Given 9²m-¹x 9⁵ = 9m+², calculate the value of m.​

The equivalent equations are A. 56 + 8x = 80,  B. 14 = 20 – 8x, and

D. 2x = 6

The equations which have the same set of solutions are known as Equivalent equations. This means that any value that satisfies one of the equations will also satisfy the others.

To determine if two equations are equivalent, we can simplify or transform one equation into another using various algebraic operations.

Some common algebraic operations include adding, subtracting, multiplying, and dividing both sides of an equation by the same non-zero value.

Here we have

1/4 (8x + 56) = 20  

Which can be simplified as follows

=> (8x + 56) = 80

=>  8x + 56 = 80

=>  8x = 80 - 56

=>  8x = 24

=>  2x = 6  

To find the equivalent equations simplify each option as follows

A. 56 + 8x = 80

=> 8x = 24

=> 2x = 6      [ Which is an equivalent equation ]

B. 14 = 20 – 8x

=> 8x = 6      [ Which is an equivalent equation ]

C. 2x + 14 = 5

=> 2x = -9     [ Which is not equivalent equation ]

D. 2x = 6       [ Which is an equivalent equation ]  

Therefore,

The equivalent equations are A. 56 + 8x = 80,  B. 14 = 20 – 8x, and

D. 2x = 6

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Answer:

The answer should be -1 degree

Step-by-step explanation:

Combine all temperatures then divide by amount added together in this case five

Answer:

54 sqrt Mr multiple question is whether you are a man or a boy are you ok

Answer:

\(\\\sf7x^3 - 2x^2 - 5\)

Step-by-step explanation:

\(\\\sf(6x^3 + 3x^2 - 2) + (x^3 - 5x^2 - 3)\)

Remove parenthesis.

6x^3 + 3x^2 - 2 + x^3 - 5x^2 - 3

Rearrange:

6x^3 + x^3 + 3x^2 - 5x^2 - 2 - 3

Combine like terms to get:

----------------------------------------

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Answer:

7x³ - 2x² - 5

Step-by-step explanation:

(6x³ + 3x² - 2) + (x³ - 5x² - 3)

Remove the round brackets.

= 6x³ + 3x² - 2 + x³ - 5x² - 3

Put like terms together.

= 6x³ + x³ + 3x² - 5x² - 2 - 3

Do the operations.

= 7x³ - 2x² - 5

____________

hope this helps!

Answer:

x < -7/3 or x > 5

Answer:

The slope is -1/2

Step-by-step explanation:

slope is found by putting the rise over run, which is -2/4 or -1/2

The value of C is acos(±√(1/10)). In spherical coordinates, the cone 9z^2=x^2+y^2 has the equation phi = c, where phi represents the angle between the positive z-axis and the line connecting the origin to a point on the cone.

To find c, we can use the relationship between Cartesian and spherical coordinates:

x = rho sin(phi) cos(theta)
y = rho sin(phi) sin(theta)
z = rho cos(phi)

Substituting x^2+y^2=9z^2 into the Cartesian coordinates, we get:

rho^2 sin^2(phi) cos^2(theta) + rho^2 sin^2(phi) sin^2(theta) = 9rho^2 cos^2(phi)

Simplifying this equation, we get:

tan^2(phi) = 1/9

Taking the square root of both sides, we get:

tan(phi) = 1/3

Since we know that phi = c, we can solve for c:

c = arctan(1/3)

Therefore, the equation of the cone 9z^2=x^2+y^2 in spherical coordinates is phi = arctan(1/3).

In spherical coordinates, the cone 9z^2 = x^2 + y^2 can be represented by the equation φ = c. To find the constant c, we first need to convert the given equation from Cartesian coordinates to spherical coordinates.

Recall the conversions:
x = r sin(φ) cos(θ)
y = r sin(φ) sin(θ)
z = r cos(φ)

Now, substitute these conversions into the given equation:

9(r cos(φ))^2 = (r sin(φ) cos(θ))^2 + (r sin(φ) sin(θ))^2

Simplify the equation:

9r^2 cos^2(φ) = r^2 sin^2(φ)(cos^2(θ) + sin^2(θ))

Since cos^2(θ) + sin^2(θ) = 1, the equation becomes:

9r^2 cos^2(φ) = r^2 sin^2(φ)

Divide both sides by r^2 (r ≠ 0):

9 cos^2(φ) = sin^2(φ)

Now, use the trigonometric identity sin^2(φ) + cos^2(φ) = 1 to express sin^2(φ) in terms of cos^2(φ):

sin^2(φ) = 1 - cos^2(φ)

Substitute this back into the equation:

9 cos^2(φ) = 1 - cos^2(φ)

Combine terms:

10 cos^2(φ) = 1

Now, solve for cos(φ):

cos(φ) = ±√(1/10)

Finally, to find the constant c, we can calculate the angle φ:

φ = c = acos(±√(1/10))

So the cone equation in spherical coordinates is φ = c, where c = acos(±√(1/10)).

