Answer:
n > 13.7
Step-by-step explanation:
Writing a symbolic statement, we get:
n - 9.1 < 4.6
Multiplying all three terms by 10 removes fractions:
10n - 91 > 46
Adding 91 to both sides isolates the 10n term:
10n > 46 + 91, or 10n > 137
Then n > 137/10, or n > 13.7
Answer:
"between 30 yards and 150 yards"
Step-by-step explanation:
Let one side of a triangle be x and another side be y. To find the possible lengths of the third side, it is given by:
<u><em>Possible length of 3rd side would be between "x - y" and "x + y"</em></u>
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Here, given x = 90 and y = 60, so the possible length of 3rd side would be:
90 - 60 = 30,
90 + 60 = 150
Hence, in between 30 and 150
You can solve this either just plain algebra or with the use of trigonometry.
In this case, we'll just use algebra.
So, if we let M be the the point that partitions the segment into a ratio of 3:2, we have this relation:
KM/ML = 3/2
KM = 1.5 ML
We also have this:
KL = KM + ML
Substituting KM,
KL = (3/2) ML + ML
KL = 2.5 ML
Using the distance formula and the given coordinates of the K and L, we get the length of KL
KL = sqrt ( (5-(-5)^2 + (1-(-4))^2 ) = 5 sqrt(5)
Since,
KL = 2.5 ML
Substituting KL,
ML = (1/2.5) KL = (1/2.5) 5 sqrt(5) = 2 sqrt(5)
Using again the distance formula from M to L and letting (x,y) as the coordinates of the point M
ML = 2 sqrt(5) = sqrt ( (5-x)^2 + (1-y)^2 ) [let this be equation 1]
In order to solve this, we need to find an expression of y in terms of x. We can use the equation of the line KL.
The slope m is:
m = (1-(-4))/(5-(-5) = 0.5
Using the general form of the linear equation:
y = mx +b
We substitue m and the coordinate of K or L. We'll just use K.
-5 = (0.5)(-4) + b
b = -1.5
So equation of the line is
y = 0.5x - 1.5 [let this be equation 2]
Substitute equation 2 to equation 1 and solving for x, we get 2 values of x,
x=1, x=9
Since 9 does not make sense (it does not lie on the line), we choose x=1.
Using the equation of the line, we get y which is -1.
So, we get the coordinates of point M which is (1,-1)
Answer:
domain is always the x values and y values are the range of x.
It's option A
Answer:
Option B is correct
Left 1 unit.
Explanation:
According to the graph theory of transformation:
y = f(x+k)=
Given the parent function: 
and the function 
we can write it as:
g(x)= 
[ ∴
]
Therefore, vertex of the graph of the function 
is 1 units to the left of the vertex of the graph of the function .
