The U and inverted U symbols, ∪ and ∩, are mathematical symbols used to denote union or intersection, respectively. For example, when a rational algebraic equation is graphed, there may be some points where the equation is undefined. Visually, we see it as breaks or discontinuities. We use the ∪ symbol to express union. For example, {-∞,2)∪(4,+∞). That means that the graph passes at all x values except x=3.

The ∩ symbol is used for intersection of two lines, for instance. When equation A and equation B are graphed, they can intersect at points (x,y). It is therefore expressed as: A∩B = (x,y).

8 0

3 years ago

Pythagoras question plz help

motikmotik

From the two right triangles, you can write the following equations using the Pythagorean theorem. Let's call that shared leg in the middle "y"

y^2 + b^2 = a^2
y^2 + c^2 = x^2

y^2 + b^2 = a^2
re-write this to get "y" alone for substitution.
y^2 = a^2 - b^2
substitute (a^2 - b^2) for y^2 in the other equation. y^2 + c^2 = x^2

a^2 - b^2 + c^2 = x^2

Now put in the values given for a,b,c to solve for x

(7.1)^2 - (5.6)^2 + (5.7)^2 = x^2
51.54 = x^2
square root
7.2 = x

6 0

3 years ago

A path is 0.75 m wide. Mr. Kassel extends the width by placing blocks 20 cm wide on each side of the pathl. What is the new widt

Nuetrik [128]

We know that there are 100 cm in 1 m. We can convert 0.75 m to cm by multiplying by 100 to give us:

$0.75m*100=75cm$

Therefore the path before the addition is 75 cm wide.

Mr. Kassel added 20 cm of blocks on each side of the path, meaning that the added width is actually 40 cm total (20 on each side, and there are 2 sides).

So we need to add 40 cm to the original 75 cm:

$40cm+75cm=115cm$

So now we have the width of the path in cm, the question asks for the width in meters. We can do this by dividing the width in cm by 100 to get the width in meters:

$\frac{115cm}{100}=1.15m$

Now we know that the new width of the path is 1.15 m.

3 0

3 years ago