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The tree house will be 8 feet off the ground. Peter will hang a rope, with knots tied for foot holds. Each knot uses an additional 2 inches of rope. Write an expression for the length of the rope needed if Peter ties n knots and wants the rope to touch the ground. How many inches of rope are needed if there are 8 knots? Explain.

The product of a fraction and its reciprocal is 1

In mathematics, we know that the fraction that is obtained by swapping or interchanging the numerator and the denominator with each other is known as the Reciprocal of the given fraction.

For example, if we have the fraction 3/5, it is safe to say that the reciprocal of this fraction will be 5/3.

Now, this means that 3/5 * 5/3 = 1.

Thus, we can say that the product of a fraction and its' reciprocal is the same as 1.

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Complete question is;

The _____ of a fraction and its reciprocal is 1. (a) sum (b) difference (c) product (d) quotient​

The number of small candles (x) and large candles (y) that were

sold 16 large candles and 12 small candles were sold.

number of small candles (x)

large candles (y)

4x+6y=144  ....equation 1.

x+y=28  ....equation 2.

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The slope ratio for a line that makes an angle of 30 with the positive direction of the x-axis is 1:√3

The slope of a line is nothing but the change of the line in the y-coordinate concerning the change in the x-axis. So the slope is simply nothing but a ratio of change in the y-axis to change in the x-axis which is also called slope ratio.

m = change in y / change in x

tan 30= 1/√3 = change in y / change in x

tan 30= 1: √3

So the ratio of an angle of 30-degree slope will be 1:√3

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The limiting speed of particle can be obtained as 12 cm/sec.

A linear equation for the given case can be written by assuming any variable as the unknown quantity. Then, as per the given data the required operations are done and it is equated to some value.

The mass of particle is given as 6 grams.

Suppose the limiting speed be x cm/s.

As per the given question, the following equation can be formed as below,

6 × 980 = 490x

⇒ x = (6 × 980)/490

⇒ x = 12

Hence, the value of the limiting speed is 12 cm/sec.

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The entire numbers, which consist of positive integer numbers and zero, are the number without any fractions. It is denoted by the letter "W," and the set of numbers is "0, 1, 2, 3, 4, 5, 6, 7, 8, 9,...." So, the first five whole numbers are 0 through 4, respectively.

An integer is either zero, a positive natural number, or a negative integer denoted by a minus sign. The inverse additive of the matching positive integers is represented by the negative numbers. The blackboard bold  Z boldface Z is a common way to represent the set of integers in mathematical notation.

Whole numbers refer to the entire set of natural numbers, including "0." Here are some examples: 0, 11, 25, 36, 999, 1200, etc.

The entire numbers, which consist of positive integer numbers and zero, are the number without any fractions.

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(3,0) is an x-intercept of the continuous function in the table.

If the graph of a function crosses the x-axis, then the function has an x-intercept. The x-intercept(s) of a function are called the zeros or the roots of the function.

If the graph of function crosses the y-axis, then the function has a y-intercept. A function can have at most one y-intercept.

Given that,

The table with x as the domain and f(x) as the range.

To find the x-intercepts, we need to find all the x-values that support the equation; f(x) = 0. An x-intercept is the first component of the ordered pair (k,0). Where k is any real number.

A y-intercept is the second component of the ordered pair (0,c), where c is any real number.

From the table provided, stated that:

So, the x-intercept becomes: (3,0).

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The complete question is as follows:

Which is an x-intercept of the continuous function in the table? (0,-6) (3,0) (-6, 0) (0, 3)

Knowing merely angle-angle-angle (AAA) does not work, because it can result in triangles that are similar but not congruent.

A set of triangles must have equal sides and angles in order for them to be congruent. The sides of the triangles may or may not be equal in the case of a triangle with all of the corresponding angles equal, or the AAA condition.

Only if the two triangles are similar would the congruence be true for two triangles with identical respective angles. Thus, we are unable to utilize AAA to establish the congruence of two triangles.

