Which of the following is the y-intercept of the line with the equation 2y=6x+4

vodka [1.7K]

$\dfrac{2}{3}[(5+3)^{-3}]=\dfrac{2}{3}(8)^{-3}\\\\\text{use}\ a^{-n}=\dfrac{1}{a^n}\\\\=\dfrac{2}{3}\cdot\dfrac{1}{8^3}=\dfrac{2}{3\cdot512}=\dfrac{1}{3\cdot256}=\dfrac{1}{768}$

7 0

3 years ago

For the given table of values for a polynomial function, where must the zeros of the function lie?

Jet001 [13]

Answer:

A. Between 3.0 and 3.5 and between 4.0 and 4.5

Step-by-step explanation:

The zeroes of a function occur whenever a value of x returns zero. To predict where the zeroes lie, determine the interval(s) where the function crosses the x-axis. This occurs when either $f(x)$ goes from a negative value to a positive value or vice versa.

From $x=3.0$ and $x=3.5$ , the y-values go from 4.0 (positive) to -0.2 (negative), respectively. Therefore, there must be a zero in this interval.

From $x=4.0$ and $x=4.5$ , the y-values go from -0.8 (negative) to 0.1 (positive), respectively. Therefore, there must also be a zero in this interval.

Thus, the zeros of this function occur between 3.0 and 3.5 and between 4.0 and 4.5, leading to answer choice A.

7 0

2 years ago

Jane needs open-topped boxes to store her excess inventory at year's end. She purchases large

Debora [2.8K]

Answer:

x = 1,6 in ( the side of the corner squares )

V(max) = 67,58 in³

Step-by-step explanation:

The cardboard is:

L = 12 in w = 8 in

Let´s call "x" the side of the square from the corner:

Then the sides of the base of the open box are:

( L - 2*x ) and ( w - 2*x ) and x is the height

( 12 - 2*x ) and ( w - 2*x )

V(ob) = (L - 2*x ) * ( - 2*x ) * x

Wich is a function of x

V(x) = [( 12 - 2*x ) * ( 8 - 2*x ) ]*x

V(x) = ( 96 - 24*x - 16*x + 4*x²) * x

V(x) = 96*x - 40*x² + 4*x³

Tacking derivatives on both sides of the equation

V´(x) = 12*x² - 80*x + 96

V´(x) = 0 12*x² - 80*x + 96 = 0

Solving for x

x₁,₂ = 80 ± √ 6400 - 4608 / 24

x₁,₂ = 80 ± 42,33 / 24

x₁ = 5,10 We dismiss this solution since 2*x becomes 2*5,10 = 10,20

ant this value is bigger than 8 inches

x₂ = 1,60 in

Therefore dimensions of the box

a = 12 - 2*x ; a = 12 - 3,20 ; a = 8,8 in

b = 8 - 2*x ; b = 8 - 3,20 ; b = 4,80 in

And the volume of the open box is:

V(max) = 8,8*4,8*1,6

V(max) = 67,58 in³

How do we Know that is the maximun value for V?

We find V´´(x) = 24*x - 80 for x = 1,6 is negative ( V´´(x) = - 41,6 therefore V (x) has a local maximun for a value of x = 1,6

3 0

3 years ago

Graph h(x)=0.5(x+2)^2 -4 by following these steps:

Goshia [24]

Answer:

Step 1: Identify a, h, and k.

a=0.5, h= -2, k= -4

Step 3: The axis of symmetry is the line x= -2

Step 4: h(-4)= -2 h(-6)= 4

The graph should have points plotted at (-6, 4), (-4, -2), (-2, -4), (0, -2), and (2, 4)

Step-by-step explanation: The answers were already there, just here to repeat for others who are confused.

4 0

3 years ago

Pls help<br> First, correct answer will get brainliest

kozerog [31]

Answer:

A for the first one.

Second one, I'm not sure, but I'd guess it'd be A

Step-by-step explanation:

7 0

3 years ago