Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 3 ≤ x ≤ 6.
Answer:
OC
1
2
ين
3
4
5
6
f(x)
69
64
59
54
49
44


Need Help

Answer:

3[tex]\sqrt{10}[/tex] ≈ 9.45

Step-by-step explanation:

calculate the distance d between the points using the distance formula

d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]

with (x₁, y₁ ) = (- 1, 8 ) and (x₂, y₂ ) = (8, 5 )

d = [tex]\sqrt{(8-(-1))^2+(5-8)^2}[/tex]

   = [tex]\sqrt{(8+1)^2+(-3)^2}[/tex]

   = [tex]\sqrt{9^2+9}[/tex]

   = [tex]\sqrt{81+9}[/tex]

   = [tex]\sqrt{90}[/tex]

   = [tex]\sqrt{9(10)}[/tex]

   = [tex]\sqrt{9}[/tex] × [tex]\sqrt{10}[/tex]

   = 3[tex]\sqrt{10}[/tex] ← exact value

   ≈ 9.49 ( to 2 dec. places )

Answer:

1

Step-by-step explanation:

We can find the slope using the slope formula, which is [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

The order of the points doesn't matter, but the points that are farthest right (8, 8) can be our y2 and x2 and the points that are farthest left (5, 5) can be our y1 and x1.

Thus, we have [tex]\frac{8-5}{8-5}=\frac{3}{3}=1[/tex]

The correct answer is x = 2

(x + 1 < 4) ∩ (x-8>-7)

Make x the subject in each case:

(x<4-1)(x>-7+8)

        (x<3)∩(x>1)

If x<3, then x could be 2, 1, -1, etc.

If x>1, then x could be 2, 3, 4, etc.

Thus (x<3)∩(x>1) = 2

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Answer:

x = 2

Step-by-step explanation:

Hello!

We are looking at the intersection of two sets, or common values found between two sets of data.

We can solve for x on each side and find any common values between.

As you can see, the intersection occurs at the common values. The only value that is common between the two sets is 2.

Therefore, the intersection of these sets is 2.

Answer:

r is -11

Step-by-step explanation:

Move the like terms to the same side. 4r-6r is -2r

14 + 8 is 22

22/-2 is -11

Answer:

64:27

Step-by-step explanation:

If the ratio between the old and new radius is described with the ratio: 4:3, then if the first radius was 3, then the new radius is 4.

Also if you multiply 3 by (4/3) it also equals 4

The volume of a sphere is described as:  [tex]\frac{4}{3} \pi r^{3}[/tex]

So let's plug in 3 and 4 and see their ratio.

[tex]\frac{\frac{4}{3}\pi 4^{3} }{ \frac{4}{3}\pi 3^{3} }} = \frac{4^{3} }{3^{3} } = \frac{64}{27}[/tex]

The answer is 64/27 or (4/3)^3

Answer:

by a factor of 64/27   or   64:27

Step-by-step explanation:

Volume of a sphere = 4/3  pi  r^3    

    now increase the radius  by 4/3      ( this is  4:3)

               new volume = 4/3 pi  (4/3 r)^3  

                                     = 64/27  *  4/3 pi r^3

so the original volume is increased by  64/27

Answer:

[tex]x \leq \frac{7 - x}{3}[/tex]

Step-by-step explanation:

This expression is an inequality which is a relation that makes a non-equal comparison between two numbers/expressions

we want x to be alone in one side, y + 3x ≤ 7

Subtract y from both sides,

y + - y + 3x ≤ 7 - y

3x ≤ 7 - y

divided both sides by 3 to get x alone

3x / 3 ≤ 7 - y / 3

x ≤ 7 - y / 3

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W is the width of the quilt, the restrictions are given by the inequality:

7.7ft ≤  W ≤  8.9 ft

Remember that for a rectangle of length L and width W, the area is:

A = L*W

In this case, we know that:

L = 1.2*W

Replacing that we get:

A = 1.2*W²

And we know that the area must be between 72 square feet and 96 square feet, then:

72ft² ≤  1.2W² ≤ 96ft²

Now we can divide all by 1.2:

(72ft²)/1.2 ≤  W² ≤ (96ft²)/1.2

60ft² ≤  W² ≤ 80ft²

If we apply the square root in the 3 sides of the inequality, we get:

√60ft² ≤  √W² ≤ √80ft²

7.7ft ≤  W ≤  8.9 ft

These are the restrictions on the width such that the quilt will meet the required area.

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Answer:

y = 4/5x + 2

Step-by-step explanation:

Standard equation given slope and y-intercept -> y = mx + b

After substituting variables m and b, you get y = 4/5x + 2.

Step-by-step explanation:

118+2×=180

180-118=62

62÷2(×)=31

×=31

Answer:

x + x + 118 = 180

Step-by-step explanation:

...........

