A sheet of graph paper is placed with its
x
-axis pointing due East and its
y
-axis pointing due North. A sluggish snail starts at points (0,0) and slowly, but smoothly, slithers 1 unit North, 2 units East, 3 units South, 4 units West, 5 units North, 6 units East, 7 units South, 8 units West, 9 units North and (lastly!) 10 units East. At which point does the snail finally arrive?
Coordinates: (__,__)

The equation is y = 2.2x. Yes, it represents a linear function.

What is a linear function?

A linear function is one that has the highest degree of 1 possible. This indicates that there are no variables in a linear function with exponents greater than 1. Such an equation on the graph, forms a straight line.

We are given that

Stopper is applied at t = 0

At t = 5 minutes ; water in tub = 11 gallons

At t = 10 minutes ; water in tub = 22 gallons

We know that a general form of a linear function is y = mx + c.

Where c is the intercept ; m is the Slope ; y and x are dependent and independent variables respectively

Here, the intercept is gallon of water at t = 0 ;

Since, it is not mentioned, therefore it will  be taken as 0.

Slope = change in y / change in x

Slope = (22 - 11) / (10 - 5)

Slope = 11 / 5

Slope = 2.2

Therefore, the equation becomes

y = 2.2x + 0

y = 2.2x

Yes, it represents a linear function because the highest degree is 1.

Hence, the equation is y = 2.2x. and it represents a linear function.

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The intensity of an earthquake decided on the Richter scale by the following formula,

10ᴬ⁻ᴮ , where A and B are magnitude of earthquake recorded by Richter Scale.

The Richter magnitude scale was developed in 1935 by Charles F. Richter of the California Institute of Technology as a mathematical device for comparing the magnitude of earthquakes. The size of an earthquake is determined from the logarithm of the amplitude of the waves recorded by seismographs. Adjustments are included for the change in distance between different seismographs and the epicenter of the earthquake. The Richter scale is a logarithmic scale with a base of 10, meaning that each order is 10 times more intense than the previous one. In other words, a two is 10 times more intense than a one, and a three is 100 times greater. In the case of the Richter scale, there is an increase in the amplitude of the wave.The Formula used to measured the intensity of an earthquake is A is x times intense than B, x = 10ᴬ⁻ᴮ.

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The initial value of b = $3.50 represents the cost of renting skates, while the rate of change m = $3.0 represents the rate per hour.

The initial value, b = $3.50 is the skate rental fee

The rate of change, 'm' is $3.0 is the hourly rate charged by the roller skating rink based on the query we have;

The roller skating rink's fees are comprised of a skate rental fee and an hourly rate.

Skating for two hours will cost you a total of $9.50.

Five hours of skating will cost you $18.50 in total.

Skating's overall cost and its duration in hours are related in a linear fashion.Let 'x' be the number of hours spent skating, and 'y' denote the overall cost;

The equation has the form y = mx + b.

Where;

m = The linear relationship's rate of change

b = The starting point (y-intercept)

X = 2 and Y = 9.50

Consequently, we can write;

9.50 = 2·m + b..(1) (1)

X = 5 and Y = 18.50

Consequently, we can write;

18.50 = 5·m + b..(2) (2)

Equation (1) minus equation (2) results in;

18.50 - 9.50 = 5·m - 2·m + b - b = 3·m

9.0 = 3 × m

∴ m = 9.0/3 = 3.0

m = 3.0 is the rate of change.

Likewise, we have;

We obtain from equation (1);

9.50 = 2·m + b = 2 × 3.0 + b = 6.0 + b

9.50 = 6.0 + b

∴ b = 9.50 - 6.0 = 3.50

The starting point is 3.50.

As a result, the initial value of b = $3.50 represents the cost of renting skates, while the rate of change m = $3.0 represents the rate per hour.

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Answer: view below

Step-by-step explanation:

a. [tex]-\frac{2}{3}x \geq 7[/tex]

[tex]x\leq -\frac{21}{2}[/tex]

b. 32>23-x

x>-9

c. 2(x+6)<10

x+6<5

x<-1

d. 15-4x[tex]\leq 3x-6[/tex]

21[tex]\leq[/tex]7x

3[tex]\leq[/tex]x

x[tex]\geq[/tex]3

The formula for finding the axis of symmetry for a quadratic function in standard form is y = a (x-h)² + k

The term axis of symmetry in math is defined as an imaginary straight line that divides a shape into two identical parts hereby creating one part as the mirror image of the other part.

Here we need to identify the formula for finding the axis of symmetry for a quadratic function in standard form.

According to the definition of axis of symmetry, the general formula is written as

Here the quadratic equation in vertex form is written as,

=> y = a (x-h)² + k

Here the values (h, k) refers the vertex of the parabola.

And here we have also given that the axis of symmetry formula is x = h.

