 = 6.73/3 = 9/4 = 2.25.

Meaning that the function is defined as follows:

y = 2.25x.

The function is graphed for a domain of x ≥ 0, as the number of cups of sugar must be a countable, non-negative amount.

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Answer:

4.42857142857

Rounded:

4.4

Answer:

6

Step-by-step explanation:

x² + 8² = 10²

x² + 64 = 100

x² = 36

x = 6

Answer:

See below

Step-by-step explanation:

Anything that makes the equation true works. For example, you can use the x-intercept (5,0) or the y-intercept (0,-1).

a. The ratio of rows of corn to beans is 13 : 12 or 13/12 or 13 to 12.

b. The ratio of rows of lettuce to the total number of rows in the garden is 5 : 52 or 5 to 52 or 5/52.

a. The ratio using the word 'to' is corn to beans.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

We know a ratio between a and b can be written as a : b, a/b or a to b.

From the given information the ratio of rows of corn to beans is,

corn/beans = 13/12 Or 13 : 12 Or 13 to 12.

The ratio of rows of lettuce to the total number of rows in the garden is,

lettuce/total number of rows in the garden = 5/52 Or 5 : 52 Or 5 to 52.

The ratio using the word 'to' is corn to beans.

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Answer:

i am not to sure but if i am corroct it IS polynomial

Step-by-step explanation:

hope this helps

The bearing of point Y from point Z is 30 degrees.

What is the bearing of a point?

The bearing of a point is the angle measured in degrees clockwise from a reference direction (usually north). To find the bearing of point Y from point Z, we need to determine the angle between the line connecting point Z to point Y and the reference direction.

we know that the bearing of point X from point Z is 135 degrees, and the bearing of point X from point Y is 105 degrees.

we can use the following mathematical relationship to find the bearing of point Y from point Z:

Bearing of Y from Z = (Bearing of X from Z) - (Bearing of X from Y)

Substituting the values we know:

Bearing of Y from Z = 135 - 105 = 30 degrees

Hence, the bearing of point Y from point Z is 30 degrees.

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The value of a and b are respectively 15 and 17 respectively.

What are trigonometry ratios?

The trigonometric functions in mathematics are real functions that connect the right-angled triangle's angle to the ratios of its two side lengths. They are extensively employed in all fields of geometry-related study, including geodesy, solid mechanics, celestial mechanics, and many others.

Given that csc θ = 17/8 and cos θ = a/b.

The reciprocal of sin θ is csc θ.

Therefore,

1/sinθ = 17/8

or, sin θ = 8 /17

Applying the trigonometry identity cos²θ = 1- sin²θ

cos²θ = 1- (8/17)²

cos²θ = 1- 64/289

cos²θ = 225/289

cos θ = 15/17

The value of a is 15 and the value of b is 17.

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Answer:

Both x - 5, and 4x-5-3x are equivalent to (1/3x+2x−5/3x)−(−1/3x+5)

Step-by-step explanation:

Let's reorganize the given expression:

(1/3x+2x−5/3x)−(−1/3x+5)

1/3x+2x−5/3x + 1/3x-5       [Expand the parentheses]

2/3x+2x−5/3x -5       [Combine like terms]

-3/3x+2x -5

-x + 2x - 5

x - 5                       One of the equivalent expressions

The option 4x-5-3x also reduces to x - 5

The phrase b2 - 4ac is referred to as the discriminant for the quadratic equation ax2 + bx + c = 0.

The phrase b2 - 4ac is known as the discriminant for the quadratic equation ax2 + bx + c = 0. How many roots f(x) has is shown by the discriminant's value: - The quadratic function has two unique real roots if b2 - 4ac > 0 A repeated real root exists in the quadratic function if b2 - 4ac = 0.

D=b2 - 4ac, discriminatory

The constant term c.

In mathematics, a discriminant is a parameter of an object or system that is calculated to help with its classification or solution. For the cubic equation x3 + ax2 + bx + c = 0, the discriminant is a2b2 + 18abc 4b3 4a3c 27c2, while the discriminant for the quadratic equation ax2 + bx + c = 0 is b2 4ac.

