Describe the similarities and differences between finding the slope of a linear equation from a graph that has x and y scales that are 1:1, and from a graph that has x and y scales that are not 1:1 (say your x and y scales are 2, 4, 6).

The next five terms are ← ↑ → ↓ ← and the conjecture is each arrow is rotated 90 degrees clockwise to get the next

The first three terms are given as

↑ → ↓

From the above pattern, we have the following highlights:

Each arrow is rotated 90 degrees clockwise to get the next

Using the above as a guide, we have the next five terms to be:

← ↑ → ↓ ←

Also, we have the conjecture to be:

Each arrow is rotated 90 degrees clockwise to get the next

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Answer: she would have sent 133 text messages

hope this helps

The product of the numbers written as a scientific notation is 1.36 × 10²²

From the question, we are to determine the product of the given numbers

The given numbers are

3.2 x 10¹² and 4.25 x 10⁹

The product of the numbers can be determined as shown below

3.2 × 10¹² × 4.25 × 10⁹

= 3.2 × 4.25 × 10¹²  × 10⁹

= 13.6 × 10¹² ⁺ ⁹

= 13.6 × 10²¹

= 1.36 × 10¹ × 10²¹

= 1.36 × 10¹ ⁺ ²¹

= 1.36 × 10²²

Hence, the product of the numbers written as a scientific notation is 1.36 × 10²²

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The equation that can be used to model the total number of yards of fabric, y. needed to make x curtain panels is y = (10 2/4 ÷ 4) × x

It should be noted that Mary used 10 2/3 yards of fabric to make 4 identical curtain panels.

Therefore, the equation that can be used to model the total number of yards of fabric, y. needed to make x curtain panels will be:

y = (10 2/4 ÷ 4) × x

where

y = number of yards

x = number of panels

Therefore, the equation is y = (10 2/4 ÷ 4) × x

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Vectors is a quantity that has both magnitude and direction as well. A vector that has 1 magnitude is called unit vector. Unit vector is represented by the symbol '^'.

To find a Unit vector we divide the vector by its magnitude.

First find the slope of the tangent line, slope of a tangent line for a point f(x) is given by f'(x). Hence at point (π/6,1) where x = π/6, the slope of the tangent line is :

[tex]f(x)=2sinx\\f'(x)=2cosx\\f'(\pi /6)=2cos(\pi /6)=2.\frac{\sqrt{3} }{2}=\sqrt{3}[/tex]

The slope of the tangent line at this point is [tex]m=\sqrt{3}[/tex]

Finding a unit vector parallel to the tangent line. since slope is the ratio y and x then we can set an arbitrary vector with slope 4 by letting x=1 and y = √3 or v=[1,√3]. this vector has slope √3 and this is parallel to the tangent line, However this is not unit vector because its magnitude is not equal to 1 so we can divide this vector by its magnitude to find the unit vector.

[tex]u_v=\frac{v}{|v|} =\frac{1 \sqrt{3} }{\sqrt{1^{2}+(\sqrt{3})^2 } } \\=\frac{1}{\sqrt{4} } ,\frac{\sqrt{3} }{\sqrt{4} } =\frac{1}{2}, \frac{\sqrt{3} }{2} =[\frac{1}{2},\frac{\sqrt{3} }{2} ][/tex]

If a line has slope of m then all lines perpendicular of it will have a slope of  -1/m

So we are looking for a unit vector of slope of -1/√3

Using the same logic we have unit vector that are perpendicular to the tangent line are [tex][\frac{\sqrt{3} }{2},-\frac{1}{2} ][/tex]

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The solution to the given  equation is 8±2√2 i

An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations

Given the equation below

(x - 8)^2 = -8

Take the square root of both sides to have:

√(x-8)^2 = √-8

x-8 = ±√-8

x-8=±2√2 i

x = 8±2√2 i

Hence the solution to the given  equation is 8±2√2 i

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Answer:

10.375ft/s

Step-by-step explanation:

We need to read the number from the plot. The range from 10 to 11 is divided into 8 segments, so each segment is (11-10)/8=0.125

The answer is at 10 + 3 segments, so 10 + 3*0.125 = 10.375

Write the phrase as an expression the quotient of 22 and a number [tex]a[/tex].The quotient of 22 and  [tex]a[/tex]  number = 22/[tex]a[/tex]

Given that

number = 22

quotient =   [tex]a[/tex]

To find

The mathematical equation or relation between quotient of 22 and a number [tex]a[/tex].

