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Minchanka [31]
3 years ago
13

Given: X = r + 2, Y = 2r - 9, and Z = r 2 + 17r + 30. Simplify [X · Y - Z] ÷ X.

Mathematics
1 answer:
musickatia [10]3 years ago
8 0

Answer: r - 24

Step-by-step explanation:

X=r+2;Y=2r-9;Z=r^2+17x+30

\frac{x*y-z}{x}

\frac{[(r+2)(2r-9)]-(r^2+17r+30)}{r+2}

\frac{(2r^2-9r+4r-18)-(r^2+17r+30)}{r+2}

\frac{(2r^2-5r-18)-(r^2+17r+30)}{r+2}

\frac{2r^2-5r-18-r^2-17r-30)}{r+2}

Combine like terms;

\frac{r^2-22r-48}{r+2}

Solve the quadratic equation;

\frac{(r-24)(r+2)}{r+2}

Simplify;

r-24

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Answer:

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Step-by-step explanation:

We know that,

Speed=\dfrac{Distance}{Time}

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Let d be the distance and t be the time.

2.5=\dfrac{d}{t}

2.5t=d      ...(1)

On his return journey, he increased his speed by 4 km/h and saved 15 minutes. So, distance is d and times is t-15.

4=\dfrac{d}{t-15}

4(t-15)=d      ...(2)

From (1) and (2), we get

4(t-15)=2.5t

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Put t=40 in (1).

d=2.5(40)=100

So, t=40 and d=100.

Now,

Total distance = d + d = 100 + 100 = 200

Total time = t + t - 15 = 40 + 40 - 15 = 65

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\text{Average speed}=\dfrac{\text{Total distance}}{\text{Total time}}

\text{Average speed}=\dfrac{200}{65}

\text{Average speed}\approx 3.08

Therefore, the average speed is 3.08 km/h.

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