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3 years ago

What rules change the input numbers to output numbers

Mathematics

2 answers:

barxatty [35]3 years ago

8 0

2x-10 is the answer b

klio [65]3 years ago

6 0

The answer to that is 2x - 10

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What are the solutions to the equation (x + 2)^2 = 49?

Mekhanik [1.2K]

Answer:

X= 5, -9

Step-by-step explanation:

(X+2)² =49

Expand the bracket,

 (X+2) (X+2)= 49

Apply the distributive property;

X(X+2) +2 (X+2) =49

X²+2X+2X+4=49

X²+4X+4=49

Move 49 to the left side of the equation;

X²+4X+4-49=0

X²+4X-45=0

Apply Factorisation method;

Consider the form

a²+bx+c=0

Find two numbers whose sum is equal to b and whose product is equal to c. Comparing with our equation;

B =4 and C =45

We can use 9 and -5, this is because ;

9+(-5)=4 and 9*(-5)= 45.

Replace X +4X-45=0 with (X-5) (X+9)=0

Therefore;

X-5=0

X+9=0

Moving to the left side of the equation;

Therefore X= 5 and -9

8 0

3 years ago

Read 2 more answers

2. The functions ???? and ???? represent the population of two different kinds of bacteria, where x is the time (in hours) and ?

klio [65]

Answer:

(a) Bacterial 1 had a faster rate of growth.

(b) The population of f(x) always exceed the population of g(x). In other words, population of g(x) cannot exceed the population of f(x).

Step-by-step explanation:

Consider the given functions are

$f(x)=2x^2+7$

$g(x)=2x$

where, x is the time (in hours) and f(x) and g(x) are the number of bacteria (in thousands).

(a)

The rate of change of a function f(x) on [a,b] is

$m=\frac{f(b)-f(a)}{b-a}$

Rate of change between third and sixth hour of first function is

$m_1=\frac{f(6)-f(3)}{6-3}$

$m_1=\frac{(2(6)^2+7)-(2(3)^2+7)}{6-3}$

$m_1=\frac{79-25}{3}$

$m_1=\frac{54}{3}$

$m_1=18$

Rate of change between third and sixth hour of second function is

$m_2=\frac{g(6)-g(3)}{6-3}$

$m_2=\frac{2(6)-2(3)}{6-3}$

$m_2=\frac{12-6}{3}$

$m_2=\frac{6}{3}$

$m_2=2$

Since $m_1>m_2$ , therefore bacterial 1 had a faster rate of growth.

(b)

The initial population of f(x) is 7 and it increases exponentially.

The initial population of g(x) is 0 and it increases linearly.

It means population of f(x) always exceed the population of g(x).

In other words, population of g(x) cannot exceed the population of f(x).

8 0

3 years ago

Ben earns $750 a month plus 4% commission on all his sales over $900. Find the minimum sales that will allow Ben to earn at leas

e-lub [12.9K]

$750 + s x 4% = $2,500 | - $750

s x 4% = $1,750 | : 4%

s = $43.750

4 0

3 years ago

What is y= -x^2-2x+3 in vertex form

IgorC [24]

y = -x² - 2x + 3
  y - 3 = -x² - 2x + 3 - 3
  y - 3 = -x² - 2x
y - 3 - 1 = -x² - 2x - 1
  y - 4 = -(x²) - (2x) - (1)
  y - 4 = -(x² + 2x + 1)
  y - 4 = -(x² + x + x + 1)
  y - 4 = -(x(x) + x(1) + 1(x) + 1(1))
  y - 4 = -(x(x + 1) + 1(x + 1))
  y - 4 = -(x + 1)(x + 1)
  y - 4 = -(x + 1)²
y - 4 + 4 = -(x + 1)² + 4
y = -(x + 1)² + 4

6 0

3 years ago

Solve: 9^(2x + 1) = 9^(3x – 2)

Stella [2.4K]

Answer:

Step-by-step explanation:

The same bases (9) needs the same exponents to be equal:

$\big9^{2x + 1}=\big9^{3x-2}\quad\iff\quad 2x+1=3x-2\\\\2x+1=3x-2\\\\2x-3x=-2-1\\\\-x=-3\\\\x=3$

5 0

3 years ago