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Y_Kistochka [10]
3 years ago
12

Solve by factoring s^2-14s+45=0

Mathematics
1 answer:
Maurinko [17]3 years ago
4 0

Answer:

s = 5, s = 9

Step-by-step explanation:

To factor the quadratic

Consider the factors of the constant term (45) which sum to give the coefficient of the s- term (- 14)

The factors are - 9 and - 5

since - 9 × - 5 = + 45 and - 9 - 5 = - 14, hence

s² - 14s + 45 = 0

(s - 9)(s - 5) = 0

Equate each factor to zero and solve for s

s - 9 = 0 ⇒ s = 9

s - 5 = 0 ⇒ s = 5

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The product of two consecutive integers is equal to 14 more than 4 times the sum. This can be simplified to x²-7x-18=0. What are
WITCHER [35]

Answer:

-1 and -2, or 9 and 10

Step-by-step explanation:

If x is the smaller integer:

x (x + 1) = 14 + 4 (x + x + 1)

x² + x = 14 + 4 (2x + 1)

x² + x = 14 + 8x + 4

x² − 7x − 18 = 0

Factor using AC method:

(x − 9) (x + 2) = 0

x = -2 or 9

x is the smaller integer, so the larger integers are -1 and 10.  Check each pair of solutions.

-1 and -2:

(-2) (-1) = 14 + 4 (-2 + -1)

2 = 14 + 4 (-3)

2 = 2

9 and 10:

(9) (10) = 14 + 4 (9 + 10)

90 = 14 + 4 (19)

90 = 90

Both solutions work.

7 0
3 years ago
A forest cover 43,000 acres. A survey finds that 0.2% of the forest is old growth tress. How many acres of old growth trees are
Sveta_85 [38]

Given:

Total forest area = 43,000

Old growth trees forest = 0.2%

To find:

The area of the old growth trees.

Solution:

We have,

Total forest area = 43,000

Old growth trees forest = 0.2%

Area of the old growth trees = 0.2% of 43,000

                                               = \dfrac{0.2}{100}\times 43000

                                               = 86

Therefore, the area of the old growth trees is 86 acres.

6 0
3 years ago
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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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