A set of triangles must have equal sides and angles in order for them to be congruent. The sides of the triangles may or may not be equal in the case of a triangle with all of the corresponding angles equal, or the AAA condition. Only if the two triangles are similar would the congruence be true for two triangles with identical respective angles.

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1 you are offered a gamble on the toss of a coin. if the coin shows tails, you lose $100. if the coin shows heads, you win $150. Yes one can  accept it.

As per the given data:

If you toss the coin.

Coin shows tails [tex]$\rightarrow$[/tex] lose $ 100

Coin shows heads [tex]$\rightarrow$[/tex] win $ 150

We would consider expected gain for us in each scenario.

Since, the probability of head is,

[tex]P(H) = \frac{1}{2}[/tex]

The probability of Tail is,

[tex]P(T)=\frac{1}{2}[/tex]

Therefore, expected gain [tex]$=150 \times \frac{1}{2}+(-100) \times \frac{1}{2}$$$[/tex]

= 75 - 50

= $ 25

Since, gain is positive number of 25 .

We can say on an average we can gain some Profit.

Hence one would accept the offer.

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Answer: It would take the snake approximately 14 hours to travel 686 centimeters

Step-by-step explanation:

At a rate of 49 centimeters per hour, it would take the snake approximately 14 hours to travel 686 centimeters. To find this, we can divide the distance the snake needs to travel by the rate at which it can travel to find the time it would take: 686 centimeters / 49 centimeters/hour = approximately 14 hours

Answer:

3,5,7,9

Step-by-step explanation:

Let x be an odd integer

given that, consider four consecutive odd integers, which are

x , (x +2), (x+4), (x+6)

Now we have to determine these odd integers such that five times the second is equal to one more than eight times the smaller

5(x+2) = 1 + 8x

5x + 10 = 1 + 8x

10 - 1 = 8x - 5x

9 = 3x

x = 3

Answer:

y=-3x-1, or 3x+y=-1

Step-by-step explanation:

well uh hopefully you don't need this

Answer: y=-3x+

Step-by-step explanation:

take the slope and the y and plug it into the equation y=mx+

The documents needed for SSS loan sickness benefit are as follows :

                 - Driver’s License

                 - Passport

                 - Voter’s ID Card

                 - National Bureau of Investigation (NBI) Clearance

                 - Postal Identity Card

                 - Any other government-issued (secondary) ID      cards/documents

                 - Laboratory, X-ray, ECG, and other diagnostic results

                 - Operating room/clinical record that will support the diagnosis

For illnesses or injuries that occurred abroad, the issuing nation's official documentation must include an English translation and be properly authenticated by the Philippine Embassy or Consulate Office or properly certified by a notary public of the receiving nation.

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The AAA (angle-angle-angle) similarity theorem can be used to express it as follows: two triangles have equal corresponding angles if and only if their corresponding sides are proportionate.

The Angle-Angle-Angle (AAA) criterion for the similarity of triangles states that “If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar”.

Proof:

Consider two triangles ABC and DEF, such that ∠A = ∠D, ∠B = ∠E and ∠C = ∠F as shown in the figure.

Now, cut DP= AB and DQ= AC and join PQ. Hence, we can say that a triangle ABC is congruent to the triangle DPQ.

(i.e) ∆ ABC ≅ ∆ DPQ, which gives ∠B = ∠P = ∠E and also, the line PQ is parallel to EF.

Therefore, by using the basic proportionality theorem, we can write

DP/PE = DQ/QF.

(i.e) AB/DE = AC/DF. …(1)

Similarly,

AB/DE = BC/EF …(2)

From (1) and (2), we can write:

AB/DE = BC/EF = AC/DF.

Therefore, the two triangles ABC and DEF are similar.

Hence, AAA(Angle-angle-angle) is proved.

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Answer:

Below

Step-by-step explanation:

3 * 2/4  =

3/1   * 1/2

(3*1) / (2*1) =  3/2 = 1  1/2

Answer:

2 linear equations can only have 1 solution.

