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mars1129 [50]
2 years ago
6

Determine the value of a and b so that x^4 6x^3 +7x^2+ax+b is a perfect square

Mathematics
1 answer:
posledela2 years ago
3 0

Step-by-step explanation:

(Ax² + Bx + C)²

= (Ax² + Bx + C)(Ax² + Bx + C)

= Ax⁴ + 2ABx³ + 2ACx² + 2BCx + C².

By Comparing Coefficients, we have:

A = 1

2AB = 6

2AC = 7

2BC = a

C² = b

Solving them we get A = 1, B = 3 and C = 3.5.

Therefore a = 2BC = 2(3)(3.5) = 21,

b = C² = (3.5)² = 12.25.

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What is the value of n? n–2=10n+4/2 n =
slamgirl [31]

simplify


n-2 = 10n/2 + 4/2


n-2 = 5n + 2


subtract 5n to both sides


n - 2 - 5n = 5n + 2 - 5n


simplify


-4n - 2 = 2


add 2 to both sides


-4n - 2 + 2 = 2 + 2


simplify


-4n = 4


divide both sides by -4


-4n/-4 = 4/-4


simplify


n = -1




                             hope it helps



8 0
3 years ago
From a list of ten books, how many groups of 4 books can be selected
andreyandreev [35.5K]

First you have all ten books, but then every time after, you loose one because you can't put the same book in the group twice.

10 * 9 * 8 * 7 = 5040 groups

6 0
3 years ago
At a display booth at an amusement park, every visitor gets a gift bag. Some
kotegsom [21]

The bag will often contain all three items every 70 bags ⇒ answer C

Step-by-step explanation:

At a display booth at an amusement park, every visitor gets a gift bag

according to these information:

1. Hat Every 2nd visitor

2. T-shirt Every 7th visitor

3. Backpack Every 10th visitor

We need to know how often a bag will contain all three items

To solve this problem you must find a number divisible by 2, 7, and 10

To find that number start with the multiples of the largest one and

check them with the other two numbers

∵ The largest number is 10

∵ The multiples of 10 are 10 , 20 , 30 , 40 , 50 , 60 , 70 , 80 , .......

- Look for the first multiple of 10 is divisible by 7

∵ 70 is the first multiple of 10 divisible by 7

∵ 70 is divisible by 2 because its even number

∴ 70 is the smallest number divisible by 2, 7 and 10

The bag will often contain all three items every 70 bags

Learn more:

You can learn more about numbers in brainly.com/question/537998

#LearnwithBrainly

4 0
3 years ago
The number - 12/16 can be reduced as​
liberstina [14]

Answer:

3/4

Step-by-step explanation:

<u>1</u><u>2</u> divide 4 <u>3</u>

16 divide 4 4

5 0
3 years ago
Read 2 more answers
| x - 1 | = 5x + 10<br> Check for extraneous solutions.
Ronch [10]
[x-1]=5x+10

We have two equations:
1) x-1=5x+10

x-1=5x+10
x-5x=10+1
-4x=11
x=-11/4

2) x-1=-(5x+10)

x-1=-(5x+10)
x-1=-5x-10
x+5x=-10+1
6x=-9
x=-9/6=-3/2

we have two  possible solutions:
solution₁;       x=-11/4
solution₂:       x=-3/2

we check it out:
1) x=-11/4
[x-1]=5x+10
[-11/4  - 1]=5(-11/4)+10
[(-11-4)/4]=-55/4  + 10
[-15/4]=(-55+40) /4
15/4≠-15/4   This solution don´t work.

2) x=-3/2
[x-1]=5x+10
[-3/2  - 1]=5(-3/2)+10
[(-3-2)/2]=-15/2  + 10
[-5/2]=(-15+20)/2
5/2=5/2; this solution works.

Therefore:

Answer: x=-3/2.
8 0
3 years ago
Read 2 more answers
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