Answer:
I believe its (- 2, 2 )
Step-by-step explanation:
Assuming the dilatation is centred at the origin, then multiply the coordinates of B by the scale factor 2, that is
B(- 1, 1 ) → B'(2(- 1), 2(1) ) → B'(- 2, 2 )
7) Certainly there is a typo in the statement, just see that the expression of item (ii) is different from that of item (i). Probably the correct expression is:
. With this consideration, we can continue.
(i) Let E the expression that we are analyzing:
Since (x-1)² is a perfect square, it is a positive number. So, E is a result of a sum of two positive numbers, 2(x-1)² and 3. Hence, E is a positive number, too.
(ii) Manipulating the expression:
So, it's the case when E=0. However, E is always a positive number. Then, there is no real number x that satisfies the expression.
8) Let E the expression that we want to calculate:
Multiplying by (2-1) in the both sides:
Repeating the process, we obtain:
Answer:
SITE A
Step-by-step explanation:
Given :
proposed-site Area-Served
1 2 3 4
A 5.2 4.4 3.6 6.5
B 6.0 7.4 3.4 4.0
C 5.8 5.9 5.9 5.8
D 4.3 4.8 6.5 5.1
Area 1 2 3 4
Number-runs 150 65 175 92
Computing the weighted average for the 4 sites :
Site A:
((150*5.2) + (65*4.4) + (175*3.6) + (92*6.5)) / (150 + 65 + 175 + 92)
= 2294 / 482
= 4.7593
Site B:
((150*6.0) + (65*7.4) + (175*3.4) + (92*4.0)) / (150 + 65 + 175 + 92)
= 2344/ 482
= 4.863
Site C:
((150*5.8) + (65*5.9) + (175*5.9) + (92*5.8)) / (150 + 65 + 175 + 92)
= 2819.6/ 482
= 5.850
Site D:
((150*4.3) + (65*4.8) + (175*6.5) + (92*5.1)) / (150 + 65 + 175 + 92)
= 2563.7/ 482
= 5.319
From the weighted average response time computed for the different sites ;
The best location for the emergency facility would be one with the least average response time; which is SITE A.
Y = x - 28/5. The slope here is 1. A perpendicular line will have a negative reciprocal slope. So our perpendicular line will have a slope of -1.
slope = (y2 - y1) / (x2 - x1)
(k,2)....x1 = k and y1 = 2
(7,0)...x2 = 7 and y2 = 0
sub
slope = (0 - 2) / (7 - k)
slope = -2 / ?......now if we want the slope to be -1..that means the number where the question mark is has to be 2....for that to happen, k has to be 5...because 7 - 5 = 2.
so ur answer is : k = 5
Smaller Angle: 49 degrees
Bigger Angle: 131 degrees
Note that supplementary angles add up to be 180 degrees. Knowing this and the information provided in the question, we can use the following system of equations:
x + y = 180 (showing they both add up to 180)
x + 82 = y (to show one angle is 82 more than the other)
We can use the substitution method to solve. Since the second equation ends in "= y" we can substitute the value of it into y for the first equation.
x + y = 180; x + 82 = y ==> x + (x + 82) = 180
And now, solve for x:
x + (x + 82) = 180
x + x + 82 = 180 > combine like terms
2x + 82 = 180
2x = 98
x = 49
So now we have the value for one of the angles! Remembering that the other angle is 82 degrees bigger, dd 49 + 82, which equals 131.
So, our two angle values are 131 and 49! This is correct since both angle measures add up to be 180, which also makes them supplementary!