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Answer:

Step-by-step explanation:

The longer you study the more you can remember so if she studied for 3.50 hrs she is more likely to get a grade in the 90s

If wrong im sry

checkers, also called drafts, board game, one of the oldest games in the world. Checkers are played by two people facing each other on a chessboard with 64 light and dark squares, just like a chessboard.

with n=0 clearly 1 path.

with n=1 clearly 0 ways.

with n=2 clearly 0 ways.

with n=3 clearly 0 ways.

If n=4, then the columns must be 2,2,0 and the rows must be 2,2,0. So the tiles must form the corners of the rectangle, there are 3 ways to select the top and bottom sides of the rectangle and 3 ways to select the left and right sides of the rectangle. So a total of 9.

If n=5, consider how many per row, it can only be 3,2,0. And clearly this means that one column has exactly one chip, so zero paths.

If n=6, consider how many per row, it could be 3,3,0 or 2,2,2. If it is 3,3,0 then there are clearly 3 ways. If it is 2,2,2, there are two possible column arrangements: 3,3,0 or 2,2,2. The first produces 3 arrangements and the second 6 arrangements. 12 ways in total.

If n=7 then it doesn't just work that the two "missing" squares are in the same row/column, there are obviously 6×3=18 ways to pick the two missing tiles, so there are (97) −18=18 correct arrangements .

If n=8 each method clearly works, then 9.

If n=9 each method clearly works, then 1.

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Answer:I=(PxRxT)/100

I=(10000x20x1)/100x2

I=200000/200

I=1000

Step-by-step explanation:

Answer:

1/2

Step-by-step explanation:

We know the total amount of marbles in the bag, 6. Now, we need to make a fraction, there are 3 blue marbles, so our fraction is 3/6. This can be simplified to 1/2.

The required probability of the blue marble in the bag is 1 / 3.

Given that,
A bag with 6 marbles has 2 blue marbles, 1 red marble, and 3 yellow marbles. A marble is chosen from the bag at random, what is the probability that it is blue is to be determined.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
Total number of marble in the bag = 6
Total number of blue marble in the bag = 2
Probability of the blue marble in the bag = 2 / 6 = 1 / 3

Thus, the required probability of the blue marble in the bag is 1 / 3.

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TransE, RotatE, and QuatE are three popular models used in knowledge graph embeddings. Each model offers unique characteristics and approaches to representing entities and relations in a knowledge graph. In comparing these models, it is important to consider their capabilities in capturing different types of relationships, their expressiveness, and their computational efficiency.

TransE is a simple yet effective model that represents entities and relations as low-dimensional vectors. It assumes that the relation vector can be obtained by translating the entity vectors. This model performs well in capturing one-to-one and many-to-one relations but may struggle with modeling more complex relationships.

RotatE is a rotational model that represents relations as complex rotations in a low-dimensional space. It excels in capturing symmetric, antisymmetric, and asymmetric relations. The rotational nature of RotatE allows it to model diverse relationships accurately.

QuatE is a quaternion-based model that represents entities and relations using quaternions. It captures complex relations by leveraging quaternion algebra and has shown promising results in capturing hierarchical relationships and multi-relational patterns.

In conclusion, the choice between TransE, RotatE, and QuatE depends on the specific requirements of the knowledge graph and the types of relationships it contains. TransE is suitable for simple relationships, RotatE excels in capturing various types of relationships, and QuatE is advantageous for hierarchical relationships and multi-relational patterns. Understanding the strengths and limitations of each model is crucial in selecting the most appropriate one for a given knowledge graph application.

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Answer: A. the product of 19 and 76 is 1444 B. the product is -1444 C.the product is -1444 D. the product is 1444 E. the product is -1444 D the product is 1444

Step-by-step explanation:

Answer:

\(A.\) \(y = \frac{5}{2}x + 1\)

Step-by-step explanation:

Because if look closely at the top arrow it lines on 5 and 2 so that would be \(\frac{5}{2}\) and then + 1 because it is also on the 1.