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Yes, Y = -3x + 10 is a linear function.

A linear function is a function that can be written in the form of y = mx + b, where m is the slope (or rate of change) and b is the y-intercept (the point where the line crosses the y-axis). The equation Y = -3x + 10 can be written in this form, with m = -3 (the coefficient of x) and b = 10 (the constant term).

Linear functions represent straight lines on a graph, and their slope and y-intercept can be used to determine the characteristics of the line, such as its direction and position. In this case, the slope of the function is -3, which means that for every unit increase in x, there is a corresponding decrease of 3 units in y. The y-intercept of this function is (0,10), which means that the line crosses the y-axis at the point (0, 10)

In summary, Y = -3x + 10 is a linear function because it can be written in the form of y = mx + b, and it represents a straight line on a graph.

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The mathematical symbol ∑∑ is used to represent a double summation. It is a way of expressing the sum of two series of numbers.

Double summation is a way of expressing the sum of two series of numbers, written as ∑∑. The upper sigma symbol represents the outer summation, while the lower sigma symbol represents the inner summation. The two series of numbers that form the double summation can be related or unrelated.

The double summation is written in the following form: ∑∑ aij, where aij is an element from the two series of numbers, i and j are the upper and lower limits of the double summation, respectively.

This type of expression is used to find the sum of a set of numbers that are related to each other in some way, such as the sum of the elements in a matrix or a table, or the sum of two series of numbers that are not related. The double summation is a useful tool for expressing the sum of two series of numbers and is widely used in mathematics and science.

Complete answer:

What does ∑∑ mean?

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Step-by-step explanation:

a function with a single input variable x is usually defined like

y = f(x) = expression in x

to "solve" it means either to have a value for x and then calculate y.

or to have a value for y and find the corresponding value for x, so that f(x) = y. this usually involves finding and using the inverse function of f(x).

the details depend on the functions and operations used in the function expression.

Answer:

A, C, E

Step-by-step explanation:

From the box-and-whisker plot of the data, the Interquartile range is 6.

What is the Interquartile range?

An interquartile range is finding the median of the first half of the data set, and the second half, then subtracting the first median from the second one.

Steps to create a box-and-whisker plot and find the interquartile range.

Step 1: Sort the data in ascending order: 7, 7, 9, 10, 11, 12, 12, 12, 12, 13, 15, 15, 17, 18, 18

Step 2: Find the median (middle value) of the data: 12

Step 3: Divide the data into two halves:

Lower half: 7, 7, 9, 10, 11, 12, 12

Upper half: 12, 12, 13, 15, 15, 17, 18, 18

Step 4: Find the median of the lower half (Q1) and the median of the upper half (Q3).

Q1: 9

Q3: 15

Step 5: Draw a box-and-whisker plot:

Draw a number line and mark the minimum, Q1, median, Q3, and maximum values.

Draw a box between Q1 and Q3 and a vertical line inside the box to represent the median.

Draw lines (whiskers) from the box to the minimum and maximum values.

Step 6: Find the interquartile range (IQR) by subtracting Q1 from Q3: 15 - 9 = 6.

Hence, the Interquartile range is 6.

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Answer:

Step-by-step explanation:

To find the volume of concrete needed to make this block, you need to calculate the volume of the block using the formula:

Volume = Length x Width x Height

In this case:

Volume = 18 yd x 23 yd x 16 yd = 7,648 cubic yards

So, 7,648 cubic yards of concrete are needed to make this block.

Alternatively, you can use the formula:

V=LWH, where V is the volume, L is the length, W is the width and H is the height.

Since a square is either positive or zero, negative numbers don't have real square roots.

No, we are unable to compute the negative number's square root. Positive is always the result of adding two numbers with the same sign.

Theorem: Square Roots of a Negative Number Simplifying an expression involving the square root of a negative number by simplifying the number as if it were a positive number and putting an i in front of it as a coefficient is one method. To put it another way, x=ix x = i x for every x where x is a positive number and where x is a negative number.

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The inequality that represents the maximum amount of apples and grapes they can buy will be 5a + 3.99 ≤ 11.

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Therefore, the inequality that represents the maximum amount of apples and grapes they can buy will be 5a + 3.99g ≤ 11.

where a= Apple

g = grape.

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No, 45 and 36 are not a Co-prime numbers, because the two numbers have a common prime factor i.e., 9 .

A co-prime number is a number that has exactly one common divisor, which is 1. This means that a pair of numbers is co-prime if their greatest common divisor is 1. Consider x and y are two positive integers, they are called relatively prime if and only if their only common divisor is 1, so gcd(x, y) = 1. There are two numbers 45 and 36. First we determine the divisors of both numbers, then check the greatest common divisor. So, the factors of 45 are 1,3,5,9,15,45.

