Answer:
Yes
Step-by-step explanation:
They are proportional by a scale of 1.5
12
because it is the only number that appears more than once which is basically the definition of mode.
Answer:
The correct order is:
a
c
d
b
Step-by-step explanation:
First, let's write 1/x in a convenient way for us:
a) Substitute 1/x = p/q, to obtain x = 1/(1/x) = 1/(p/q) = q/p.
Now we assume that 1/x is rational (we want to prove that this implies that x will be also rational and because we know that x is irrational assuming that 1/x is rational will lead to an incongruence), then:
c. If 1/x is rational, then 1/x = p/q for some integers p and q with q ≠ 0. Observe that p is not 0 either, because 1/x is not 0.
Now we know that we can write x as a quotient of two integers, we need to imply that, then the next one is:
d) Observe that x is the quotient of two integers with the denominator nonzero.
And that is the definition of rational, then we end with:
b) Hence x is rational.
Which is what we wanted to get.
This question is referred to two similar triangles.
One triangle has sides x and x - 2.
The other triangle has the respective sides x + x + 5 and x - 2 + x + 1
Then you can state a proportionality relation between the sides>
[x + x + 5] / x = [x - 2 + x + 1] / [x - 2]
=> [2x + 5] / x = [2x - 1] / [x - 2]
=> (2x + 5)(x - 2) = (2x - 1)x
=> 2x^2 - 4x + 5x - 10 = 2x^2 - x
=> x - 10 = - x
=> 2x = 10
=> x = 10 / 2
=> x = 5
Answer: x = 5
