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3 years ago

Use the given graph to determine the limit, if it exists.

Mathematics

1 answer:

Aleksandr-060686 [28]3 years ago

6 0

As x approaches 3 from the right, the limit is 3. There is a closed hole up there AT x=3 y=7, but we don't care about what happens AT x=3, only what happens as x APPROACHES 3.

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Let A be a 3 by 6 , B be a 6 by 7 and C be a 7 by 3 matrix. Determine the size of the following matrices (if they do not exist,

kozerog [31]

Answer:

a. AB: 3 by 7

b. BA: N by N

c. A^TB: N by N

d. BC: 6 by 3

Step-by-step explanation:

Given

$A =3\ by\ 6$

$B =6\ by\ 7$

$C =7\ by\ 3$

Required

The dimension of the following matrices

As a general rule:

For A * B to be successful, the columns in a must equal the rows in B

Using this rule, we have:

$A_{m*n} * B_{n * p} = AB_{m*p}$

So:

$(a)\ AB$

$A_{3*6} * B_{6*7} \to AB_{3 * 7}$

$(b)\ BA$

$B_{6*7} * A_{3*6} \to AB_{N * N}$

The column numbers of B does not equal the row numbers of A.

Hence, BA does not exist

$(c)\ A^TB$

$A^T$ implies that:

If $A =3\ by\ 6$ , then

$A^T = 6\ by\ 3$

So:

$A^T_{6*3} * B_{6,7} \to A^TB_{N*N}$

The column numbers of A^T does not equal the row numbers of B.

Hence, $A^TB$ does not exist

$(d)\ BC$

$B_{6*7} * C_{7*3} \to BC_{6,3}$

6 0

3 years ago

X + 3y = 14 -5x + 6y = -28 Solve systems by substitution

mote1985 [20]

Rearrange the first system to get x = -3y + 14. Substitute that into the other system.

$-5x+6y=-28\\\\-5(-3y+14)+6y=-28\\\\15y-70+6y=-28\\\\15y-70+6y=-28\\\\21y-70=-28\\\\21y=42\\\\y=2$

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4 0

3 years ago

This figure shows △XYZ . MZ¯¯¯¯¯¯ is the angle bisector of ∠YZX . What is XM ? Enter your answer, as a decimal, in the box. unit

astraxan [27]

Answer:

Length of XM is 5.5 units.

Step-by-step explanation:

Given △XYZ where MZ is the angle bisector of ∠YZX . we have to find the length of XM.

A triangle with vertices X, Y, and Z. Side XZ is base. A line segment drawn from Z to M bisects ∠YZX into two parts ∠YZM and ∠XZM.

YZ=7 units, XZ=11 units and YM=3.5 units

By angle bisector theorem which states that an angle bisector of an angle divides the opposite side in two segments that are proportional to the another two sides of the triangle.

Hence, $\frac{YM}{MX}=\frac{YZ}{XZ}$