Answer:
D. Y+5=-(1/2)*(x+3)
Step-by-step explanation:
Perpendicular Lines are those with the following condition:
y=a*x+b (1)
y=c*x+d (2)
Where 'a' and 'c' are the respective slope
If These two lines are perpendicular, then
a=- 1/c
Equation (1) for our case is written as y=2x-8, meaning that a=2 and b = -8
Using those principles we have that the slope for our needed line ('c') has to be -(1/2).
Now we most use the given point to find the remaining term of the equation (d) so, evaluate (-3,-5) in eq (2) to have this:
-5=(-1/2)*(-3)+d
resulting that d=-5-(3/2)
Eq (2) is written now as the following: y= (-1/2)*x - (5+3/2)
Rearranging terms, we have the following:
y+5=(-1/2)*x-(3/2)
where you can obtain a more pretty expression:
y+5=(-1/2)*(x+3)
Answer:
B. (-0.73, 0), (2.73, 0)
Step-by-step explanation:
vertex form of a parabola
y = a(x-h)^2 +k
y = a(x-1)^2 -9
substitute the point in to find a
-6 = a (0-1) ^2 -9
-6 = a *1 -9
add 9 to each side
-6+9 = a -9+9
3 =a
y = 3(x-1)^2 -9
FOIL
y = 3(x-1)(x-1) -9
y = 3(x^2-2x+1) -9
distribute
y = 3x^2-6x+3-9
combine like terms
y = 3x^2 -6x -6
factor out 3
y= 3(x^2 - 2x -2)
set = 0
0 = 3(x^2 - 2x -2)
x^2 - 2x -2 =0
using the quadratic formula
-b±sqrt(b^2 -4ac)
----------------------
2a
-(-2) ± sqrt(2^2 - 4(1)(-2))
-------------------------------
2(1)
2 ± sqrt(4+8)
------------------
2
2±sqrt(12)
---------------
2
2±2sqrt(3)
----------------
2
1±sqrt(3)
roots: 2.73, and -.73
★ Sigma Operator ★
Option C is the correct answer of the above summation series
Description -
Upper limit of sigma - ∞ [ where to stop ]
Lower Limit - 10 [ Where to start ]
Argument = n²
Hence we'll obtain - 100 + 121 + ... ∞
Answer:
The 80% confidence level estimate for how much a typical parent would spend on their child's birthday gift is between $33.954 and $35.246.
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution should be used to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 28 - 1 = 27
80% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 27 degrees of freedom(y-axis) and a confidence level of
. So we have T = 1.314
The margin of error is:

In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 34.6 - 0.646 = $33.954
The upper end of the interval is the sample mean added to M. So it is 34.6 + 0.646 = $35.246
The 80% confidence level estimate for how much a typical parent would spend on their child's birthday gift is between $33.954 and $35.246.