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4 years ago

If α , β are roots of x2 + 5x + a =0 and 2α + 5β = -1 then α is equal to _____?

Mathematics

1 answer:

ELEN [110]4 years ago

3 0

9514 1404 393

Answer:

-8

Step-by-step explanation:

If α and β are roots of x^2 +5x +a = 0, then we must have ...

(x -α)(x -β) = x^2 +5x +a

x^2 -(α+b)x +αβ = x^2 +5x +a

Then ...

α + β = -5

Together with the other relation between the roots, we have a system of equations in α and β.

Using the above to write an expression for β, we get ...

β = -α -5

Substituting this into the given relation, we have an equation for α:

2α +5(-α -5) = -1

-3α -25 = -1 . . . . . . eliminate parentheses

-24 = 3α . . . . . . . . add 3α +1

-8 = α

The root α is equal to -8.

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Is 8, 11.5, 8.5 a right triangle?

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Answer:

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Step-by-step explanation:

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3 years ago

How to turn 1/4÷9/10 into a mixed fractions

sashaice [31]

First, change the division sign to multiplication, and flip the second fraction

(1/4)/(9/10) = 1/4 x 10/9

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7 0

4 years ago

Cho surveyed a random sample of 60 students in the school's library about whether they read the newest magazine. Fifteen of the

Softa [21]

Answer:

90 students.

Step-by-step explanation:

Given that Cho surveyed a random sample of 60 students in the school's library, of which 15 said they read the newest magazine, and that a total of 360 students attend the library every day, to determine how many of the 360 students can have expect to read the newest magazine the following calculation should be performed:

60 = 100

15 = X

15 x 100/60 = X

1,500 / 60 = X

25 = X

Thus, 25 percent of the students in the sample read the newest magazine. Since 25% of 360 is 90 (360 x 0.25), that is the number of students he can expect to have read the magazine.

8 0

3 years ago

All of the coats in a clothing store were on sale for 30% off the original price. Carlotta paid $41.30 for a coat after the disc

Yakvenalex [24]

(original price) -0.30*(original price) = $41.30
(original price)*0.7 = $41.30
(original price) = $41.30/0.70 = $59.00

The coat's original price was $59.00.

6 0

3 years ago

Please help me (please dont send links)

Burka [1]

Answer:

Part A

79.4

Part B

Part C

The science class

Step-by-step explanation:

The linear function representing the average test score in the math class, after taking x number of tests, f(x) = 0.2·x + 79

The science class average test score, after taking x number of tests, is given by the linear function g(x)

The values of g(x) are presented as follows;

x; 1, 2, 3

g(x); 86, 84, 82

Part A

By using the given function for the test average for the math class, f(x), when x = 2, we have;

f(2) = 0.2 × 2 + 79 = 79.4

The test average for the math class after completing test 2 = 79.4

Part B

The test average for the science class after completing test 2 from the table is 84

Part C

After completing test 4, the test average for the math class, f(4), is given as follows;

f(4) = 0.2 × 4 + 79 = 79.8

The test average for the science class after the completing test 4 is found by noting that the test average, g(x) decreases by 2 for each increase in the number of test taken, x, by 1

Given that the test average of the science, g(3) class after taking test 3 is 82, the test average after taking test 4, g(4) = g(3) - 2 = 82 - 2 = 80

g(4) = 80

Therefore, after completing test (4), the science class has a higher test average g(4) = 80, than the math class f(x) = 79.8

3 0

3 years ago