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3 years ago

Solve this problem. A number c decreased by 9 is less than or equal to 20. Find c.

Mathematics

1 answer:

Lady_Fox [76]3 years ago

5 0

So c-9 is less than or equal to 20 so c is less than or equal to 29. So the correct answer is c. Hope this helps :)

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What is the true solution to the equation below?

Marina CMI [18]

Answer:

The solution is:

$x=4$

Step-by-step explanation:

Considering the expression

$lne^{lnx}+lne^{lnx}^{^2}=2ln8$

$\ln \left(e^{\ln \left(x\right)}\right)+\ln \left(e^{\ln \left(x\right)\cdot \:2}\right)=2\ln \left(8\right)$

$\mathrm{Apply\:log\:rule}:\quad \:log_a\left(a^b\right)=b$

$\ln \left(e^{\ln \left(x\right)}\right)=\ln \left(x\right),\:\space\ln \left(e^{\ln \left(x\right)2}\right)=\ln \left(x\right)2$

$\ln \left(x\right)+\ln \left(x\right)\cdot \:2=2\ln \left(8\right)$

$\mathrm{Add\:similar\:elements:}\:\ln \left(x\right)+2\ln \left(x\right)=3\ln \left(x\right)$

$3\ln \left(x\right)=2\ln \left(8\right)$

$\mathrm{Divide\:both\:sides\:by\:}3$

$\frac{3\ln \left(x\right)}{3}=\frac{2\ln \left(8\right)}{3}$

$\ln \left(x\right)=\frac{2\ln \left(8\right)}{3}.....A$

Solving the right side of the equation A.

$\frac{2\ln \left(8\right)}{3}$

$\ln \left(8\right):\quad 3\ln \left(2\right)$

Because

$\ln \left(8\right)$

$\mathrm{Rewrite\:}8\mathrm{\:in\:power-base\:form:}\quad 8=2^3$

⇒ $\ln \left(2^3\right)$

$\mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right)$

$\ln \left(2^3\right)=3\ln \left(2\right)$

$\frac{2\ln \left(8\right)}{3}=\frac{2\cdot \:3\ln \left(2\right)}{3}$

$\mathrm{Multiply\:the\:numbers:}\:2\cdot \:3=6$

$=\frac{6\ln \left(2\right)}{3}$

$\mathrm{Divide\:the\:numbers:}\:\frac{6}{3}=2$

$=2\ln \left(2\right)$

So, equation A becomes

$\ln \left(x\right)=2\ln \left(2\right)$

$\mathrm{Apply\:log\:rule}:\quad \:a\log _c\left(b\right)=\log _c\left(b^a\right)$

$=\ln \left(2^2\right)$

$=\ln \left(4\right)$

$\ln \left(x\right)=\ln \left(4\right)$

$\mathrm{Apply\:log\:rule:\:\:If}\:\log _b\left(f\left(x\right)\right)=\log _b\left(g\left(x\right)\right)\:\mathrm{then}\:f\left(x\right)=g\left(x\right)$

$x=4$

Therefore, the solution is

$x=4$

6 0

3 years ago

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carol is excited to get a new kitten from the animal shelter. the kitten had an $299 adoption fee. carol had $50 off coupon for

Molodets [167]

Answer:

1 month

Step-by-step explanation:

249 is the amount she spends for buying the kitten, (299-50=249) which she only has to pay once.

20 is the amount she has to spend every month, the rate of change.

The problem can be modeled with the general equation:

y = 20x + 249

In this equation, x the the time in months and y is the amount of money spent.

Substitute 250 for y.

y = 20x + 249

250 = 20x + 249 <= isolate x to get the number of months

1 = 20x

x = 1/20

Carol will only spent money every month, not for 1/20 of a month.

It will only take Carol 1 month to spent $250.

Check answer:

Substitute x for 1

y = 20x + 249

y = 20(1) + 249

y = 269

269 is more than 250 already.

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3 years ago

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5,395<br> - 2,697<br> How do you solve?

sashaice [31]

Answer:

2698

Step-by-step explanation:First you take 1000 from 5000 and then distribute it to 395

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Some more free-points education is important

makkiz [27]

Answer:

Thank you for the free-points!!! <3

Step-by-step explanation:

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3(x+3)-5x simplify<br> Answer

Lelu [443]

Answer: -2x + 9

First, Use the distributive property: 3(x+3)-5x (3 multiplied by x is 3x and 3 multiplied by 3 is 9

Next, subtract the variable x: 3x+9-5x (3x-5x=-2x

The answer is -2x+9

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3 years ago

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