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For which values of a does ????3a 2a − 6<br> 6a 4a − 12<br> ???? have an inverse matrix?

likoan [24]

Answer:

The matrix does not have an inverse.

Step-by-step explanation:

$A=\begin{bmatrix}3a & 2a-6\\ 6a & 4a-12\end{bmatrix}$

$det\ A=3a(4a-12)-6a(2a-6)\\\Rightarrow det\ A=12a^2-36a-(12a^2-36a)\\\Rightarrow det\ A=12a^2-36a-12a^2+36a\\\Rightarrow det\ A=0$

Since the determinant of the matrix is zero it is called a singular matrix.

Singular matrices do not have an inverse.

Hence, the matrix does not have an inverse.

7 0

3 years ago

Ginger’s baby weighed only 3 3/8 pounds when it was born. The doctor said it could not leave the hospital until it weighed 5 1/5

Zigmanuir [339]

To subtract 3 3/8 from 5 1/2,by turning into fractions[(5x2)+1]/2 = 11/2[(3x8)+3]/8 = 27/8 11/2 - 27/8To subtract fractions, your denominator needs to have the same number. so multiply it by 4 44/8 - 27/8 = (44-27)/8 = 17/8.17 / 8 pounds or 2 and 1/8 because 17 / 8 = 2 remainder 1. In terms of weight that is 2.125 pounds.

5 0

3 years ago

A salesperson travels from city A to city B and then to city C. From city C, the salesperson travels directly back to city A

swat32

Answer:

1) city C to city A

2) city A to city B

3) city B to city C

Step-by-step explanation:

step 1

Find the value of x

Remember that

The sum of the interior angles of a triangle must be equal to 180 degrees

so

A+B+C=180°

substitute the given values and solve for x

(2x-5)°+(x-1)°+(x+2)°=180°

Group terms

4x-4=180

4x=180+4

4x=184

x=46

step 2

Find the measure of each angle

A=(2x-5)°------> A=2(46)-5=87°

B=(x-1)° -------> B=46-1=45°

C=(x+2)° -----> C=46+2=48°

Let

a ------> travel from city B to city C

b -----> travel from city C to city A

c -----> travel from city A to city B

we know that

If one angle of a triangle has a greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle

so

The greater angle is angle A, the side opposite the greater angle is the side a (travel from city B to city C)

The lesser angle is angle B, the side opposite the greater angle is the side b (travel from city C to city A)

therefore

The lengths of the legs of the trip in order from least to greatest is

1) city C to city A

2) city A to city B

3) city B to city C

7 0

3 years ago

A roulette wheel has the numbers 1 through 36, 0, and 00. A bet on three numbers pays 11 to 1 (that is, if you bet $1 and one of

OLga [1]

Answer:

You are expected to lose $0.05 (or win -$0.05)

Step-by-step explanation:

Since the roulette wheel has the numbers 1 through 36, 0, and 00, there are 38 possible outcomes.

In this bet, you are allowed to pick 3 out of the 38 numbers. Thus, your chances of winning (P(W)) and losing (P(L)) are:

$P(W)=\frac{3}{38}\\P(L) = 1 - P(W)\\P(L) = \frac{35}{38}\\$

The expected value of the bet is given by the sum of the product of each outcome pay by its probability. Winning the bet means winning $11 while losing the bet means losing $1. The expected value is:

$EV = (11*\frac{3}{38}) -(1*\frac{35}{38})\\EV = -\$0.0525$

Therefore, with a $1 bet, you are expected to lose roughly $0.05

5 0

3 years ago

What is the length of de

Dima020 [189]

Answer:

x = 6

Step-by-step explanation:

Since <F = <F, this shows that the triangles are similar. Therefore:

XZ/DF = XY/DE

12/8 = 9/X

Cross multiply

12X = 9*8

12X = 72

X = 72/12

X = 6

Hence the value of x is 6

5 0

3 years ago