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3 years ago

Line AB goes through the points (0,-4) and B (6,2). Which equation represents line AB?

1 answer:

4 0

The answer is y = x - 4. The points already have the y-intercept which is -4, and to solve for the slope you must do 6-0 divided by 2 - (-4) which is equal to 6/6 which is equal to 1.

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Convert 8^12 = 3x - 5 to corresponding logarithmic function.

julia-pushkina [17]

Answer:

Step-by-step explanation:

$8^{12}=3x-5\quad :\quad x=\frac{8^{12}+5}{3}\quad \left(\mathrm{Decimal}:\quad x=22906492247\right)$

$8^{12}=3x-5\\\\\mathrm{Add\:}5\mathrm{\:to\:both\:sides}\\3x-5+5=8^{12}+5\\Simplify\\\mathrm{Divide\:both\:sides\:by\:} 3\\\frac{3x}{3}=\frac{8^{12}}{3}+\frac{5}{3}\\\mathrm{Simplify}\\x=\frac{8^{12}+5}{3}$

6 0

2 years ago

Read 2 more answers

Differentiating a Logarithmic Function in Exercise, find the derivative of the function. See Examples 1, 2, 3, and 4.

wlad13 [49]

Answer:

$\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}$

Step-by-step explanation:

To solve the question we refresh our knowledge of the quotient rule.

For a function f(x) express as a ratio of another functions u(x) and v(x) i.e

$f(x)=\frac{u(x)}{v(x)}\\$ , the derivative is express as

$\frac{df(x)}{dx}=\frac{v(x)\frac{du(x)}{dx}-u(x)\frac{dv(x)}{dx}}{v(x)^{2} }$

from $y=lnx/x^{2}$

we assign u(x)=lnx and v(x)=x^2

and the derivatives

$\frac{du(x)}{dx}=\frac{1}{x}\\\frac{dv(x)}{dx}=2x\\$ .

Note the expression used in determining the derivative of the logarithm function.it was obtain from the general expression of logarithm derivative i.e $y=lnx\\\frac{dy}{dx}=\frac{1}{x}$

If we substitute values into the quotient expression we arrive at

$\frac{dy}{dx}=\frac{(x^{2}*\frac{1}{x})-(2x*lnx)}{x^{4}}\\\frac{dy}{dx}=\frac{x-2xlnx}{x^{4}}\\\frac{dy}{dx}=\frac{x(1-2lnx)}{x^{4}}$

8 0

3 years ago

Adele and her best friend, Valentina, want to rent a canoe to explore the lake by their campsite. The Boat Bunker charges $27 fo

LiRa [457]

Answer:

Oar City

Step-by-step explanation:

Divide the first expense (27) by the time you ride (3 hours) and you get 9 dollars an hour

Divide the second expense (45) by the time you ride (9 hours) and you get 5 dollars an hour

6 0

3 years ago

Tina plans on going bowling this weekend, and there are two bowling alleys in her town. The Bowling Pin charges $5 for shoe rent

DanielleElmas [232]

Answer:

Step-by-step explanation:

the options A and B are the ones that make sense

to get rid of one of the options, you have to substitute.

lets try 6

5+ 3.5(6)= 5+21= 26

3+ 4(6)= 3+24 = 27

in that example, the Bowling Pin is the best deal for Tina

6 0

2 years ago

Segment A'B' is parallel to segment AB.<br>What is the length of segment AB?

Nonamiya [84]

Answer:

7.5

Step-by-step explanation:

5/6=x/9

cross multiply

6x=45

x=45/6

x=7 3/6 = 7 1/2 = 7.5

7 0

3 years ago