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Question 3

Examining the given polynomial we arrive at the various parameters

The degree refers to the maximum power to which the equation is raised. We can see that the term 2x⁴ bears the maximum power and it is 4 hence the equation is degree 4

The end behavior refers to how the equation relates at the extremes. The extremes a big positive value and big negative value.

Big positive value say x = 1000

f(x)=8x³+2x⁴-5x²+9

f(1000) = 2.008x10^12

Big negative value say x = -1000

f(x)=8x³+2x⁴-5x²+9

f(-1000) = 1.992x10^12

comparing the two values shows that the value is increasing in both positive and negative, hence we write the end behavior as x → ∞ f(x) → ∞,  x → - ∞ f(x) → ∞

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The inverse of the given function is f-1(x)= x²+4.

A function that "undoes" another function in mathematics is known as an inverse. In other words, if f(x) produces y, then y entered into the inverse of f produces x. An invertible function is one that has an inverse, and the inverse is represented by the symbol f-1.

To calculate the inverse of a function:

Consider f(x)=y

And interchange the variables.

So given f(x)= √x-4 becomes

y=√x-4 ⇒ x=√y-4

Now on squaring both sides we get,

x²= y-4

⇒ y = x²+4

Replace y by f-1(x)

So the equation becomes,

f-1(x) = x²+4

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a

so the first one is 817(the amount at the beginning) +19x

817+19x

the second pool is 38x, cause there's no water at the start.

38x

b

it would be 817+19x=38x

Answer:

x = 16.4

Step-by-step explanation:

From the diagram, we can see that the radius of the circle is 19.4 as the line labelled 19.4 goes from the centre to the edge of the circle.

Therefore the length of the line marked in green is also 19.4 units, as it is also a radius of the circle.

Now we can simply use the Pythagorean Theorem to calculate the value of [tex]x[/tex]:

[tex]19.4^2 = x^2 + 10.3^2[/tex]

⇒ [tex]x^2 = 19.4^2 - 10.3^2[/tex]

⇒ [tex]x = \sqrt{19.4^2 - 10.3^2}[/tex]

⇒ [tex]x = \bf 16.4[/tex]

Therefore the length of the indicated segment is 16.4 units.

Answer:

Rational

Step-by-step explanation:

- √225 = -15

Answer:

x = 18

Step-by-step explanation:

the angles pictured are supplementary angles.

supplementary angles are angles whose sum equals 180°

ex: <1 + <2 = 180°

[tex]5x - 11 + 6x - 7 = 180[/tex]

[tex]11x - 18 = 180[/tex]

[tex]11x = 198\\x = 18[/tex]

Answer:

[tex]\boxed{\sf{x=18}}[/tex]

Step-by-step explanation:

To find the value of x, you have to use the supplementary angles which is equal to 180°.

Supplementary angles = 180°

5x-11+6x-7=180

Combine like terms.

[tex]\sf{5x+6x-11-7=180}[/tex]

5x+6x=11x

[tex]\sf{11x-11-7=180}[/tex]

Subtract the numbers from left to right.

-11-7=-18

[tex]\sf{11x-18=180}[/tex]

You have to add by 18 from both sides.

11x-18+18=180+18

Solve.

Add the numbers from left to right.

180+18=198

11x=198

Divide by 11 from both sides.

11x/11=198/11

Solve.

198/11=18

[tex]\rightarrow \boxed{\sf{x=18}}[/tex]

Therefore, the final answer is x=18.

Answer:

8.368, 156.8, 2.52$

Step-by-step explanation:

0.8% of 1,046 is 8.368

to get this first find 80% of 8.368 so you can get 836.8 and then you move it back 2 places to get 8.368

160% of 98 will be 156.8

first split it up into 2 problems for it to be easier

100% of 98

and 60% of 98

100% of 98 = 98

60% of 98 = 9.8*6 = 58.8

98+58.8 = 156.8

For the 3rd one it will be 2.52$ srry gtg soon so can't explain

Answer: 7

Step-by-step explanation:

Let the number of sessions be x. Then,

[tex]20+45x=90+35x\\\\10x=70\\\\x=7[/tex]

Answer:

Step-by-step explanation:

21

Answer: 21

Step-by-step explanation: To solve for AC, you will need to add segments AB and BC together. So, 9+12=21

The amount in the savings account of Mrs. Martins after 9 years will be $4081.

