140% of what number is 14?

Answers

Answer 1

Answer: 140% of 19.6 is 14 and you are very welcome

Answer 2

Answer: 140% of what number is 14
140% × number = 14
(140% = $(140)/(100)$ = 1.4)
1.4 × n = 14
Divide by 1.4 to isolate n
$(1.4n)/(1.4)$ = $(14)/(1.4)$
1.4 and 1.4 cancels out
n = 10

140% of 10 is 14

Check:
$(140)/(100)$ × 10 = 14
1.4 × 10 = 14
14 = 14

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Area of a Trapezoid = 791 square cm. Base 1 = 26.5cm, Base 2 = 30cm. What is the height?

Answers

A=1/2(h)(b1+b2)
791=1/2(h)(26.5+30)
791=1/2(h)(56.5)
1582=(h)(56.5)
28=h

Use mathematical induction to prove the statement is true for all positive integers n. The integer n3 + 2n is divisible by 3 for every positive integer n.

Answers

1. prove it is true for n=1
2. assume n=k
3. prove that n=k+1 is true as well

so

1.
$(n^3+2n)/(3)$ =
$(1^3+2(1))/(3)$ =
$(1+2)/(3)$ =1
we got a whole number, true

2.
$(k^3+2k)/(3)$
if everything clears, then it is divisble

3.
$((k+1)^3+2(k+1))/(3)$ =
$((k+1)^3+2(k+1))/(3)$ =
$(k^3+3k^2+3k+1+2k+2))/(3)$ =
$(k^3+3k^2+5k+3))/(3)$
we know that if z is divisble by 3, then z+3 is divisble b 3
also, 3k/3=a whole number when k= a whole number

$(k^3+2k)/(3) + (3k^2+3k+3)/(3)$ =
$(k^3+2k)/(3) + k^2+k+1$ =
since the k²+k+1 part cleared, it is divisble by 3

we found that it simplified back to $(k^3+2k)/(3)$

done

Answer:

We have to use the mathematical induction to prove the statement is true for all positive integers n.

The integer $n^3+2n$ is divisible by 3 for every positive integer n.