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Dennis_Churaev [7]
2 years ago
14

Which value of a would make the following expression completely factored?

Mathematics
1 answer:
ehidna [41]2 years ago
7 0

Answer:

12

Step-by-step explanation:

x^2 - a

If a is a perfect square we could factor

x^2 - b^2 = (x-b)(x+b)

So a cannot be 36,49,81 since they are perfect squares

a must be 12

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PLEASE HELP!!
Dima020 [189]

Answer:

A. 90°+m∠4

Step-by-step explanation:

Also  

∠ A + ∠ C = 180  o = ∠ B + ∠ D

⇒ 2 x+ ( 3 x − 5 ) = 180  0 = ( x + 5 ) +  ∠  C

5 x  −  5  =  180

Add 5 to both sides

5 x  =  185

Divide both sides by 5

x =  185  5  =  37

But it was A. 90°+m∠4

4 0
2 years ago
Which will result in a perfect square trinomial?
nikitadnepr [17]

Answer:

The first one

Step-by-step explanation:

For the first choice, the binomial is multiplied by itself, so it will result in a perfect square trinomial.

4 0
3 years ago
Peter went to his local zoo where 50% of its exhibits featured lions. If the zoo features 24 exhibits in total, then how many of
Sauron [17]
12 exhibits featured lions since half of 24 is 12.
3 0
3 years ago
Read 2 more answers
Ex 7) Imagine a mile-long bar of metal such as the rail along railroad tracks. Suppose that the rail is anchored on both ends an
Fantom [35]

9514 1404 393

Answer:

  about 44.5 feet

Step-by-step explanation:

We can write relations for the height of the rail as a function of initial length and expanded length, but the solution cannot be found algebraically. A graphical solution or iterative solution is possible.

Referring to the figure in the second attachment, we can write a relation between the angle value α and the height of the circular arc as ...

  h = c·tan(α) . . . . . . where c = half the initial rail length

Then the length of the expanded rail is ...

  s = r(2α) = (c/sin(2α)(2α) . . . . . . where s = half the expanded rail length

Rearranging this last equation, we have ...

  sin(2α)/(2α) = c/s

It is this equation that must be solved iteratively. We find the solution to be ...

  α ≈ 0.0168538794049 radians

So, the height of the circular arc is ...

  h = 2640.5·tan(0.0168538794049) ≈ 44.4984550191 . . . feet

The rail will bow upward by about 44.5 feet.

_____

<em>Additional comments</em>

Note that s and c in the diagram are half the lengths of the arc and the chord, respectively. The ratio of half-lengths is the same as the ratio of full lengths: c/s = 2640/2640.5 = 5280/5281.

We don't know the precise shape the arc will take, but we suspect is is not a circular arc. It seems likely to be a catenary, or something similar.

__

We used Newton's method iteration to refine the estimate of the angle from that shown on the graph. The iterator used is x' = x -f(x)/f'(x), where x' is the next guess based on the previous guess of x. Only a few iterations are required obtain an angle value to full calculator precision.

3 0
3 years ago
Determine if line AB and line CD are parallel, perpendicular, or neither.
choli [55]

Answer:

AB and CD are parallel lines

Step-by-step explanation:

• Parallel lines have equal slopes

• The slopes of perpendicular lines are negative reciprocals

Calculate the slope m using the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

let (x₁, y₁ ) = A(1, 4) and (x₂, y₂ ) = B(3, 8)

m = \frac{8-4}{3-1} = \frac{4}{2} = 2

let (x₁, y₁ ) = C(- 1, 6) and (x₂, y₂ ) = D(3, 14)

m = \frac{14-6}{3+1} = \frac{8}{4} = 2

Since slope of AB and CD are equal then lines are parallel


3 0
3 years ago
Read 2 more answers
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