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Dovator [93]
3 years ago
13

Find the two-digit number whose tens digit is 4 less than its units digits if the original number is 2 more than 3 times the sum

of the digits
Mathematics
1 answer:
frosja888 [35]3 years ago
7 0
Let the 2 digit number be ab remembering that ab=10a+b
a=b-4...........equation 1
10a+b=3(a+b)+2........... equation 2
take a's value in equation 1 and plug it into equation 2
10(b-4)+b=3(b-4)+3b+2
5b=30
b=6 units digit
a=6-4=2 tens unit
number is 26

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Determine the value of c that will result in a perfect square trinomial. <br> w^2+6w+ c =130+c
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Answer:

The value of c that will result in a perfect square trinomial is (3)^2 or 9

The perfect square trinomial is: (w+3)^2=139

Step-by-step explanation:

We need to determine the value  of c that will result in a perfect square trinomial.

w^2+6w+ c =130+c

Perfect square trinomial are of form: a^2+2ab+b^2=(a+b)^2

Now, the equation given is:

w^2+6w+ c =130+c

Looking at the term 6w, we can write it as 2(w)(3)

We are given: a = w, 2ab = 2(w)(3) so, b will be: (3)^2

So, we will be adding (3)^2 on both sides

w^2+6w+ c=130+c\\w^2+2(w)(3)+ (3)^2 =130+(3)^2\\The\:left\:side\:becomes: a^2+2ab+b^2\\We\:can\:write\:it\:as: (a+b)^2\\We\:have\:a=w\: and\: b=3\\(w+3)^2=130+9\\(w+3)^2=139

So, The value of c that will result in a perfect square trinomial is (3)^2 or 9

The perfect square trinomial is: (w+3)^2=139

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