Answer:
-1/2
Step-by-step explanation:
Answer:
Ok, first in our series we can see two numbers in the Sigma, one bellow 0, and other above, 4.
This means that the value of k will go from 0 to 4, then all the numbers in the sum are:
(-1/2)^0 + (-1/2)^1 + (-1/2)^2 + (-1/2)^3 + (-1/2)^4
So we have 5 terms in our series.
b) to see the sign in each term, we must solve the powers, remember that:
(-1)^n is -1 if n is odd, and is equal to 1 if n is even, so we have:
(-1/2)^0 + (-1/2)^1 + (-1/2)^2 + (-1/2)^3 + (-1/2)^4
= 1 -1/2 + 1/4 - 1/8 + 1/16.
So the sign in each term of the series alternates.
Answer:
Step-by-step explanation:
EXAMPLE #1:
What number is 75% of 4? (or Find 75% of 4.)
The PERCENT always goes over 100.
(It's a part of the whole 100%.)
4 appears with the word of:
It's the WHOLE and goes on the bottom.
A proportion showing one fraction with PART as the numerator and 4 as the denominator equal to another fraction with 75 as the numerator and 100 as the denominator.
We're trying to find the missing PART (on the top).
In a proportion the cross-products are equal: So 4 times 75 is equal to 100 times the PART.
The missing PART equals 4 times 75 divided by 100.
(Multiply the two opposite corners with numbers; then divide by the other number.)
4 times 75 = 100 times the part
300 = 100 times the part
300/100 = 100/100 times the part
3 = the part
A proportion showing the denominator, 4, times the diagonally opposite 75; divided by 100.
You didn't provide more information regarding triangle but from given options, it seems that triangle has ratio from shortest side to longest side would be 5 : 12 : 13
So 13 would be hypotenuse since it is longest.
Now A cannot be right angle because tangent is not defined at 90°.
Also tan(A) would be ratio of opponent side to adjacent side (think SOH CAH TOA)
So either opposite side would be 5 or 12, and adjacent side would be 12 or 5 respectively.
So the answer is either 5 / 12 or 12 / 5 but only option provided is 12/5 so that would be your answer.
Final answer: 12 / 5
You labeled the triangle wrong sides 'a' and 'b' are supposed to be the sides that make the right angle. the other side is called the hypotenuse which is the longest side which you should have labeled 'c'
so Pythagorean theorem says
a^2+b^2=c^2
so
(2x+1)^2+(11x+5)^2=(12x+1)^2
distribute
(4x^2+4x+1)+(121x^2+110x+25)=(144x^2+24x+1)
add like terms
125x^2+114x+26=144x^2+24x+1
subtract 125x^2 from both sides
114x+26=19x^2+24x+1
subtract 114x from both sides
26=19x^2-90x+1
subtract 26 from both sides
0=19x^2-90-25
factor
(x-5)(19x+5)=0
therefor x-5=0 and/or 19x+5=0
so
x-5=0 add 5 to both sides
x=5
19x+5=0
subtract 5 from both sides
19x=-5
divide both sides by 19
x=-5/19
since side legnths can't be negative, we can cross this solution out
so x=5
subtitute
1+2x
1+2(5)
1+10=11
side a=11
11x+5
11(5)+5
55+5=60
side b=60
12x+1
12(5)+1
60+1=60
side c=61
add them all up
side a+b+c=11+60+61=132=total legnth
