What is the GCF of 6 and 18

Mathematics

2 answers:

eimsori [14]3 years ago

4 0

Find the factors. 1,2,3, and 6. Six is the greatest

olya-2409 [2.1K]3 years ago

3 0

The answer is 6 for the GCF

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you buy a baseball and a bat and spend $31. the bat costs $19 more than the baseball. what is the price of the baseball? What is

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The bat costs $25.50 and the baseball costs $5.50

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2 years ago

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How to solve logarithmic equations as such

Serga [27]

$\bf \textit{exponential form of a logarithm} \\\\ \log_a b=y \implies a^y= b\qquad\qquad a^y= b\implies \log_a b=y \\\\\\ \begin{array}{llll} \textit{Logarithm of exponentials} \\\\ \log_a\left( x^b \right)\implies b\cdot \log_a(x) \end{array} ~\hspace{7em} \begin{array}{llll} \textit{Logarithm Cancellation Rules} \\\\ log_a a^x = x\qquad \qquad \stackrel{\textit{we'll use this one}}{a^{log_a x}=x} \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \log_2(x-1)=\log_8(x^3-2x^2-2x+5) \\\\\\ \log_2(x-1)=\log_{2^3}(x^3-2x^2-2x+5) \\\\\\ \log_{2^3}(x^3-2x^2-2x+5)=\log_2(x-1) \\\\\\ \stackrel{\textit{writing this in exponential notation}}{(2^3)^{\log_2(x-1)}=x^3-2x^2-2x+5}\implies (2)^{3\log_2(x-1)}=x^3-2x^2-2x+5$

$\bf (2)^{\log_2[(x-1)^3]}=x^3-2x^2-2x+5\implies \stackrel{\textit{using the cancellation rule}}{(x-1)^3=x^3-2x^2-2x+5} \\\\\\ \stackrel{\textit{expanding the left-side}}{x^3-3x^2+3x-1}=x^3-2x^2-2x+5\implies 0=x^2-5x+6 \\\\\\ 0=(x-3)(x-2)\implies x= \begin{cases} 3\\ 2 \end{cases}$

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3 years ago

Solve for x: sinx-cosx=√2

kvv77 [185]

sinx - cosx =sqrt(2)
Taking square on both sides:
(sinx - cosx)^2 =sqrt(2)^2
sin^2(x) -2cos(x)sin(x) + cos^2(x) = 2
Rearranging the equation:
sin^2(x)+cos^2(x) -2cos(x)sin(x)=2
As,
sin^2(x)+cos^2(x) = 1
So,
1-2sinxcosx=2
1-1-2sinxcosx=2-1
-2sinxcosx = 1
Using Trignometric identities:
-2(0.5(sin(x+x)+sin(x-x))=1
-sin2x+sin0=1
As,
sin 0 = 0
So,
sin2x+0 = -1
sin2x = -1
2x=-90 degrees + t360
Dividing by 2 on both sides:
x=-45 degrees + t180
or 2x=270 degrees +t360
x= 135 degrees + t180 where t is integer

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2 years ago

Consider the equation v + 4 + v = 8. What is the resulting equation after the first step in the solution?

Kryger [21]

Answer:

Letter D

Step-by-step explanation:

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3 years ago

0.65x + 5 = 0.45x+ 10

aleksley [76]

Answer:25

Step-by-step explanation:

Move the variable to one side by subtracting 0.45x from 0.65x and you get 0.20 the divide 5 by 0.20

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2 years ago

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