If a and b are positive integers such that [tex]a^{3b}[/tex] = x and [tex]a^{b}[/tex] = y, then [tex]\frac{x}{y^{2} }[/tex] = ?

Answer:8

Step-by-step explanation:

The transformations that result in similar triangles are dilations, rotations, reflections, and translations.

A transformation that conserves the shape, but not necessarily the size, of a figure is called a similarity transformation. Rotation, reflection, and translation are rigid motions, which means they preserve both size and shape, on the other hand, dilation only ensures that the shape is preserved. As the rigid motions are congruence transformations, all congruent figures are also similar.

A similarity transformation is a dilation or a combination of rigid motions and dilations. Two geometric figures are similar if and only if there is a similarity transformation that maps one of the figures onto the other. Similar figures have the same shape but necessarily not the same size.

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An inequality is a mathematical statement that compares two expressions and expresses the relationship between them. It is represented by a symbol such as ">", "<", "≥", or "≤" and can be thought of as a generalization of an equation.

Unlike an equation, which has one unique solution, an inequality can have multiple solutions or no solution at all. The solutions of an inequality are the values that make the inequality true.

Inequalities are used to model real-world situations where there are constraints or limitations, such as determining the range of possible values for a variable. They are also used to describe relationships between variables, such as when one variable is greater than or less than another variable.

There are different types of inequalities, such as linear inequalities, quadratic inequalities, and absolute value inequalities, each with their own set of rules and methods for solving them.

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today fever is 100.7 F, today is 2.5 higher than yesterday

yesterday is 2.5 lower than today.

x = temperature of yesterday

x + 2.5 = 100.7

x = 98.2 F

Answer:

B)  Let x = yesterday's body temperature

         x + 2.5° = 100.7 °F

         x = 98.2 °F

Step-by-step explanation:

We want to determine Dud's body temperature yesterday.  Therefore, the unknown variable is:

If Dud's body temperature today is 2.5° higher than yesterday's body temperature, then his body temperature today is the sum of yesterday's body temperature and the increase:

To solve the equation, subtract 2.5° from both sides of the equation:

Therefore, Dud's body temperature yesterday was 98.2 °F.

Answer:

2.44444

but rounded to 2.4 (tens place)

Step-by-step explanation:

hope this helps!:)

The coordinate of point A are (-2,1), Point B are (-4,-2), Point C are (-4,-6), and Point D are (-1,-3).

A coordinate of a graph is defined as the point where the line of X axis and y axis meets to form a location on the graph.

To find the coordinates of a point in the coordinate system, you do the opposite. Start at one point and follow the vertical axis vertically up or down. You have x-coordinates. Then do the same thing, but with a horizontal line to find the y-coordinate.

Thus, the coordinates of the following points include the following:

Point A: (-2,1)

Point B: (-4,-2)

Point C: (-4,-6)

Point D: (-1,-3)

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The value of cos(Z) is 12/13.

Since both triangles are similar, △ABC ~ △XYZ, the corresponding angles are congruent. It means:

m∠C = m∠Z, and

cos C = cos Z

The ratio for cosine is adjacent/hypotenuse. In a right triangle, the hypotenuse is the longest side, while an opposite side is the one across from a given angle, and an adjacent side is the one next to a given angle.

Since the side marked 12 is adjacent to angle C and 13 is the hypotenuse of this triangle; so, we know that:

cos C = 12/13

Thus, because of the angles and cosines for C and Z will be the same, it makes:

cos Z = cos C = 12/13

Hence, the value of cos(Z) is 12/13.

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There are 180 lines of longitude in total.

Longitude is a geographic coordinate that specifies the east-west position of a point on the Earth's surface. Lines of longitude run in a north-south direction and measure the angular distance of a location east or west of the Prime Meridian, which is located at 0 degrees longitude. Lines of longitude are also known as meridians. Lines of longitude are drawn on the map and divided into 180 sections of exactly equal size. Each line of longitude is assigned a numerical value of 0 to 180 degrees east or west of the Prime Meridian. In total, there are 180 lines of longitude, which form a band around the Earth and divide it into eastern and western hemispheres. Lines of longitude are important for navigation, since they act as reference points for sailors and pilots, who use them to locate their position. They are also used to measure the time of day across different regions of the world.

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The requried value of the proportional value of p when q = 2 is given as 245.

proportionality is defined as between two or more sets of values, and how these values are related to each other in the sense are they directly proportional or inversely proportional to each other.

here,
p ∝ 1 / q²

So,
p₁/p₂ = q₂² / q₁²
Substitute value in the above equation,
20/p = 2²/7²
20 ×49 / 4 = p
p = 245

Thus, the requried value of p when q = 2 is given as 245.

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Actually forget this answer

Prime numbers are called prime as they come multiplicative first and other numbers are multiples of prime numbers.

As given in the question,

Prime numbers are called prime:

Therefore, prime numbers are called prime as they are multiplicative first numbers other numbers are multiples of prime number other than one.

