3. Solve the formula v + f -e = 2 for e
O Ae-v-f-2
O BC v+f-2
O ce-v-f+2
O De-u+f+2

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:

Step-by-step explanation:

the answer is 30

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:

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 .

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

Answer:

g = -4

Step-by-step explanation:

Hope this helps :)

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:

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

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:

$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

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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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.

[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]