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TEA [102]
2 years ago
12

Which of the following is equivalent to (mn)³?a. 3mnb. m³nc. mn³d. m³n³

Mathematics
1 answer:
Alla [95]2 years ago
4 0

Answer:

Step-by-step explanation:

d is correct

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Which expression is equivalent to the following complex fraction?
svlad2 [7]

Consider the <em>fraction</em> first ;

{:\implies \quad \sf \dfrac{\dfrac{3}{(x-1)}-4}{2-\dfrac{2}{(x-1)}}}

{:\implies \quad \sf \dfrac{\dfrac{3-4(x-1)}{\cancel{(x-1)}}}{\dfrac{2(x-1)-2}{\cancel{(x-1)}}}}

{:\implies \quad \sf \dfrac{3-4x+7}{2(x-1-1)}}

{:\implies \quad \boxed{\bf{\dfrac{-4x+7}{2(x-2)}}}}

<em>Hence, Option B) is </em><em>required</em><em> </em><em>answer</em>

4 0
2 years ago
6. Fill in the smallest digit to make the number divisible by:
Degger [83]

Answer:

(i) 7164<u>0</u>, 32197<u>0</u>

(ii) 1<u>1</u>43, 47<u>2</u>05, <u>2</u>316

(iii) <u>1</u>428, 9<u>2</u>52, 721<u>2</u>

(iv) 2462<u>0</u>, 91<u>00</u>, 670<u>0</u>

(v) 1232<u>0</u>, 59<u>0</u>16, 4642<u>4</u>

Step-by-step explanation:

(i) In order for any number to be divisible by 5, its last digit must be <u>either 0 or 5</u>.

In this case, we should add a last digit, so we opt for <u>0</u> without any doubt since it gives a smaller number than <u>5</u> as the last digit: 71640 is smaller than 71645, the same way as 321970 is smaller than our second option, 321975.

(ii) If the sum of a number's digits gives a number divisible by 3, then the main number is also divisible by 3.

This means that we have to do some addition:

1_43: 1 + 4 + 3 = 8. Eight is not divisible by 3. But <u>9</u> is. So the smallest digit we can add for it to be divisible by three is <u>1</u>: <em>1143.</em>

47_05: 4 + 7 + 0 + 5 = 16. Since 16 is not, the next number that is divisible by 3 is 18, and therefore, the smallest digit we need here is <u>2</u>: <em>47205.</em>

_316: 3 + 1 + 6 = 10. Twelve is the next number divisible by 3, and that means <u>2</u> is the digit we choose: <em>2316.</em>

(iii) Only numbers that are divisible by both <u>2 and 3</u> are also divisible by 6.

_428: In order for a number to be divisible by 2, its last digit must be 0 or divisible by 2. That is already the case here.

4 + 2 + 8 = 14 which is not divisible by 3. But 15 is. So the smallest digit we need is <u>1</u>: <em>1428.</em>

9_52: The number will be divisible by 2. And 9 + 5 + 2 = 16 which is not divisible by 3 but 18 is. This means the smallest digit we need is <u>2</u>: <em>9252.</em>

721_: Since the last digit can be any of these <u>0, 2, 4, 6, 8</u> for the number to be divisible by two, we will first see what digit we need for it to be divisible by 3.

7 + 2 + 1 = 10 which is not divisible by 3 but 12 is. We will then choose to add <u>2</u>: <em>7212.</em>

(iv) A number is divisible by 4 only if the number that is formed by its two last digits is also divisible by 4..

2462_: Since we need to add a last digit, this should be easy. The smallest two-digit-number that starts with 2 and is divisible by four is <u>20</u>: <em>24620. </em>

91__: Here we need to add both of the two last digits, and this should be the easiest example! All numbers that end in <u>00</u>, meaning they have a round number of hundreds, are divisible by 4! Therefore our option is: <em>9100.</em>

670_: In this case, we apply the same rule from the last example - and we choose <u>0</u>: <em>6700.</em>

(v) In order for a number to be divisible by 8, its last three digits need to be divisible by 8, or it can end in <u>000,</u> since every number having a round number of thousands is also divisible by 8.