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If P(terriers) = 15%, the interpretation of the likelihood of randomly selecting a terrier from the shelter is; Unlikely

Probability of selection is one that defines the probability that a population unit is included in a sample generated by probability sampling.

For any population, the probability of any element within that population to be selected into a sample is calculated as the sample size divided by the population size.

In this case, we are told that the dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. There are three types of dogs.

We are given;

P(terriers) = 15%

This means the probability of randomly selection the other 2 dogs is way higher than that to select terriers.

Thus, we conclude that the probability of selecting terriers is unlikely due to its' low probability.

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Answer: B: Unlikely

Step-by-step explanation:

Answer:

Summary: The polygons are similar but not necessarily drawn to scale, the value of x is 13 units.

Step-by-step explanation:

pls follow 4 more :) tysm

The length of the third side can be in range of [1, 17].

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane

Given is that in triangle ABC, AB = 6 and BC = 11.

In a triangle, the sum of two sides of a triangle is always greater than the third side. This means -

AB + BC > AC

(6 + 11) > AC

AC < 17

Therefore, the length of the third side can be in range of [1, 17].

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A lossless compression algorithm preserves all of the original data, while a lossy compression algorithm may discard some of the original data.

A lossless compression algorithm is a type of data compression algorithm that preserves all of the original data without any loss. This means that when the original data is uncompressed, it is exactly the same as when it was compressed. On the other hand, a lossy compression algorithm is a type of data compression algorithm that discards some of the original data in order to reduce the size of the file. This means that when the original data is uncompressed, it may not be exactly the same as when it was compressed.

The advantage of a lossless compression algorithm over a lossy compression algorithm is that it preserves all of the original data, while a lossy compression algorithm may discard some of the original data.

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Answer: likely

Step-by-step explanation:

50/50

Answer: 50/50

Step-by-step explanation: It Is equally likely because it is 50% of the total.

The numeric value of the expression A = LW, when L = 50 and W = 15, is given as follows:

A = 750.

To find the numeric value of a function or of an expression, we replace each instance of the variable in the function or in the expression by the value at which we want to find the numeric value.

The expression for this problem is defined as follows:

A = LW.

The input values of L and W are given as follows:

L = 50, W = 15.

Then the numeric value of the expression is found replacing the lone instance of L by 50 and the lone instance of W by 15, as follows:

A = 50 x 15

A = 750.

As there is only a single multiplication operation, precedence is not relevant for this problem.

The problem asks for the numeric value of the expression A = LW when L = 50 and W = 15.

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If we evaluate the ∫(2to1)(v^6+v^5)/4 dv  the answer would be 7.16

An integral gives numerical values to functions to represent concepts like volume, area, and displacement that result from combining infinite small amounts of data. Integration is the action of locating integrals.

The signed area of the region in the plane that is circumscribed by the graph of a specific function between two points on the real line can be used to represent definitive integrals.

Traditionally, portions above the plane's horizontal axis are positive, and those below it are negative.

First, calculate the corresponding indefinite integral.

∫(v^6+v^5)/4 dv= v^6(6v+7)/168

According to the Fundamental Theorem of Calculus, ∫(b to a) F(x)dx=f(b)−f(a), so just evaluate the integral at the endpoints

(v^6(6v+7)/168)at (v=2)=152/21.

(v^6(6v+7)/168)at (v=1)=13/168

∫(2to1)(v^6+v^5)/4 dv= (v^6(6v+7)/168)at (v=2) - (v^6(6v+7)/168)at (v=1) = 401/56 = 7.16

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If Mike pitches a ridge tent. The tent is 16 yards wide and the slope of the tent measures 23 yards, the height of the tent is 28.07 cm

The solution for the height would be gotten with the Pythagorean theorem. The theorem states that in a right angled triangle the sum of the square on the hypotenuse is equal to the sum of the square of the two other sides of same triangle.

This is illustrated mathematically as

C² = A² + B²

where C is the height

A is the width in yards

B is the slope.

Then we have

C² = 16² + 23²

C = √785

C = 28.07 yards

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The simplified exponential notation of the given expression is 9[tex]a^{2}b[/tex].The following polynomials, then put the resolution in the right spot.

A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x. This statement is written as x/2 + 6 in a mathematical expression.

given

the expression as:

=[tex](\frac{18}{2})( \frac{a^{3} }{a})(\frac{b^{2} }{b})[/tex]

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

So,   =[tex](\frac{18}{2})( \frac{a^{3} }{a})(\frac{b^{2} }{b})[/tex] =  9[tex]a^{2}b[/tex].

The simplified exponential notation of the given expression is 9[tex]a^{2}b[/tex].The following polynomials, then put the resolution in the right spot.

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The solution to the system of equations, x = 7y - 3 and x + 7y = 8, is: (5/2, 11/14).

One way to solve a system of equations is to use substitution.

