What is the length of the square's side? (Show Work)

Sum of first n natural numbers, i.e., n(n + 1)/2 is an example of sum of numbers.

Sum is defined as a way of putting all the things like numbers, quantities, etc. together. Alternate words used for sum are “all together, “put together,” and “total,” etc. For example, the sum of first five natural numbers. First five natural numbers are 1, 2, 3, 4, and 5, then sum of first five natural numbers is written as 1 + 2 + 3 + 4 + 5 = 15

Similarly, Sum of First n Natural Numbers :

We have to calculate the sum of the sequence of first n natural numbers. Consider the first n natural numbers as 1, 2, 3, 4,…., n. This represents an AP with first term a = 1 and last term l = n. As we know Sum formula for Arithmetic Progression, S = (n/2) (a + l)

= (n/2)(1 + n)

= n(n + 1)/2

Therefore, the sum of the first n natural numbers is given by n(n + 1)/2.

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Answer: 3 , 1 1/2

Step-by-step explanation:

Solve for

x

by simplifying both sides of the equation, then isolating the variable.

Exact Form:

x

=

3

,

3

2

Decimal Form:

x

=

3

,

1.5

Mixed Number Form:

x

=

3

,

1

1

2

The volume of a cube that has an edge length of 6 inches is 216 inches cubed.

The formula for the volume of a cube is V = s^3, where s is the length of one of the edges of the cube.

In this case, the edge length of the cube is given as 6 inches. To find the volume, we can substitute that value into the formula:

V = 6^3 = 216

Key points:

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The steps for dividing the 3 digit numbers by 3 digit numbers is solved with the help of multiplication and subtraction.

The process of division is defined as  the process of breaking a number up into equal parts, and finding out how many equal parts can be made.

Here we need to find the way to divide 3 digit numbers by 3 digit numbers.

The steps to solve the given division is written as,

The first steps is to take the first digit of the dividend from the left and then we have to  check if this digit is greater than or equal to the divisor.

Now then we have to divide it by the divisor and write the answer on top as the quotient.

Then we have to do the subtract operation the result from the digit and write the difference below.

Then the final steps is to bring down the next digit of the dividend and this process is repeated until we get the remainder as zero.

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In maths, equivalent is different from equality. The same means the same in all respects, but equivalent means similar but not identical.

Equivalent generally refers to two numbers, terms, or expressions that have the same value. There are many ways to express equivalent quantities.

Equivalent formulas : Two formulas are said to be equivalent if they give the same result when solved. For example, suppose the number 2 is equivalent to 1 + 1.

Equivalent Fractions: Two fractions are equivalent if they represent the same value, proportion, or amount. Equivalent fractions are present with different numerators and denominators. Example: 2/5 = 4/10 = 6/15.

Equivalence ratio: An equivalence ratio is a ratio that can express a similarity between numbers or values. They are similar in proportion and have the same value. For example, 1:3 and 2:6 are equivalent ratios.

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A positive and negative angle that are coterminal to angle 2π / 7 are 16π / 7 and - 12π / 7, respectively.

Two consecutive angles are coterminal if and only if the difference between their measures equals 2π radians. Given an angle θ, then the family of coterminal angles can be derived from following equation:

θ' = θ + 2π · i, where i is an integer.

Where θ' is a coterminal angle, in radians.

First, determine a positive coterminal angle: (i = 1)

θ' = 2π / 7 + 2π

θ' = 16π / 7

Second, determine a negative co-terminal angle: (i = - 1)

θ' = 2π / 7 - 2π

θ' = - 12π / 7

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The shortest side of the right-angle triangle is its base therefore the shortest side is XY.

There are various different kinds of triangles that exists for example there is an isosceles triangle, right angle triangle equilateral triangle acute angle triangle, obtuse angle triangle hey and many more many. So in a right angle triangle the size of each side is different. As we know that the side opposite to the right angle is known as hypotenuse which is the longest side of the rightangle triangle and the adjacent side the hypotenuse is called base which is the shortest side of a right-angle triangle XYZ.

Also the sum of all the interior angles of a triangle should be equal to 180 degrees.

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The greater than sign is '>' . If one value is greater than the other, use greater than. For example, 8 is greater than 7. Therefore, we can write greater than 7 is x >7.

Greater than symbol:

In mathematics, the greater than sign is placed between two values ​​where the first number is greater than the second number. For example, 10 > 5. Here 10 is greater than 5. For inequalities, the greater-than sign always refers to the greater value, and the sign consists of two equal length dashes joined at an acute angle on the right.

As we know math problems don't always end evenly. We may need to include inequalities such as greater than and less than signs. Statements can be expressed as mathematical expressions.

Example: 'x' is the number of students in the class. If she has more than 45 students in her class, and she has 5 students join her class again, then she has more than 50 students in her class. This statement is expressed mathematically as x + 5 > 45. fish . Crocodiles always want to eat more fish, so they can eat more fish, regardless of how many mouths they have open.

One of the best ways to remember the "greater than" and "less than" signs is to think of them as little alligators (or crocodiles). The numbers on either side represent the number of fish. Crocodiles always want to eat more fish, so they can eat more fish, regardless of how many mouths they have open.

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C is calculated from solving simultaneous equation generated, the value of C is equal to 10

The information from the problem helps to derive the equations which are solved simultaneously to get A and B then substituted to solve for C

A + A + B = 17and A + B + B = 13 are the given equations

2A + B = 17

A + 2B = 13

solving with calculator will result to

A = 7 and B = 3

substitution to solve for C

and C = A + B

C = 7 + 3

C = 10

hence c is equal to 10

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The adjacent angle to ∠PSL is ∠KRM which is ∠2

what is adjacent angle?

Adjacent angles are two angles that share a common vertex and have a common side (or arm) but no common interior points. They are side by side angles and are next to each other. They are not always congruent but they share a common side, usually represented by a line. They can be acute, obtuse or right angles. They can also be complementary angles, meaning they add up to 90 degrees. For example, in a rectangle, the angles across from each other are called adjacent angles, they are both right angles.

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[tex]g(x) = 4x^2 + 3x[/tex]

So, [tex]g(x+a) = 4(x+a)^2 + 3(x+a)[/tex], since we're just substituting (x+a) for x.

If we clean that up a bit,

    [tex]\begin{aligned}g(x+a) &= 4(x+a)^2 + 3(x+a)\\[0.5em] &= 4(x^2+2xa+a^2) + 3x+3a\\[0.5em] &= 4x^2+8xa+4a^2 + 3x+3a\end{aligned}[/tex]

Now putting this all together:

    [tex]\begin{aligned}g(x+a)-g(x) &= ( 4x^2+8xa+4a^2 + 3x+3a) - (4x^2+3x)\\[0.5em] &= 4x^2+8xa+4a^2 + 3x+3a - 4x^2-3x\\[0.5em]&= 8xa+4a^2 +3a\end{aligned}[/tex]

Remember that [tex](x+a)^2 = (x+a)(x+a) = x^2+2xa+a^2[/tex]

The mirror image of (3,2) in X-axis => (-3,-2), Y-axis => (3,-2).

The term mirror image of the point is a reflected duplication that appears identical but in reverse.

Here we have given points (3,2).

And we have to find the mirror image of this point with respect to the y-axis that is the mirror image is a point whose distance is the same from the origin O (0, 0) and the same from both axes as of the point (3,2).

As we all know that (3,2) lies on the first quadrant, then the mirror image with respect to the y-axis must lie on the second quadrant.

And we all also know that In the second quadrant, here the x-coordinate of any point (x, y) is negative.

Therefore, while we looking into the given graph we have identified that the mirror image is (-2, 3).

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To prove that if KB = (p ⇒ q)∧(r∨s)∧(¬p)∧(¬ ⇒ ¬t)∧(¬q∨t)∧(¬p∧r ⇒ u)∧(w∨t), then KB |= (u ∧ w) using resolution, we can start by assuming the negation of the conclusion, (¬u ∨ ¬w)

Then use the resolution to derive the empty clause, which would mean that our assumption is false and therefore the conclusion is true.

