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Question 170193: Add. Simplify if possible. 7v/v^2-49 + v/v-7 (this is a fraction)


Find the polynomial for the perimeter and for the area z+8 (top of square) z (side of square).


Subtract by simiplifying collecting like radical terms if possible 4 square root sign 80 - 6 square root sign 5.


If the sides of a square are lengthened by 7cm, the area becomes 196cm^2.
Find the length of a side of the oringinal square.


Please help I have to submit by tomorrow.
Thank you in advance
: Add. Simplify if possible. 7v/v^2-49 + v/v-7 (this is a fraction)


Find the polynomial for the perimeter and for the area z+8 (top of square) z (side of square).


Subtract by simiplifying collecting like radical terms if possible 4 square root sign 80 - 6 square root sign 5.


If the sides of a square are lengthened by 7cm, the area becomes 196cm^2.
Find the length of a side of the oringinal square.


Please help I have to submit by tomorrow.
Thank you in advance

Answer by jim_thompson5910(9929) About Me  (Show Source):
You can put this solution on YOUR website!
# 1


7v/(v^2-49) + v/(v-7) Start with the given equation


7v/((v-7)(v+7)) + v/(v-7) Factor the first denominator


Take note that the LCD is (v-7)(v+7)


7v/((v-7)(v+7)) + (v(v+7))/((v-7)(v+7)) Multiply the second fraction by (v+7)/(v+7) to make the denominators equal.


7v/((v-7)(v+7)) + (v^2+7v)/((v-7)(v+7)) Distribute


(7v+v^2+7v)/((v-7)(v+7)) Combine the fractions.


(v^2+14v)/((v-7)(v+7)) Combine like terms.


(v^2+14v)/(v^2-49) FOIL the denominator.


So 7v/(v^2-49) + v/(v-7) simplifies to (v^2+14v)/(v^2-49)





# 2


Area: A=Length*Width=z(z+8)=z^2+8z


So the area is A=z^2+8z square units


Perimeter: P=2*length+2*width=2(z)+2(z+8)=2z+2z+16=4z+16


So the perimeter is P=4z+16 units





# 3


sqrt(80)-6*sqrt(5) Start with the given expression


4*sqrt(5)-6*sqrt(5) Simplify sqrt(80) to get 4*sqrt(5). Note: If you need help with simplifying square roots, check out this solver.


Since we have the common term sqrt(5), we can combine like terms


(4-6)sqrt(5) Combine like terms. Remember, 5x+3x-4x=(5+3-4)x=4x


-2*sqrt(5) Now simplify 4-6 to get -2


So sqrt(80)-6*sqrt(5) simplifies to -2*sqrt(5).


In other words, sqrt(80)-6*sqrt(5)=-2*sqrt(5)





# 4


Area of original square A[1]=s^2


Area of new square: A[2]=(s+7)^2


Since the "area becomes 196cm^2", this means that A[2]=196


A[2]=(s+7)^2 Start with the second equation


196=(s+7)^2 Plug in A[2]=196


196=s^2+14s+49 FOIL


0=s^2+14s+49-196 Subtract 196 from both sides.


0=s^2+14s-147 Combine like terms.


Notice we have a quadratic equation in the form of as^2+bs+c where a=1, b=14, and c=-147


Let's use the quadratic formula to solve for s


s = (-b +- sqrt( b^2-4ac ))/(2a) Start with the quadratic formula


s = (-(14) +- sqrt( (14)^2-4(1)(-147) ))/(2(1)) Plug in a=1, b=14, and c=-147


s = (-14 +- sqrt( 196-4(1)(-147) ))/(2(1)) Square 14 to get 196.


s = (-14 +- sqrt( 196--588 ))/(2(1)) Multiply 4(1)(-147) to get -588


s = (-14 +- sqrt( 196+588 ))/(2(1)) Rewrite sqrt(196--588) as sqrt(196+588)


s = (-14 +- sqrt( 784 ))/(2(1)) Add 196 to 588 to get 784


s = (-14 +- sqrt( 784 ))/(2) Multiply 2 and 1 to get 2.


s = (-14 +- 28)/(2) Take the square root of 784 to get 28.


s = (-14 + 28)/(2) or s = (-14 - 28)/(2) Break up the expression.


s = (14)/(2) or s = (-42)/(2) Combine like terms.


s = 7 or s = -21 Simplify.


So the possible answers are s = 7 or s = -21


However, since a negative side length is NOT possible, this means that the only answer is s = 7


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Answer:

So the original side length is 7 centimeters