If algebraic expressions are a³ᵇ = x and aᵇ = y, then, by algebra properties, x / y² is equal to aᵇ.
How to find the result of an algebraic expression based on two given expression by algebra properties
Herein we find the following two algebraic expressions with two positive integers a and b:
a³ᵇ = x
aᵇ = y
From these equation we need to find the result associated to algebraic expression x / y² in terms of the integers given. This can be done by means of algebra properties. First, square the second expression:
(aᵇ)² = y²
Second, divide the first expression by the given formula found in previous step:
x / y² = a³ᵇ / (aᵇ)²
Third, simplify the resulting expression to a single power:
x / y² = a³ᵇ / a²ᵇ
x / y² = a³ᵇ - ²ᵇ
x / y² = aᵇ
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please answer this question and I will give you a brainlist!
The coordinate of point A are (-2,1), Point B are (-4,-2), Point C are (-4,-6), and Point D are (-1,-3).
What is a coordinate of a graph?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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Given △abc ~ △xyz, what is the value of cos(z)? five-thirteenths five-twelfths twelve-thirteenths twelve-fifths
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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What is inequality give answer?
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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mala walk her dog 3 times a day each walk is 3/4 mile. which expression tell how many mile mala walks her dog each day
3×3/4 is the expression which gives the 2.25 miles mala walks her dog each day.
What is Expression?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 dog shelter has Labradors, Terriers, and Golden Retrievers available for adoption. If P(terriers) = 15%, interpret the likelihood of randomly selecting a terrier from the shelter. Likely Unlikely Equally likely and unlikely This value is not possible to represent probability of a chance event
If P(terriers) = 15%, the interpretation of the likelihood of randomly selecting a terrier from the shelter is; Unlikely
How to find the probability of selection?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:
Mike pitches a ridge tent. The tent is 16 yards wide and the slope of the tent measures 23 yards. What is the height of the tent?
I need help
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
How to solve for the heightThe 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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What transformations result in similar triangles?
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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Task #3: Felicia's Drive
As Felicia gets on the freeway to drive to her cousin's house, she notices that she is a little low on gas. There is a gas station at the exit she normally takes, and she wonders if she will have to get gas before then. She normally sets her cruise control at the speed limit of 70mph and the freeway portion of the drive takes about an hour and 15 minutes. Her car gets about 30 miles per gallon on the freeway, and
gas costs $3.50 per gallon.
a. Describe an estimate that Felicia might do in her head while driving to decide how many gallons of gas she needs to make it to the gas station at the other end.
b. Assuming she makes it, how much does Felicia spend per mile on the freeway?
Therefore , the solution of the given problem of unitary method comes out to be A.$10.5 total cost and $ 0.12 .
What is a unitary method, exactly?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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Please help!!! 30+ points! Thank you so much! :)
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.
Perpendicular lines have slopes that are negative reciprocals of each other, so the answer for the first question is 8/5.Parallel lines have the same slope, so the answer to the second question is -5/8.The polygons are similar, but not necessarily drawn to scale. Find the value of x.
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
If AB=6 A B = 6 and BC=11 B C = 11 ,what is the length of AC A C ?
The length of the third side can be in range of [1, 17].
What are triangles?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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please help me with this question thank you very much
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:
Let x = yesterday's body temperatureIf 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:
x + 2.5° = 100.7 °FTo solve the equation, subtract 2.5° from both sides of the equation:
x + 2.5° - 2.5° = 100.7 °F - 2.5°x = 98.2 °FTherefore, Dud's body temperature yesterday was 98.2 °F.
!!HELP!! evaluate using order of operations: A = L=50 W= 15 give your answer in simplest form
The numeric value of the expression A = LW, when L = 50 and W = 15, is given as follows:
A = 750.
How to find the numeric value of a function or of an expression?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.
Missing Information
The problem asks for the numeric value of the expression A = LW when L = 50 and W = 15.
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Can a triangle be constructed with sides 2.5 cm 3.0 cm and 6.5 cm give reason?
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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How many lines of longitude are there in total Class 6?
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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Jason is designing a new board game and is trying to figure out all the possible outcomes how many different possible outcomes are there if he spent a spinner with five equal sized labeled Monday, Tuesday Wednesday, Thursday Friday and spent a spinner with three equal sides section labeled walk when I stop
Answer:8
Step-by-step explanation:
what is the decimal form of this mixed fraction: 2 4/9 (four over nine)
Answer:
2.44444
but rounded to 2.4 (tens place)
Step-by-step explanation:
hope this helps!:)
Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the
correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag
the item to the trashcan. Click the trashcan to clear all your answers.
Add the following polynomials, then place the answer in the proper location on the grid. Write answer in descending
powers of x.
Add: x5-4x4+7x³ + 8, 9x³ +7x2-10, and -2x 5 +7x4-3x + 8.
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.
what is expression ?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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Someone help me pleaseeeee
What is the mean of the values below (48,59,70,27,61)
Why is it called a prime number?
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:
Meaning of prime is known as first.Prime numbers are multiplicatively first numbers .All the other numbers are multiples of prime numbers other than one.'1' is neither a prime number nor a composite number.prime numbers represents such numbers which has only two factors one and the number itself.Example of prime numbers : 2, 3, 5, 7,.... so on.Other numbers : 4 = 2 × 2 , 12 = 2× 2 × 3 so on.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 is inversely proportional to the square of q, and p is 20 when q is 7, determine p when q is equal to 2.
The requried value of the proportional value of p when q = 2 is given as 245.
What is proportionality?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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Which geometric series diverges? three-fifths + three-tenths + three-twentieths + startfraction 3 over 40 endfraction + ellipsis negative 10 + 4 minus eight-fifths + startfraction 16 over 25 endfraction minus ellipsis sigma-summation underscript n = 1 overscript infinity endscripts two-thirds (negative 4) superscript n minus 1 sigma-summation underscript n = 1 overscript infinity endscripts (negative 12) (one-fifth) superscript n minus 1.
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
What are divergent geometric series?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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HELP PLEASE
The baker made a batch of chocolate chip, oatmeal raisin, and sugar cookies. if
P(chocolate chip) = 0.50, interpret the likelihood of randomly selecting a chocolate chip cookie from the batch.
Equally likely and unlikely
Likely
Unlikely
This value is not possible to represent probability of a chance event.
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.
Determine which representation has the greatest rate of change.
The representation that has the greatest rate of change is y = 2 + 3.5x
How to find the representation that has the greatest rate of changeThe 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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HELP PLS
Sid has a baseball cap collection. 75% of his caps have sports team symbols. If 24 of the caps have the team symbols, how many total caps does Sid have?
Actually forget this answer
If polygons are similar then what do you know about the corresponding sides and the corresponding angles ?
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.
evaluate the integral (2 to 1)( v5 + v6) / 4 dv
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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Find the solution to the system of equations.
The solution to the system of equations, x = 7y - 3 and x + 7y = 8, is: (5/2, 11/14).
How to Find the Solution tp a System of Equations?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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Which of the following is an advantage of a lossless compression algorithm over a lossy compression algorithm
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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