Sparkles the Clown makes balloon animals for children at birthday parties. At Kelsey's party, she made 4 balloon poodles (x) and
2 answers:
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First set up equation
x times y=xy
so
xy=-29
and
x+y=1
subtract x from both sides
y=1-x
subsitute 1-x for y in first equation
x(1-x)=-29
distribute
x-x^2=-29
add x^2 to both sides
x=-29+x^2
subtract x from both sides
0=x^2-x-29
so we can use the quadratic formula to solve for x if the equation=0 and it is in ax^2+bx+c form so
if
ax+bx+c=0 then x=
that means x=
or x=
so
x^2-x-29
a=1
b=-1
c=-29
=![\frac{ +1-\sqrt{1^2-(-116)} }{2(1)}=\frac{ +1-\sqrt{1^2+116} }{2}=\frac{ +1-\sqrt{117} }{2}= \frac{1-10.816653826392}{2} = [tex] \frac{-9.816653826392}{2}= -4.908326913196](https://tex.z-dn.net/?f=%5Cfrac%7B%20%2B1-%5Csqrt%7B1%5E2-%28-116%29%7D%20%7D%7B2%281%29%7D%3D%5Cfrac%7B%20%2B1-%5Csqrt%7B1%5E2%2B116%7D%20%7D%7B2%7D%3D%5Cfrac%7B%20%2B1-%5Csqrt%7B117%7D%20%7D%7B2%7D%3D%20%5Cfrac%7B1-10.816653826392%7D%7B2%7D%20%3D%20%5Btex%5D%20%5Cfrac%7B-9.816653826392%7D%7B2%7D%3D%20-4.908326913196)
the second number is
the two numbers are
5.908326913196 and
-4.908326913196
x times y=xy
so
xy=-29
and
x+y=1
subtract x from both sides
y=1-x
subsitute 1-x for y in first equation
x(1-x)=-29
distribute
x-x^2=-29
add x^2 to both sides
x=-29+x^2
subtract x from both sides
0=x^2-x-29
so we can use the quadratic formula to solve for x if the equation=0 and it is in ax^2+bx+c form so
if
ax+bx+c=0 then x=
x^2-x-29
a=1
b=-1
c=-29
the second number is
the two numbers are
5.908326913196 and
-4.908326913196
(AAA) Corresponding angles are congruent.
Therefore, the sides of the triangles are proportional:
cross multiply
use distributive property
subtract 100 from both sides
divide both sides by 100
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(SAS)
If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.
Therefore we have the equation:
The perimeter of △PQR:
Substitute the value of y to the expression: