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3 years ago

The circle below is centered at the point (-1,3) and has a radius of length 4

1 answer:

6 0

(x-h)^2 + (y-k)^2 = r^2 where h & k are the x,y values of the center point

(x + 1)^2 + (y-3)^2 = 4^2
(x + 1)^2 + (y-3)^2 = 16

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The diagram shows the graph of y = 2x + c, where c is a constant find the value of K.

mote1985 [20]

Answer:

$k=\frac{13}{2}$

Step-by-step explanation:

The equation $y=2x+c$ is a linear equation. By definition, the independent term on this equation (that is, the number that is not being multiplied by $x$ ) is the y-intercept, which is a fancy way of saying "the point where the line crosses the y-axis".

By looking at the equation, we know that our y-intercept is c. By looking at the graph, we can see that the y-intercept is -3. Therefore, $c=-3$ and we get the complete version of our linear equation:

$y=2x-3$

Now, looking at the graph we can see that the point $(k,10)$ lies on the line of the equation, which means that the point is a solution to our equation. All we have to do is replace $x$ and $y$ by the values of the given point (which are $k$ and $10$ , respectively), and then solve for $k$ :

$10=2k-3\\10+3=2k\\13=2k\\2k=13\\k=\frac{13}{2}$

And we are done!

4 0

3 years ago

Read 2 more answers

Please choose the answer that describes the scientific notation for 5,098,000.

avanturin [10]

Scientific notation is the representation of a number in a power of ten, with a sequence of digits placing the comma after the first digit, and the power or then that is mathematically consistent with the number. For example 400 is 4.00 * 10^2; 3100 is 3.100 * 10^4; 13421 = 1.3421 * 10 ^4. It is important that you have only one digit before the comma. So, 5,098,00 is 5.098 * 1,000,00 = 5.098 * 10^6. The answer is the option c. 5.098 * 10^6.

8 0

3 years ago

PLEASE HELP ASAP!!!

barxatty [35]

Answers:

24000 dollars invested at 4%
18000 dollars was invested at 7%

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

Work Shown:

x = amount invested at 4%

If she invests x dollars at 4%, then the rest (42000-x) must be invested at the other rate of 7%

She earns 0.04x dollars from that first account and 0.07(42000-x) dollars from the second account

This means we have

0.04x+0.07(42000-x)

0.04x+0.07*42000-0.07x

0.04x+2940-0.07x

-0.03x+2940

This represents the total amount of money earned after 1 year.

We're told the amount earned in interest is $2220, so we can say,

-0.03x+2940 = 2220

-0.03x = 2220-2940

-0.03x = -720

x = -720/(-0.03)

x = 24000 dollars is the amount invested at 4%

42000-x = 42000-24000 = 18000 dollars was invested at 7%

----------------------

As a check, we can see that

18000+24000 = 42000

and also

0.04x = 0.04*24000 = 960 earned from the first account

0.07*18000 = 1260 earned from the second account

1260+960 = 2220 is the total interest earned from both accounts combined

This confirms our answers.

7 0

3 years ago

Simplify (3/2x+5) + (5/x-5)

tia_tia [17]

Answer:

(3x + 10) / (2x + 5)(x - 5).

Step-by-step explanation:

(3/2x+5) + (5/x-5)

= [3(x - 5) + 5(2x + 5) ] / [ (2x + 5)(x - 5)]

= 3x - 15 + 10x + 25 / (2x + 5)(x - 5)

= 13x + 10 / (2x + 5)(x - 5).

6 0

3 years ago

Michael and Tyler both ran a half marathon Michael finished in 1 hour 42 minutes and 13 seconds Tyler finished in 97 minutes and

xxMikexx [17]

Answer:

Step-by-step explanation:

From the question, we are informed that Michael and Tyler both ran a half marathon and that Michael finished in 1 hour, 42 minutes and 13 seconds while Tyler finished in 97 minutes and 49 seconds.

First, we should know that 60 minutes makes 1 hour, therefore we need to change Tyler's time taken to finish the marathon appropriately. Since Tyler finished in 97 minutes and 49 seconds, this will be converted to 97 minutes equals 1 hour 37 minutes. Therefore, Tyler used 1 hour, 37 minutes and 49 seconds.

Since Michael finished in 1 hour, 42 minutes and 13 seconds while Tyler finished in 1 hour, 37 minutes and 49 seconds. We can see that Tyler is faster than Michael.

To know how much faster Tyler was, we subtract Tyler's time from Michael's. This will be:

= (1 hour, 42 minutes 13 seconds) - (1 hour, 37 minutes, 49 seconds)

= 4 minutes, 24 seconds.

Tyler was faster by 4 minutes, 24 seconds.

4 0

3 years ago