MATHEMATICS HIGH SCHOOL

If f(x) = x² – 3, where x is an integer, which of the following could be a value of f(x)?a. 6
b. 0
c. -6

It would be great if you could add a few words of explanation

Answers

Answer 1
Answer: f (x) = x^2 - 3 \n \n a.\ 6 \n \nf(x)=6\n \n 6=x^2-3\n \n6+3= x^2

x^2=9 \n \nx^2-9=0\n \n(x-3)(x+3)=0 \n \nx-3=0 \ \ or \ \ x+3 =0 \n \nx=3 \ \ or \ \ x= -3 \n \n Answer : \ Possible .


b.\ \ 0 \n \nf(x)=0\n \n 0=x^2-3\n \n(x-√(3)) (x+√(3))=0 \n \n x-√(3)=0 \ \ or \ \x+√(3) =0

x=√(3) \ \ or \ \x=-√(3) \n \nAnswer : \ x \ is \ not \ an \ integer,\ not \ possible


c.\ \ -6 \n \nf(x)= -6\n \n -6=x^2-3\n \n x^2=-6 +3 \n \nx^2=-3\n \nAnswer: \ square \ of \ an \ integer \ can \ not \ be \ negative

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Find the solution to the following equation by transforming it into a perfect square trinomial. x2 – 10x = 39
Question number 1 is attached below.
Which inequality will have a dashed boundary line with a shaded area above its graph? 7x − y ≤ 3 x − y ≤ 4 2x − 9y > 2 4x + 7y > 3

Simplify (3+4i) +(5-2i)

Answers

first Simplify
3+4i +5−2i3 +4i+5−2i

next Gather like terms
(3+5)+(4i−2i)(3+5)+(4i−2i)

then Simplify
8+2i
(3+4i) + (5-2i)
3+4i+5-2i
8+2i

Find four consecutive integers such that twice the sum of the two greater integers exceeds three times the first by 91

Answers

Answer:

81, 82, 83, 84.

Step-by-step explanation:

Let x represent 1st integer. Then the next three consecutive integers would be x+1,x+2\text{ and }x+3.

We have been given that twice the sum of the two greater integers exceeds three times the first by 91. We can represent our given information in an equation as:

2(x+2+x+3)=3x+91

Let us solve for x.

2(2x+5)=3x+91

4x+10=3x+91

4x-3x+10=3x-3x+91

x+10=91

x+10-10=91-10

x=81

Therefore, the 1st integer would be 81.

The next three consecutive integers would be:

81+1=82\n81+2=83\n81+3=84

Therefore, our required four consecutive integers are 81, 82, 83, 84.

Final answer:

To find four consecutive integers, set up an equation using the given information and solve for x. The four consecutive integers are -86, -85, -84, and -83.

Explanation:

To find four consecutive integers, we can let the first integer be x. The next three consecutive integers would then be x+1, x+2, and x+3. According to the given condition, twice the sum of the two greater integers (x+2 + x+3 = 2x+5) exceeds three times the first integer (3x) by 91. So, we can set up the equation 2x+5 = 3x + 91 and solve for x.

Subtracting 2x from both sides yields 5 = x + 91. Subtracting 91 from both sides gives -86 = x. Therefore, the four consecutive integers are -86, -85, -84, and -83.

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in a two digit number the tens digit is 6 more than the units digit. if the digits are interchanged, the sum of the new and the original number is 132. Determine the original number.​

Answers

Given:

In a two digit number the tens digit is 6 more than the units digit.

If the digits are interchanged, the sum of the new and the original number is 132.

To find:

The original number.

Solution:

Let the unit digit of the original number be x. So, the tens digit is (x+6) and the value of the number is:

m=(x+6)* 10+x* 1

m=10x+60+x

m=11x+60

If we interchange the digits, then the value of new number is:

n=x* 10+(x+6)* 1

n=10x+x+6

n=11x+6

The sum of the new and the original number is 132.

m+n=132

11x+60+11x+6=132

22x+66=132

22x=132-66

22x=66

Divide both sides by 22.

x=(66)/(22)

x=3

So, the unit digit of the original number is 3 and the tens digit is:

x+6=3+6

x+6=9

Therefore, the original number is 39.

Find (f×g)(x) when f(x)=x^2+8x+15 and g(x)=5 over x^2-9

Answers

look at the picture......

Final answer:

To find the product of two functions, substitute the given functions into the expression and simplify.

Explanation:

To find (f×g)(x), we need to multiply the functions f(x) and g(x). First, let's substitute f(x) = x^2 + 8x + 15 and g(x) = 5/(x^2 - 9) into the expression. (f×g)(x) = (x^2 + 8x + 15) × (5/(x^2 - 9)).

Next, we simplify the expression by multiplying the numerators and denominators. (f×g)(x) = 5(x^2 + 8x + 15) / (x^2 - 9).

We can further simplify by factoring the numerator and denominator if possible. If not, we can leave the expression as is. Therefore, (f×g)(x) = 5(x + 5)(x + 3) / (x - 3)(x + 3).

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Show the check. 3B -12/3B + 12 = -2 + 1B + 6The solution to this problem is B=4
But I don’t know how to check the answer, please help and explain, PLEASE!

Answers

Answer:

i got 4

Step-by-step explanation:

thats all i could tell u i don't know how to explain it nor check it but i got 4 so thats all i can tell u bestie sorry

Which of the following is the radical expression of a to the four ninths power ?

Answers

first if a>0 sqrta=a^(1/2), and (a^p)^q=a^pxq

sqrt(a^4/9)= (a^4/9)^1/2=a^4/9x1/2=a^(2/9)
so the answer is a^(2/9)
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