Step-by-step explanation:

⭐ What is a linear equation?

⭐What does "solution" mean?

Thus, when 2 linear equations intersect, they can only have 1 solution, because straight lines can only meet at 1 point.

Radius, diameter, center, and circumference--all are parts of a circle .Every point in the plane that is a certain distance away from a certain point forms a circle (center).

Every point in the plane that is a certain distance away from a certain point forms a circle (center). It is, thus, a curve formed by points moving in the plane at a fixed distance from a point. A circle is a closed two-dimensional object where every pair of points in the plane are equally spaced out from the "center." A line that goes through the circle creates a specular symmetry line. At every angle, it is also rotationally symmetric about the center.

Area of circle =  

[tex]\pi r^2\\r = 10\\A = 3.14 X 10 X 10\\A = 314 unit sq\\[/tex]

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Answer: (16 + -4)

Step-by-step explanation:

You have to swap the negative numbers with positives and positive numbers for negative.

Answer:

no solutions

Step-by-step explanation:

y = -x + 4

y=-x+1

-x+1 = -x+4  ==> since y=-x+1 and y=-x+4, -x+1=-x+4

-x+1-1 = -x+4-1  ==> isolate x on one side by subtracting 1 on both sides

-x = -x+3

-(-x) = -(-x+3)

x = x - 3  ==> this isn't equal since a number won't have the same value if

                     you take away 3 from it.

Hence, there are no solutions.

Answer:

There is no solution

Step-by-step explanation:

y = -x + 4

y=-x+1

If we solve

-x + 4 = -x +1

Add x to both sides and it will be 0

So, there is no solution!

The features of the sinusoidal function are given as follows:

The general definition of the sine function in this problem is given as follows:

y = asin(b(x+c))+d.

The parameters of the general function are explained as follows:

The equation in this problem is given as follows:

y=−1/2sin(3πx−5)−2​.

From the vertical shift, the midline is given as follows:

y = -2.

The period is calculated as follows:

p = 2π/3π = 2/3.

The phase shift and the amplitude are given, respectively, by:

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Answer:

⭐Congruent is another word for "same"

In a grouped data,

it is not possible to find the median for the given observation by looking at the cumulative frequencies.

The middle value of the given data will be in some class interval. So, it is necessary to find the value inside the class interval that divides the whole distribution into two halves.

In this scenario, we have to find the median class.

To find the median class, we have to find the cumulative frequencies of all the classes and n/2.

After that, locate the class whose cumulative frequency is greater than (nearest to) n/2. The class is called the median class.

After finding the median class, use the below formula to find the median value.

[tex]Median = l +(\frac{\frac{n}{2}- cf}{f} )*h[/tex]

Where

l is the lower limit of the median class

n is the number of observations

f is the frequency of median class

h is the class size

cf is the cumulative frequency of class preceding the median class.

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The ideal way to find the intercepts of an equation with the "x" and "y" axes is to evaluate both values when the image is 0, as described below:

First let's define equation

An equation is the equality that has mathematical expressions on both sides of it, they can be functions, polynomials or others, there are no limits for them.

  Equations can be graphed, just like a function.

Now that we know what an equation is and its structure, let's explain it with an example.

Let the equation

2y = 4x + 2, determine its intersections with the axes "x" and "y".

First, we clear:

y = (4x + 2)/2

y = 2x + 1

0 = 2x + 1

2x = -1

x = -1/2

y = 2(0) + 1

y = 1

As we can see, to find the intercepts, we only have to evaluate the equation when y = 0 and when x = 0.

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The formula of r in term ∅ of is [tex]\frac{∅}{360} * 2\pi r[/tex]

What is circle?

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

What is arc in circle?

The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that could be drawn by connecting the two ends of the arc is known as a chord of a circle. 

The whole circle of 360 makes arc length of 2πr.

Thus angle of θ will make a length = [tex]\frac{∅}{360} * 2\pi r[/tex].