According to the question,

We have the following details:

The amount deposited in the savings account or the principal amount = $2,650

Interest per year = 6%

Time = 9 years

(It is given that the interest is not compounded.)

Now, using the formula of simple interest, we will first find the total interest after 9 years,

Simple Interest (S.I.) = (Principal * Rate * Time)/100

S.I. = (2650*6*9)/100

S.I. = (2650*54)/100

S.I. = 143100/100

S..I. = $ 1,431

Now, the total amount in the savings account would be the sum of the principal amount and the total interest.

So, we have:

Total amount = Principal + S.I.

Total amount = $ (2,650+1,431)

Total amount = $ 4,081

Hence, the total amount in Mrs. Martins's savings account is $ 4,081.

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Step-by-step explanation: I hope this helps.

Answer:

There are 2 ³⁷ bytes in 128 gigabytes.

Bytes, which typically contain eight bits, are the basic building blocks of digital information.

We know that 128 = 2⁷

Now each gigabyte = 2³⁰ bytes

So the total number of bytes in 128 gb is

2⁷ × 2³⁰  = 2³⁰⁺⁷ = 2 ³⁷

Therefore there are 2³⁷ bytes in 128 gigabytes.

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Answer:

The sequence is arithmetic.

-2 , 8 , 18 , 28 , 38 , 48 , 58 , 68 , 78 , . . .

21st term value is 198.

Step-by-step explanation:

Answer:

(0,2)

Step-by-step explanation:

Answer:X squared =4/9 is c

              X to the third power is a

               X squared =81/46 is b or d

               X to the third power is d or b

Answer:

x= 2/3 or x= −4

Explanation:
3x2+16x−10=6x−2

Step 1: Subtract 6x-2 from both sides.

3x2+16x−10−(6x−2)=6x−2−(6x−2)

3x2+10x−8=0

Step 2: Factor left side of equation.

(3x−2)(x+4)=0

Step 3: Set factors equal to 0.

3x−2=0 or x+4=0

x=2/3 or x= −4

The correct option is A. 1.4 x 10^3

Exponents: The exponent of a number indicates how many times a number has been multiplied by itself. For instance, 3^4 indicates that we have multiplied 3 four times. Its full form is 3 3 3 3. Exponent is another name for a number's power. A whole number, fraction, negative number, or decimal are all acceptable.

The first number = 72,980,001

The second number = 54908

Dividing the first number by the second number we get:

=72980001/54908 = 1329.13

Which is equivalent to 1.4 x 10^3

So, 72,980,001 is 1.4 x 10^3 times greater than 54,908

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[tex]x\leq -18[/tex]

Graph Displayed Below

Hope this helps!

The solution to the given inequality [tex]3x \leq -54[/tex] is [tex]x \leq \frac{-54}{3}[/tex] .

Inequality is a fine statement that compares two values, showing if one is lower than, lesser than, or simply not equal to another value. Inequalities are frequently used to represent connections between amounts, similar to the relationship between the height and weight of a person, or the relationship between the speed and time of an object in stir.

We first divide the inequality [tex]3x \leq -54[/tex] by 3 on both sides to obtain:

[tex]x \leq \frac{-54}{3}[/tex] .

Then, we plot the line [tex]x = \frac{-54}{3}[/tex] on the graph. The region left to the line thus obtained is the solution of the given question.

Thus, the line [tex]x \leq \frac{-54}{3}[/tex] is plotted in the graph.

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This is not a function, we know this because the input x = 1 is mapped into two different outputs.

A relation maps elements from one set, the domain, into elements from another set, the range. A relation is only a function if each element of the domain is mapped into only one element of the range.

In this case, we have the relation:

x: 1, -2, 1, -3

y: 2, 1, 3, -2

The input x = 1 is mapped into two different values, y =2 and y = 3.

Thus, the relation is not a function.

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The solution to given inequality 2(4x + 1) < 3(2x - 3) is x < -11/2

In this question, we have been given an inequality  2(4x + 1) < 3(2x - 3)

We need to solve given inequality.

2(4x + 1) < 3(2x - 3)                          ..............(Given inequality)

8x + 2 < 6x - 9               .............(simplify both sides of the inequality)

8x + 2 - 6x < 6x - 9 - 6x             ............(subtract 6x from both the sides)

2x + 2 < -9

2x + 2 - 2 < -9 - 2                       ............(subtract 2 from each side)

2x < -11

2x/2 < -11/2                               ................(Divide each side by 2)

x < -11/2

Therefore, the solution to given inequality 2(4x + 1) < 3(2x - 3) is x < -11/2

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Answer:

5 minutes and 20 seconds

Step-by-step explanation:

basically your equation is: (rate of filling container) x (time to fill container)

- (minus)

(rate of leaking from container) x (time to fill container)

=

(the size of the container in gallons)

--------------------

step 1 - so t = the time in minutes to fill14 gallon container

step 2 - convert 2 3/4 to quarters so:

2 • 4 = 8 and it’s in quarters so 8/4 then

8/4 + remaining 3/4 = 11/4

step 3 -  so then you fill in the equation:(11/4)•t - (1/8)•t = 14

step 4 - multiply both sides of the equation by 8:

(11/4) = 2.75 • 8 = 22

(1/8) = 0.125 • 8 = 114 • 8 = 112

so the equation is:

22t - t = 112

step 5 - divide both sides of the equation by 22:

22t / 22 = t 

112 / 22 = 5.333

so t = 5.333 

step 6 - convert 

so 5.333 has a repeating decimal of 0.3 which is 1/3. so to convert that to seconds, take 1/3 of  60:

 60 / 3 = 20 

so it takes 5 minutes and 20 seconds to fill the 14 gallon container

hope this helps :)

The given function f(x) =3x² - 48/2x+8 has no Horizontal asymptote.

A horizontal asymptote may be defined as a horizontal line at which the graph of the function will appear to meet but will not actually meet. It is a tool to determine the end behavior of the function. We are given the function f(x) = 3x² - 48/2x+8. Now to find horizontal asymptote of this function we first find lim ₓ→∞ f(x) that is

lim ₓ→∞ (3x² - 48)/(2x + 8)

lim ₓ→∞ 3/2(x - 4) = ∞

Now, we calculate lim ₓ→-∞ f(x) that is

lim ₓ→-∞ (3x² - 48)/(2x + 8)

lim ₓ→-∞ 3/2(x - 4) = -∞

Since, both the limits are different therefore function does not have any horizontal asymptote.

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To purchase a mobile set with the cost of Rs 18000 and VAT 13% , Mrs Sharma needs to pay Rs 20,340.

As given in the question,

Cost of the mobile set Mrs Sharma purchase = Rs 18000

VAT added on purchasing a mobile set is equal to 13%

Amount of VAT on mobile set is equal to

= 13% of 18000

= (13/100) × 18000

= 13 ×180

= Rs 2340

Mrs Sharma needs to pay amount to purchase a mobile set

=18000 + 2340

= Rs 20,340

Therefore, to purchase a mobile set with the cost of Rs 18000 and VAT 13% , Mrs Sharma needs to pay Rs 20,340.

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Answer:

b = 4.472 and h = 4.472

Step-by-step explanation:

Area of a parallelogram is A = bh

Find b and h where the area is 20 square inches

So, to find the equal value of both b and h take square root of 20

➟ √20

➟ 4.472

So, b = 4.472 and h = 4.472

Checking

A = 4.472 × 4.472

A = 19.9 ≈ 20

If Martin earned $8.75 an hour plus another $18 in tip and Lawrence earned $9.25 an hour and spent $2 on a soda, then the inequality represents the situation is 8.75x+18 < 9.25x-2

The payment of Martin per hour = $8.75

The addition tip he got = $18

The payment of Lawrence per hour = $9.25

The amount he spend for soda = $2

x represents the number of hours worked

Lawrence had more money than Martin

Then the inequality will be

8.75x+18 < 9.25x-2

Hence, if Martin earned $8.75 an hour plus another $18 in tip and Lawrence earned $9.25 an hour and spent $2 on a soda, then the inequality represents the situation is 8.75x+18 < 9.25x-2

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Answer:

7 People is they all go in the same car and pay only for 1 parking space.

Step-by-step explanation:

23.25x + 7.25 ≤ 170  Subtract 7.25 from both sides of the equation

23.25x ≤ 170  Divide both sides by 23.25

x ≤ 7

Answer:

1, 2, 8

Step-by-step explanation:

Corresponding angles lie on the same side of the parallel lines and on the same side of the transversal.

1, 2, and 8 are corresponding angles.

Answer:

-4 2/21

Step-by-step explanation:

-2 3/7 - 1 2/3

Change to improper fraction

-2 3/7 = -17/7

- 1 2/3 =-5/3

-17/7-5/3

L.C.M=21

-51-35/21

= -86/21

= -4 2/21

Hope it helps..

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