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Advocard [28]
3 years ago
12

Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions. x + 2y – 3z

= 4 3x – y + 5z = 2 4x + y +(a– 14)z = a +2
Mathematics
1 answer:
Luden [163]3 years ago
5 0

Answer:

a) If a=20 the system has no solutions.

b) If a≠20 the system has exactly one solution.

Step-by-step explanation:

The augmented matrix of the system is \left[\begin{array}{cccc}1&2&-3&4\\3&-1&5&2\\4&1&a-14&a+2\end{array}\right].

Using rows operations we obtain the echelon form of the matrix, ie,

\left[\begin{array}{cccc}1&2&-3&4\\0&-7&-4&-10\\0&0&a-20&a+4\end{array}\right]

Since the echelon form of the matrix does not have free variables then the problem has exactly one solution or has no solutions.

a) If a=20 the system has no solutions because in the last equation solving for x3 it has that 0=24. Then the system is inconsistent.

b) If a≠20, the the system has exactly one solution that is obtained solving the system of the echelon form matrix.

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I am Lyosha [343]

Answer:

y = -3x  

Step-by-step explanation:

(a) Slope

y = mx + b

Choose points (-3, 9) and (3, -9)

m = (-9 - 9)/(3 – (-3))

m = -18/(3 + 3)

m = -18/6

m = -3

=====

(b) y-intercept

y = mx +b

Choose point (0,0).

0 = 0 + b

b = 0

=====

(c) Equation of line

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y = -3x

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3 years ago
The wading pool shown is a trapezoidal prism with a total volume of 286 cubic feet. What is the missing dimension? First base: 8
harkovskaia [24]
To find the missing dimension you will use the formula for finding the volume of a prism and solve for the missing dimension.  In this case 2ft is how deep the pool is and you will solve for the width of the pool.

V = Bh, where B is the area of the base.  In this case, use the area of a trapezoid formula.

286 = 1/2h(8 +13)2
<u>286</u> = <u>21h</u>
21      21
h = 13.6

The width of the wading pool is approximately 13.6 feet.
5 0
3 years ago
A construction crew has just finished building a road. the crew worked for 10 days. if they build 2 3/4 kilometers of road each
tatuchka [14]
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7 0
2 years ago
Read 2 more answers
Can someone explain me how do i do (ii)?
Varvara68 [4.7K]

Answer:

(only ii right?)

Since we have the total number is 360° and our section is 72°, we know that the percentage of students who choose the cinema should be the number that we have divided to the total amount and then multiply the result by 100 ( it's fine if you write 100%, but when you actually calculate it, it's only 100, not 100%):

(72/360) . 100 = 20%

6 0
3 years ago
hich equation represents a line that passes through (5, 1) and has a slope of ? y – 5 = (x –1) y – = 5(x –1) y – 1 = (x –5) y –
gtnhenbr [62]

Answer:

The equation that would represent it would be y - 1 = (x - 5)

Step-by-step explanation:

In order to get this, we can start with the base form of point-slope form.

y - y1 = m(x - x1)

Now put the point in for (x1, y1)

y - 1 = (x - 5)

3 0
3 years ago
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