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2 years ago

How to write “6 times the quantity two x plus three y” in a Algebraic expression.

Mathematics

2 answers:

Schach [20]2 years ago

8 0

Answer:

6(2x + 3y)

Step-by-step explanation:

6 × 2x + 6 × 3y

6(2x + 3y)

kolbaska11 [484]2 years ago

6 0

Algebraic expression: 6*2x + 3y

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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

2 years ago

Read 2 more answers

Click the picture that I sent you

Digiron [165]

Answer: 1211.6585 years

<u>Step-by-step explanation:</u>

The equation for exponential growth is: $P=P_oe^{kt}$

P: final population
P₀: initial population
k: rate of decay (or growth)
t: time

Use the half life information to find k:

$\dfrac{1}{2}P_o=P_oe^{k(800)}\\\\\\\dfrac{1}{2}=e^{800k}\qquad \rightarrow \qquad \text{divided both sides by}\ P_o\\\\\\ln\bigg(\dfrac{1}{2}\bigg)=800k\qquad \rightarrow \qquad \text{applied ln to both sides}\\\\\\\dfrac{ln(\frac{1}{2})}{800}=k\qquad \rightarrow \qquad \text{divided both sides by 800}\\\\\\\large\boxed{-0.000867=k}$

Next, input the information (65% decayed = 35% remaining) and the k-value to find your answer.

$.35P_o=P_oe^{-0.000867t}\\\\\\.35=e^{-0.000867t}\\\\\\ln(.35)=-0.000867t\\\\\\\dfrac{ln(.35)}{-0.000867}=t\\\\\\\large\boxed{1211.6585=t}$

5 0

3 years ago

The variables x and y have a proportional relationship, and y=5/6 when x=3/4. Which equation represents this relationship?

seropon [69]

Answer:

y = 1 1/9

BRO MAKE ME THE BRAINLIEST PLS

4 0

2 years ago

Find the volume of this sphere please <br><br> As soon as possible.

seropon [69]

<h3>Answer: 30</h3>

==========================================================

Explanation:

"Use 3 for pi" is something I've never seen a teacher do before. Usually it's "use 3.14 for pi".

Anyway, the diameter of this cylinder is 2 inches, which cuts in half to 1 inch. This is the radius.

The height is 10 inches.

So we have r = 1 and h = 10

V = pi*r^2*h

V = 3*1^2*10

V = 30 cubic inches approximately

3 0

2 years ago

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The animal department wants to estimate baboon population. So they paint 50 baboons with a mark. These baboons were then release

Svet_ta [14]

Answer:

600 baboons

Step-by-step explanation:

Half the number of marked baboons showed up in the sample, so we expect the sample size to be about half of the total population. 300 is half of 600.

___

Many assumptions are involved in such an experiment and analysis. Not the least of which are the assumptions that the marked baboons end up evenly distributed through the population, and that the sample is a fair sample of the entire population.

3 0

2 years ago