Answer:
(3, 3 )
Step-by-step explanation:
Given the 2 equations
3x - y = 6 → (1)
6x + y = 21 → (2)
Adding the 2 equations term by term will eliminate y, that is
(6x + 3x) + (y - y) = (21 + 6), that is
9x = 27 (divide both sides by 9 )
x = 3
Substitute x = 3 into either (1) or (2) and solve for y
Using (2), then
(6 × 3) + y = 21
18 + y = 21 ( subtract 18 from both sides )
y = 3
Solution is (3, 3 )
Probablity is (desired outcomes)/(total) possible outcomes
so the dice
1 is desired and the total poassible outcomes is 6 since 6 numbers
so probailty of rolling a 1 is 1/6
then flippin heads
desired outcome=1
total possible=2
probabilty is 1/2
so we have 1/6 and 1/2
now we mulitply them
1/6 times 1/2=1/12
the answer is A
The dimensions of the prism can be 2x, 2x+3 and x+6.
We first factor out the GCF of the trinomial. The GCF of the coefficients is 2. Each term has an x in common as well, so the GCF is 2x.
Factoring out the 2x, we have
2x(2x²+15x+18).
To factor the remaining trinomial, we find factors of 2*18=36 that sum to 15. 12*3 = 36 and 12+3 = 15. We split up 15x into 12x and 3x:
2x(2x²+12x+3x+18)
Now we group together the first two terms in parentheses and the last two:
2x((2x²+12x)+(3x+18))
Factor out the GCF of the first group:
2x(2x(x+6)+(3x+18))
Factor out the GCF of the second group:
2x(2x(x+6)+3(x+6))
Factoring out what these have in common,
2x(x+6)(2x+3)
Based on the given variation, y does not vary directly with x and the constant of variation are 8, 3.2 and 1.25 respectively.
<h3>Variation</h3>
y = k × x
where,
k = constant of proportionality
y = -40
x = -5
y = k × x
-40 = k × -5
-40 = -5k
k = -40/-5
k = 8
when,
y = 8 and x = 2.5
y = k × x
8 = k × 2.5
8 = 2.5k
k = 8/2.5
k = 3.2
when,
y = 5 and x = 4
y = k × x
5 = k × 4
5 = 4k
k = 5/4
k = 1.25
Learn more about variation:
brainly.com/question/6499629
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