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3 years ago

What’s the equation of the line

Mathematics

2 answers:

vova2212 [387]3 years ago

4 0

Answer:

$y = - \frac{1}{3}x + 5$

Step-by-step explanation:

Consider two points through which the line passes.

Let it be ( 0 , 5 ) and ( 6 , 3 )

Step 1 : Find slope

$Slope, m = \frac{y_2 - y_ 1 }{x_2 - x_1}$

$= \frac{3-5}{6-0} \\\\=\frac{-2}{6}\\\\= -\frac{1}{3}$

Step 2 : Find the equation of the line passing through the points.

$( y - y_1) = m (x - x_1)\\\\(y - 5) = -\frac{1}{3} ( x - 0) \\\\y = -\frac{1}{3}x + 5$

Sergio039 [100]3 years ago

3 0

Answer:

y=8 and x =10

Step-by-step explanation:

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stellarik [79]

To model this situation, we are going to use the compound interest formula: $A=P(1+ \frac{r}{n} )^{nt}$
where
$A$ is the final amount after $t$ years
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$r$ is the interest rate in decimal form
$n$ is the number of times the interest is compounded per year
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For account A:
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For account B:
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$A=2000(1+ \frac{0.03}{12} )^{12t}$

Since we want to find the time, $t$ , when the sum of the balance in both accounts is at least 5000, we need to add both accounts and set that sum equal to 5000:
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Now that we have our equation, we just need to solve for $t$ :
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$(1+ \frac{0.0225}{12} )^{12t}+(1+ \frac{0.03}{12} )^{12t}= \frac{5000} {2000}$
$(1.001875)^{12t}+(1.0025 )^{12t}= \frac{5}
{2}$
$ln(1.001875)^{12t}+ln(1.0025 )^{12t}=ln( \frac{5} {2})$
$12tln(1.001875)+12tln(1.0025 )=ln( \frac{5} {2})$
$t[12ln(1.001875)+12ln(1.0025 )]=ln( \frac{5} {2})$
$t= \frac{ln( \frac{5}{2} )}{12ln(1.001875)+12ln(1.0025 )}$
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We can conclude that after 17.47 years the sum of the balance in both accounts will be at least 5000.

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