Hope I Helped! :)

Answer:

8) y = x/2 + 6

9) x = -(7/4)

Step-by-step explanation:

for (8), start with point-slope form and enter -2, 5, and 1/2 into the appropriate places:

y-5 = (1/2)(x- -2)

simplify by distributing (1/2)

y-5 = x/2 + 1

add 5 to both sides to get yourself in slope-intercept form

y = x/2 + 6

for 9, start by distributing the 3 and the 2

6x-12 = 10x-8+3

combine like terms

6x-12 = 10x-5

subtract 6x from both sides

-12 = 4x-5

add 5 to both sides

-7=4x

divide both sides by 4

-(7/4) = x

Answer:

Choice A. The shading in the Venn Diagram shown in the first attachment represents the set \((K \cup M) \; \cap \; (K \cup L)\).

Step-by-step explanation:

Let \(A\), \(B\), and \(C\) be sets. By the distributive law of sets, \(A \cup (B \cap C)\) and \((A \cup B) \cap (A \cup C)\) refer to the same set.

Apply this property to simplify the given expression:

\(\begin{aligned}(K \cup M) \; \cap\; (K \cap L) = K\cup (M \cap L)\end{aligned}\)

\(M \cap L\) refers to the intersection between the two lower circles. The union of that intersection with set \(K\) (the upper circle) would be the shaded region seen in choice A.

Answer:

a)

Domain : All Real Numbers

Range : All Real Numbers

b)

Domain : All Real Numbers

Range : y\(\geq\)0

Answer:

2,040,816 days ≈ 2.04 × 10⁶ days

Step-by-step explanation:

To calculate the time it takes for light to travel from the Sun to the Andromeda galaxy, we need to use the formula:

\(\boxed{\sf Time = \dfrac{Distance}{Speed}}\)

Given:

Substitute these values into the formula:

\(\sf Time=\dfrac{1.2 \times 10^{19}\;miles}{5.88 \times 10^{12}\;miles/day}\)

Simplify the calculation:

\(\sf Time=\dfrac{1.2}{5.88} \times \dfrac{10^{19}}{10^{12}}\;days\)

Divide the numbers 1.2 and 5.88:

\(\sf Time=0.204081632...\times \dfrac{10^{19}}{10^{12}}\;days\)

\(\textsf{Apply the exponent rule:} \quad \dfrac{a^b}{a^c}=a^{b-c}\)

\(\sf Time= 0.204081632...\times 10^{19-12}\;days\)

Therefore:

\(\begin{aligned}\sf Time&=\sf 0.204081632...\times 10^{7}\;days\\&=\sf 2.04081632...\times 10^{6}\;days\\&=\sf 2,040,816\;days\end{aligned}\)

Therefore, it takes approximately 2.04 million days for light to travel from the Sun to the Andromeda galaxy.

The median is not affected by an extreme value in the data set, while the standard deviation, range, and mean can all be influenced by extreme values.

An extreme value refers to a data point that significantly deviates from the other values in a data set. When considering the impact of extreme values, it is important to understand their effect on different statistical measures.

The median, which represents the middle value in a sorted data set, is not affected by extreme values. The median only considers the position of the data points and is not influenced by their actual values. Therefore, even if there are extreme values present, the median will remain unchanged.

On the other hand, the standard deviation, range, and mean can all be affected by extreme values. The standard deviation measures the dispersion of data points around the mean. Extreme values can significantly impact the spread of the data, leading to a larger standard deviation. The range, which is the difference between the maximum and minimum values in a data set, is directly influenced by extreme values. A single extreme value can greatly expand the range. Additionally, the mean, or the average of all data points, is sensitive to extreme values. Since the mean considers the actual values, extreme values can skew the average towards higher or lower values, depending on the nature of the extreme value.

Therefore, the correct answer is option c. The median is not affected by an extreme value in the data set, while the standard deviation, range, and mean can all be influenced by extreme values.

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a) The mass of a grain of rice in standard form; 0.3×10⁻¹ gram.

b) The mass, in grams, of rice eaten in the USA each year: 4.6×10¹² grams.

For the given question;

a) Weight of the rice grain is  0.03 g.

Shift the point to one decimal of the right and replace it with 10⁻¹ for this.

= 0.3×10⁻¹

Thus, the number in standard form becomes 0.3×10⁻¹ grams.

b) In USA, the rice eaten per year = 4.3 million tonnes.

1 tonne = 1 million grams

And, we know, one million can be written as.

1 million = 10⁶

4.3 million tonnes = 4.6×10⁶ tonnes.

