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3 years ago

Solve each equation for the given variable: 1) 6a+5a=-11

Mathematics

2 answers:

ivanzaharov [21]3 years ago

4 0

$6a+5a=-11 \\
(6+5)a=-11 \\
11a=-11 \\
a=\frac{-11}{11} \\
a=-1$

LUCKY_DIMON [66]3 years ago

3 0

$6a + 5a=-11. So, 11a=-11 => a = \frac{-11}{11} , and a =-1.$

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How do I solve this?

zmey [24]

Hey there!!

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8 0

4 years ago

The population of mosquitoes in a certain area increases at a rate proportional to the current population, and in the absence of

Alexandra [31]

Answer:

Population of mosquitoes in the area at any time t is:

$P(t) =504,943.26 -104,943.26e^{0.693t}$

Step-by-step explanation:

assume population at any time t = P(t)

population increases at a rate proportional to the current population:

⇒dP/dt ∝ P

$\implies \frac{dP}{dt} =kP$ ----(1)

where k is constant rate at which population is doubled

solving (1)

$ln|P(t)|=kt +C\\P(t)= e^{kt+C}\\P(t)=Ce^{kt}$

$t=0\\P(0) = P_{o}\\\implies C= P_{o}\\P(t) =P_{o}e^{kt}\\$ ---- (2)

initial population = 400,000

population is doubled every week

⇒P(1)=2P(0)

Using (2)

$P_{o}e^{k(1)} = 2P_{o} e^{k(0)}\\$

$e^{k} =2\\k=ln|2|\\$

In presence of predators amount is decreased by 50,000 per day

Then amount decreased per week = 350,000

In this case (1) becomes

$\frac{dP}{dt}=kP-350,000\\\frac{dP}{dt} - kP=-350,000\\$ ---(3)

solving (3) by calculating integrating factor

$I.F=e^{\int-k dt}$

Multiplying I.F with all terms of (3)

$e^{-kt}\frac{dP}{dt} - ke^{-kt}P =-350,000 e^{-kt}\\\frac{d}{dt}(e^{-kt}P) = -350,000 e^{-kt}$

Integrating w.r.to t

$e^{-kt}P(t)= \frac{350,000e^{-kt}}{k} +C$

$P(t) =\frac{350,000}{k} +Ce^{kt}\\$

$k=ln|2| =0.693$

$P(t) =504,943.26 + Ce^{0.693t}\\$

at t=0

$P(0) =504,943.26 + Ce^{0.693(0)}$

$400,000 =504,943.26 + C$

$C = -104,943.26$

So, population of mosquitoes in the area at any time t is

$P(t) =504,943.26 -104,943.26e^{0.693t}$

6 0

3 years ago

y=-3x-6(-3,2)Write the equation of a line parallel to the given line and passing through the given point

Ede4ka [16]

Slope of required equation = slope of given line = -3( since both lines are parallel). By slope point form, y - y1 = m( x - x1). y-2 = -3(x-(-3)). y-2 = -3x - 9. y = -3x - 7. Required equation is y= -3x - 7.

8 0

3 years ago

State the hypothesis and the conclusion in each conditional statement.

saveliy_v [14]

Step-by-step explanation:

Hypothesis - Statement following the word 'Íf'

Conclusion - Statement after the word 'Then'

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Conclusion - then you are at least 5’9” tall.

27. If three points lie on a line, then they are collinear.

Hypothesis - If three points lie on a line

Conclusion - then they are collinear.

28. If you are 13 years old, then you are a teenager.

Hypothesis - If you are 13 years old

Conclusion - then you are a teenager.

29. 9x=36 implies x=4.

Hypothesis - 9x=36

Conclusion - x=4

30. A =+~ B only if mA =+~mB

Hypothesis - if mA =+~mB

Conclusion - A =+~ B

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3 years ago

The least-squares regression line is ________.

Murljashka [212]

Answer:

a. the line that passes through the most data points.

Step-by-step explanation:

Regression analysis, is used to draw the line of‘ best ﬁt’ through co-ordinates on a graph. The techniques used enable a mathematical equation of the straight line form y=mx+c to be deduced for a given set of co-ordinate values, the line being such that the sum of the deviations of the co-ordinate values from the line is a minimum, i.e.

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3 years ago