Answer:
10 years.
Step-by-step explanation:
Present age of Mr. Tanaka = 35 years
Present age of his son = 5 years
Now let the number of years be x. As after x years both of their age will increased by x years, therefore
After x years age of Mr. Tanaka = 35 + x
After x years age of his son = 5 + x
According to question,
Mr.Tanaka's age after x years = 3 (His son's age after x years)
35 + x = 3 (5 + x)
Further solving,
35 + x = 15 + 3x
3x - x = 35 - 15
2x = 20
x = 10
Therefore after 10 years Mr. Tanaka's age will be exactly three times as old as his son. As after 10 years Mr. tanaka's age will be 45 and his son's age will be 15.
Answer:
5
Step-by-step explanation:
There are two ways you can solve this. First is to just count all the numbers in the list given that are within the range 15-19. This is an inclusive range meaning the numbers 15 and 19 are a part of it. The second method is to count how many numbers are in the list given and count all the numbers that have already been put on the table. There are 19 total numbers, and 14 have already been counted. If you subtract you are left with 5 numbers that are within the range. So the answer is 5.
The correct answer is: [D]: " 4x² − 12x − 4 " .
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Explanation:
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Given:
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" (16x² − 16) + ( -12x² − 12x + 12) " ; Simplify.
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Note the "distributive property of multiplication:
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a(b + c) = ab + ac ;
a(b − c) = ab − ac .
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So we can rewrite the expression as:
" (16x² − 16) + 1( -12x² − 12x + 12) " ;
{The "1" is implied; since "1", multiplied by any value, results in the exact same value.}.
Let us examine the following part of the expression:
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" + 1 ( -12x² − 12x + 12 ) " ;
Using the distributive property of multiplication:
" + 1 ( -12x² − 12x + 12 ) = (1 * -12x²) − (1 * 12x) + (1 * 12) ;
= " − 12x² − 12x + 12 " ;
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Now, bring down the other part of the expression; & rewrite:
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→ " (16x² − 16) − 12x² − 12x + 12 " ;
→ " 16x² − 16 − 12x² − 12x + 12 " ;
Now, combine the "like terms" :
+ 16x² − 12x² = 4x² ;
− 16 + 12 = -4 ;
and we have " − 12x" ;
So we can rewrite the expression as:
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→ " 4x² − 12x − 4 " ;
→ which is: "Answer choice: [D]: " 4x² − 12x − 4 <span>" .
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Use the cosine rule.
c=AB=7
b=AC=8
a=BC=3
a^2=b^2+c^2-2bc(cos(A))
=>
cos(A)=(b^2+c^2-a^2)/(2bc)
=(7^2+8^2-3^2)/(2*7*8)
=13/14
=0.9286
Step-by-step explanation:
sin(2x) + cos(3x)
Use double angle formula sin(2x) = 2 sin x cos x.
Use triple angle formula cos(3x) = 4 cos³x − 3 cos x.
Substitute:
2 sin x cos x + 4 cos³x − 3 cos x
