A student is trying to solve the set of two equations given below:Equation A: x + z = 6
Equation B: 2x + 4z = 1

Which of the following is a possible step used in eliminating the z-term?

Multiply equation B by 4.
Multiply equation A by 2.
Multiply equation A by −4.
Multiply equation B by 2.

Answers

Answer 1

Answer:

If you would like to eliminate the z-term, you can do this using the following steps:

x + z = 6 /*(-4)
2x + 4z = 1
_____________
-4x -4z = -24
2x + 4z = 1
_____________
-4x + 2x = -24 + 1
-2x = -23

x = 23/2

The correct result would be x + z = 6 /*(-4); multiply equation A by -4.

Answer 2

Answer:

A possible step which can be used in eliminating the z-term is: C. multiply equation A by -4.

Given the following data:

x + z = 6 ........equation A.

2x + 4z = 1 ......equation B.

What is a set of equations?

A set of equations is also referred to as a system of equations and it can be defined an algebraic equation that has only two (2) variables, which can be solved simultaneously.

In order to eliminate the z-term, we would subtract the second equation from 4 times the first equation:

Multiplying the first equation by 4, we have:

4[x + z = 6] = 4x + 4z = 24

Subtracting the two equations, we have:

[4x + 4z - 24 - 2x - 4z - (-1)] = 0

2x - 23 = 0

2x = 23

x = 23/2

x = 11.5.

In conclusion, a possible step which can be used in eliminating the z-term is to multiply equation A by -4.

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A bond quoted at 93 (1/8) is equal to ___ per 1,000.00 of the face amount.

Answers

Answer:

$931.25

Step-by-step explanation:

Given a bond is quoted at $93(1)/(8)$

let the Face value of the amount = $1000

therefore, the price/cost = $(93.125)/(1000)*100$

= $931.25

Therefore, the bond quoted at $93(1)/(8)$ is equal to $931.25 per 1000 of the face value.

Hope you got the point, feel free to ask doubts

The number a bond is the percentage of the value of the bond that the bond is worth. Because the bond is quoted at 93, the bond is worth $930 per $1,000.

Which equation shows an example of the associative property of addition? (–4 + i) + 4i = –4 + (i + 4i) (–4 + i) + 4i = 4i + (–4i + i) 4i × (–4i + i) = (4i – 4i) + (4i × i) (–4i + i) + 0 = (–4i + i)

Answers

(–4 + i) + 4i = –4 + (i + 4i) is the associative property of addition. Thus, option A is correct.

What is the associative property of addition?

According to the associative property of additionally, whenever at least three figures are added together, the outcome is unaffected by the sequence in which the individual numbers are added.

In the first given condition is is stated:

(–4 + i) + 4i = –4 + (i + 4i)

-4 + i + 4i = -4 + i + 4i

5i - 4 = 5i - 4

As the LHS = RHS, the property is said to be valid for the associative property of addition.

Therefore, option A is the correct option.

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Which equation shows an example of the associative property of addition?

(–4 + i) + 4i = –4 + (i + 4i)

(–4 + i) + 4i = 4i + (–4i + i)

4i × (–4i + i) = (4i – 4i) + (4i × i)

(–4i + i) + 0 = (–4i + i)

A. (–4 + i) + 4i = –4 + (i + 4i)

Step-by-step explanation:

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How many times would a coin have to show heads in 50 tosses to have an experimental probability of 20% more than the theoretical probability of getting heads?

Answers

The theoretical probability of getting heads is 50%. 50% of 50 is 25. So, 20 % more than 50% is 20% * 25 + 25 = 5 + 25 = 30. That means that the coin should show 30 heads fo have an experimental probability of 20% more than the theoretical probability. You can check that 30 out of 50 is 0.6. Which is 0.1 more than 0.5. And 0.1 is 20% of 0.5. Then 0.6 is 20% more than 0.5.

Final answer:

In a series of 50 coin tosses, a coin needs to land heads 30 times to have an experimental probability 20% greater than the theoretical probability.

Explanation:

The subject of focus here is the allusion to the theory of probability, particularly in relation to a fair coin flip. The theoretical probability of obtaining either heads or tails in a coin flip is 0.5. However, the student is interested in having an experimental probability 20% greater than the theoretical probability.

We can first calculate the theoretical counts of expected heads per 50 tosses, which is (0.5 * 50) = 25. This result represents the notion that if a coin is thrown 50 times, on average, will land heads 25 times based on the theoretical probability.

To achieve an experimental probability 20% greater than the theoretical probability, we need to find a count of heads that corresponds to a probability that is 20% more than 0.5 (the theoretical probability). This new probability is therefore 0.6 and the corresponding count of heads required would be (0.6 * 50) = 30. Hence, in 50 tosses, the coin would need to show heads 30 times to have an experimental probability 20% greater than the theoretical probability of getting heads.

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A rectangular ballroom is being carpeted. The room measures 32 feet by 24 feet. If the carpet costs $3.60 per square foot, then what is teh cost of the carpet?

Answers

Answer:

$2764.8

Step-by-step explanation:

32ft * 24ft = 768ft²

1ft² = 3.6

768*3.6 = 2764.8

How do I Find the slope and Y intercept of each equation:1. Y= 2x +1
2. Y= 1/3x _3
3. Y=_2x + 1
4. _2x +5y=10
5. 4x _2y _5=0
6. Y= _4x _3
7. 3x_ 5y=20

Answers

$1.\n \n the \ slope \ intercept \ form \ is : \n \n y= mx +b \n \ny=2x+1 \n \n the \ slope \ (the multiplier \ of \ x \ represented \ by \ m ) \ is \ 2 \n \n and \ the \ y-intercept \ (the constantrepresented \ by \ b \ ) \ is \ 1$

$2.\n \n y= (1)/(3)x-3 \n \n the \ slope \ m = (1)/(3) \ \ and \ y = -3$

$3.\n \n y= -2x + 1\n \n the \ slope \ m = -2 \ \ and \ y = 1$

$4.\n \n-2x +5y=10\n \n5y=2x +10 \ \ /:5\n \ny = (2)/(5)x +2\n \n the \ slope \ m =( 2)/(5) \ \ and \ y = 2$

$5.\n \n 4x-2y-5=0\n \n-2y =-4x +5 \ \ /:(-2)\n \ny=2x-(5)/(2) \n \n the \ slope \ m = 2 \ \ and \ y = -(5)/( 2)$

$6.\n \n y=-4x-3 \n \n the \ slope \ m =-4 \ \ and \ y = -3$

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H(n) = n^2+ 4n
g(n)= 2n -3
Find h(g(-2))