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4 years ago

Decide which part of the quadratic formula tells you whether the quadratic equation can be solved by factoring.

1 answer:

4 0

Hello,

if b²-4ac>0 then the equation has 2 reals roots
if b²-4ac=0 then the equation has one real root with multiplicity 2
if b²-4ac<0 then no real root.

4x²+6x+2=0

Δ=6²-4*4*2=36-32=4=2² ==> 2 reals roots

==>x=(-6-2)/8=-1 or x=(-6+2)/8=-1/2

One other way is:

4x²+6x+2=0
==>2(2x²+3x+1)=0
==>2x²+3x+1=0
==>2x²+2x+x+1=0
==>2x(x+1)+1(x+1)=0
==>(x+1)(2x+1)=0
==>x=-1 or x=-1/2

Answer B

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3 years ago

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3 years ago

Suppose that news spreads through a city of fixed size of 900000 people at a time rate proportional to the number of people who

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4 years ago

Show work and explain with formulas.

Natasha_Volkova [10]

23 Answer: $\bold{\dfrac{29,524}{9}}$

Step-by-step explanation:

$\dfrac{1}{9}+\dfrac{1}{3}+1+...+2187\\\\\\a_1=\dfrac{1}{9}=3^{-2}\qquad r=3\qquad a_n=2187\\\\\underline{\text{Find n:}}\\a_n=a_1\cdot r^{n-1}\\2187=3^{-2}(3)^{n-1}\\2187=3^{n-3}\\3^7=3^{n-3}\\7=n-3\\10=n$

$\underline{\text{Find the sum:}}\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\\\S_{10}=\dfrac{\frac{1}{9}(1-3^{10})}{1-3}\\\\\\.\quad =\dfrac{1-59,049}{(9)(-2)}\\\\\\.\quad =\dfrac{-59,048}{9(-2)}\\\\\\.\quad =\large\boxed{\dfrac{29,524}{9}}$

24 Answer: $\bold{\dfrac{364}{9}}$

Step-by-step explanation:

$a_1=27\qquad r=\dfrac{1}{3}\qquad n=6\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\\\S_6=\dfrac{27(1-\frac{1}{3}^6)}{1-\frac{1}{3}}\\\\\\.\quad =\dfrac{27(\frac{728}{729})}{\frac{2}{3}}\\\\\\.\quad =\dfrac{27(728)}{729}\cdot \dfrac{3}{2}\\\\\\.\quad =\large\boxed{\dfrac{364}{9}}$

25 Answer: n=7

Step-by-step explanation:

$\{-6,\ -12,\ -24,\ ...\ \}\\\\a_1=-6\qquad r=2\qquad S_n=-762\\\\S_n=\dfrac{a_1(1-r^n)}{1-r}\\\\\\-762=\dfrac{-6(1-2^n)}{1-2}\\\\\\-762=\dfrac{-6(1-2^n)}{-1}\\\\\\\dfrac{-762}{6}=1-2^n\\\\-127=1-2^n\\\\-128=-2^n\\\\128=2^n\\\\2^7=2^n\\\\\large\boxed{7=n}$

3 0

3 years ago

Read 2 more answers