Life , Health , Car are considered to be very important insurance ,  Rental Car Damage , Travel Insurance has no usage.

Insurance is safe guarding any thing which has some monetary or emotional value to it , It can be life , health , car , house , your gold etc.

Insurance protects you against something you can never predict .The life is unpredictable and Insurance is a cover to that .

As given in the question , a person can be lucky enough that he never gets to use the money that he invested in the Insurance , but not investing due to this is wrong.

This is not difference of opinion but lack of prediction of future and lack of understanding the needs of life.

Life , Health , Car , Home , Fire etc . insurance that protects the basic amenities of life are considered to be very important ,

while nowadays insurance of Rental Car Damage , Travel Insurance , these are some which has no usage beyond the fact that they cover nothing.

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Answer:

Step-by-step explanation:

it should be sth like green graph

Answer:

121 i.e. 11²

Step-by-step explanation:

(a+b)² = a² + 2ab + b²

x² + 2 × x × 11 + 11² = (x + 11)²

Answer:

Step-by-step explanation:

The question is asking you to identify the domain for each of the parts of the piecewise-defined function. This means you need to identify the corresponding part on the graph, and determine its horizontal extent.

The first step in solving a problem is to look at the given information. The graph is shown as three (3) non-overlapping horizontal line segments. The open- or filled-circle end points tell you whether that x-value is part of the line segment.

The blanks in the function definition are where the domain descriptions go for the piecewise-defined function. This means you have to match the function description to the left of "if x ∈" with the set of x-values it corresponds to. The "x ∈" notation suggests you want to specify the domain in "interval notation," rather than as an inequality.

The first part of the function definition is ...

  f(x) = -4

This matches the horizontal line segment at the bottom of the graph. The closed dots at its ends mean it is defined for ...

  -6 ≤ x ≤ -2

In interval notation, a square bracket is used when the end point is included in the interval.

  f(x) = -4  if x ∈ [-6, -2]

The second part of the function definition is ...

  f(x) = -3

This matches the horizontal line segment in the middle of the graph. The open dot at the left end, and the closed dot at the right end mean it is defined for ...

  -2 < x ≤ 1

We use a round bracket (parenthesis) when an end point is not included in the interval.

  f(x) = -3  if x ∈ (-2, 1]

The third part of the function definition is ...

  f(x) = 4

This matches the horizontal line segment at the top of the graph. The open dot at the left end, and the closed dot at the right end mean it is defined for ...

  1 < x ≤ 5

In interval notation, this is ...

  f(x) = 4  if x ∈ (1, 5]

The number of prime divisors of "6n" is 2 numbers 2 and 3

Given

"n"  = 6    

thus 6n  = 6(6) = 36

The positive divisors are   1, 2, 3, 4, 6, 9, 12, 18 and 36

So, the number of prime divisors of "6n" is 2 numbers 2 and 3.

The prime factors of a positive integer are the top numbers that divide that integer exactly. The technique of finding those numbers is known as integer factorization or prime factorization.

The fundamental theorem of mathematics says that every positive integer has a completely unique prime factorization.

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The ordered pair on the inequality y < 2/3x + 2 is D. (1,2)

The inequality is given as:

y < 2/3x + 2

Next, we test the options:

A. (0,3)

3 < 2/3 * 0 + 2

3 < 2 --- false

B. (-3,1)

1 < 2/3 * -3 + 2

1 < 0 --- false

C. (3,5)

5 < 2/3 * 3 + 2

5 < 4 --- false

D. (1,2)

2 < 2/3 * 1 + 2

2 < 2.67 --- true

Hence, the ordered pair on the inequality y < 2/3x + 2 is D. (1,2)

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The explicit formula that is equivalent to aₙ = -6aₙ₋₁  is; aₙ = 1(-6)ⁿ⁻¹

We are given;

a₁ = 1

aₙ = -6aₙ₋₁

Thus, for second term;

a₂ = -6a₁

a₂ = -6

For the third term;

a₃ =  -6a₂

a₃ = 36

The resulting sequence is 1, -6, 36,......

The sequence is a geometric sequence with;

a = 1

r = -6

The explicit rule will be aₙ = 1(-6)ⁿ⁻¹

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Answer:

4 m/s

Step-by-step explanation:

Well the constant rate of change can be defined as the slope or rise/run. This can be calculated using any two points. So I'll use (10, 40) and (20, 80). the seconds increased by 10 (run) and the meters increased by 40 (rise) This gives you the equation 40/10 which simplifies to 4. That is the constant rate of change

Probability that Martin passed the exam when he attend the class daily is given by 1/3.

Probability is the possibility to occurrence of an event.

In other words, Probability is the ratio of number of favorable cases under an event to total number of cases under that event.

Let P be the event that Martin passed the exam and A be the event that he attend the class daily.

Given that,

40% of students passed tbe exam.

The probability to pass the exam is given by,

[tex]P(P)=40%=\frac{40}{100}=\frac{4}{10}[/tex]

90% students attend the class daily

probability to attend the class daily is given by,

[tex]P(A)=90%=\frac{90}{100}=\frac{9}{10}[/tex]

30% student both passed the exam and attended class

So probability to both passed the exam and attend the class is given by,

[tex]P(P\cap A)=30%=\frac{30}{100}=\frac{3}{10}[/tex]

Now conditional probability that Martin will passed the exam if he attend class daily is given by,

[tex]P(P|A)=\frac{P(P\cap A)}{P(A)}=\frac{\frac{3}{10}}{\frac{9}{10}}=\frac{3}{9}=\frac{1}{3}[/tex]

Hence the required pobability that Martin passed the exam when he attend the class daily is given by 1/3.

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The height of the new photo must be 945 pixels (option B).

To calculate the height of the photograph, we must first know what proportion the sides of the previous photo have, for this we do the following operation:

According to the above, the height of the photo is equal to 75% of the width. So to find the height of the new photograph we must do the following operation:

So the height of the new photo should be 945 pixels.

Note: This question is incomplete. Here is the missing part:

Question

Jorge wants to determine the enlarged dimensions of a digital photo to be used as wallpaper on his computer screen. The original photo was 800 pixels wide by 600 pixels high. The new photo will be 1,260 pixels wide. What will the new height be?

Options

460 pixels

945 pixels

1,680 pixels

1,860 pixels

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Answer: 5

Step-by-step explanation:

By the inscribed angle theorem.

[tex]\frac{9}{15}=\frac{2x-1}{3x}\\\\27x=30x-15\\\\-3x=-15\\\\x=5[/tex]

Answer:

1/8 of the pizza

Step-by-step explanation:

whole pizza=1

5/8 is gone so 1-5/8=8/8-5/8=3/8

3/8-1/4 = 3/8-2/8=1/8

hope this helps

Answer:

h = 5t

Step-by-step explanation:

So basically, its a slope problem again. You are trying to find the equation that equals hits. So you can cross off t = 5h and t = h + 5. So now, you need to find the most reasonable answer by calculating the slope.

If you try h = t + 5,

Put in 3 - you get 8

Put in 7 - you get 12

But on the table you get 15, 36 respectively.

If you try h = 5t,

Put in 3 - you get 15

Put in 7 - you get 35

Which is much closer to the numbers in the table, therefore it is the answer.

The rule is n/(-2)

A geometric progression is a sequence in which any element after the first is obtained by multiplying the preceding element by a constant called the common ratio which is denoted by r.

Given:

64, -32,16,-8

r= 64/-32

r= -2

again, r= -32/16

r= -2

By above we concluded that the common ratio is is -2.

If n is natural numbers for finding geometric progression the rule which defines it n/(-2).

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Answer:

Keep in mind the rules.

When we multiply terms with same bases we keep one base and add the exponents.

Step-by-step explanation:

Answer:

bro tbh just use like or

Step-by-step explanation:

its not that deep

Answer:

B

Step-by-step explanation:

7/20 x 1/2 x 1/6

Answer:

I don't understand the formatting of the possible answers.  Below is a solution.

Step-by-step explanation:

906,060 is the same as 9.0606 x 10^5

The given number is equal to [tex]-9.0606 * 10^5[/tex]

Scientific notation is a way to write numbers in an abbreviated way, making it easier to work with these numbers.

The primary reason for converting numbers into scientific notation is to make calculations with unusually large or small numbers less cumbersome. Because zeros are no longer used to set the decimal point, all of the digits in a number in scientific notation are significant.

A widely used floating-point system in which numbers are expressed as products consisting of a number between 1 and 10 multiplied by an appropriate power of 10

Converting –906,060 into scientific notation, we get

-906060/100000

= - 9.06060*10^5

Thus, The given number is equal to -9.06060*10^5

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Answer:Tangent ratio of an angle

Step-by-step explanation:

Tangent ratio of an angle  the ratio of the length of the opposite side of an angle divided by the length of the adjacent side.

Answer:

w(w-5)

Step-by-step explanation:

Given Width of rectangle = w

Length of rectangle is 5 less than width of rectangle = w - 5

Area of Rectangle = Length x Width = w * w-5 = w(w-5)

Answer:

the second answer option

Step-by-step explanation:

the area of a rectangle is

length × width

or

l × w

l = w - 5

so, when we use the second in the first equation, we get

(w - 5)×w

or

w(w - 5)