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lisabon 2012 [21]
3 years ago
5

Ms. Ortiz is painting her canoe. Two-fifths of gallon of paint covers ¼ of the canoe.

Mathematics
1 answer:
madreJ [45]3 years ago
6 0

Answer: 8/5 or 1 3/5

Step-by-step explanation:

2/5 + 2/5 + 2/5 + 2/5

8/5 which is 1 3/5

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What is the value of the rational expression below when x is equal to 4? 12+x/4+x
riadik2000 [5.3K]
12+4=16
4+4=8
16/8=2

C!
8 0
3 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
Mariana plans to visit an amusement park where she must pay for admission and purchase tickets to go on the rides. Mariana wants
Ivanshal [37]

Answer: The number 12 represents admission charge in Mariana's equation.

Step-by-step explanation:

As per given ,

Total cost = ( Charge per ticket) (Number of tickets) +  (Admission fees)  (i)

For x = Number of tickets, the total cost (c) for a day at the amusement park is given as

c = 1.50x + 12                                       (ii)

Here, 12 = Admission fees                 [Comparing (i) and (ii)]

Hence, the number 12 represents admission charge in Mariana's equation.

3 0
3 years ago
Find the slope between the pair of points (1,3) and (7,2)
agasfer [191]

Answer:

             \bold{m=-\dfrac16}

Step-by-step explanation:

\bold{slope\, (m)=\dfrac{change\ in\ Y}{change\ in\ X}=\dfrac{y_2-y_1}{x_2-x_1}}

(1, 3)    ⇒   x₁ = 1,  y₁ = 3

(7, 2)    ⇒   x₂ = 7,  y₂ = 2

So the slope:

                    \bold{m=\dfrac{2-3}{7-1}=\dfrac{-1}6=-\dfrac16}

5 0
3 years ago
1/4×10/12 simplest form
Mashcka [7]

Answer:

10/48 - 2/24 - 1/12

Step-by-step explanation:

answer is 1/12

3 0
2 years ago
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