1232_: 320 is divisible by 8 since 8 × 40 gives 320. Therefore, our smallest digit here is <u>0</u>: <em>12320.</em>

59_16: If we add a <u>0</u> here, the last three digits form the number 016, which is divisible by 8. Our choice is again zero: <em>59016.</em>

4642_: Unfortunately, 420 is not divisible by 8. The next number closest to 420 and which is divisible by 8 is 424. Its division by 8 gives 53. Therefore we should add <u>4</u>: <em>46424.</em>

7 0
2 years ago
What is the area of a regular hexagon (6 sides) whose
Ganezh [65]

Step-by-step explanation:

With reference to the regular hexagon, from the image above we can see that it is formed by six triangles whose sides are two circle's radii and the hexagon's side. The angle of each of these triangles' vertex that is in the circle center is equal to 360∘6=60∘ and so must be the two other angles formed with the triangle's base to each one of the radii: so these triangles are equilateral.

The apothem divides equally each one of the equilateral triangles in two right triangles whose sides are circle's radius, apothem and half of the hexagon's side. Since the apothem forms a right angle with the hexagon's side and since the hexagon's side forms 60∘ with a circle's radius with an endpoint in common with the hexagon's side, we can determine the side in this fashion:

tan60∘=opposed cathetusadjacent cathetus => √3=Apothemside2 => side=(2√3)Apothem

As already mentioned the area of the regular hexagon is formed by the area of 6 equilateral triangles (for each of these triangle's the base is a hexagon's side and the apothem functions as height) or:

Shexagon=6⋅S△=6(base)(height)2=3(2√3)Apothem⋅Apothem=(6√3)(Apothem)2

=> Shexagon=6×62√3=216

8 0
2 years ago
The cheetah traveled 1.75 times faster for the first 8 minutes than it did for the second 8 minutes. Was the distance traveled d
IgorC [24]
Yes,

Step-by Step explaination:

If the cheetah is going at a faster rate of speed the first run it has a farther distance

So it collects more distance. The slower they run in the short period of time, the less distance they rank up.
8 0
3 years ago
1. Jack and Jill purchased a $125,000 house making a 20% down payment and paying the closing
kherson [118]

Answer:

The month payment amount is $897.589

Interest amount is $61,566

Step-by-step explanation:

Given as :

The price of the house = $125,000

The down payment amount for house = 20% of total price

i.e The down payment amount for house = 20% × $125,000

Or, The down payment amount for house = \dfrac{20}{100} × $125,000

Or, The down payment amount for house = $25,000

Now, Balance amount = total price - down payment

Or, Balance amount = $125,000 - $25,000

Or, Balance amount = $100,000

So, The balance amount is bring finance

The finance principal amount = p = $100,000

The rate of interest applied = r = 3.25%

The time period of mortgage = t = 15 years = 15 × 12 = 180 months

Let The Amount of mortgage after 15 years = $A

<u>From Compound Interest method</u>

Amount = Principal × (1+\dfrac{\textrm rate}{100})^{\textrm time}

Or, A = p × (1+\dfrac{\textrm r}{100})^{\textrm t}

Or, A = $100,000 × (1+\dfrac{\textrm 3.25}{100})^{\textrm 15}

Or, A = $100,000 × (1.0325)^{15}

Or, A = $100,000 × 1.61566

Or, A = $161,566

So,The Amount of mortgage after 15 years = $161,566

Interest applied = Amount - principal

Or, I = $161,566 - $100,000

∴ Interest = $61,566

<u>Again</u>

The month payment amount = \dfrac{\textrm amount after 15 years}{number of months of mortgage}

i.e The month payment amount = \dfrac{161566}{180}

Or, The month payment amount = $897.589

Hence The month payment amount is $897.589 and interest amount is $61,566  . Answer

6 0
3 years ago
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