If n and t are positive integers, what is the greatest prime factor of the product nt ?

Answers

Answer 1

Answer: Positive turn in too a negative

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You add two numbers together, and the total is 122. If you triple the smaller number and subtract 34, it will equal the larger number. What are the two numbers?

Answers

Answer: 39 and 83

Step-by-step explanation:

Let's assume the smaller number is represented by 'x' and the larger number is represented by 'y'.

According to the given information, we have two equations:

Equation 1: x + y = 122

Equation 2: 3x - 34 = y

We can solve this system of equations to find the values of 'x' and 'y'.

Substituting Equation 2 into Equation 1, we get:

x + (3x - 34) = 122

Combining like terms:

4x - 34 = 122

Adding 34 to both sides:

4x = 122 + 34

4x = 156

Dividing both sides by 4:

x = 39

Substituting the value of 'x' back into Equation 1:

39 + y = 122

Subtracting 39 from both sides:

y = 122 - 39

y = 83

Therefore, the smaller number is 39 and the larger number is 83.

Which of the the following could be the ratio between the lengths of the two legs of a 30-60-90?Check all that apply. (A)Sqrt2:Sqrt3 (B)1:Sqrt2 (c)Sqrt2:Sqrt2 (D)2Sqrt3:Sqrt6 (E)1:Sqrt3 (F)Sqrt3:Sqrt3

Answers

This is worth remembering:

In a 30-60-right triangle,
-- the side opposite the 30 is 1/2 the hypotenuse
-- the side opposite the 60 is (1/2 the hypotenuse) times (square root of 3).

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I believe Choice-'E' is the only one you could make with the above rule.

$(a)/(a √(3) ) = (1)/( √(3) ) \ \ \ \Rightarrow\ \ \ Ans.\ E\n\n(2a)/(a √(3) ) = (2)/( √(3) )=(2\cdot √(2) )/( √(3)\cdot √(2) )=(2 √(2) )/( √(6) ) \neq (2 √(3) )/( √(6) ) \n\n (a)/(2a ) = (1)/( 2 )$

Suppose a parabola has vertex (–4, 7) and also passes through the point (–3, 8). Write the equation of the parabola in vertex form.

Answers

The equation for a parabola can also be written in the "vertex form":
$y = a (x-h) ^ 2 + k$
Where,
the vertex of the parabola is the point (h, k).
The value of a is the term that accompanies x ^ 2
Substituting values we have:
$y = a (x - (- 4)) ^ 2 + 7$
Rewriting we have:
$y = a (x + 4) ^ 2 + 7$
For the point (-3, 8) we have:
$8 = a (-3 + 4) ^ 2 + 7$
From here, we clear the value of a:
$8 = a (1) ^ 2 + 7 8 = a + 7 a = 8 - 7 a = 1$
Then, the equation is given by:
$y = (x + 4) ^ 2 + 7$
Answer:
The equation of the parabola in vertex form is:
$y = (x + 4) ^ 2 + 7$

y=a(x-h)^2 +k
in the vertex (h, k) given that vertex (-4, 7)
we get y=(x-(-4))^2 +7
y=(x+4)^2 +7
hope it helps

Which of the following is a polynomial with roots 4, –2i, and 2i ?

Answers

(x - 4)(x + 2i)(x - 2i) = 0
x(x^2 + 4) - 4(x^2 + 4) = 0
x^3 + 4x - 4x^2 - 16 = 0
x^3 - 4x^2 + 4x - 16 = 0

Use the percent proportion to find each
10. 25 is what percent of 125?

Answers

25/125 x 100% = 20%.

Twice a certain number is 44. What is the number?
equation:
n=

Answers

2n = 44
n = 22 (Divide by 2)

Hope I helped.

equation: n = 2n = 44
To work this out, do the opposite of multiplication on both sides of the equation.
This means:
2n/2 = 44/2

^ a rule is, what you do to one side, you must do to the other.

This leaves you with n = 22.

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