Solve the matrix equation for a, b, c, and d. [1 2] [a b] [6 5][3 4] [c d]= [19 8]

Answers

Answer 1

Answer:

Answer:

The answer is " $\bold{\left[\begin{array}{cc}a&b\nc&d\end{array}\right] = \left[\begin{array}{cc}7&-2\n -(1)/(2)&(7)/(2)\end{array}\right]}$ ".

Step-by-step explanation:

$\bold{\left[\begin{array}{cc}1&2\n3&4\end{array}\right] \left[\begin{array}{cc}a&b\nc&d\end{array}\right] = \left[\begin{array}{cc}6&5\n 19&8\end{array}\right]}$

Solve the L.H.S part:

$\left[\begin{array}{cc}1&2\n3&4\end{array}\right] \left[\begin{array}{cc}a&b\nc&d\end{array}\right]\n\n\n\left[\begin{array}{cc}a+2c&b+2d\n3a+4c&3b+4d\end{array}\right]$

After calculating the L.H.S part compare the value with R.H.S:

$\left[\begin{array}{cc}a+2c&b+2d\n3a+4c&3b+4d\end{array}\right]= \left[\begin{array}{cc}6&5\n 19&8\end{array}\right]} \n\n$

$\to a+2c =6....(i)\n\n\to b+2d =5....(ii)\n\n\to 3a+4c =19....(iii)\n\n\to 3b+4d = 8 ....(iv)\n\n$

In equation (i) multiply by 3 and subtract by equation (iii):

$\to 3a+6c=18\n\to 3a+4c=19\n\n\text{subtract}... \n\n\to 2c = -1\n\n\to c= - (1)/(2)$

put the value of c in equation (i):

$\to a+ 2 (- (1)/(2))=6\n\n\to a- 2 * (1)/(2)=6\n\n\to a- 1=6\n\n\to a =6 +1\n\n\to a = 7\n$

In equation (ii) multiply by 3 then subtract by equation (iv):

$\to 3b+6d=15\n\to 3b+4d=8\n\n\text{subtract...}\n\n\to 2d = 7\n\n\to d= (7)/(2)\n$

put the value of d in equation (iv):

$\to 3b+4 ((7)/(2))=8\n\n\to 3b+4 * (7)/(2)=8\n\n\to 3b+14=8\n\n\to 3b =8-14\n\n\to 3b = -6\n\n\to b= (-6)/(3)\n\n\to b= -2$

The final answer is " $\bold{\left[\begin{array}{cc}a&b\nc&d\end{array}\right] = \left[\begin{array}{cc}7&-2\n -(1)/(2)&(7)/(2)\end{array}\right]}$ ".

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Answers

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Brian and Jennifer are planning to get married at the end of the year. They read that certain diets are healthier for specific blood types and hope that they both have the same blood type. Unfortunately, neither Brian nor Jennifer can remember their blood type.Suppose a recent study shows that 29% of adults have blood type A, 35% of adults have blood type B, 24% of adults have blood type AB, and 12% of adults have blood type O. The tree diagram shows the possible outcomes for Brian and Jennifer along with their associated probabilities.
What is the probability that Brian and Jennifer share the same blood type?

Answers

The probability that they both have type A: 0.29 x 0.29 = 0.0841

The probability that they both have type A: 0.35 x 0.35 = 0.1225

The probability that they both have type AB: 0.24 x 0.24 = 0.0576

The probability that they both have type O: 0.12 x 0.12 = 0.0144

The probability that they both have the same:

0.0841 + 0.1225 + 0.0576 + 0.0144 = 0.2786

The probability that Brian and Jennifer share the same blood type is approximately 0.2786 or 27.86%.The probability that Brian and Jennifer share the same blood type can be calculated by considering all the possible cases where they can have the same blood type.

There are four blood types: A, B, AB, and O. Since there are 4 possibilities for Brian's blood type and 4 possibilities for Jennifer's blood type, there are a total of $4 * 4 = 16$ equally likely outcomes for their blood types.

Out of these 16 possible outcomes, there are two cases where Brian and Jennifer share the same blood type: either both have the same blood type A, B, AB, or O.

1. Both have blood type A:Probability = Probability(Brian has A) × Probability (Jennifer has A) = 0.29 × 0.29 = 0.0841.

2. Both have blood type B:Probability = Probability(Brian has B) × Probability (Jennifer has B) = 0.35 × 0.35 = 0.1225.

3. Both have blood type AB:Probability = Probability(Brian has AB) × Probability (Jennifer has AB) = 0.24 × 0.24 = 0.0576.

4. Both have blood type O:Probability = Probability(Brian has O) × Probability (Jennifer has O) = 0.12 × 0.12 = 0.0144.

Now, add up the probabilities of these four cases:

$0.0841 + 0.1225 + 0.0576 + 0.0144 = 0.2786.$

Therefore, the probability that Brian and Jennifer share the same blood type is approximately 0.2786 or 27.86%.

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Cot^2x+1 please simplify

Answers

csc^2(x)

Explanation:
We have:
cot
2
(
x
)
+
1

This expression can be simplfiified by applying one of the Pythagorean identities:
1
+
cot
2
(
x
)
=
csc
2
(
x
)
=
csc
2
(
x
)

An architect uses a scale of 3 4 inch to represent 1 foot on a blueprint for a building. If the east wall of the building is 24 feet long, how long (in inches) will the line be on the blueprint?

Answers

The length of the line on the blueprint of the wall will be 18 inches.

What is dilation?

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered.

There is no effect of dilation on the angle.

An architect uses a scale of 3/4 inches to represent 1 foot on a blueprint for a building.

Then the scale factor of the blueprint will be

Scale factor = 3/4 inches per foot

If the east wall of the building is 24 feet long.

Then the length of the line on the blueprint of the wall will be

Length = 24 feet x scale factor

Length = 24 x (3/4)

Length = 6 x 3

Length = 18 inches

Thus, the length of the line on the blueprint of the wall will be 18 inches.

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Answer:

16 in.

Step-by-step explanation:

We have the ratio

How about let's make this easier. Easier is better, right? Let's get rid of the fraction 2/3. We will do that by multiplying 2/3 by 3 and 1 by 3 to get the equivalent ratio of

Now we need to know how many inches there would be if the number of feet is 24:

Cross multiply to get

3x = 48 so

x = 16 in.

About 70,000 people live in a 6-mile radius of a city's town hall. Find the population density in people per square mile. Round your answer to the nearest whole number.The population density is about _
people per square mile.