What is √84 simplified

Answer:   False

The correct expression is -4(x-1)^3+2

====================================================

Work Shown:

[tex]f(x) = x^3\\\\f(x-1) = (x-1)^3\\\\-4f(x-1) = -4(x-1)^3\\\\-4f(x-1)+2 = \boldsymbol{-4(x-1)^3+2}\\\\[/tex]

So the error is with the stuff in the parenthesis. Instead of (x^3-1) it should be (x-1)^3

Side note:  (x-1)^3 expands to x^3-3x^2+3x-1

The reminder by dividing f(x)= x⁴ + 7x³ + 17x² + 20x is divided by x² + 4 is x² + 7x + (-13x² - 8x)/(x² + 4) so none of the given option is correct.

The number system is a way to represent or express numbers.

Any of the multiple sets of symbols and the guidelines for utilizing them to represent numbers are included in the Number System.

Given the dividend f(x)= x⁴ + 7x³ + 17x² + 20x and diviser x² + 4

The first time it will go to x²

Then,

Quotient = x²

Remainder = 7x³ - 13x²

The second time goes to 7x

Quotient = 7x

Remainder = -13x² - 28x

The third time it is not divisible so  (-13x² - 8x)/(x² + 4) will be the reminder.

Together it is  x² + 7x + (-13x² - 8x)/(x² + 4).

Hence "The reminder by dividing f(x)= x⁴ + 7x³ + 17x² + 20x is divided by x² + 4 is x² + 7x + (-13x² - 8x)/(x² + 4)".

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Answer:

A.

         √10 ≈ 3

          2 × 3 ≈ 6

         √25 = 5

         √4 = 2

          5 × 2 = 10

         [tex]\frac{300}{3}=100\\\sqrt{100}\\100=10^2\\\sqrt{10^2}\\\sqrt{10^2}=10[/tex]

         [tex]1000=10^3\\\sqrt[3]{10^3}\\\sqrt[3]{10^3}=10(\mathrm{Radical\:rule)}\\[/tex]

Thus,

option A. is correct.

The amount of Lemon's commission is $4.7

According to the question we have been given that

     Commission earned by Lemon = 3.2%

     Selling price of drone which is sold by Lemon  = $146.97

We need to find the amount of commission she earned by selling the drone.

The formula to be used to find the amount of commission is

                =  percentage of commission * selling price

putting the required value we get

               = 3.2% of $146.97

here 'of' is denoted as multiplication

thus,        =0.032 * 146.97

               = $4.7

Hence the amount of Lemon's commission is $4.7

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The Slope of the line passing through the points (-2,1) and (2,-1) is -1/2 .

The Slope(m) of the line is defined as the change in y coordinate with respect to change in x coordinate ,

The Slope(m) of line passing through the points A(a,b) and B(c,d) is calculated using the formula

m = (d-b)/(c-a)

In the question

it is given that the line passes through the points (-2,1) and (2,-1) .

name the points as A(-2,1) and B(2,-1) .

the values are a=-2  ,  b=1  ,  c=2  ,  d=-1 .

Substituting the values in the formula of Slope we get

m = (-1-1)/(2-(-2))

= -2/(2 + 2)

= -2/4

= -1/2

Therefore , the slope of the line passing through the points (-2,1) and (2,-1)  is -1/2 .

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Answer:

Step-by-step explanation:

The Slope of the line passing through the points (-2,1) and (2,-1) is -1/2 .

[tex]x^2 + 18x=-79 \\ \\ x^2 + 18x+81=2 \\ \\ \boxed{(x+9)^2=2} \\ \\ x+9=\pm \sqrt 2 \\ \\ x=-9 \pm \sqrt{2} \\ \\ \boxed{x=-9+\sqrt{2}, -9-\sqrt{2}}[/tex]

The value of the expression 2^6 × 2^2 is 8^2 * 4

Expressions are mathematical statements that are represented by variables, coefficients and operators

The expression is given as

2^6 × 2^2

Apply the product law of indices to the above expression

So, we have

2^6 × 2^2 = 2^(6 + 2)

Evaluate the sum in the above expression

So, we have

2^6 × 2^2 = 2^8

Expand the expression

So, we have

2^6 × 2^2 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2

This gives

2^6 × 2^2 = 8 * 8 * 4

So, we have

2^6 × 2^2 = 8^2 * 4

Hence, the value of the expression 2^6 × 2^2 is 8^2 * 4

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The probability that the sum of the two rolls equals 5 is 1/16.

Probability is defined as the ratio of the number of favorable outcomes to the total number of outcomes in other words the probability is the number that shows the happening of the event.

Probability = Number of favorable outcomes / Number of sample

Given a single die with 8 sides (numbered 1, 2, 3, ..., 8) is rolled twice, the total outcome will be:

Total outcome = 8^2

Total outcome = 64

For the sum of two rolls, the expected outcome will be:

E = {(1, 4), (4, 1), (3, 2), (2, 3)}

n(E) = 4

Pr(sum of the two rolls is 5) = 4/64

Pr(sum of the two rolls is 5) = 1/16

Hence the probability that the sum of the two rolls equals 5 is 1/16

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The monthly payment will be $1454.06048

You can calculate the Car Loan EMI Amount with the help of the mathematical formula: EMI Amount = [P x R x (1+R)^N]/[(1+R)^N-1] , where P, R, and N are the variables. This also means that the EMI value will change, each time you change any of the three variables. Let’s discuss these three variables in detail.

‘P’ stands for the Principal Amount. It is the original loan amount given to you by the bank on which the interest will be calculated.

‘R’ stands for the Rate of Interest set by the bank.

N is the number of years given for the repayment of the loan. As you must pay the EMIs each month, the duration is calculated in the number of months.

Here , P=$50000,R=3/12/100=0.0025,N=36 Months.

EMI=[50000 x 0.0025 x (1+0.0025)^36]/[(1+0.0025)^36-1]

= $1454.06048

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The flipped shape has a pair of parallel line

A pair of line is said to be parallel lines when the lines tend to maintain equal distance apart and never intersect at any point. such lines has peculiar properties and are useful in mathematics.

Since a pair of parallel line do not intersect their is not angle between them.

Flipping a shape will change the position of the flipped shape to a new one. This activity does not add to the size of a shape or to the property of the shape.

Margot flipping a pair of parallel lines will not add or reduce the number of the parallel lines. It however creates point of intersection between the parallel line and horizontal line crossing the parallel line.

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150 Minutes

We need to find the Lcm of 25 and 30

Student 1 and Student 12 start from the same point, at same time and in same direction.  So they meet again after lcm of the times taken by them individually.

What is LCM?

Least common multiple

To get the LCM we have to factorize the numbers,

25=5*5

30=2*5*3

LCM of 25 and 30 is 5*2*3*5 is 150

Therefore in 15 minutes they meet each other at the starting point

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Answer: 175

Step-by-step explanation:

Answer: Determine the mid-point.

Determine the slope between the two points.

The slope of perpendicular is negative reciprocal

Use slope and mid-point is point slope form.

Step-by-step explanation:

Answer:

Step-by-step explanation:

the answer is 30

The new coordinates are A'(-21, 7), B'(0, -28), C'(14, 28).

Dilating the given triangle by the scale factor means multiplying each coordinate by the given scale factor.

Given coordinates are A(-3, 1), B(2, 4), and C(0, -4).

The scale factor k = 7.

Let, the new coordinate obtained by dilating A with scale factor k be A'.

Then x-coordinate of A' = k × x-coordinate of A

⇒ x-coordinate of A' = 7 × (-3)

⇒ x-coordinate of A' = -21

And y-coordinate of A' = k × y-coordinate of A

⇒ y-coordinate of A' = 7 × 1

⇒ y-coordinate of A' = 7

So, A' → (-21, 7)

Let, the new coordinate obtained by dilating B with scale factor k be B'.

Then x-coordinate of B' = k × x-coordinate of B

⇒ x-coordinate of B' = 7 × 2

⇒ x-coordinate of B' = 14

And y-coordinate of B' = k × y-coordinate of B

⇒ y-coordinate of B' = 7 × 4

⇒ y-coordinate of B' = 28

So, B' → (14, 28)

Let, the new coordinate obtained by dilating C with scale factor k be C'.

Then x-coordinate of C' = k × x-coordinate of C

⇒ x-coordinate of C' = 7 × 0

⇒ x-coordinate of C' = 0

And y-coordinate of C' = k × y-coordinate of C

⇒ y-coordinate of C' = 7 × -4

⇒ y-coordinate of C' = -28

So, C' → (0, -28)

Refer to the image attached for the new triangle formed.

Therefore, the new coordinates are A'(-21, 7), B'(0, -28), C'(14, 28).

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The relationships

a. the distance traveled on a trip and the travel time

c. the amount of money spent and the number of shirts bought

are have the positive associations.

Positive associations:

Two variables have a positive association when the values of one variable tend to increase as the values of the other variable increase.

Given,

Here we have the following relationships,

a. the distance traveled on a trip and the travel time

b. the distance remaining on a trip and the travel time

c. the amount of money spent and the number of shirts bought

d. the height of an eighth- grade student and the time to complete a puzzle

e. the amount of money owed on a computer and the time making payments

We need to find the positive associations in it.

Based on the definition of positive association,

The options (a) and (c) are the relationships that are in positive association.

Because while we look into the option (a),

When the traveling distance is increased then the time taken for it also increased.

Similarly in option (c),

While we increase the amount then the number of shirt we brought will also be increased.

The other options are not fit in this case.

So, option (a) and (c) are in positive association.

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Answer:

B is the correct answer.

Step-by-step explanation:

Add -2+e to both sides

v + f − e -2+e = 2 -2+e

Which will give you v + f -2 = e.

Answer:

$14.67

Step-by-step explanation:

The value of the discount is,

→ (10/100) × 16.30

→ 0.1 × 16.30

→ $1.630

Then the amount he should pay is,

→ 16.30 - 1.630

→ $14.67

Hence, he must pay $14.67.

Answer:

=14.67

Step-by-step explanation:

0.10×16.30=1.63 or

16.30-1.63=14.67 or[tex]\frac{1467}{100}[/tex]

i

4.05 with (05) repeating if converted to a fraction or mixed number will be

[tex]4\frac{5}{99}[/tex].

As per the question statement, we are provided with a repeating decimal, 4.05 with (05) repeating.

We are required to convert the repeating decimal into a mixed number.

To solve this question, we need to know the formula to convert any repeating decimal number to a fraction which goes as:

[tex]\frac{[(DN*F)-NRF]}{D}[/tex]

Where, DN denoted the concerned Decimal Number,

(F = 10) if one repeating is number, 100 if two repeating numbers, 1000 if three repeating numbers and so on.

NRP denotes the Non-repeating part of decimal number.

And, D = 9 if one repeating number, 99 if two repeating numbers, 999 if three repeating numbers, and so on, similar to F.

Then, using our given data in the above formula, we get

4.05 with (05) repeating = [tex]\frac{(4.05*100)-4}{99}=\frac{(405-4)}{99}=\frac{401}{99}=4\frac{5}{99}[/tex].

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Answer:

please demonstrate how tha triangle looks like

The proportion which falls within the range is 0.9.

Given that data:

x : 7, 5, 11, 8, 14, 19, 16, 15, 13, 27

Mean = Σx / n

Using calculator :

Mean (m) = 13.5

Standard deviation (s) = 6.433

Proportion that lies in mean ± 2s

Lower = Mean - 2s

13.5 - 2(6.433) = 0. 632

Upper = Mean + 2s

13.5 + 2(6.433) = 26.376

Mean ± 2(sd) = (0.632, 26.276)

The only digit from the data which falls outside the defined range = 27

Proportion within interval = 9 / n

Proportion which falls within range = 9/10 = 0.9

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The assumption that the population variances are not equal and that the two populations are normally distributed is −35.713332; 0.313332.

To assume that the population variances are not equal and that the two populations are normally distributed:

Given:

So, df = n1 + n2 - 2; 11 + 18 - 2 = 27.

T critical = T0.01, 27 = 2.473

Let,

Then,

Now,

Therefore, the assumption that the population variances are not equal and that the two populations are normally distributed is −35.713332; 0.313332.

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Answer:

x = -∛115

Step-by-step explanation:

x^3 - (-115) = 0

= x^3 + 115

Factoring

(a+b) • (a^2-ab+b^2) =

   a^3-a^2b+ab^2+ba^2-b^2a+b^3 =

   a^3+(a^2b-ba^2)+(ab^2-b^2a)+b^3=

   a^3+0+0+b^3=

   a^3+b^3

(115 isn't a cube.)

Polynomial roots

P: -1, -5, -23, -115, 1, 5, 23, 115

Q: 1

P/Q: -1, -5, -23, -115, 1, 5, 23, 115

Divisor(s): None

In these sets of data, there are no rational roots shown.

Step-by-step explanation(part 2):

x^3 + 115 = 0

x^3 = -115

x  =  ∛-115

Negative numbers will always have real cube roots.

∛ -115 = ∛ -1 × 115  = ∛ -1 × ∛ 115 = (-1) × ∛ 115

Therefore,

x = -∛115

Answer:

-63, -90, -1924. -|63|, etc

Step-by-step explanation:

Answer:

x = 18

Step-by-step explanation:

Vertical angles are congruent.

4x + 3 = 75  Subtract 3 from both sides of the equation

4x = 72  Divide both sides by 4

x = 18

The minimum and maximum allowed baseball masses are 143 grams and 147 grams

The given parameters are

Mass = 145 grams

Vary = 2 grams

This means that the allowed baseball masses are

Allowed baseball masses = Mass  ± Vary

This gives

Allowed baseball masses = (145 - 2, 145 + 2) grams

Evaluate

Allowed baseball masses = 143 grams, 147 grams

Hence, the minimum and maximum allowed baseball masses are 143 grams and 147 grams

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3. A pair of adjacent complementary angles is: ∠LJM and ∠NJM.

4. A pair of adjacent supplementary angles is: ∠KJL and ∠NJL

5. A pair of nonadjacent complementary angles is: ∠EGF and ∠NJP

6. A pair of nonadjacent supplementary angles is: ∠FGH and ∠LJM

Supplementary angles have a sum that is equal to 180 degrees, while complementary angles equal 90 degrees.

Angles that share the same side and vertex are adjacent angles.

3. m∠LJM + m∠NJM = 56 + 34 = 90°

A pair of adjacent complementary angles is: ∠LJM and ∠NJM.

4. m∠KJL + m∠NJL = 90 + (56 + 34) = 180°

A pair of adjacent supplementary angles is: ∠KJL and ∠NJL

5. m∠EGF + m∠NJP = 41 + 49 = 90°

A pair of nonadjacent complementary angles is: ∠EGF and ∠NJP

6. m∠FGH + m∠LJM = 124 + 56 = 180°

A pair of nonadjacent supplementary angles is: ∠FGH and ∠LJM

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The difference between 0.2 and 0.2 repeating is that 0.2 is that rational number and 0.2 repeating is the rational number.

For the two given values;

0.2 is the rational number as it can written in the fraction form as;

0.2 = 2/10

0.2 = 1/5 which is in the p/q form.

For the value of 0.2... repeating is also the rational number as it can be also written in the form of p/q.

0.2... = 0.2 bar is the correct representation.

Therefore, the number 0.2 and 0.2 repeating are the rational numbers.

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Answer:

g = -4

Step-by-step explanation:

Hope this helps :)