Answer:
B.
Step-by-step explanation:
a function is continuous, if the functional values are the same at the "connection" points of the various segments (and the segments themselves are continuous).
"continuous" simply means that the graph of the function is a continuous line without any "rips". it can have corners and such, but no "interruptions".
specifically it means : for every possible y value in the defined range of the function there is an x value that causes this y.
all defined segments are continuous functions.
so, let's look at
A. the first connection point is x=-2.
-2 + 6 = 0.5×(-2)²
4 = 0.5×4 = 2
4 = 2 is wrong. => here, at this point, the function "rips" apart and is not continuous.
B. x=-2
-2 + 4 = 0.5×(-2)²
2 = 2 is correct. continuous at this point.
second connection point x=4
0.5×4² = 20 - 3×4
0.5×16 = 20 - 12
8 = 8 is correct. continuous at this point
C. x=-2
-2 - 2 = 0.5×(-2)²
-4 = 2 is wrong. not continuous
D. x=-2
-2 + 4 = 0.5×(-2)²
2 = 2 is correct. continuous here.
now for x=4
4 + 4 = 25 - 3×4
8 = 25 - 12 = 13
8 = 13 is wrong. not continuous.
Answer:
A=4, B=3, C=2, D=7 or A=2, B=7, C=4, D=3
Step-by-step explanation:
To factor this, you are looking for factors of 8×21 = 168 that have a sum of 34.
168 = 1×168 = 2×84 = 3×56 = 4×42 = 6×28 = 7×24 = 8×21 = 12×14
The sums of these factor pairs are 169, 86, 59, 46, 34, 31, 29, 26. The factor pair whose sum is 34 is 6×28. This means we can rewrite the expression as ...
8x² +28x +6x +21
Factoring by pairs gives ...
4x(2x +7) +3(2x +7)
(4x +3)(2x +7) ⇒ A=4, B=3, C=2, D=7 or A=2, B=7, C=4, D=3
Answer:
31.6 feet by 15.8 feet.
Step-by-step explanation:
Area of a Rectangle = Length X Breadth = LB
The area of the playground is to be 500 square feet
Therefore:
LB=500
Perimeter of the Rectangle = 2(L+B)
The Chain link fence that costs $2 per linear foot on three sides and a fancier wooden fence that costs $6 per linear foot on the fourth side.
Cost = ${2(L+2B)+6L}=2L+4B+6L=8L+4B
Cost= $(8L+4B)
From: LB=500, B=500/L
Substitute B into 8L+4B
C(L) =
C(L)=
The minimum cost of the fencing occurs when the dimensions are minimum.
If we take the derivative of C(L)
At
Recall: B=500/L
The dimensions that minimizes the total cost of the fencing are 31.6 feet by 15.8 feet.
Answer:
both angles are 92 degrees
Step-by-step explanation:
88+c=180
c=92
c and b are vertical angles and all vertical angles are equal