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dalvyx [7]
3 years ago
6

If, in a quadratic equation, the values of a and c have opposite signs, the solutions of the equation are real numbers.

Mathematics
1 answer:
Virty [35]3 years ago
4 0
Ax²+bx+c=0 , a>0, c<0 (or a<0, c>0)
D=b²-4ac ≥ 0 always will be positive
because negative*positive = negative, 
a*c -negative, so (-4ac) positive 
So,
<span>If, in a quadratic equation, the values of a and c have opposite signs, the solutions of the equation are real numbers. 
</span>True
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Divide 29 into two parts so that the sun of the squares of the parts is 425.Find the value of each Part.
Taya2010 [7]

Answer:

13 and 16

Step-by-step explanation:

let the 2 parts be x and y, then

x + y = 29 → (1) and

x² + y² = 425 → (2)

From (1) → x = 29 - y → (3)

substitute x = 29 - y into (2)

(29 - y)² + y² = 425 ( expand factor )

841 - 58y + y² + y² = 425 ( rearrange into standard form )

2y² - 58y + 416 = 0 ← in standard quadratic form

divide all terms by 2

y² - 29y + 208 = 0

Consider the factors of 208 which sum to - 29

These are - 13 and - 16, hence

(y - 13)(y - 16) = 0

equate each factor to zero and solve for y

y - 13 = 0 ⇒ y = 13

y - 16 = 0 ⇒ y = 16

substitute these values into (3)

x = 29 - 13 = 16 and x = 29 - 16 = 13

The 2 parts are 13 and 16


4 0
3 years ago
Read 2 more answers
If f(a)=(a•a•a)-(a•a) + a-1 what is the value of f(-3)?
Elena L [17]

Answer:

-40

Step-by-step explanation:

f(a) = a³ - a² + a - 1

f(-3) = (-3)³ - (-3)² + (-3) - 1

f(-3) = (-27) - (9) + (-3) -1

f(-3) = -27 - 9 -3 - 1

f(-3) = -40

3 0
3 years ago
Patrick is building a fence for his backyard. He bought wood planks that have a base length of 1/2 a foot and a height of 6 feet
miss Akunina [59]

Answer:

72 ft^2

Step-by-step explanation:

area = length x width

1/2 x 8 = 3

3 x 24 = 72

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2 years ago
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AlladinOne [14]

Answer:

Linear

Step-by-step explanation:

It is linear as it has degree 1.

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Amy ran 2/3 of a marathon. Beth ran 5/6 of a marathon. Who ran farther ? How much farther?
Ymorist [56]
2/3 is equal to 4/6. 

So, Beth ran further by 1/6 of the marathon
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3 years ago
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