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Leokris [45]
3 years ago
9

What is the set of integers?

Mathematics
1 answer:
stepladder [879]3 years ago
7 0

Answer:

The set of counting numbers, their opposites, and 0 is the set of integers. Integers are counting numbers, their opposites, and zero.

Step-by-step explanation:

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Solve the following equation by completing the square. 3x^2-3x-5=13
mr Goodwill [35]

we'll start off by grouping some

\bf 3x^2-3x-5=13\implies (3x^2-3x)-5=13\implies 3(x^2-x)-5=13 \\\\\\ 3(x^2-x)=18\implies (x^2-x)=\cfrac{18}{3}\implies (x^2-x)=6\implies (x^2-x+~?^2)=6

so we have a missing guy at the end in order to get the a perfect square trinomial from that group, hmmm, what is it anyway?

well, let's recall that a perfect square trinomial is

\bf \qquad \textit{perfect square trinomial} \\\\ (a\pm b)^2\implies a^2\pm \stackrel{\stackrel{\text{\small 2}\cdot \sqrt{\textit{\small a}^2}\cdot \sqrt{\textit{\small b}^2}}{\downarrow }}{2ab} + b^2

so we know that the middle term in the trinomial, is really 2 times the other two without the exponent, well, in our case, the middle term is just "x", well is really -x, but we'll add the minus later, we only use the positive coefficient and variable, so we'll use "x" to find the last term.

\bf \stackrel{\textit{middle term}}{2(x)(?)}=\stackrel{\textit{middle term}}{x}\implies ?=\cfrac{x}{2x}\implies ?=\cfrac{1}{2}

so, there's our fellow, however, let's recall that all we're doing is borrowing from our very good friend Mr Zero, 0, so if we add (1/2)², we also have to subtract (1/2)²

\bf \left( x^2 -x +\left[ \cfrac{1}{2} \right]^2-\left[ \cfrac{1}{2} \right]^2 \right)=6\implies \left( x^2 -x +\left[ \cfrac{1}{2} \right]^2 \right)-\left[ \cfrac{1}{2} \right]^2=6 \\\\\\ \left(x-\cfrac{1}{2} \right)^2=6+\cfrac{1}{4}\implies \left(x-\cfrac{1}{2} \right)^2=\cfrac{25}{4}\implies x-\cfrac{1}{2}=\sqrt{\cfrac{25}{4}} \\\\\\ x-\cfrac{1}{2}=\cfrac{\sqrt{25}}{\sqrt{4}}\implies x-\cfrac{1}{2}=\cfrac{5}{2}\implies x=\cfrac{5}{2}+\cfrac{1}{2}\implies x=\cfrac{6}{2}\implies \boxed{x=3}

6 0
3 years ago
Which transformation of y = f(x) moves the graph 7 units to the left and 3 units down?
Svetlanka [38]

Answer:

b) y = f(x - 7) - 3

Step-by-step explanation:

it adds  if its goes to the right and subtracts if it goes to the left

And when it goes down then it will also decrease in number.

that is why b) y = f(x - 7) - 3 is the correct answer to put

8 0
2 years ago
Help help help help help
Ugo [173]

Answer:

I'm pretty sure it's c but I'm not sure

8 0
2 years ago
A. x 1 2 3 y 1 4 9 B. x 1 2 3 y 2 5 10 C. x 1 2 3 y 3 6 9 D. x 1 2 3 y 0 3 8 Which table can be represented by a line? A) B) C)
nata0808 [166]
A.)
x  y
1  1
2  4
3  9
dx=2-1→dx=1   dy=4-1→dy=3
dx=3-2→dx=1   dy=9-4→dy=5 different to 3, then this table can not be represented by a line

B.)
x  y
1  2
2  5
3  10
dx=2-1→dx=1   dy=5-2→dy=3
dx=3-2→dx=1   dy=10-5→dy=5 different to 3, then this table can not be represented by a line

C.)
x  y
1  3
2  6
3  9
dx=2-1→dx=1   dy=6-3→dy=3
dx=3-2→dx=1   dy=9-6→dy=3, then this table can be represented by a line

D.)
x  y
1  0
2  3
3  8
dx=2-1→dx=1   dy=3-0→dy=3
dx=3-2→dx=1   dy=8-3→dy=5 different to 3, then this table can not be represented by a line

Answer: Option C. x 1 2 3 y 3 6 9
6 0
3 years ago
The probability that you roll a two on a six-sided die is 1/6 If you roll the die 60 times, how many twos can you expect to roll
steposvetlana [31]
Roughly 1/6 x 60 so 10 on average
8 0
3 years ago
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