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3 years ago

Solve for x [Sigma Notion and the Nth term] [VERY URGENT]

Mathematics

1 answer:

Sonja [21]3 years ago

8 0

The answer Is D I hope this helps!

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The denominator of a fraction is two more than the numerator. If both numerator and denominator are decreased by six, the simpli

ira [324]

Answer:

$\dfrac{40}{42}$

Step-by-step explanation:

Let the numerator of the fraction=x

Since the denominator of a fraction is two more than the numerator.

Denominator=x+2

The fraction is therefore:

$\dfrac{x}{x+2}$

If both numerator and denominator are decreased by six, the fraction becomes:

$\dfrac{x-6}{x+2-6}$

The simplified result is $\dfrac{17}{18}$

Therefore:

$\dfrac{x-6}{x+2-6}=\dfrac{17}{18}\\$Next, we solve for x\\Cross multiply\\18(x-6)=17(x+2-6)\\18(x-6)=17(x-4)\\Expand the bracket\\18x-108=17x-68\\Collect like terms\\18x-17x=-68+108\\x=40$

Substituting x=40 into the initial fraction

$\dfrac{x}{x+2}=\dfrac{40}{40+2}=\dfrac{40}{42}$

Therefore, the original fraction is $\dfrac{40}{42}$

4 0

3 years ago

1. Simplify the expression below.<br> 2(x + 2) + 3(-x-7) -5 ( 2x - 4)

MrMuchimi

Answer: -11x+15

Step-by-step explanation: distributed property: 2x+2-3x-7-10x+20, -11x+15

5 0

3 years ago

In 2015, I’m buffalo, New York, there were 8,625 arrest, 2,678 robberies, 865 assaults, and 20 murders. The population of Buffal

Nutka1998 [239]

865:2678 is the answer

8 0

3 years ago

90 POINTS| PLEASE ANSWER ASAP|

shtirl [24]

For A:

You add the probabilities to get the answer to A: = .75, or 3/4

Note that the probability of ALL THREE of them hitting would be 1/3 x 1/4 x 1/5.

For B:

2/3 and 3/4 is the probability of the other two people MISSING (the remainder of 1/3, 1/4)

1.0 = 100% chance to hit the target, so 1.0 x 2/3 x 3/4 = 1/2

Mark's chance of hitting is 1/5, so do 1/2 x 1/5, = 1/10

5 0

3 years ago

Please help! A-level maths.

astra-53 [7]

$x+y=k\implies y=k-x$

Substitute this into the parabolic equation,

$k-x=6-(x-3)^2\implies x^2-7x+(k+3)=0$

We're told the line $x+y=k$ intersects $C$ twice, which means the quadratic above has two distinct real solutions. Its discriminant must then be positive, so we know

$(-7)^2-4(k+3)=49-4(k+3)>0\implies k$

We can tell from the quadratic equation that $C$ has its vertex at the point (3, 6). Also, note that

$-1\le\sin t\le1\implies3\le3+2\sin t\le5\implies3\le x\le5$

and

$-1\le\cos2t\le1\implies2\le4+2\cos2t\le6\implies2\le y\le6$

so the furthest to the right that $C$ extends is the point (5, 2). The line $x+y=k$ passes through this point for $2+5=k\implies k=7$ . For any value of $k$ , the line $x+y=k$ passes through $C$ either only once, or not at all.

So $7\le k$ ; in set notation,

$\{k\mid 7\le k$

4 0

3 years ago