So according the question

We have

quotient = 22

divisor =   [tex]a[/tex]

For finding the relation between given quotient and divisor, let's firstly know about Dividend, Divisor, Quotient and Remainder,

In Mathematics, the dividend is the value that is divided by another value to get the result. The dividend is the base of any division method.

An integer that divides another integer to obtain a result is called a divisor. The result of this division, or quotient, is the dividend, which is the original number that was divided.

Quotient = Dividend ÷ Divisor

When we divide one number by another, the result is a quotient. As an illustration, when we divide 6 by 3, we obtain the answer 2, which is the quotient. A decimal or an integer can both be used as the quotient. When dividing exactly, as when 10 ÷5 = 2, the quotient is an integer, whereas when dividing roughly, as when 12÷ 5 = 2.4, the quotient is a decimal. Although a quotient can be greater than the divisor, it will never be greater than the dividend.

The value remaining after division is known as the Remainder. After division, we are left with a value if a number (dividend) cannot be divided entirely by another number (divisor). This value is called the remainder.

Now, from question  

We have a quotient of 22 that is [tex]a[/tex].

So, 22 fully divided by [tex]a[/tex].

In mathematical form,

                        = 22/[tex]a[/tex]

The quotient of 22 and [tex]a[/tex]  number = 22/[tex]a[/tex]

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Answer:

so i the answer is 216 only

This geometric progression has 5 terms

This is a geometric progression or geometric series whose sum of n terms is given by the formula

Sn = a[([tex]r^{n\[/tex] – 1)/(r – 1)]

Where Sn is sum of n terms of geometric progression, a is the first term of the series , r is the common ratio

Here we are required to find the number of terms in the geometric progression whose first term is -3 and common ratio is 6

-4665 = -3 [( [tex]6^{n}[/tex]-1)/(6-1)

1555=( [tex]6^{n}[/tex]-1)/5

7775= [tex]6^{n}[/tex]- 1

7776 = [tex]6^{n}[/tex]

[tex]6^{5}[/tex] = [tex]6^{n}[/tex]

So, n=5

Therefore this geometric progression has 5 terms

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The numbers that neither terminate nor repeat are called irrational numbers.

What are irrational numbers?

Any real number that is not rational is called an irrational number. These numbers can not be expressed in the form of p/q, where q is not equal to 0. Sometimes, irrational numbers are also called non-terminating and non-repeating numbers.

Filling the blank with an appropriate term

The decimal representation of ___Irrational__ number neither terminates nor repeats.

Hence, the answer is irrational.

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Answer:

Step-by-step explanation:

18x^2 + 22x + 81x + 99

18x^2 + 103x + 99

Using the distance formula, the approximate distance between the points (1, -2) and (-9, 3) is: 11 units.

To find the distance of two points on a coordinate grid, the distance formula that is employed is: d = [tex]\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}[/tex].

Given the points are on a coordinate grid:

(1, -2) = (x1, y1)

(-9, 3) = (x2, y2)

Plug in the  values into the distance formula:

d = √[(−9−1)² + (3−(−2))²]

d = √[(−10)² + (5)²]

d = √(100 + 25)

d = √125

d = 11.18034

d ≈ 11 units.

Therefore, using the distance formula, the approximate distance between the points (1, -2) and (-9, 3) is: 11 units.

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Answer:

B

Step-by-step explanation:

7.5cm - 5cm = 2.5cm

So it is B :)

By unitary method we can say that it is better to buy the 4 inch radius pizza for $3.

According to the given question.

The price of 4 inch radius pizza = $3

And, the price of 8 inch radius pizza = $14

As we know that, the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Therefore, by unitary method.

Cost of 1inch radius pizza, when the price of 4 inch radius pizza is $3

= 3/4

= $0.75

And the cost of 1 inch radius pizza, when the price of 8 inch radius pizza is $ 14

= 14/8

= $ 1.75

Hence, by unitary method we can say that it is better to buy the 4 inch radius pizza for $3.

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The coordinates of the midpoint of a segment with the given endpoints (-8.4, -5.6)

The endpoints are given as

J(-11.2,-3.4), K(-5.6,-7.8)

The coordinates of the midpoint is calculated as

Midpoint = 0.5(x1 + x2, y1 + y2)

So, we have

Midpoint = 0.5(-11.2 - 5.6, -3.4 - 7.8)

This gives

Midpoint = (-8.4, -5.6)

Hence, the coordinates of the midpoint of a segment with the given endpoints (-8.4, -5.6)

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Bro each ticket is 4$. You just divide the money she earned with how much a ticket costs;

284/4 = 71 tickets

According to the given statement the values are:

The range = 19

Interquartile Range will be = 8.25

Sample Variance =33.93

Sample Standard deviation = 5.82

The dispersion of your data's middle quartile is measured by the interquartile range (IQR). It is the range for your sample's middle 50%. Assess geographical variability where the majority of your numbers are by using the IQR. Larger numbers suggest a wider dispersion of your data's center region.