The formula of r in term ∅ of is [tex]\frac{∅}{360} * 2\pi r[/tex]

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Answer:

C. BA ≅ DA

Step-by-step explanation:

⭐ What is the HL theorem?

✔️In this problem, it is already established that ΔABC and ΔADC are right triangles because they have a right angle.

✔️ΔABC and ΔADC have congruent hypotenuses because they both share hypotenuse AC, and by the reflexive property of congruence, AC ≅ AC

❌There is no indication that their corresponding legs are congruent, and that is what we need for the HL theorem.

The only answer option that mentions their corresponding legs being congruent is option C.

Trigonometry Examples Popular Issue Trigonometry Solve the Triangle tri {} {30} {} {60} {} {90} Side Angle is given as b = c = a = A = 30 B = 60 C = 90 Side Angle b = c = a = A = 30 B = 60 C = 90

30 60 90 triangle sides If we know the shorter leg length a, we can find out that: b = a√3 c = 2a If the lasting leg length b is the one parameter given, then:

a = b√3/3 c = 2b√3/3 For hypotenuse c known, the legs formulas Now as follows: a = c/2 b = c√3/2 Or simply type your given values and the 30 60 90 triangle calculator will do the rest!

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The system of the equation's solution is x = -6 and y = 4 which is determined by graphically.

The system of equations is given in the question as:

y = 1/6 x + 5

4x + 3y = -12

For the first equation, y = 1/6x + 5, we can plug in two values for x and solve for y to find two points on the line. Let's plug in x = 0 and x = 1 to find two points:

When x = 0, y = 1/6(0) + 5 = 5. So the point (0, 5) lies on the line.

When x = 1, y = 1/6(1) + 5 = 5 + 1/6 = 5 1/6. So the point (1, 5 1/6) lies on the line.

For the second equation, 4x + 3y = -12,

Let's plug in y = 0 and y = 1 to find two points:

When y = 0, 4x + 3(0) = -12.

4x = -12, so x = -3. So the point (-3, 0) lies on the line.

When y = 1, 4x + 3(1) = -12.

4x + 3 = -12, so x = -4. So the point (-4, 1) lies on the line.

To solve these equations graphically, we plotted the lines on the coordinate plane, found the point of intersection, and then found the coordinates of that point.

Thus, the solution to the system of equations is x = -6 and y = 4.

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The quadratic solution of the linear system of equations y = x2 + 5x - 3 is y = (x+3)(x-1).

1. Rewrite the equation as y = x2 + 5x - 3

2. Factor the equation by grouping the terms: y = (x+3)(x-1).

3. Set each factor equal to 0 and solve for x: x+3 = 0 and x-1 = 0

4. Solve each equation: x = -3 and x = 1

5. Substitute the values of x into the original equation to find the corresponding values of y:

y = (-3+3)(-3-1) = (-3)(-4) = 12

y = (1+3)(1-1) = (4)(0) = 0

Therefore, the solution of the linear quadratic system of equations y = x2 + 5x - 3 is y = (x+3)(x-1).

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When resolving an inequality, you can, add the same amount to each side, take away the same amount from each side, multiply or divide each side by the same positive amount.

The complete question is,

How do you resolve an inequality equation?

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Sometimes the triangle's circumcenter is outside of it. In actuality, it may lie outside the triangle, as in the case of an acute triangle, or it may land at the midway of the hypotenuse of a right triangle.

the location that is equally spaced from each of a triangle's three vertices and where the three perpendicular bisectors of its sides meet.

The circumcenter of a triangle is found at the junction of all sides' perpendicular bisectors, or lines that are at right angles to each side's midpoint. The triangle's perpendicular bisectors are shown to be contemporaneous by this (i.e. meeting at one point).

Sometimes the triangle's circumcenter is outside of it. In actuality, it may lie outside the triangle, as in the case of an acute triangle, or it may land at the midway of the hypotenuse of a right triangle.

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