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Given equation 3 = 3 is an identity, so it has infinite solutions.

Consider the given mathematical equation 3 = 3

We need to check whether the given mathematical equation has solution or not.

We know that a statement 3 = 3 's true no matter what.

We can observe that for given statement 3 = 3, there's no variable in sight.

This means, 3 = 3 must has infinite solutions.

We know that an equation which is always true, no matter what values we substituted is called as an identity.

This equation is an identity, all real numbers are solutions.

Therefore, the equation 3 = 3 have infinitely many solutions.

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The builder needs building sand weighing 6.3 * 10⁶ g and contains 9 * 10¹⁰ grains

An equation is used to show the relationship between numbers and variables.

A brick layer needs 6300 kg of building sand

The conversion from kg to g is:

1 kg = 1000 g

a) 6300 kg in grams is:

6300 kg = 6300 kg * 1000 g per 1 kg = 6,300,000 g = 6.3 * 10⁶ g

b) 1 grain = 7 * 10⁻⁵ g

6.3 * 10⁶ g = 6.3 * 10⁶ g * 1 grain / (7 * 10⁻⁵ g) = 9 * 10¹⁰ grain

The builder needs 6.3 * 10⁶ g of building sand

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There is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.

At the null hypothesis, it is tested if there is no evidence of different performance, that is, the mean is of 8.5 hours, hence:

[tex]H_0: \mu = 8.5[/tex]

At the alternative hypothesis, it is tested if there is evidence of different performance, with a mean different of 8.5 hours, hence:

[tex]H_1: \mu \neq 8.5[/tex]

We have a two-tailed test, as we are testing if the mean is different of a value, with a significance level of 0.05, hence the critical value is of:

|z| = 1.96.

(p-value of 1 - (0.05/2)).

Hence the decision rule is given as follows:

The population standard deviation is known, hence the z-distribution is used to obtain the test statistic.

The equation is given as follows:

[tex]z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}[/tex]

In which:

The parameters for this problem are given as follows:

[tex]\overline{x} = 8.8, \mu = 8.5, \sigma = \sqrt{1.21} = 1.1, n = 21[/tex]

Hence the test statistic is of:

[tex]z = \frac{8.8 - 8.5}{\frac{1.1}{\sqrt{21}}[/tex]

z = 1.24.

|z| < 1.96, hence there is not enough evidence at the 0.05 level that the technique performs differently than the traditional method.

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The 4 ways to solve a problem are understanding the problem, devising a plan, carrying out the plan, look back.

A problem is any type of disruption from normality that is impeding progress. A problem can be time-consuming and requires too much energy to solve it.

Polya created his famous four-step process for problem-solving, which is used all over to aid people in problem-solving:

Step 1. Understand the problem.

x = a number

Step 2. Devise a plan (translate).

Twice the difference between a number and 1 is equal to 4 more than that number

Step 3. Carry out the plan (solve).

2(x - 1) = (x + 4)

2x - 2 = x + 4

2x - 2 - x = x + 4 - x

x - 2 + 2 = 4 + 2

x = 6

Step 4. Look back (check and interpret).

If we take twice the difference of 6 and 1, that is the same as 4 more than 6. Thus the final answer is 6.

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Relief refers to the highest and lowest point elevation in an area.

Relief

Relief is the term used for the differences in height from place to place on the land’s surface and it is greatly affected by the underlying geology. Relief relies on the hardness, permeability and structure of a rock.

elevation

The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface.

geology

Geology describes the structure of the Earth on and beneath its surface, and the processes that have shaped that structure. It also provides tools to determine the relative and absolute ages of rocks found in a given location, and also to describe the histories of those rocks.

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Answer: Relief

Step-by-step explanation:

Relief refers to the highest and lowest point elevation in an area.

Slope is the measure of steepness

Topography refers to the arrangement of the land in an area

Elevation on the other hand is the distance above sea level