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3 years ago

Find the length of the segment with endpoint Y(4, 3) and midpoint M(1, 7).

Mathematics

1 answer:

inessss [21]3 years ago

5 0

Answer:the length is 10

Step-by-step explanation:

since m is the midpoint it is 3 away from y on the x axis and 4 away on the y axis

so if you go the same distance away from the midpoint you get -2, 11

so -2 is 6 away from 4 away and 3 is 8 away from 11

6^2 = 36

8^2 = 64

36+64= 100

the square root of 100 is 10

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Convert the following systems of equations to an augmented matrix and use Gauss-Jordan reduction to convert to an equilivalent m

Rasek [7]

Answer:

System of equations:

$x_1+2x_2+2x_3=6\\2x_1+x_2+x_3=6\\x_1+x_2+3x_3=6$

Augmented matrix:

$\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right]$

Reduced Row Echelon matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right]$

Step-by-step explanation:

Convert the system into an augmented matrix:

$\left[\begin{array}{cccc}1&2&2&6\\2&1&1&6\\1&1&3&6\end{array}\right]$

For notation, R_n is the new nth row and r_n the unchanged one.

1. Operations:

$R_2=-2r_1+r_2\\R_3=-r_1+r_3$

Resulting matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&-3&-3&-6\\0&-1&1&0\end{array}\right]$

2. Operations:

$R_2=-\frac{1}{3}r_2$

Resulting matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&-1&1&0\end{array}\right]$

3. Operations:

$R_3=r_2+r_3$

Resulting matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&2&2\end{array}\right]$

4. Operations:

$R_3=\frac{1}{2}r_3$

Resulting matrix:

$\left[\begin{array}{cccc}1&2&2&6\\0&1&1&2\\0&0&1&1\end{array}\right]$

4 0

3 years ago

If f(x) = 2х2 +1 and g(x) = х2 -7, find (f-g)(x).

Nookie1986 [14]

Option A

If f(x) = $2x^2 + 1$ and g(x) = $x^2 - 7$ then $(f - g)(x) = x^2 + 8$

<em><u>Solution:</u></em>

Given that f(x) = $2x^2 + 1$ and g(x) = $x^2 - 7$

To find: (f - g)(x)

We know that,

(f – g)(x) = f (x) - g(x)

Let us substitute the given values of f(x) and g(x) in above formula,

$(f - g)(x) = 2x^2 + 1 - (x^2 - 7)$

For solving the brackets in above expression,

There are two simple rules to remember:

When you multiply a negative number by a positive number then the product is always negative.

When you multiply two negative numbers or two positive numbers then the product is always positive.

So the expression becomes,

$(f - g)(x) = 2x^2 + 1 -x^2 + 7$

Combining the like terms,

$(f - g)(x) = 2x^2 - x^2 + 1 + 7\\\\(f - g)(x) = x^2 + 8$

Thus option A is correct

8 0

2 years ago

PLSSS ANSWER JUST PUT THE NUMBER OF THE QUESTION THEN THE ANSWER PLS HELP ITS OVERDUE AND IM GONNA FAIL 7TH GRADE :(

yanalaym [24]

Answer:

11= 21

12= -12

13= -72

14= -1

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

7. If every short side is 1.5 inches and every long side is 3 inches, what is the perimeter?

hjlf

The answer 2 your question is 24in

6 0

2 years ago

Read 2 more answers

Mo puts $1,600.00 into savings bonds that pay a simple interest rate of 3.5%. How much money will the bonds be worth at the end

BabaBlast [244]

18.5 I think so if not then sorry

5 0

3 years ago