Now, if  1 tonne = 1 million grams.

Then, multiply both side by 4.6×10⁶.

4.6×10⁶ × 1 tonne = 4.6×10⁶×1 million grams.

4.6×10⁶ tonnes = 4.6×10⁶ million grams.

Again convert million as 10⁶.

= 4.6×10⁶×10⁶

= 4.6×10⁶⁺⁶

= 4.6×10¹²

Thus, in USA 4.6×10¹² grams of rice is eaten each year.

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Answer:

11x^2y^2-11xy

Step-by-step explanation:

The correct formula to calculate the number of tires, t, needed for c cars per day is t = c/4, which is option b).


The formula that shows how to calculate the number of tires, t, needed for c cars per day is option b) t = c/4.

To understand this formula, let's break it down step by step:

1. Each car needs four regular tires and one spare tire for the trunk. So, the total number of tires needed for one car is 4 + 1 = 5.

2. If we want to calculate the total number of tires needed for c cars, we can multiply the number of cars by the number of tires needed per car, which is 5. So, the formula becomes t = 5c.

3. However, we need to find the number of tires needed, which is represented by t. Since we have t on the left side of the equation, we can rearrange the formula by dividing both sides by 5: t/5 = c.

4. Now, we have the number of tires needed (t) expressed in terms of the number of cars (c), but we want to find the number of cars needed given the number of tires (t).


To do this, we can rearrange the formula again by dividing both sides by 4: t/4 = c/4.

Therefore, the correct formula to calculate the number of tires, t, needed for c cars per day is t = c/4, which is option b).

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The formula A = | ax (by - cy) + bx (cy - ay) + cx (ay - by) | / 2 is used to find the area of a parallelogram whose vertices are given. The vertices are (-2, 0), (0, 3), (1, 3), and (-1, 0). The area of the parallelogram is 11/2 square units.

To find the area of a parallelogram whose vertices are given, we use the formula

A = | ax (by - cy) + bx (cy - ay) + cx (ay - by) | / 2 .

Here, ax and ay are the x and y coordinates of vertex A, bx and by are the x and y coordinates of vertex B, and cx and cy are the x and y coordinates of vertex C. Given the vertices are (-2, 0), (0, 3), (1, 3), and (-1, 0).We will use the above formula to find the area of the parallelogram.

Area = |(-2(3)-0(1)+1(0)) + (0(0)-3(-1)+(-1)(-2))|/2

=|(-6+0+0)+ (0+3+2)|/2

=11/2 square units.

Hence, the area of the parallelogram whose vertices are (-2, 0), (0, 3), (1, 3), and (-1, 0) is 11/2 square units.

Therefore, the answer is: The area of the parallelogram whose vertices are (-2, 0), (0, 3), (1, 3), and (-1, 0) is 11/2 square units.

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Answer:

1/4

Step-by-step explanation:

There are 2 yellow, 3 red and 5 blue for a total of 10 marbles.

The probability  of drawing a blue marble is 5/10 = 1/2

If the marble is replaced, then there are 10 marbles in the bag.

So, the probability of drawing another blue marble is 1/2

Now, multiply the two probabilities together to get the final probability.

1/2(1/2) = 1/4

The probability of drawing two blue marbles if the first marble is placed back in the bag before the second draw is 1/4.

It is a branch of mathematics that deals with the occurrence of a random event.

There are a total of 10 marbles in the bag.

If one marble is drawn and then placed back in the bag before the second draw, there are still 5 blue marbles in the bag,

The probability of drawing a blue marble on the first draw is 5/10 = 1/2.

Since the marble is placed back in the bag, there are still 5 blue marbles in the bag for the second draw

The probability of drawing another blue marble on the second draw is also 5/10 = 1/2.

To find the probability of drawing two blue marbles.

We multiply the probability of the first draw being blue by the probability of the second draw being blue, assuming that the first marble is replaced back in the bag:

P(2 blue marbles) = P(blue on first draw) × P(blue on second draw)

P(2 blue marbles) = (1/2) × (1/2) = 1/4

Therefore, the probability of drawing two blue marbles if the first marble is placed back in the bag before the second draw is 1/4.

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Answer: -4

Explanation: To find the rate of change, notice that the y values in the

table decrease by 4 each time and the x values increase by 1 each time.

Therefore, the rate of change, or the change in y / change in x is 4/-1 or -4.

Answer:

2x + 10

_______

x^3 - 4x

Step-by-step explanation:

this is the answer