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2 years ago

Find the value of k so that the two given lines are parallel. -5x+kx=4 2y-9x=11

Mathematics

1 answer:

vladimir1956 [14]2 years ago

5 0

The value of k so that the two given lines are parallel is; k = 22.5

First, the correct question is;

-5y+ kx = 4 and

2y-9x=11

In line segment geometry;

The slopes of two or more parallel lines are equal

First, we must determine the slope of the lines by rewriting the equations to resemble the equation of a line in the slope-intercept form; y = mx + c

Therefore, we have;

y = (k/5)x - 4/5.................eqn(1)

and y = (9/2)x + 11/2....,........eqn(2)

Evidently, the slope of the line in equation 2 is; 9/2

And since the slope of parallel lines are equal;

k/5 = 9/2

By cross product;

2k = 45

k = 22.5

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A population of bacteria is initially 6000. After three hours the population is 3000. If this rate of decay continues, find the

tester [92]

Answer:

The equation is $A=6000e^{-0.23t}$ at a rate of -23%.

Step-by-step explanation:

Decay can be represented by the equation $A=A_0e^{rt}$ . We can find the rate at which it decays by using t=3 hours and A=3000. This means $A_0=6000$ in this context.

$A=A_0e^{rt}\\3000=6000e^{r(3)}$

$0.5=e^{(24.5)r}$

After substituting, we divided by 6000 to each side to get 0.5 on the left. Now to solve for r, we will take the natural log of both sides and use log rules to isolate r.

$ln 0.5=ln e^{(3)r}\\ln 0.5=3r (ln e)\\\frac{ln0.5}{3} =r$

We know $lne=1$ so we were able to cancel it out and divide both sides by 3.

We solve with a calculator $\frac{ln0.5}{3} =r\\-0.23=r$

We change -0.23 into a percent by multiplying by 100 to get -23% as the rate.

The equation is $A=6000e^{-0.23t}$

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3 years ago

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denpristay [2]

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4 years ago

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Nine less than two-thirds a number is greater than twenty-five. Which inequality best represents the situation?

Rudik [331]

To solve this problem you must apply the proccedure shown below:

1. First, you must understand the information given in the exercise. You have that: nine less than two-thirds a number is greater than twenty-five.

2. Let's call $x$ to the number mentioned above. You have that "nine less than two-thirds a number" means a substraction and " is greater than twenty-five" can be expressed with the symbol >.