There are many systems of equation that will satisfy the requirement for Part A.
an example is y≤(1/4)x-3 and y≥(-1/2)x-6
y≥(-1/2)x-6 goes through the point (0,-6) and (-2, -5), the shaded area is above the line. all the points fall in the shaded area, but
y≤(1/4)x-3 goes through the points (0,-3) and (4,-2), the shaded area is below the line, only A and E are in the shaded area.
only A and E satisfy both inequality, in the overlapping shaded area.
Part B. to verify, put the coordinates of A (-3,-4) and E(5,-4) in both inequalities to see if they will make the inequalities true.
for y≤(1/4)x-3: -4≤(1/4)(-3)-3
-4≤-3&3/4 This is valid.
For y≥(-1/2)x-6: -4≥(-1/2)(-3)-6
-4≥-4&1/3 this is valid as well. So Yes, A satisfies both inequalities.
Do the same for point E (5,-4)
Part C: the line y<-2x+4 is a dotted line going through (0,4) and (-2,0)
the shaded area is below the line
farms A, B, and D are in this shaded area.
Answer:
(x+3)m
Step-by-step explanation:
Area of a rectangle = Length × width
Given the area = (x²-9)m²
Width = (x-3)m
Length of the rectangle = Area/Width
Length of the rectangle = x²-9/x-3
= x²-3²/x-3
Note that according to different of two square, a²-b² = (a+b)(a-b)
Therefore x²-3² = (x+3)(x-3)
Length of the rectangle
= (x+3)(x-3)/x-3
= x+3
The length of the rectangle is (x+3)m
This is done by solving the question using the linear equation. If x=0 then y = -43,886 udring the year 1900. If x=88, then y=1698. The difference between the observed value and tthe predicted value at the value of x is 42,188.
It gives you the y-intercept in the question: (0,1)
Use (y2-y1)/(x2-x1) to find the slope:
= (1-7) / (0-2)
= -6 / -2
= 3
Your answer is y=3x+1
Answer:
the number of circles is 3
the number of square is 9
the number of triangle is 10
Step-by-step explanation:
Let the number of square = s
let the number of circle = c
let the number of triangle = t
let the total number of the shapes = y
15 < y < 25
y = s + c + t ---- (i)
s = c + 6 ------ (ii)
c + 7 = t ------ (iii)
y = (s) + (c) + (t)
y = (c + 6) + (c) + (c + 7)
y = 3c + 13
15 < y < 25
15 < 3c + 13 < 25
15 - 13 < 3c < 25 -13
2 < 3c < 12
2/3 < c < 12/3
0.67 < c < 4
Thus, number of circle is greater 1 but less than 4
c = 3
s = 3 + 6 = 9
t = 3 + 7 = 10
