Answer:
x = - 2.5
Step-by-step explanation:
Given that the sketch represents
y = x² + bx + c
The graph crosses the y- axis at (0 , - 14), thus c = - 14
y = x² + bx - 14
Given the graph crosses the x- axis at (2, 0), then
0 = 2² + 2b - 14
0 = 4 + 2b - 14 = 2b - 10 ( add 10 to both sides )
10 = 2b ( divide both sides by 2 )
b = 5
y = x² + 5x - 14 ← represents the graph
let y = 0 , then
x² + 5x - 14 = 0 ← in standard form
(x + 7)(x - 2) = 0 ← in factored form
Equate each factor to zero and solve for x
x + 7 = 0 ⇒ x = - 7
x - 2 = 0 ⇒ x = 2
The x- intercepts are x = - 7 and x = 2
The vertex lies on the axis of symmetry which is midway between the x- intercepts, thus
the x- coordinate of the turning point is 
= 
= - 2.5
Answer:
<h2>11/19</h2>
Step-by-step explanation:
= 11/19
Answer:
A) 420 seconds = 7 minutes
B) 8 times
Step-by-step explanation:
A) After how many second would all three things happen together again?
Solution:
His clock ticked every 5 seconds , a tap was dripping every 7 seconds and his pet dog snored every 12 seconds. It all happens simultaneously = 5*7*12=420 seconds
B) How many times would all three things happen together again between midnight and one o'clock
Since all these events happen together after every 420 sec = 7 mins and there are 60 mins between midnight and 1 o'çlock , thus 60/7 = 8 times ....
Answer:
- As the slopes of both lines 'm' and 'n' are the same.
Therefore, we conclude that the equation x-2y=4 represents the equation of the line 'n' if lines m and n are parallel to each other.
Step-by-step explanation:
We know that the slope-intercept of line equation is
Where m is the slope and b is the y-intercept
Given the equation of the line m
y = 1/2x - 4
comparing with the slope-intercept form of the line equation
y = mx + b
Therefore,
The slope of line 'm' will be = 1/2
We know that parallel lines have the 'same slopes, thus the slope of the line 'n' must be also the same i.e. 1/2
Checking the equation of the line 'n'
solving for y to writing the equation in the slope-intercept form and determining the slope
Add -x to both sides.
Divide both sides by -2
comparing ith the slope-intercept form of the line equation
Thus, the slope of the line 'n' will be: 1/2
- As the slopes of both lines 'm' and 'n' are the same.
Therefore, we conclude that the equation x-2y=4 represents the equation of the line 'n' if lines m and n are parallel to each other.
Answer:
$3.60.
Step-by-step explanation:
If you want to tip 15%, then the total tip amount would be $2.40 plus half of that again ($1.20), which is $3.60.
