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Airida [17]
3 years ago
12

x+ y+(k −5)z=k where k is an arbitrary constant. For which value(s) of k does this system have a unique solution? For which valu

e(s) of k does the system have infinitely many solutions? For which value(s) of k is the system inconsistent?
Mathematics
1 answer:
sergeinik [125]3 years ago
6 0

Answer: Lets rewrite our equation.

x + y + kz - 5z =k

x + y -5z = k(1-z)

k = \frac{x + y - 5z}{1 - z}

so the only problem with the equation is that z can't be equal to one.

but x and y are free, so you have two free variables and one equation,

that means that for any k the system has infinitely many solutions.

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Merritt is driving to Mount Shasta. On her map, she is a distance of 7 inches away. The scale of the map is 2 inches is to 50 mi
Alisiya [41]

Answer:

7 inches on the map is 175 miles.

Step-by-step explanation:

2 inches equals 50 miles.  Use 50 divided by 2 to find the 1-inch scale which is 1:25 ( one inch to 25 miles)

7 0
3 years ago
Which of the following is a point-slope equation of a line that passes through the points (-1, 4) and (8,-2)?
yan [13]

Answer:

B

Step-by-step explanation:

We want to find the point-slope equation of a line that passes through the points (-1, 4) and (8, -2).

Point-slope form is given by:

y-y_1=m(x-x_1)

Where <em>m</em> is the slope and (<em>x₁, y₁</em>) is a point.

So, let's find the slope of the line first. We can use the slope formula:

\displaystyle m=\frac{\Delta y}{\Delta x}=\frac{-2-4}{8-(-1)}=\frac{-6}{9}=-\frac{2}{3}

We can choose (-1, 4) as our point. So, (<em>x₁, y₁</em>) = (-1, 4).

Substitute:

\displaystyle y-(4)=-\frac{2}{3}(x-(-1))

Simplify:

\displaystyle y-4=-\frac{2}{3}(x+1)

Therefore, our answer is B.

7 0
3 years ago
What is the median of the data set? <br><br> {16, 15, 17, 19, 12, 11, 14, 14, 13, 11, 18, 15}
RUDIKE [14]
The median is the numeric value separating the higher half of a sample data set from the lower half. The median of a data set can be found by arranging all the values from lowest to highest value and picking the one in the middle. If there is an odd number of data values then the median will be the value in the middle. If there is an even number of data values the median is the mean of the two data values in the middle. For the data set 16, 15, 17, 19, 12, 11, 14, 14, 13, 11, 18, 15 the median is 14.5. It is the mean of 14 and 15 or, (14+15)/2 = 14.5.
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KengaRu [80]
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4 0
3 years ago
An multiple of 10 to the 2 power
Margaret [11]
10 to the second power means
10^2 = 10×10 = 100
Your answer is 100.
3 0
3 years ago
Read 2 more answers
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