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3 years ago

Determine what type of number the solutions are and how many exist for the equation 3x^2+7x+5=0

Mathematics

1 answer:

Hitman42 [59]3 years ago

6 0

Answer:

Two complex (imaginary) solutions.

Step-by-step explanation:

To determine the number/type of solutions for a quadratic, we can evaluate its discriminant.

The discriminant formula for a quadratic in standard form is:

$\Delta=b^2-4ac$

We have:

$3x^2+7x+5$

Hence, a=3; b=7; and c=5.

Substitute the values into our formula and evaluate. Therefore:

$\Delta=(7)^2-4(3)(5) \\ =49-60\\=-11$

Hence, the result is a negative value.

If:

The discriminant is negative, there are two, complex (imaginary) roots.
The discriminant is 0, there is exactly one real root.
The discriminant is positive, there are two, real roots.

Since our discriminant is negative, this means that for our equation, there exists two complex (imaginary) solutions.

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When the members of a family discussed where their annual reunion should take place, they found that out of all the family mem

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Answer:

The total number of family members is 21.

Step-by-step explanation:

To solve this problem, we must build the Venn's Diagram of these sets.

I am going to say that:

-The set A represents those that would not go to a park.

-The set B represents those who would not go to a beach.

-The set C represents those who would not go to the family cottage.

The value d represents those who would go to all three places.

We have that:

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

In which a are those that would only not go to a park, $A \cap B$ are those who would not got to a park or to the beach, $A \cap C$ are those who would not go to a park or to the famili cottage. And $A \cap B \cap C$ are those that would not go to any of these places.

By the same logic, we have:

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

This diagram has the following values:

$a,b,c,d,(A \cap B), (A \cap C), (B \cap C), (A \cap B \cap C)$

The total number of family members is the sum of all these values:

$T = a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

We start finding the values from the intersection of the three sets

5 would not go to a park or a beach or to the family cottage.

This means that $A \cap B \cap C = 5$

1 would go to all three places. This means that $d = 1$ .

8 would go to neither a park nor the family cottage

This means that:

$A \cap C + (A \cap B \cap C) = 8$

$A \cap C = 3$

8 would go to neither a beach nor the family cottage

$B \cap C + (A \cap B \cap C) = 8$

$B \cap C = 3$

7 would go to neither a park nor a beach

$A \cap B + (A \cap B \cap C) = 7$

$A \cap B = 2$

15 would not go to the family cottage

$C = 15$

$C = c + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

$15 = c + 3 + 3 + 5$

$c = 4$

12 would not go to a beach

$B = 12$

$B = b + (B \cap C) + (A \cap B) + (A \cap B \cap C)$

$12 = b + 3 + 2 + 5$

$b = 2$

11 would not go to a park

$A = 11$

$A = a + (A \cap B) + (A \cap C) + (A \cap B \cap C)$

$11 = a + 2 + 3 + 5$

$a = 1$

Now, we can find the total number of family members.

$T = a + b + c + d + (A \cap B) + (A \cap C) + (B \cap C) + (A \cap B \cap C)$

$T = 1 + 2 + 4 + 1 + 2 + 3 + 3 + 5$

$T = 21$

The total number of family members is 21.

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Answer:

Step-by-step explanation:

i quessed

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12. Answer: 2130

Step-by-step explanation:

T = -0.01y + 10.6

9.2 = -0.01y + 10.6

-10.6 -10.6

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÷-0.01 ÷-0.01

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1990 + 140

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**************************************************************

13. Answer: -0.0036° per foot

Step-by-step explanation:

Since the relationship is linear, then we can set up the values as x, y coordinates and use the slope formula to find the rate of degrees over feet.

(6562, 63) and (16405, 28)

rate = $\frac{28 - 63}{16405-6562}$

= $\frac{-35}{9843}$

= $\frac{-0.0036}{1}$

**************************************************************

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Step-by-step explanation:

Same reason as #13

(200, 55) and (500, 140)

rate = $\frac{140-55}{500-200}$

= $\frac{85}{300}$

= $\frac{0.28}{1}$

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3 years ago