The greatest common factor of 76 and 675 is 1
<u>Answer:</u>
The available amount for the down payment of car and invested $3,200 at 3.75% interest compounded continuously is 3449.23$
<u>Explanation:</u>
We know final amount is given by
Where,
A = final amount
P = initial principal balance = $3200
r = interest rate = 3.74%
t = number of time periods elapsed = 2 years
Substituting the values in the formula
A=
We know, e = 2.72
So we get A = 3449.23$ which is the available amount for the down payment of car .
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To answer if they are right triangles or not use the Pythagorean theorem which states that the square of the hypotenuse equals the sum of the square of the legs.
a) 25² = 20² + 7²
625 = 400 + 49
625 ≠ 449 It is not a right triangle
b) 26² = 24² + 10²
676 = 576 + 100
676 = 676 it is a right triangle
c) 13² = 8² + (√10)²
169 = 64 + 10
169 ≠ 74 it is not a right triangle
d) 52² = 48² + 20²
2704 = 2304 + 400
2704 = 2704 it is a right triangle
Absolute value of any number is always positive because it represent distance and distance will always positive.
To place chimney at least 30 feet , the distance along the width of the roof (x) will be x = 17.5 feet or x = 2.5 feet.
Since, The height of the roof is described by the function f(x)=−4/3|x−10| + 40
Since, minimum height is 30 feet.
So , substitute f(x)=30 in above expression.
30=−4/3|x−10| + 40
4/3|x−10| = 10
|x−10|=30/4
|x−10| = 7.5
Taking positive case,
x−10 = 7.5
x = 17.5 feet
Taking negative case,
x−10 = - 7.5
x = 10 - 7.5
x = 2.5 feet
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