Answer:
7
/10 0.7
Step-by-step explanation:
To add fractions, find the LCD and then combine.
This question was posted almost a week ago, and I am not sure if you still need the answer, but I'll explain it.
The total number of all of the shapes were placed in the bag are equal to 100. The number comes from adding 32+20+48=100.
This is our total number and will be the denominator.
There are a total of 32 cards which have a hexagon, this number will be our numerator.
So far we have 32/100 , but this is not simplest form.
Next to reduce the fraction, the GCF must be found.
32: 1, 2, 4, 8, 32
100: :
If x is a real number such that x3 + 4x = 0 then x is 0”.Let q: x is a real number such that x3 + 4x = 0 r: x is 0.i To show that statement p is true we assume that q is true and then show that r is true.Therefore let statement q be true.∴ x2 + 4x = 0 x x2 + 4 = 0⇒ x = 0 or x2+ 4 = 0However since x is real it is 0.Thus statement r is true.Therefore the given statement is true.ii To show statement p to be true by contradiction we assume that p is not true.Let x be a real number such that x3 + 4x = 0 and let x is not 0.Therefore x3 + 4x = 0 x x2+ 4 = 0 x = 0 or x2 + 4 = 0 x = 0 orx2 = – 4However x is real. Therefore x = 0 which is a contradiction since we have assumed that x is not 0.Thus the given statement p is true.iii To prove statement p to be true by contrapositive method we assume that r is false and prove that q must be false.Here r is false implies that it is required to consider the negation of statement r.This obtains the following statement.∼r: x is not 0.It can be seen that x2 + 4 will always be positive.x ≠ 0 implies that the product of any positive real number with x is not zero.Let us consider the product of x with x2 + 4.∴ x x2 + 4 ≠ 0⇒ x3 + 4x ≠ 0This shows that statement q is not true.Thus it has been proved that∼r ⇒∼qTherefore the given statement p is true.
Answer:Find the distance between the parallel lines m and n whose equations are y = x + 4 and y = x - 6, respectively.
There are several ways to do this...here's one
Let (0, 4) be a point on the first line
Then.......a line with a negative reciprocal slope going through this point will have the equation :
y = -x + 4........so......we can find the intersection of this line with y = x - 6....set both equations equal
-x + 4 = x - 6 add x, 6 to both sides
10 = 2x divide both sides by 2
5 = x
So...using -x + 4, the y value at intersection = -1.......
So...we just need to find the distance from (0,4) to ( 5, -1) =
√[ (5)^2 + (4 + 1)^2 ] = 5√2 ≈ 7.07 units
Here's a pic....AB is the distance with A = (0,4) and B = (5, -1)
Step-by-step explanation:
<h3>
Therefore 24 students take a car to school. </h3>
Step-by-step explanation:
Given, Total number of students is 80.
and 30% of the total students take a car to school
30% of 80
=24
Therefore 24 students take a car to school.
