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3 years ago

If angle LNM =8x+12 and angle JNL =12x-32, find the measure of angle JNP.(JNP and LNM are congruent.

1 answer:

3 0

$Sum\ of\ congrugent\ angles\ is\ 180^{\circ}.\\\\
LNM+JNL=180^{\circ}\\\\
8x+12+12x-32=180\\\\
20x-20=180 \ \ \ |Add\ 20\\\\
20x=200\ \ \ |Divide\ by\ 20\\\\
x=10\\\\
JNL=12x-32=12*10-32=120-32=88^{\circ}$

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A fisherman traveled in a boat from point N upstream. After having traveled 6 km, he stopped rowing and 2 hour 40 min after firs

Nat2105 [25]

Answer:

The speed of the river's current is 4.5 km/hr.

Step-by-step explanation:

Given : A fisherman traveled in a boat from point N upstream.

After having traveled 6 km, he stopped rowing and 2 hour 40 min after first leaving N, he was brought back to N by the current.

Knowing that the speed of the boat in still water is 9 km/hour

To find : The speed of the river’s current.

Solution :

Let the speed of current = x km/h

Speed of boat = 9 km/h

Thus, the speed in upstream = (9 - x) km/h

Also, the speed in downstream = x km/h (because the boat is stationary in downstream)

Total distance = 6 km ( from N to the point he reached )

Total time = 2 hours 40 minutes

$\text{2 hours 40 minutes}=2\frac{40}{60}=2 \frac{2}{3} \\\\\text{2 hours 40 minutes}=\frac{8}{3} \text{ hours}$

We know, $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$

According to the question,

$\frac{6}{9-x}+\frac{6}{x}=\frac{8}{3}$

Taking LCM and 6 common

$6[\frac{x+9-x}{(9-x)x}]=\frac{8}{3}$

Take 6 to another side,

$\frac{9}{9x-x^2}=\frac{8}{3\times 6}$

Cross multiply,

$9\times 18=8\times(9x-x^2)$

$162=72x-8x^2$

Taking 4 common and cancel out

$4x^2-36x+81=0$

Solve quadratic equation by middle term split,

$4x^2-18x-18x+81=0$

$2x(2x-9)-9(2x-9)=0$

$(2x-9)(2x-9)=0$

$\Rightarrow 2x-9=0$

$\Rightarrow x=\frac{9}{2}=4.5$

Therefore, The speed of the river's current is 4.5 km/hr.

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3 years ago

When a certain polynomial is divide by binomial x-3, the result is 4x-5+6/x-3. What is the polynomial

Dmitry_Shevchenko [17]

$\frac{p(x)}{x-3} = 4x-5 + \frac{6}{x-3}$

The polynomial p(x) can be found by multiplying 'x-3' to every term
$p(x) = (4x-5)(x-3) + 6$

Now distribute and you have your answer.
$p(x) = 4x^2 -12x-5x+15 +6 \\ \\ p(x) = 4x^2 -17x+21$

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Factor 1 - 2.25x^8.

sleet_krkn [62]

<span>1 - 2.25x</span>⁸ =
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