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user100 [1]
4 years ago
9

What is the product of the two integer values for $x$ for which $|x^2 - 16|$ is a prime number?

Mathematics
1 answer:
Nana76 [90]4 years ago
8 0

Answer:

-9

Step-by-step explanation:

x² -16 = (x -4)(x +4)

This magnitude of this product can only be prime if one of the factors is ±1. Any other integer value of x will produce a composite number (or zero).

... For x-4 = ±1, x = 3 or 5

... For x+4 = ±1, x = -3 or -5

The values of x that are ±3 both give |x²-16| = 7, a prime.

The values of x that are ±5 both give |x²-16| = 9, not a prime.

The two values of x that are of interest are x=-3 and x=3. Their product is ...

... (-3)·(3) = -9

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Given that (2,8) is on the graph of f(x),find the corresponding point for the function -3/4 f(x)
yuradex [85]

Answer:

Corresponding point to (2,8) along -3/4 f(x) = ( -1.5 , -6 )

Explanation:

 When a graph f(x) is multiplied by a factor k, the points on the graph also changes by (kx, ky).

Here it is given that (2,8) is on the graph of f(x)

Now we need to find corresponding point to (2,8) along -3/4 f(x)

x - coordinate = \frac{-3*2}{4} =-1.5

y - coordinate = \frac{-3*8}{4} =-6

So corresponding point to (2,8) along -3/4 f(x) = ( -1.5 , -6 )

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3 years ago
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Select all quantities that are proportional to the diagonal length of a square.
horsena [70]

Answer:

B. Perimeter of a square and

C. Side length of a square​

Step-by-step explanation:

if n= side length of square then

  • Area of square is n^{2}
  • Perimeter of a square is 4×n
  • diagonal length of a square is \sqrt{2} × n

Thus,

Perimeter of square can be expressed as

2\sqrt{2}×diagonal length of a square

Side length of a square can be expressed as

\frac{1}{\sqrt{2} }×diagonal length of a square

but Area of square is

\frac{1}{\sqrt{2} }×n×diagonal length of a square

As a Result,  Area of square is <em>also dependent of the value n</em>, wheras in other cases it is <em>a proportion of diagonal length of a square</em>

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3 years ago
Given that f(x)=x2-1 and g(x)=2x+8 find (g-f)(10)
irga5000 [103]

Answer:

<h2>(g-f)(10) = - 71</h2>

Step-by-step explanation:

f(x) = x² - 1

g(x) = 2x + 8

To find (g-f)(10) first find ( g - f)(x)

To find ( g - f)(x) subtract f(x) from g(x)

That's

( g - f)(x) = 2x + 8 - ( x² - 1)

Remove the bracket

( g - f)(x) = 2x + 8 - x² + 1

Simplify

( g - f)(x) = - x² + 2x + 9

To find (g-f)(10) substitute the value in the bracket that's 10 into ( g - f)(x)

That is

(g-f)(10) = -(10)² + 2(10) + 9

= - 100 + 20 + 9

= - 100 + 29

= - 71

Hope this helps you

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If the mean, median and mode of a distribution are 5, 6, 7 respectively, then the distribution is:
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<span>the distribution is 43

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