=> 45 = 1× 3×3× 5

and factors of 36 are 1, 3,2,4,6,9,12,36

=> 36 = 1×2×2×3×3

Now, greatest commen factor between 45 and 36 is 9, i.e., gcd(45,36) = 9 ≠ 1. Therefore, 45 and 36 are not co-prime numbers.

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Complete question:

Are 45 and 36 a Coprime number?.

The evaluation of the expression 12.75 ÷ 1.5 is 51  / 6.

To evaluate an algebraic expression means to find the value of the expression when the variable is replaced by a given number.

Therefore, let's evaluate the expression as follows:

Hence,

12.75 ÷ 1.5

Let's convert each decimal to fractions for easy evaluation

Therefore,

12.75  = 1275 / 100

1.5 = 15 / 10

Therefore,

1275 / 100 ÷ 15 / 10

Let's change the division sign to multiplication sign.

1275 / 100 × 10 / 15

1275 / 150

Therefore,

255 / 30 = 51 / 6

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a) The amount in the account at the end of this year after the interest is paid will be 1.04x.

b) The amount in the account at the end of this year after the interest is paid will be 1.08x.

c) The expression for the amount in the account after N years will be x + 0.04xn.

a) From the information, Mybankaccount pays 4% interest at the end of each year. The person has $x in the bank account at the start of this year. The amount in the account at the end of this year after the interest is paid will be:

= x + (x*0.04*1)

= x + 0.04x

= 1.04x

b) The amount in the account at the end of 2 years after the interest is paid will be:

= x + (x*0.04*2)

= x + 0.08x

= 1.08x

c) The expression for the amount in the account after N years will:

= x + (x*0.04*n)

= x + 0.04xn

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Answer:

n_(n-1)+6

Step-by-step explanation:

n_(n-1)+6

im pretty sure?

The values of x for which the product:

√(5x)*√(x + 3)

Is defined are:

x ≥ 0

Here we want to see for which values of x is the following product not defined.

√(5x)*√(x + 3)

Ok, remember that the argument of the square root must be zero or larger, then we have two inequalities here:

5*x ≥ 0

x + 3≥ 0

We can simplify both of these inequalities to get:

x ≥0

x≥ -3

We take the first one, which is more restrictive, the values of x for which the product is defined are:

x ≥0

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Answer:

f=32

Step-by-step explanation:

11f = 352

11x32=352

Answer:

[tex] \sf \: f = 32[/tex]

Step-by-step explanation:

Now we have to,

→ find the required value of f.

The equation is,

→ 11f = 352

Then the value of f will be,

→ 11f = 352

→ f = 352 ÷ 11

→ [ f = 32 ]

Hence, the value of f is 32.

The formula for the sum of an arithmetic sequence is [tex]S_n[/tex]=[tex]n/2[/tex][2a+(n−1)d], [tex]S_n[/tex] = [tex]n/2[/tex] [2a +( n − 1 )d ], where: n = the number of terms to be added. a = the first term in the sequence. d = the constant value between terms.

In arithmetic, a chain is an enumerated series of gadgets in which repetitions are allowed and order matters. Like a hard and fast, it consists of contributors (additionally referred to as elements, or terms). The quantity of elements (possibly endless) is called the duration of the series.

Unlike a fixed, the same factors can appear a couple of times at distinct positions in a chain, and unlike a fixed, the order does be counted. formally, a chain can be described as a function from herbal numbers (the positions of elements inside the collection) to the factors at each position. The belief of a sequence may be generalized to a listed family, defined as a character from an arbitrary index set.

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A triangle with a right angle is a 3 4 5 triangle.

A right triangle is a particular kind of triangle that only has one right (90°) angle.A mathematical formula for determining the length of the third side of a right triangle given the lengths of the other two sides was developed by the Greek mathematician Pythagoras.

The sides of variables a and b make up the right angle of the triangle. Any side may make use of any variable. The variable c stands for the left side, or the side that leans away from the right angle. The longest side, or side c, is always present and is known as the hypotenuse.

So the right angle triangle is a triangle with sides of 3, 4, and 5.

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Left Column: AC bisects ZBCA ZDCA. Right Column: Angle ZBAC = Angle ZDCA (Angle Bisector Theorem).

Angle bisector theorem states that in any triangle, the line that bisects an angle also divides the opposite side into two segments that are proportional to the other two sides of the triangle. This theorem can be used to prove that the angle bisector of any triangle is the perpendicular bisector of the opposite side. In other words, the line that bisects the angle of a triangle will also divide the opposite side into two segments with lengths that are equal to the ratio of the other two sides of the triangle.

Left Column                                           Right Column

1. AC bisects ZBAD                                    1. AC bisects ZBCA ZDCA

2. ZBAD = ZBCA + ZDCA                                 2. Angle ZBAC = Angle ZDCA (Angle Bisector Theorem)

3. Angle ZBAC = Angle ZBCA + Angle ZDCA               3. BC = DC (Congruent Sides of Congruent Triangles)

4. Angle ZBCA = Angle ZDCA                            

5. BC = DC (Congruent Sides of Congruent Triangles)  

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From the given proof below, we have shown that AB is parallel to CD.

