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3 years ago

13

The table shows the total distance (in meters) an athlete ran over a 3- second sprint. What is the athletes average speed betwee

n points A and B

1 answer:

siniylev [52]3 years ago

5 0

Answer:

Step-by-step explanation:

18 meters

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In Exercises 40-43, for what value(s) of k, if any, will the systems have (a) no solution, (b) a unique solution, and (c) infini

svet-max [94.6K]

Answer:

If k = −1 then the system has no solutions.

If k = 2 then the system has infinitely many solutions.

The system cannot have unique solution.

Step-by-step explanation:

We have the following system of equations

$x - 2y +3z = 2\\x + y + z = k\\2x - y + 4z = k^2$

The augmented matrix is

$\left[\begin{array}{cccc}1&-2&3&2\\1&1&1&k\\2&-1&4&k^2\end{array}\right]$

The reduction of this matrix to row-echelon form is outlined below.

$R_2\rightarrow R_2-R_1$

$\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\2&-1&4&k^2\end{array}\right]$

$R_3\rightarrow R_3-2R_1$

$\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&3&-2&k^2-4\end{array}\right]$

$R_3\rightarrow R_3-R_2$

$\left[\begin{array}{cccc}1&-2&3&2\\0&3&-2&k-2\\0&0&0&k^2-k-2\end{array}\right]$

The last row determines, if there are solutions or not. To be consistent, we must have k such that

$k^2-k-2=0$

$\left(k+1\right)\left(k-2\right)=0\\k=-1,\:k=2$

Case k = −1:

$\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-1-2\\0&0&0&(-1)^2-(-1)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&-3\\0&0&0&-2\end{array}\right]$

If k = −1 then the last equation becomes 0 = −2 which is impossible.Therefore, the system has no solutions.

Case k = 2:

$\left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&2-2\\0&0&0&(2)^2-(2)-2\end{array}\right] \rightarrow \left[\begin{array}{ccc|c}1&-2&3&2\\0&3&-2&0\\0&0&0&0\end{array}\right]$

This gives the infinite many solution.

5 0

3 years ago

If I put 1500 into my savings account and 180 of interest at 4% simple interest how long was my money in my bank

stealth61 [152]

10,800 I think that's the answer

6 0

3 years ago

Please help, will give brainliest

Goryan [66]

Uhhh i think the answers A

3 0

3 years ago

Find the face value of the 20-year zero-coupon bond at 4.4%, compounded semiannually, with a price of $8,375.

umka21 [38]

<u>Given</u>:

Time,

t = 20 years

Rate,

r = 4.4%

Price

= $8,375

Now,

The yield will be:

= $\frac{4.4}{2}$

= $1.1$ (%)

Time will be:

= $20\times 2$

= $40 \ periods$

As we know the formula,

⇒ $Price \ of \ bond = \frac{Face \ value}{(1+\frac{r}{2} )^{n\times 2}}$

By substituting the values, we get

$8375=\frac{Face \ value}{(1+\frac{0.044}{2} )^{20\times 2}}$

$8375=\frac{Face \ value}{(1.022)^{40}}$

$8375=\frac{Face \ value}{2.3880083}$

The face value will be:

$Face \ value = 2.3880083\times 8375$

$=20,000$ ($)

Learn more about face value here:

brainly.com/question/14862802

5 0

3 years ago

Scott earned 20 points more on his most recent math test than he earned on the previous test. If he earned at least 80 points on

NARA [144]

9514 1404 393

Answer:

s ≥ 60

Step-by-step explanation:

If Scott earned 20 points more on this test, then he earned 20 points less on the last test. 20 points less than "at least 80" is "at least 60."

s ≥ 60

7 0

3 years ago