Lucas had $272 and Kelly had $804. Both of them spent the same amount of money. The ratio of Lucas' to Kelly's money than became 2:9. How much did they spend altogether?

Answers

Answer 1

Answer: $x-\ money\ spend\n\n(272-x)/(804-x)=(2)/(9)\ \ \ \ | cross\ multiplication\n\n9(272-x)=2(804-x)\n\n2448-9x=1608-2x\ \ \ | add\ 2x\n\n2448-7x=1608 \ \ \ | subtract\ 2448\n\n-7x=-840\ \ \ | divide\ by\ -7\n\nx=120\n\nThey\ spend\ together\ 240\$$

Answer 2

Answer:

Answer:

the answer for the question is 240$

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Write the equation for a parabola with the focus at(-1, 4) and the equation of the directrix x = 5.
(x + 1)2 = 3(y-4)
(y-4)2 = 12(x + 1)
(y-2)2 = -3(x – 4)
(y-4)2 = –12(x - 2)

Answers

The answer is (y - 4)2 = -12(x - 2)
Since the graph is facing the left, the starting equation would be (y - k)2 = -4p(x - h).
(h, k) is the vertex of the graph. If you plot the focus and the directrix, you can see that the distance is 6. Divide 6 by 2, thus the vertex should be 3 squares away from the focus and 3 squares away from the directrix. The vertex is (2, 4). And since the distance from the focus to the vertex and the distance from the directrix to the vertex is 3, P = 3.
Insert the numbers in and you should get the last choice.

A deposit of $7,000 at 6.5% for 120 days. 151.67 358.97

Answers

120 days is approximately equals to 4 months. (30 days * 4 = 120 days)
Now you deposited 7000 dollars at 6.5% interests.
IN 1 months
=> 7000 * .065 = 455 dollars in 1 month is the interest
=> 455 * 4 months = 1820 dollars n 4 months
=> 7000 + 1820 = 8820 dollars.

Marina is currently 14 years older than her cousin joey. in 5 years she will be 3 times as old as joey. if you let x represent joey's current age, what expression can you use to represent marina's current age?

Answers

The expression is 14x

a 3-inch candle burns down in 12 hours.Assuming the candles are the same thickness and make (that is, directly proportional),how long would it take for a 1-inch candle to burn down?

Answers

Answer: 4 hours

Step-by-step explanation:

Derivative of R=(100+50/lnx)

Answers

Answer:

$\displaystyle R' = (-50)/(x(\ln x)^2)$

General Formulas and Concepts:

Calculus

Differentiation

Derivatives
Derivative Notation

Derivative Property [Multiplied Constant]: $\displaystyle (d)/(dx) [cf(x)] = c \cdot f'(x)$

Derivative Property [Addition/Subtraction]: $\displaystyle (d)/(dx)[f(x) + g(x)] = (d)/(dx)[f(x)] + (d)/(dx)[g(x)]$

Basic Power Rule:

f(x) = cxⁿ
f’(x) = c·nxⁿ⁻¹

Derivative Rule [Quotient Rule]: $\displaystyle (d)/(dx) [(f(x))/(g(x)) ]=(g(x)f'(x)-g'(x)f(x))/(g^2(x))$

Step-by-step explanation:

Step 1: Define

Identify

$\displaystyle R = 100 + (50)/(\ln x)$

Step 2: Differentiate

Derivative Property [Addition/Subtraction]: $\displaystyle R' = (d)/(dx)[100] + (d)/(dx) \bigg[ (50)/(\ln x) \bigg]$
Rewrite [Derivative Property - Multiplied Constant]: $\displaystyle R' = (d)/(dx)[100] + 50 (d)/(dx) \bigg[ (1)/(\ln x) \bigg]$
Basic Power Rule: $\displaystyle R' = 50 (d)/(dx) \bigg[ (1)/(\ln x) \bigg]$
Derivative Rule [Quotient Rule]: $\displaystyle R' = 50 \bigg(((1)' \ln x - (\ln x)')/((\ln x)^2) \bigg)$
Basic Power Rule: $\displaystyle R' = 50 \bigg( (-(\ln x)')/((\ln x)^2) \bigg)$
Logarithmic Differentiation: $\displaystyle R' = 50 \bigg( ((-1)/(x))/((\ln x)^2) \bigg)$
Simplify: $\displaystyle R' = (-50)/(x(\ln x)^2)$

Topic: AP Calculus AB/BC (Calculus I/I + II)

Unit: Differentiation

8)What is the equation of a line that goes through the point (3, 12) and is perpendicular to the line given by the equation y = -1/3x - 7?(A) y = -3x - 12
(B )y = -1/3x + 6
(C) y = 3x + 3
(D) = (1/3x) - 6

Answers

The slope of the first line is $m_1=(-1)/(3)$ .
To be perpendicular the slope of the second line must be the negative reciprocal of the first: $m_2=3$
Use the slope-intercept formula:
$y=mx+b$
Substitute known values:
$12=3(3)+b$
Solve for $b$ :
$b=3$
Complete the formula:
$y=3x+3$

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