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2 years ago

What is the greatest common factor GCF of 30,66. 84

Mathematics

1 answer:

Anon25 [30]2 years ago

8 0

Answer:

Step-by-step explanation:

Factorize of the above numbers :

30 = 2 • 3 • 5

66 = 2 • 3 • 11

84 = 22 • 3 • 7

Build a prime factors table

Number of times each prime factor

appears in the factorization of :

Prime

Factor Number

30 Number

66 Number

84 G.C.F

(min)

2 1 1 2 1

3 1 1 1 1

5 1 0 0 0

7 0 0 1 0

11 0 1 0 0

GCF = 2 • 3

Greatest Common Factor is :

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Which system of equations is inconsistent?

Agata [3.3K]

Answer:

Option A is correct.

The system of equation is inconsistent is;

2x+8y=6

5x+20y=2

Explanation:

* A system of equations is called an inconsistent system, if there is no solution because the lines are parallel.

* If a system has at least one solution, it is said to be consistent .

*A dependent system of equations is when the same line is written in two different forms so that there are infinite solutions.

(A)

2x+8y=6

5x+20y=2

This is inconsistent, because as shown below in the graph of figure 1 that the lines do not intersect, so the graphs are parallel and there is no solution.

(B)

5x+4y=-14

3x+6y=6

this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 2 and also it is independent.

(C)

x+2y=3

4x+6y=5

this system of equation is Consistent because it has exactly one solution as shown below in the graph of Figure 3.

(D)

3x-2y=2

6x-4y=4

this is a consistent system and has an infinite number of solutions, it is dependent because both equations represent the same line. as shown below in the graph of Figure-4.

Therefore, the only Option A system of equation is inconsistent.

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2 years ago

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Consider the table representing a rational function.

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Answer:

The function has a hole when x = 0 and a vertical asymptote when x = 4.

Step-by-step explanation:

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1 year ago

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Bonita has a standard of 2 hours of labor per unit, at $12 per hour. In producing 2600 units, Bonita used 5050 hours of labor at

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1800

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2 years ago

A pound of oranges costs $2 less than a pound of pears. Together, ten pounds of oranges and eight pounds of pears cost $61. How

Thepotemich [5.8K]

Let us say that:

o = cost of oranges per pound

p = cost of pears per pound

so that:

o = p – 2

Therefore:

10o + 8p = 61

10 (p – 2) + 8p = 61

10p – 20 + 8p = 61

18p = 81

p = 4.5

p = $4.5 per pound

So 3 pounds of pears would cost:

total cost = 3 * 4.5

total cost = $13.5

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2 years ago

The aquarium at Sea Critters Depot contains 140 fish. Eighty of these fish are green swordtails (44 female and 36 male) and 60 a

maxonik [38]

Given that:

Total number of fish = 140

Fish are green swordtails female = 44

Fish are green swordtails male = 36

Fish are orange swordtails female = 36

Fish are orange swordtails male = 24

Solution:

A. We have to find the probability that the selected fish is a green swordtail.

$\text{P(green swordtail)}=\dfrac{\text{Total green swordtail fish}}{\text{Total fish}}$

$\text{P(green swordtail)}=\dfrac{80}{140}$

$\text{P(green swordtail)}=\dfrac{4}{7}$

Therefore, the probability that the selected fish is a green swordtail is $\dfrac{4}{7}.$

B. We have to find the probability that the selected fish is male.

$\text{P(Male fish)}=\dfrac{\text{Total male fish}}{\text{Total fish}}$

$\text{P(Male fish)}=\dfrac{36+24}{140}$

$\text{P(Male fish)}=\dfrac{60}{140}$

$\text{P(Male fish)}=\dfrac{3}{7}$

Therefore, the probability that the selected fish is a male, is $\dfrac{3}{7}.$

C. We have to find the probability that the selected fish is a male green swordtail.

$\text{P(Male green swordtail)}=\dfrac{\text{Total male green swordtail fish}}{\text{Total fish}}$

$\text{P(Male green swordtail)}=\dfrac{36}{140}$

$\text{P(Male green swordtail)}=\dfrac{9}{35}$

Therefore, probability that the selected fish is a male green swordtail is $\dfrac{9}{35}.$

We have to find the probability that the selected fish is either a male or a green swordtail.

$\text{P(Male or green swordtail)}=\dfrac{\text{Total male or green swordtail fish}}{\text{Total fish}}$

$\text{P(Male or green swordtail)}=\dfrac{44+36+24}{140}$

$\text{P(Male or green swordtail)}=\dfrac{96}{140}$

$\text{P(Male or green swordtail)}=\dfrac{24}{35}$

Therefore, the probability the selected fish is either a male or a green swordtail is $\dfrac{24}{35}.$

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2 years ago

What is the greatest common factor GCF of 30,66. 84​

What is the greatest common factor GCF of 30,66. 84