Convert 5.4 ⋅ 103 to standard form. 0.0054 0.00054 5,400 54,000

Let $f(x) = 12x^9 + x$. Find $f(3) + f(-3)$.

BlackZzzverrR [31]

Answer:

Ok, here goes: f(3) means take f(x) and plug in 3 wherever we see x. So

f(3) = 12*39 + 3 = 236196 + 3

f(3) = 236199

Likewise, f(-3) means take f(x) and plug in (-3) wherever we see x. So

f(-3) = 12*(-3)9 + (-3) = -236196 - 3

f(-3) = -236199

Putting those two things together, we get

f(3) + f(-3) = 236199 - 236199 = 0

Step-by-step explanation:

7 0

1 year ago

Write an equation of a parabola that passes through (3,-30) and has x-intercepts of -2 and 18. Then find the average rate of cha

Nookie1986 [14]

Answer:

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ . The average rate of change of the parabola is -4.

Step-by-step explanation:

We must remember that a parabola is represented by a quadratic function, which can be formed by knowing three different points. A quadratic function is standard form is represented by:

$y = a\cdot x^{2}+b\cdot x + c$

Where:

$x$ - Independent variable, dimensionless.

$y$ - Dependent variable, dimensionless.

$a$ , $b$ , $c$ - Coefficients, dimensionless.

If we know that $(3, -30)$ , $(-2, 0)$ and $(18, 0)$ are part of the parabola, the following linear system of equations is formed:

$9\cdot a +3\cdot b + c = -30$

$4\cdot a -2\cdot b +c = 0$

$324\cdot a +18\cdot b + c = 0$

This system can be solved both by algebraic means (substitution, elimination, equalization, determinant) and by numerical methods. The solution of the linear system is:

$a = \frac{2}{5}$ , $b = -\frac{32}{5}$ , $c = -\frac{72}{5}$ .

The equation of the parabola is $y = \frac{2}{5}\cdot x^{2}-\frac{32}{5}\cdot x -\frac{72}{5}$ .

Now, we calculate the average rate of change ( $r$ ), dimensionless, between $x = -2$ and $x = 8$ by using the formula of secant line slope:

$r = \frac{y(8)-y(-2)}{8-(-2)}$

$r = \frac{y(8)-y(-2)}{10}$

$x = -2$

$y = \frac{2}{5}\cdot (-2)^{2}-\frac{32}{5}\cdot (-2)-\frac{72}{5}$

$y(-2) = 0$

$x = 8$

$y = \frac{2}{5}\cdot (8)^{2}-\frac{32}{5}\cdot (8)-\frac{72}{5}$

$y(8) = -40$

$r = \frac{-40-0}{10}$

$r = -4$

The average rate of change of the parabola is -4.

3 0

2 years ago

A rectangle has an area of 99 square in. What is the length of the long side?

OLga [1]

Answer:

The longer length is either 99, 33 or 11 inches

Step-by-step explanation:

Given

$Area = 99$

Required

The length of the longer side

Area of a rectangle is:

$Area = Length * Width$

List out all possible products that give 99 [Assume the dimension are whole numbers]

$Length * Width = 99 * 1 = 99$

$Length * Width = 33 * 3 = 99$

$Length * Width = 11 * 9 = 99$

List out the longer factors

$L = \{99, 33, 11\}$

<em>Hence, the longer length is either 99, 33 or 11 inches</em>

8 0

3 years ago

F left parenthesis x right parenthesis equals 9 x cubed plus 2 x squared minus 5 x plus 4 and g left parenthesis x right parenth

Jet001 [13]

The answer is 2x(2x²+x+1).

When we subtract polynomials we combine like terms:
(9x³+2x²-5x+4)-(5x³-7x+4)

9x³-5x³=4x³
2x²- 0 = 2x²
-5x--7x=-5x+7x=2x
4-4=0

This gives us
4x³+2x²+2x

Each of these is divisible by 2, and each has an x, so we factor those out:
2x( )

4x³/2x = 2x²:
2x(2x² )

2x²/2x=x:
2x(2x²+x )

2x/2x = 1:
2x(2x²+x+1)

3 0

3 years ago

Please help me I’ll mark you as brainliest! Answer quickly pleaseee

Scrat [10]

Answer:

i need the triangle

Step-by-step explanation:

the question is incomplete... show the diagram of the triangle

we can't solve without that

5 0

2 years ago