According to the given data:

finding the range =  Maximum value + Minimum value

                            = 34 - 15

                            = 19

The range = 19When ordering the observations, we obtain:

15,20,24,26,26,27,30,34

Where ,

n = 8

Q1=(n+14)the observation's term value

=(94)the observation's term value

=(2.25)the observation's term value

=2nd observation +0.25[3rd-2nd]

=20+0.25[24-20]

=20+0.25(4)

=20+1

=21

Q3=(3(n+1)4)the observation's term value

=(3⋅94)the observation's term value

=(6.75)the observation's term value

=6th observation +0.75[7th-6th]

=27+0.75[30-27]

=27+0.75(3)

=27+2.25

=29.25

Now finding the Interquartile Range

= Q3 -Q1

= 29.25 - 21

=8.25

The  Interquartile Range will be = 8.25

Sample Variance S2=∑x2-(∑x)2nn-1

=5338-(202)28/7

=5338-5100.5/7

=237.57

=33.9286

Sample Variance =33.93

S=√∑x2-(∑x)2nn-1

=√5338-(202)28/7

=√5338-5100.5/7

=√237.5/7

=√33.9286

=5.8248

Sample Standard deviation = 5.82

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The experimental probability that all three of the coins will be head is 1 / 10.

The theoretical probability that all three of the coins will be head is 1/8.

Probability determines the chances that an event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.

The more likely the event is to happen, the closer the probability value would be to 1. The less likely it is for the event not to happen, the closer the probability value would be to zero.

Experimental probability is based on the result of an experiment that has been carried out multiples times.

Experimental probability = number of times all heads is gotten / total number of tosses

5/50 = 1/10

Theoretical probability = number of times all heads can be gotten / total number of possible outcomes

1/8

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Answer: 3/6 or 1/2 or 50%

Step-by-step explanation: 1, 2, 3 4, 5, 6 are each face

2, 4, and 6 are even.

3 out of the 6 are even (3/6)

reduce (1/2)

1/2 = 50%

Answer: 2 5/12

Step-by-step explanation: you multiply each number to 12 as the bottom number it’s hard to explain

-90

90

Since it is withdrawing, we are taking away -$18 every day for 5 days.

(-18)*5 = -90

Since it is a deposit, we are adding to the amount in her account, +$18 for 5 days.

18*5 = 108

The difference is that one is taking away and one is adding each day, resulting in negative or positive change.

An agreement with a bank to retain money and maintain transaction records. a plan for working with a firm on a regular basis. a set-up where a person uses a specific company's email or Internet services. The word "account" typically alludes to a ledger or record-keeping activity. In the financial sector, it can be used in a wide variety of ways. An account in banking is a contract whereby a company, generally a bank or credit union, takes a customer's financial assets and retains them on the customer's behalf at the customer's choice.

Savings accounts are one type of account that consumers can open to help them amass liquid assets.

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Using it's concepts, we have that:

A function has the following format: y = f(x).

In which each value of y is a function of one value of x, and thus, x is the independent variable and y is the dependent variable.

That is, the input of the function is the independent variable and the output is the dependent variable.

For this problem, we have that the number of swings is dependent on the mass of the pendulum, hence:

Number of Swings = f(mass).

Thus:

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There are two vertical asymptotes at angles of 0.5π radians and 1.5π radians and it occurs every π radians.

Tangent function is a kind of trigonometric function, that is, a kind of transcendent function. This function has a period of π radians and for f(x) = tan x, the vertical asymptotes are contained in the points:

x = 0.5π + i · 2π, where i is an integer.

Hence, there are two vertical asymptotes at angles of 0.5π radians and 1.5π radians and it occurs every π radians.

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Answer:

x = 5

Step-by-step explanation:

A. The integer that represents the change of altitude to avoid the storm is 8,000

B. The integer representing the altitude after passing the storm is 30,000

A. We are given that the initial altitude of the plane was 30,000 ft. The plane flew at at altitude of 38,000 feet

Change of altitude = final altitude - initial altitude

Change of altitude = 38,000 - 30,000 = 8,000 ft

Therefore, the integer representing the change of altitude to avoid the storm is 8,000

B. After the storm:

We know that, after the storm, the plane returned to its initial altitude. Given that the initial altitude is 30,000 ft, this would mean that the integer representing the altitude after passing the storm is 30,000

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Answer: 27

Step-by-step explanation: