Answer:
➩ 15 : 4 is the ratio
Step-by-step explanation:
Hari's marbles are = ¾ which is black in color.
And ⅕ of his marbles are green in color.
Forming in ratio :
Identify the interval(s) on which the function y = -x2 + 5x + 14 is positive.
1 answer:
Given:
To find:
The interval on which the given function is positive.
Solution:
We have,
Splitting the middle term, we get
Using zero product property, we get
-2 and 7 divide the number line is three interval.
Interval Signs of Result
(-∞,-2) (-)(-)(-) Negative
(-2,7) (-)(-)(+) Positive
(7,∞) (-)(+)(+) Negative
So, the function is positive for the interval (-2,7), i.e., -2 < x < 7.
Therefore, the correct option is D.
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Remember that the general equation of a line is 
, where:
is the slope, and 
is the y-intercept; so to find the y-intercept, solve for 
and identify .
Now, to find the x-intercept, just replace in your line equation with 
, and solve for 
Lets apply those procedures to our two questions:
1. - y-intercept:
Notice that now we have our line equation in the form with 
and 
; sine is the y-intercept, we can conclude that the y-intercept of our equation is 8.
x-intercept:
First, lets replace with :
And then, we can solve for to find our x-intercept:
We can conclude that our x-intercept is -4; thus the correct answer in your list is the fourth one: x-intercept is -4; y-intercept is 8.
2. y-intercept:
We can conclude that our y-intercept is 20.
x-intercept:
We can conclude that our x-intercept is 16; thus the correct answer in your list is, once again, the fourth one: x-intercept is 16; y-intercept is 20.
Now, to find the x-intercept, just replace
Lets apply those procedures to our two questions:
1. - y-intercept:
Notice that now we have our line equation in the form
x-intercept:
First, lets replace
And then, we can solve for
We can conclude that our x-intercept is -4; thus the correct answer in your list is the fourth one: x-intercept is -4; y-intercept is 8.
2. y-intercept:
We can conclude that our y-intercept is 20.
x-intercept:
We can conclude that our x-intercept is 16; thus the correct answer in your list is, once again, the fourth one: x-intercept is 16; y-intercept is 20.