We can start by substituting the first equation into the second equation:

x + 7y = 8

(7y - 3) + 7y = 8

7y + 7y - 3 = 8

14y - 3 = 8

14y = 11

y = 11/14

Now that we know the value of y, we can substitute it back into the first equation to find x:

x = 7y - 3

x = 7(11/14) - 3

x = 11/2 - 3/2

x = 8/2 - 3/2

x = 5/2

So the solution to the system of equations is (x, y) = (5/2, 11/14)

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3×3/4 is the expression which gives the 2.25 miles  mala walks her dog each day.

An expression is combination of variables, numbers and operators.

Given that mala walk her dog 3 times a day

Each walk is 3/4 mile.

We have to find the expression tell how many mile mala walks her dog each day.

The miles walk by Mala and her dog=3×3/4

=9/4

=2.25 miles.

Hence, 3×3/4 is the expression which gives the 2.25 miles  mala walks her dog each day.

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The geometric series which diverges is shown in the option number c as the absolute value of the common ratio of this series 4 is ∑∞n=1 (2/3)(-4)ⁿ⁻¹

The next term in a geometric sequence is produced by multiplying the previous term by the same number across the whole series.

It can be given as,

a+ar+ar²+ar³+...

Here,

is the sequence's (a) initial term, and (r) stands for common ratio.

It should therefore be a series as geometric series diverge.

|r|>1

the first choice is,

3/5+3/10+3/20+3/40+ ...

The common ratio in this case is,

r = (3/10)/(3/5)

r= 1/2

The average ratio is below one. Option an is therefore incorrect.

second option given as,

-10+4-8/4+18/25- ...

Here, the common ratio is,

r = (4/-10)/(-2/5)

r= -2/5

The usual ratio for the second choice is (-2/5), which is below one. This alternative is also incorrect.

The common ratio in option number c is equal to -4. The common ratio's exact value is,

|r|=|-4|

|r|= 4

This common ratio has a greater absolute value than one. This is the best choice as a result.

The absolute value of this series' common ratio, or option number c, represents the geometric series that diverges.

∑∞n=1 (2/3)(-4)ⁿ⁻¹

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Therefore , the solution of the given problem of unitary method comes out to be  A.$10.5 total cost and $ 0.12 .

By first multiply the value with one unit by the number of units needed, one can use the unit method to solve a problem. Simply put, the unit function is used to distinguish a single entity unit from a given many. 40 needles may be purchased for 400 rupees, or the price of one pen. There may be a standard method for figuring this out. only one nation. Everything has a unique quality. Algebra, its dialectic and inversion, and matrix logic are all analogous concepts.

Here,

Given:

A) Estimate :

70 * 1.25

80*1.25

=> 80 + 20 = 100

and

100/30 = 3.33

thus, approx 4 gallons of gas felicia needs

=> 4 * 3.5 = 14

thus, $14 total cost

Exact :

=> 70 * 1.25 = 87.5 miles

=> 87.5/30 = 2.92 gallons

thus, approx 3 gallons of gas felicia needs

=> 3*3.5 =10.5

thus, $10.5 total cost

B)

=> per cost / miles

=> 3.5 / 30 = 0.116

=>$ 0.12

Therefore , the solution of the given problem of unitary method comes out to be  A.$10.5 total cost and $ 0.12 .

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We cannot construct a triangle with side lengths 2.5 cm, 3.0 cm and 6.5 cm as they don't follow the Triangle Inequality Theorem.

It is not possible to construct a triangle using the given side lengths of 2.5 cm, 3.0 cm, and 6.5 cm. This is because of the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, if we take 2.5 cm and 3.0 cm as two sides, the sum of their lengths is 5.5 cm. But the length of the third side (6.5 cm) is greater than 5.5 cm, so these three side lengths cannot form a triangle.

It is important to note that this theorem applies to any triangle, whether it is acute, right or obtuse-angled triangle. It is also important to note that this theorem is necessary for the formation of a triangle, and without it, it would not be possible to form a triangle.

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The representation that has the greatest rate of change is y = 2 + 3.5x

The rate of change in the expression y = 2 + 3.5x is 3.5. This is compared with the equation y = mx + c where m is the rate of change

For the table the rate of change is calculated as follows

m = change in y / change in x

m = (20 - 8) / (5 - 1)

m = 12 / 6

m = 2

For the graph the slope is calculated using the points (2, -1) and (3, -4)

m = (-1 + 4) / (2 - 3)

m = 3 / -2

m = -1.5

The slope of 3.5 from the equation is the greatest

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Answer:

Step-by-step explanation:

In Similar polygons, the corresponding angles are congruent, but the corresponding sides are proportional. So, similar polygons have the same shape, whereas their sizes are different. There would be certain uniform ratios in similar polygons.

Answer:

8/5, -5/8

Step-by-step explanation:

[tex]5x+8y=-8 \\ \\ 8y=-5x-8 \\ \\ y=-\frac{5}{8}x-1[/tex]

So, the slope of the given line is -5/8.