Answer:
FD≈25.94.. rounded = 26
Step-by-step explanation:
FD²=12²+(4x+11)²
FD²=144+16x²+88x+121
FD²=265+16x²+88x
also
FD²=12²+(13x-16)²
FD²=144+169x²-416x+256
FD²=400+169x²-416x
thus
265+16x²+88x = 400+169x²-416x
16x²-169x²+88x+416x+265-400 = 0
-153x²+504x-135 = 0
we will solve this quadratic equation by suing the quadratic formula to find x
x=(-504±sqrt(504²-4(-153)(-135)))/2(-153)
x=(-504±
)/2(-153)
x=(-504±
)/-306
x=(-504±
)/-306
x=(-504±414)/-306
x=(-504+414)/-306 and x=(-504-414)/-306
x=-90/-306 and x=-918/-306
x= 5/17 , 3
substituting x by the roots we found
check for 5/17:
4x+11 = 4×(5/17)+11 = (20/17)+11 = (20+187)/17 = 207/17 ≈ 12.17..
13x-16 = 13×(5/17)-16 = (65/17)-16 = (65-272)/17 = -207/17 ≈ -12.17..
check for 3:
4x+11 = 4×3+11 = 12+11 = 23
13x-16 = 13×3-16 = 23
thus 3 is the right root
therfore
ED=23 and CD=23
FD²=FE²+ED² or FD²=FC²+CD²
FD²=12²+23²
FD²=144+529
FD²=673
FD=√673
FD≈25.94.. rounded = 26
Answer:
negative 16 years
Step-by-step explanation:
Answer:1.625=158
Step-by-step explanation:
Answer:
1.625=158
Showing the work
Rewrite the decimal number as a fraction with 1 in the denominator
1.625=1.6251
Multiply to remove 3 decimal places. Here, you multiply top and bottom by 103 = 1000
1.6251×10001000=16251000
Find the Greatest Common Factor (GCF) of 1625 and 1000, if it exists, and reduce the fraction by dividing both numerator and denominator by GCF = 125,
1625÷1251000÷125=138
Simplify the improper fraction,
=158
In conclusion,
1.625=158
8x² - 24 can be written in factorized form as 8 (x² - 3).
<u>Step-by-step explanation:</u>
Given expression is
8x² - 24
It can be factorized by taking the common factors as,
Since 8 is the common factor for both the terms and the expression can be written as,
8x² - 24
It can be expanded as,
= 8x² - 8×3
Now both the terms has 8, so it can be taken out and the expression can be written as,
= 8 (x² - 3)
So it can be written in factorized form as 8 (x² - 3).
