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Brums [2.3K]
3 years ago
6

Distributive property of division over subtraction

Mathematics
1 answer:
egoroff_w [7]3 years ago
5 0

<u>Distributive property of division over subtraction:</u>

We know distribution means dividing one element to multiple element. Hence distributing property means if we multiply two set of number, like two elements in bracket and one outside the bracket, then the result will  be same as the multiplication of individual elements. As example, x\times(y+z) = x\timesy + x\times z

So generally it works on multiplication over addition, and directly do not work on division over subtraction.

But division over subtraction can work only in case of reciprocals as division is opposite of multiplication and subtraction can be done by adding one positive and one negative numbers.

Example,

\frac{(x-y)}{z} = \frac{(x+(-y))}{y} = \frac{x}{z} =\frac{x}{z}-\frac{y}{z}

But \frac{z}{(x-y)} case will not work.

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Farmer frank owns a piece of grassland. The grass grows at a constant rate and each cow eats at a constant rate. 12 cows can eat
MrRa [10]

Answer: There are 36 cows that can eaten 72 acres of grass in 126 days.

Step-by-step explanation:

Let x be the amount of grass in an acre initially.

Let y be the amount of grass grown in an acre per day.

Since we have given that

12 cows can eat 10 acres of grass in 28 days

12×28  = 10x + 10×28 y

336 = 10x + 280 y----------------------------(1)

Similarly,

21 cows can eat 30 acres of grass in 63 days.

21×63  = 30x + 30×63 y

1323 = 30x +1890 y ---------------------------(2)

So, by graphing method, we get the value of x and y

x=\dfrac{126}{5},\ y=\dfrac{3}{10}

So, we have,  72 acres of grass in 126 days, we need to find the number of cows.

So, it becomes,

c×126 = 72x + 72×126 y

126c=72\times \dfrac{126}{5}+72\times 126\times \dfrac{3}{10}\\\\126x=4536\\\\x=\dfrac{4536}{126}\\\\x=36

Hence, there are 36 cows that can eaten 72 acres of grass in 126 days.

3 0
2 years ago
what is the relationship between 5.34 x 10^5 and 5.34 x 10^-2 is it greater or lesser than? for 5.34 x 10^5? will give brainlies
Romashka-Z-Leto [24]

the relationship between 5.34 x 10^5 and  5.34 x 10^-2

5.34 x 10^5 = 5.34*100000= 534000

5.34 * 10^-2  , for exponent -2 we move the decimal point 2 places to the left

5.34 x 10^-2= 0.0534

Now we compare 534000  and 0.0534

0.0534 is 10,000,000 times less than 534000

Or we can say  534000 is 10,000,000 times greater than 0.0534

5.34 x 10^5 is 10,000,000 times greater than 5.34 x 10^-2


3 0
3 years ago
Factor 9y 2 - 12y 4.
vesna_86 [32]
Hope i understand it right 

9y^2 -12y^4 = 3y^2 *(3 - 4y^2)
5 0
3 years ago
Read 2 more answers
Allied Corporation is trying to sell its new machines to Ajax. Allied claims that the machine will pay for itself since the time
kvasek [131]

Answer:

z(s) is in the acceptance region. We accept H₀  we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine

Step-by-step explanation:

We must evaluate the differences of the means of the two machines, to do so, we will assume a CI  of 95%, and as the interest is to find out if the new machine has better performance ( machine has a bigger efficiency or the new machine produces more units per unit of time than the old one) the test will be a one tail-test (to the left).

New machine

Sample mean                  x₁ =    25

Sample variance               s₁  = 27

Sample size                       n₁  = 45

Old machine

Sample mean                    x₂ =  23  

Sample variance               s₂  = 7,56

Sample size                       n₂  = 36

Test Hypothesis:

Null hypothesis                         H₀             x₂  -  x₁  = d = 0

Alternative hypothesis             Hₐ            x₂  -  x₁  <  0

CI = 90 %  ⇒  α =  10 %     α = 0,1      z(c) = - 1,28

To calculate z(s)

z(s)  =  ( x₂  -  x₁ ) / √s₁² / n₁  +  s₂² / n₂

s₁  = 27     ⇒    s₁²  =  729

n₁  = 45    ⇒   s₁² / n₁    = 16,2

s₂  = 7,56   ⇒    s₂²  = 57,15

n₂  = 36     ⇒    s₂² / n₂  =  1,5876

√s₁² / n₁  +  s₂² / n₂  =  √ 16,2  + 1.5876    = 4,2175

z(s) = (23 - 25 )/4,2175

z(s)  =  - 0,4742

Comparing z(s) and  z(c)

|z(s)| < | z(c)|  

z(s) is in the acceptance region. We accept H₀  we did not find a significantly difference in the performance of the two machines therefore we suggest not to buy a new machine

The very hight dispersion of values s₁ = 27 is evidence of frecuent values quite far from the mean

3 0
3 years ago
The surface areas of two similar hexagonal prisms are 882cm² and 1,058 cm²? What is the scale factor of the smaller
max2010maxim [7]

Answer:

scale factor of the smaller  prism to the larger prism is B. 21/23

Step-by-step explanation:

Given

surface areas of two similar hexagonal prisms are 882cm² and 1,058 cm²?

scale factor is ratio of sides of two similar objects

thus scale factor for given prism will be = side of smaller prism / side of larger prism

in general rule

If shape of solid has scale factor of k

scale factor of area = k²

scale factor of volume = k³

_____________________________

Given in the problem area of two prism is given

we know area = side^2

scale factor of area = k²

k^2 = area of smaller prism / area of larger prism

k^2 = 882 / 1058 = 441/529\\k = \sqrt{ 441/529} \\k = 21/23

Thus, correct option is B 21/23.

7 0
2 years ago
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