Here is one possible sequence of resolution steps:

step 1: Assume ¬u

step 2: ¬p∧r ⇒ u (from KB)

step 3: ¬p∧r (by resolution with step 2)

step 4: ¬p (from KB)

step 5: r (by resolution with step 3)

step 6: ¬q∨t (from KB)

step 7: t (by resolution with step 5)

step 8: ¬ ⇒ ¬t (from KB)

step 9: (by resolution with step 7)

step 10: p ⇒ q (from KB)

step 11: q (by resolution with step 9)

step 12: ¬q∨t (by resolution with step 6)

step 13: t (by resolution with step 7)

step 14: w∨t (from KB)

step 15: w (by resolution with step 13)

step 16: ¬u ∨ w (by resolution with steps 1 and 15)

step 17: (by resolution with steps 10 and 16)

Since we have derived the empty clause, our assumption (¬u ∨ ¬w) is false, and we have proven that KB |= (u ∧ w) by resolution.

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The initial height of the anchor is 75 meters.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement. It's possible to multiply, divide, add, or subtract with this mathematical operation.

Given, A big ship drops its anchor. The variable "l" models the anchor's elevation (in meters) relative to the water's surface "t" seconds after the ship drops its anchor.

l=-2.4t + 75

The initial Height of the anchor will be measured at t = 0

Thus,

the value of l at t = 0

l(0) = -2.4*0 + 75

l(0) = 75

Therefore, the Height of the anchor initially is 75 meters.

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The slope of points with same y coordinate but a different x coordinate is 0

this is because change in y is zero

The slope, m of the linear function is calculated using the formula

= change in y / change in x

This is represented mathematically as

m = (y₀ - y₁) / (x₀ - x₁)

In this case change in y is zero since it is same point

y₀ = y₁

And when a number in the numerator is zero the division will result to a quotient of zero and hence the line is a horizontal line

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Answer:

18.19

Step-by-step explanation:

15% of 20 = 3

20 - 3 = 17

7% of 17 = 1.19

17 + 1.19 = 18.19

Answer:
1. y = 1/4x-1 or y = 0.25x-1

Step-by-step explanation: Hello! You can do this by using the slope-intercept equation.  The slope-intercept formula is y = mx+b.  You have the x and y coordinates already, which is all you need to solve the equation.  m = slope, b = y-coordinate in the formula y = mx+b.  The first thing you have to do is find the slope.  To find the slope, use the formula (y2 - y1)/(x2-x1).  The y-coordinates are the second numbers in the coordinate pairs, and the x-coordinates are the first numbers in the coordinate pairs.  Put the information in the formula.  You now have: (0 - (-2))/(4 - (-4)).  Two negatives make a positive, so you can simplify this equation by writing (0 + 2)/(4 + 4).  Add both equations.  You now have 2/8.  You can simplify this even more by dividing the numerator and denominator by 2.  2/8 divided by 2/2 = 1/4.  You now know the slope is 1/4.  

The next thing you have to do is use the point-slope formula.  The point-slope formula is y - y1 = m(x - x1).  m = slope, so put the slope you know (1/4) in the equation.  y - y1 = 1/4(x - x1).  You also know that y1 = -2 and x1 = -4 from the given coordinate pairs.  Fill this information in.  
y - (-2) = 1/4(x - (-4)).  Two negatives make a positive, so you can simplify this into: y + 2 = 1/4(x + 4).  Distribute 1/4 to x and -4.  1/4 x x = 1/4x, and 1/4 x 4 = 1.  You now have y + 2 = 1/4x + 1.  Subtract 2 from both sides.  y + 2 - 2 = 1/4x + 1 - 2. You now have y = 1/4x-1.  This is in the format y = mx+b, which is what you are supposed to do.  The answer for question 1. is y = 1/4x-1.  Hope this helps you with the rest of the problems! If you still need help after this, I can teach you how to do the second question as well.

