Answer:
0.36 cents
Step-by-step explanation:
1.80/5=0.36 <----answer
To check you can do 0.36x5 and get 1.80
Answer: A=2 and B=13
Explanation: The Factor Theorem states that if a is the root of any polynomial p(x) that is if p(a)=0, then (x−a) is the factor of the polynomial p(x).
Let p(x)=x
3
+ax
2
−bx+10 and g(x)=x
2
−3x+2
Factorise g(x)=x
2
−3x+2:
x
2
−3x+2=x
2
−2x−x+2=x(x−2)−1(x−2)=(x−2)(x−1)
Therefore, g(x)=(x−2)(x−1)
It is given that p(x) is divisible by g(x), therefore, by factor theorem p(2)=0 and p(1)=0. Let us first find p(2) and p(1) as follows:
p(1)=1
3
+(a×1
2
)−(b×1)+10=1+(a×1)−b+10=a−b+11
p(2)=2
3
+(a×2
2
)−(b×2)+10=8+(a×4)−2b+10=4a−2b+18
Now equate p(2)=0 and p(1)=0 as shown below:
a−b+11=0
⇒a−b=−11.......(1)
4a−2b+18=0
⇒2(2a−b+9)=0
⇒2a−b+9=0
⇒2a−b=−9.......(2)
Now subtract equation 1 from equation 2:
(2a−a)+(−b+b)=(−9+11)
⇒a=2
Substitute a=2 in equation 1:
2−b=−11
⇒−b=−11−2
⇒−b=−13
⇒b=13
Hence, a=2 and b=13.
Answer:
3
Step-by-step explanation:
to convert the centimeters to inches, divide 137. 16 by 2.54
you should get 54
then divide by 18
you get three
1.
Since ABCD is a rectangle, then
angleABE = 90 degrees
angle ABE + angle BEA + 41 = 180
Substitute the known and solve for angle BEA
angle BEA + 41 = 90
angle BEA = 49 degrees
But,
x + angleBEA + 61 = 180 (angles in a straight line)
x = 180 - 61 - 49
x = 70 degrees
2.
triangle XYZ is equilateral, meaning all angles in it are the same, each 60 degrees.
Therefore,
Angle YZX = 60
But Angle YZX = x + 32 (exterior angles equal to the sum of the two opposite interior angles)
60 = x + 32
Therefore,
x = 28 degrees
3.
Angle QPR = Angle QRP (equal oppo sides, equal opposite angles)
Therefore, 2angleQRP + 64 = 180 (angle sum of a triangle)
Angle QRP = 58 degrees
But angle QRP = x + 35 (exterior angles equal to the sum of the two opposite interior angles)
58 = x + 35
x = 23 degrees