Help memory withmthiss

In February of 2014, gas was about $3.37 per gallon. In February 2015, gas was about 2.25 per gallon. What is the percent decrea

Sveta_85 [38]

Answer:

I don't know if its right but $1. 11

5 0

2 years ago

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

I’ll give Brainliest!!

Gnoma [55]

Answer: 1.5

Step-by-step explanation: The difference between the 2nd And 4th is 7. Divide by 2 to get 3.5. Add 3.5 to f(2) to getf(3)
The difference between f(1) and f(2) will be 3.5 and that's 5-3.5 =1.5
F(5) is 15.5 f(6) is 19

7 0

2 years ago

What is the mean, median, interquartile range, and standard deviation of 20, 20, 28, 28, 30, 30, 30, 36, 36, 40, 40

Kazeer [188]

Median is 30 range is 20 and that's all I'm gonna do sorry I have my own math hope I helped

4 0

3 years ago

Um homem está localizado a 300 m de uma estrada linear (reta). Nessa estrada está localizada a sua esposa a 500 m do homem. Ambo

lukranit [14]

Answer:

The distance of the restaurant from the man and woman = 312.5 m

Option C is correct.

A distância do restaurante do homem e da mulher = 312,5 m

A opção C está correta.

Step-by-step explanation:

English Translation

A man is located 300 m from a linear (straight) road. On that road his wife is located 500 m from the man. Both walk towards a restaurant that is on the road and is the same distance from the two. What is this distance in meters?

A) 400m

B) 300m

C) 312.5m

D) 325m

E) 87.5m

Solution

A diagram showing the scenario described, is presented the attached image.

From the attached image, x is the distance of the restaurant from both the man and the woman. So, there are two right angled triangles,

- The bigger one with hypotenuse 500 m and other side 300 m, the third side is calculated as

(Third side)² = 500² - 300² = 160000

Third side = 400 m

- The smaller right angled triangle, with hypotenuse x m and other sides 300 m & (400 - x) m

(400 - x)² + 300² = x²

160000 - 800x - x² + 90000 = x²

800x = 160000 + 90000 = 250000

x = (250000/800) = 312.5 m

Hence, the distance of the restaurant from the man and woman = 312.5 m

In Portugese/Em português

Um diagrama mostrando o cenário descrito é apresentado na imagem em anexo.

Na imagem em anexo, x é a distância do restaurante do homem e da mulher. Então, existem dois triângulos retângulos,

- Quanto maior com hipotenusa 500 me outro lado 300 m, o terceiro lado é calculado como

(Terceiro lado) ² = 500² - 300² = 160000

Terceiro lado = 400 m

- O triângulo angular direito menor, com hipotenusa x me outros lados 300 m & (400 - x) m

(400 - x)² + 300² = x²

160000 - 800x - x² + 90000 = x²

800x = 160000 + 90000 = 250000

x = (250000/800) = 312.5 m

Portanto, a distância do restaurante do homem e da mulher = 312,5 m

Hope this Helps!!!

Espero que isto ajude!!!

4 0

3 years ago