Answer: 41

Step-by-step explanation: please someone tell me is 49 or 48 because I think. It looks like 48.

90 - 48 = 41

The substitution which should be made to rewrite given equation  4x⁴ + 21x² + 20 = 0 as a quadratic equation is U = x² .

The Quadratic Equations are the type of polynomial equations which has the highest degree of 2 ,

The quadratic equations are algebraic equation of the second degree in the variable x .

given equation is ⇒ 4x⁴ + 21x² + 20 = 0 ;

we have to make this equation as a quadratic equation ,

So , we substitute , U as x² in given equation ,

we get ;

⇒ 4(x²)² + 21x² + 20 = 0 ;

⇒ 4(U)² + 21U + 20 = 0  ;

the equation becomes as  ⇒ 4U² + 21U + 20 = 0  , which is a quadratic .

Therefore , the substitution of U = x² , should be used .

The given question is incomplete , the complete question is

What substitution should be used to rewrite  4x⁴ + 21x² + 20 = 0 as a quadratic equation ?

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150

The median is where the line inside the box sits.  That's the halfway point between all of the data.  (Halfway in terms of "if you line everything up and it's the data point in the middle.")

The fraction of the fruit that Kri that is   [tex]\frac{3}{32}[/tex]. To find the fraction, you have to determine the value of the total data.

As per data given are banana = 10 and apple = 22. We will determine the fraction that Kri take by sum up the fruit and then determine the fraction where the maths as follow:

Total fruit = banana + apple

Total fruit = 10 + 22

Total fruit = 32

Then find Kri fraction as follow

Kri fraction = Kri fruit : total fruit

Kri fraction = 3 : 32 = [tex]\frac{3}{32}[/tex]

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The process of inverse the function is  f⁻¹(x) = x/2.

In math the term function is known as a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Here we have to explain the process of solve inverse functions with examples.

While we take the function for examples as

f(x) = 2x.

Now, we have to do the following steps to identify the inverse of the function,

Here the first steps is to replace f(x) by y in the equation describing the function, then we get

=>  y = 2x

Now, we have to interchange x and y in a simple terms now we have to replace replace every x by a y and vice versa, then we get,

=> x = 2y

Then the next step is to Solve for y, here we get

=> y = x/2

Finally replace y by f⁻¹(x)

Therefore, the inverse of the function is

=> f⁻¹(x) = x/2.

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Answer: 900

Step-by-step explanation:

Add 150 + 250 + 50 = 450 .

After 450 * 2 = 900

Answer:

Complementary Angles, Supplementary Angles, Adjacent Angles, Linear Pair, and vertical Angles.

Step-by-step explanation:

The triangles ΔUVW are ΔUKL discovered to be similar by AA Similarity theorem.

Similar triangles are defined as triangles that have the same shape, but then their sizes may differ. Thus, if two triangles are said to be similar, then it means that their corresponding angles are congruent and  also their corresponding sides are in equal proportion

There are three triangle similarity theorems, namely; Angle-Angle (AA), Side-Angle-Side (SAS) or Side-Side-Side (SSS).

Now, looking at the given image, we see that ∠UVW ≅ ∠UKL because they are both corresponding angles.

Similarly, we can say that ∠UWV ≅ ∠ULK because they are corresponding angles.

Thus, ΔUVW is similar to ΔUKL by AA similarity theorem.

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The true statement is "No, you cannot prove that the two right triangles are congruent with the information given."

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

As a general rule, congruent triangles would have same dimensions and angles

In the scenario, we understand that Sidewalk B and Sidewalk A form a right angle.

This and the other information does not provide information to determine the congruency because the lengths of the sides of either triangle or the angles are missing.

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Answer: D , Y + 4 = 2/3 (x-5)

Step-by-step explanation: Since the equation has to be parallel, both equations need to have the same slope; in this case it is 2/3. Then, you can plug in the point into the equations to ascertain if it’s a true statement or a false statement.