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3 years ago

Rearrange the formula a^2 + b^2 = c^2 for a.

2 answers:

6 0

We were given

$a^2 +b^2 = c^2$

Adding $b^2$ to both sides of the equation gives,

$a^2=c^2-b^2$

The Right Hand Side of the equation is a difference of two squares. So we can factor it as follows:

$a^2= (c+b)(c-b)$

Taking the square root of both sides we have,

$a=\sqrt((c+b)(c-b))$

diamong [38]3 years ago

5 0

First, subtract the term b^2 from the both sides of the equation to isolate a^2. Then, take the square root of both sides of the equation so "a" is completely isolated. And voila! You should have the simplified version of this formula.

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What is the equation of the line?

spin [16.1K]

Answer:

y=1/2x+2

Step-by-step explanation:

You want to find the equation for a line that passes through the two points:

(0,2) and (-4,0).

First of all, remember what the equation of a line is:

y = mx+b

Where:

m is the slope, and

b is the y-intercept

First, let's find what m is, the slope of the line...

The slope of a line is a measure of how fast the line "goes up" or "goes down". A large slope means the line goes up or down really fast (a very steep line). Small slopes means the line isn't very steep. A slope of zero means the line has no steepness at all; it is perfectly horizontal.

For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:

So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (0,2), point #1, so the x and y numbers given will be called x1 and y1. Or, x1=0 and y1=2.

Also, let's call the second point you gave, (-4,0), point #2, so the x and y numbers here will be called x2 and y2. Or, x2=-4 and y2=0.

Now, just plug the numbers into the formula for m above, like this:

m= 0 - 2-4 - 0 or... m= -2-4 or... m=1/2

So, we have the first piece to finding the equation of this line, and we can fill it into y=mx+b like this:

y=1/2x+b

Now, what about b, the y-intercept?

To find b, think about what your (x,y) points mean:

(0,2). When x of the line is 0, y of the line must be 2.

(-4,0). When x of the line is -4, y of the line must be 0.

Because you said the line passes through each one of these two points, right?

Now, look at our line's equation so far: y=1/2x+b. b is what we want, the 1/2 is already set and x and y are just two "free variables" sitting there. We can plug anything we want in for x and y here, but we want the equation for the line that specfically passes through the two points (0,2) and (-4,0).

So, why not plug in for x and y from one of our (x,y) points that we know the line passes through? This will allow us to solve for b for the particular line that passes through the two points you gave!.

You can use either (x,y) point you want..the answer will be the same:

(0,2). y=mx+b or 2=1/2 × 0+b, or solving for b: b=2-(1/2)(0). b=2.

(-4,0). y=mx+b or 0=1/2 × -4+b, or solving for b: b=0-(1/2)(-4). b=2.

See! In both cases we got the same value for b. And this completes our problem.

The equation of the line that passes through the points

(0,2) and (-4,0)

y=1/2x+2

4 0

3 years ago

A pet store was selling 4 lizards for $47.88. If they ended up selling 6 lizards, how much would they have earned?

fgiga [73]

Answer:

Step-by-step explanation:

Step one- Find out how much it costs for one Lizard In this case, for four lizards it costs $47.88. To find the price for one lizard you divide 47.88 by four

$47.88/4Lizards=$11.97 per lizard.

Step two- Now that we have the price for one lizard, your question asks you how much for 6 lizards. We need to find that cost. To do so you multiply $11.97 by 6 for the lizards.

Your answer is $71.82

Hope This Helped :)

4 0

3 years ago

Read 2 more answers

What number is it? the difference of 9 and three times equals 69. find the number

Mazyrski [523]

Consider the number as 'n' (for now)
3n - 9 = 69
3n = 69 + 9
3n = 78
n = 78/3
n = 26
Therefore, The number is 26

8 0

3 years ago

A population of bees is decreasing. The population in a particular region this year is 1,250. After 1 year, it is estimated tha

8_murik_8 [283]

To model this situation, we are going to use the decay formula: $A=Pe^{rt}$
where
$A$ is the final pupolation
$P$ is the initial population
$e$ is the Euler's constant
$r$ is the decay rate
$t$ is the time in years

A. We know for our problem that the initial population is 1,250, so $P=1250$ ; we also know that after a year the population is 1000, so $A=1000$ and $t=1$ . Lets replace those values in our formula to find $r$ :
$A=Pe^{rt}$
$1000=1250e^{r}$
$e^{r}= \frac{1000}{1250}$
$e^{r}= \frac{4}{5}$
$ln(e^{r})=ln( \frac{4}{5} )$
$r=ln( \frac{4}{5} )$
$r=-02231$

Now that we have $r$ , we can write a function to model this scenario:
$A(t)=1250e^{-0.2231t}$ .

B. Here we are going to use a graphing utility to graph the function we derived in the previous point. Please check the attached image.

C.
- The function is decreasing
- The function doe snot have a x-intercept
- The function has a y-intercept at (0,1250)
- Since the function is decaying, it will have a maximum at t=0:
$A(0)=1250e^{(-0.2231)(0)$
$A_{0}=1250e^{0}$
$A_{0}=1250$
- Over the interval [0,10], the function will have a minimum at t=10:
$A(10)=1250e^{(-0.2231)(10)$
$A_{10}=134.28$

D. To find the rate of change of the function over the interval [0,10], we are going to use the formula: $m= \frac{A(0)-A(10)}{10-0}$
where
$m$ is the rate of change
$A(10)$ is the function evaluated at 10
$A(0)$ is the function evaluated at 0
We know from previous calculations that $A(10)=134.28$ and $A(0)=1250$ , so lets replace those values in our formula to find $m$ :
$m= \frac{134.28-1250}{10-0}$
$m= \frac{-1115.72}{10}$
$m=-111.572$
We can conclude that the rate of change of the function over the interval [0,10] is -111.572.

7 0

3 years ago

Anyone who could do these 8 listed questions I will give a generous amount of points. Please make sure to list all the angles th

k0ka [10]

Answer:

1) 0, 180

2) 90

3) 3pi/2

4) pi/2, -3pi/2

5) 90, 270

6) 0

7) pi

8) -2pi, 0, 2pi

Step-by-step explanation:

1) sinx = 0

x = 0, 180, 360

2) sinx = 1

x = 90

3) sinx = -1

x = 270 or 3pi/2

4) sinx = 1

x = pi/2, pi/2 - 2pi = -3pi/2

5) cosx = 0

x = 90, 360

6) cosx = 1

x = 0, 360

7) cosx = -1

x = pi

8) cosx = 1

-2pi, 0 , 2pi

5 0

3 years ago