From the attached diagram showing the triangles inside the circle, we are given that;

<APC = <DQB [ Given]

Now, we know that in cyclic quadrilaterals that Equal angles subtend equal arcs and therefore; Arc(AC = BD)

From the statement above showing that Equal angles subtend equal arcs. we can conclude that AB is parallel to CD

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The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.

A set comprises elements or members that can be mathematical objects of any sort, including numbers, symbols, points in space, lines, other geometric forms, variables, or even other sets. A set is the mathematical model for a collection of various things.

An ordered pair consists of two items. The order of the objects in the pair matters because, unless a = b, the ordered pair differs from the ordered pair. Ordered pairs are also known as 2-tuples, or 2-length sequences.

An ordered pair is made up of the ordinate and the abscissa of the x coordinate, with two values given in parenthesis in a certain sequence. In order to understand a point visually, it might be helpful to position it on the Cartesian plane. An ordered pair's numerical values may be fractions or integers.

The following ordered pair is given as {(1, -1), (2,0), (3,1)} for the given data of movement of arrow.

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Answer:

D

Step-by-step explanation:

the required equation is 5x - 6y + 5z = 7

Given that;

points : (1, 4,4) and (-4, 1,2).

mid point : ( [(1-4)/2], [(4-1)/2], [(4+2)/2]

⇒ midpoint : ( -3/2, 3/2, 3 )  

                       x₀    y₀    z₀

Direction vector n = [-4-(1)], [  1-4], [ 2-4]

⇒ Direction vector n = < -5, -3, -2 >

General equation plane : n(x-x₀, y-y₀, z-z₀) = 0

so we substitute

⇒ (-5,-3,-2) (x-3/2, y-(-2), z-(-5/2) ) = 0

⇒ (-5,-3,-2) (x - 3/2, y + 2, z + 5/2) ) = 0

⇒ 5(x - 3/2) - 6(y + 2 ) + 5(z + 5/2) = 0

⇒ 5x - 15/2 - 6y - 12 + 5z + 25/2 = 0

⇒ 5x - 6y + 5z = 15/2 + 12 - 25/2

⇒ 5x - 6y + 5z = 7

Therefore, the required equation is 5x - 6y + 5z = 7

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An obtuse angle has 120 degrees in them.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.

Any angle more than 90 degrees is called obtuse: A straight angle is one with a 180° measurement: A zero angle is one with a measurement of 0°: Angles with measures that add up to 90 degrees are said to be complementary angles: Angles with measures that add up to 180° are referred to as supplementary angles.

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Answer:

y = 4

Step-by-step explanation:

21/3 = 7

7 - 3 = 4

The tip left by the family at the restaurant is 18.48% of the total bill.

To determine the percentage of the tip, we need to divide the amount of the tip by the total bill, and then multiply by 100 to get the percentage.

The amount of the tip can be calculated by subtracting the cost of the bill from the total amount paid: $49.77 - $42 = $7.77

So the percentage of the tip is:

$7.77 / $42 x 100 = 18.48%

Therefore, the tip left by the family at the restaurant is 18.48% of the total bill.

The percentage is a relative term that expresses a number as a fraction of 100. It is commonly used to express a proportion or rate in terms of a hundred. For example, 45% is equal to 45 out of 100, or 0.45. The percentage can be used to represent any ratio, such as a ratio of two numbers, a fraction of a whole, or a proportion of a total.

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When the numerator of the fraction is greater than the denominator, the the fraction is an improper fraction.

We know that the fraction is used to represent the portion or part of the whole thing.

The fraction has two parts: numerator and denominator.

The top part of fraction is numerator and the bottom part is denominator.

consider a fraction 1/6.

Here, numerator is 1, denominator is 6

When certain thing is divided into 6 equal parts then each part of is represented by fraction1/6

As we the types of fractions are: Proper fraction, Unit Fraction ,Improper fraction, Mixed fraction, Like fractions, Unlike fractions and Equivalent fractions

An improper fraction is a fracton in which the numerator of the fraction is greater than the denominator.

For example, 8/7 is an improper fraction.

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A possible tape diagram that shows the proportion of muffins with and without chocolate is one that displays 1/4 or 10 flavors with chocolate and 30 flavors without chocolate.

This is a simple diagram that uses segments of a tape to illustrate fractions.

It is known 25% of the flavors have chocolate, but let's calculate the exact number:

40/100 = 0.4 x 25= 10 flavors have chocolate and therefore 30 flavors do not have chocolate.  

Based on this, here is the diagram (green shows the chocolate flavors):

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