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4 years ago

The model bellow represents the expression 5x18 . How many tens will there be in in the final product

Mathematics

1 answer:

Leokris [45]4 years ago

7 0

Consider the expression $5 \times 18$

Expanding 18 as (10+8),

= $5 \times (10+8)$

By using distributive property, we get

= $( 5 \times 10) + ( 5 \times 8)$

= 50 + 40

By adding, we get

= 90

The digit at units place is '0' and the digit at tens place is '9'.

Therefore, there are 9 tens in the final product of $5 \times 18$ .

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Can you prove it??<br>it's hard,I tried but couldn't solve this.

BARSIC [14]

I'll abbreviate $s=\sin\theta$ and $c=\cos\theta$ , so the identity to prove is

$\dfrac{s+c+1}{s+c-1}-\dfrac{1+s-c}{1-s+c}=2\left(1+\dfrac1s\right)$

On the left side, we can simplify a bit:

$\dfrac{s+c+1}{s+c-1}=\dfrac{s+c-1+2}{s+c-1}=1+\dfrac2{s+c-1}$

$\dfrac{1+s-c}{1-s+c}=-\dfrac{-2+1-s+c}{1-s+c}=-1+\dfrac2{1-s+c}$

Then

$\dfrac{s+c+1}{s+c-1}-\dfrac{1+s-c}{1-s+c}=2\left(1+\dfrac1{s+c-1}-\dfrac1{1-s+c}\right)$

So the establish the original equality, we need to show that

$\dfrac1{s+c-1}-\dfrac1{1-s+c}=\dfrac1s$

Combine the fractions:

$\dfrac{(1-s+c)-(s+c-1)}{(s+c-1)(1-s+c)}=\dfrac{2-2s}{c^2-s^2+2s-1}$

We can rewrite the denominator as

$c^2-s^2+2s-1=c^2+s^2-2s^2+2s-1$

then using the fact that $c^2+s^2=\cos^2\theta+\sin^2\theta=1$ , we get

$1-2s^2+2s-1=2s-2s^2$

so that we have

$\dfrac1{s+c-1}-\dfrac1{1-s+c}=\dfrac{2-2s}{2s-2s^2}=\dfrac1s$

as desired.

6 0

4 years ago

Vector addition obeys rules that are different from those for the addition of two scalar quantities.

My name is Ann [436]

Answer:

false

Step-by-step explanation:

false

8 0

3 years ago

URGENT

Lynna [10]

The answer would be A. 3 1/2.
Explanation
First find a common denominator, which would be 6. You times the top number the same amount of times you times the bottom number to get the common denominator, so now it's 1 4/6 + 1 5/6 now you add, 1+1=2, now you need to add 4 and 5 together, bc they are the top numbers of the fraction. That would be 9 so now the problem is 2 9/6, now we simplify the fraction so that it is 3 3/6 now that simplifies into 1/2 so the answer is 3 1/2

4 0

3 years ago

PLEASE HELP ME AND SHOW ALL WORK THANK YOU!!!!!!

Natalija [7]

M>5=m>4
m>5 and m>7 are on line then m>5+m>7=180
by substituting
m>4+37=180
m>4=143
m>2=m>7=37
m>4=m>8
m<3+m>5=180

7 0

3 years ago

-7m²-10m+17<br> common factor

kicyunya [14]

Answer:

Greatest common factor of 17

So, the prime factors of 45 are 3, 3, and 5. The Greatest Common Factor is the greatest number that is common (that is, in both lists). It is 17. Since 17 is a factor of itself and of 51 -- which is 3 x 17 -- then the greatest possible common factor is 17!

Step-by-step explanation:

Add and subtract the second term to the expression and factor by grouping.

- (m - 1 )( 7m + 17 )

6 0

4 years ago