Long Questions

What is the y-intercept, axis of symmetry and vertex of the following function.

Pepsi [2]

Complete the square:

F(x) = -3x² - 6x - 5

F(x) = -3 (x² + 2x) - 5

F(x) = -3 (x² + 2x + 1 - 1) - 5

F(x) = -3 ((x + 1)² - 1) - 5

F(x) = -3 (x + 1)² + 3 - 5

F(x) = -3 (x + 1)² - 2

The y-intercept has x-coordinate equal to 0, so it corresponds to the value of F(0) :

F(0) = -3 (0 + 1)² - 2 = -3 - 2 = -5

The axis of symmetry is the vertical line running through the vertex of this parabola, so we'll come back to this.

The vertex of the parabola is (-1, -2). This represents the maximum value of F(x), which follows from

(x + 1)² ≥ 0 ⇒ -3 (x + 1)² ≤ 0 ⇒ -3 (x + 1)² - 2 ≤ -2

This is to say, every point on the parabola has a y-coordinate no greater than -2.

As mentioned earlier, the axis of symmetry is the vertical line through the vertex, and its equation is determined by the x-coordinate of the vertex. Hence the AoS is the line x = -1.

4 0

2 years ago

Read 2 more answers

Brandon rode in a taxi that charges a flat fee of $2.25 and an additional $0.40 per mile of his trip. If he paid $6.80 for the c

r-ruslan [8.4K]

Answer:

11 $\frac{3}{8}$ miles.

Step-by-step explanation:

To find how many miles Brandon rode, we can create an equation in slope-intercept form: y = mx + b

$2.25 is the flat fee, or the unchanging variable. This is our y-intercept, or b.

$0.40 is the changing variable, as it changes value depending on the amount of miles ridden. This is our slope, or m.

We know Brandon spent $6.80 on the cab ride. So, this is our y.

We get the equation: 6.80 = 0.40x + 2.25.

To solve, first subtract 2.25 from both sides of the equation:

6.80 - 2.25 = 0.40x + 2.25 - 2.25

We get: 4.55 = 0.40x

Now, just divide by 0.40 on both sides:

4.55 ÷ 0.40 = 0.40x ÷ 0.40

We get: 11.375 = x

So, Brandon rode for 11.375 miles. When converted to a mixed number, we get 11 $\frac{3}{8}$ .

<em>I would appreciate brainliest, if not that's ok!</em>

6 0

3 years ago

WHAT IS EQUIVALENT TO THE INEQUALITY y/2 -6 <8 ? PLEASE HURRY ITS DUE 10:50

Oksanka [162]

Y/2 - 6 < 8
y/2 < 14
y < 7

6 0

3 years ago

Read 2 more answers

A used car was purchased in July 1999 for $11,900. If the car depreciates 13% of it's value each year, what is the value of the

trapecia [35]

1999 price = 11900
it depreciates 13%
$\frac{13}{100} \times 11900 = 1547$
year 2000 cost = 11900 - 1547 = 10353
it depreciates 13%
$\frac{13}{100} \times 10353 = 1345.89$
year 2001 cost = 10353 - 1345.89 = 9007.11
it depreciates 13%
$\frac{13}{100} \times 9007.11 = 1170.92$
year 2002 cost = 9007.11 - 1170.92 = 7836.19
pls mark as brainliest

8 0

3 years ago

Evaluate the surface integral. s y ds, s is the helicoid with vector equation r(u, v) = u cos(v), u sin(v), v , 0 ≤ u ≤ 6, 0 ≤ v

Juliette [100K]

Compute the surface element:

$\mathrm dS=\|\vec r_u\times\vec r_v\|\,\mathrm du\,\mathrm dv$