Answer:
AC = 6.05 cm
Step-by-step explanation:
We can draw two different trapeziums with the information given.
The possible drawings of the trapezium ABCD are in the image attached.
In both trapeziums, the length of AC is the same, and we can calculate this length using the law of cosines in the triangle ABC:
AC^2 = AB^2 + BC^2 - 2 * AB * BC * cos(B)
AC^2 = 4.8^2 + 6.8^2 - 2 * 4.8 * 6.8 * cos(60)
AC^2 = 23.04 + 46.24 - 65.28 * 0.5
AC^2 = 36.64
AC = 6.05 cm
Answer:
a = 5
Remainder when p(x) is divided by x+2 = 62
Step-by-step explanation:
Given:
P(x) = x⁴-2x³+3x²-ax+3a-7
When x+1 divides the polynomial p(x) the ramainder is 19.
Applying remainder theorem,
x = -1
p(-1) = 19
Substitute the x = -1 into the polynomial expression
p(-1) = (-1)⁴-2(-1)³+3(-1)²-a(-1)+3a-7 = 19
1+2+3+a+3a-7 = 19
6-7+4a = 19
4a-1 = 19
4a = 19+1
4a = 20
a = 20/4
a = 5.
Hence, a = 5
p(x) = x⁴-2x³+3x²-5x+8
If p(x) is divided by x+2,
Then the remainder is p(-2)
p(-2) = (-2)⁴-2(-2)³+3(-2)²-5(-2)+8
p(-2) = 16+16+12+10+8
p(-2) = 62
Hence the remaider when p(x) is divided by x+2 is 62
IF:
|1/2.x -2/3.y = 7 and
|a.x - 8.y = -1
have no solution, that means these 2 linear equations ARE PARALLEL (since they can never meet). Reminder: 2 equations are parallel if they have the same coefficient , so let write each of the equation in the normal form:
a)1/2.x -2/3.y = 7→ -2/3.y = -1/2.x + 7 → y = 3/4.x - 21/2
b) a.x - 8.y = -1 → - 8.y = -a.x - 1 → y= a/8.x + 1
a) and b) are // if (3/4) = (a/8), [the 2 coefficient OR the 2 slopes)
a/8 = 3/4 → a = 24/4 and a = 6 (Answer D)
