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3 years ago

The points (10,8) and (4,5) fall on a particular line. What is its equation in point-slope form?

Mathematics

1 answer:

FinnZ [79.3K]3 years ago

7 0

Answer:

y-8=1/2(x-10)

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(5-8)/(4-10)

m=-3/-6

simplify

m=1/2

y-y1=m(x-x1)

y-8=1/2(x-10)

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How do you find the missing height of a triangle?

g100num [7]

Answer:

Use the Pythagorean theorem

Step-by-step explanation:

The pythagorean theorem is $a^{2} +b^{2} =c^{2}$ where a is a height, b is a height, and c is the hypotenuse, which is the longest side of a triangle. For example, if the triangle has two side with lengths of three and four we would put them into the equation to get:

$3^{2} +4^{2} =c^{2}$

Simplify the equation to get:

$9+16=c^2$

Add 16 and 9 to get 25 and take the square root of both sides:

$\sqrt{25} =c$

The sqrt of 25 is 5. Therefore, the length of the hypotenuse, or c, is 5.

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3 years ago

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In how many ways can 3 Americans, 4 Frenchmen, 4 Danes and 2 Italians be seated in a row so that those of the same nationality s

kaheart [24]

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3 years ago

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What’s Distribute -x(5x+2)

MaRussiya [10]

Answer:

-5x^2-2x

Step-by-step explanation:

When distributing, you multiply the term outside the brackets to all the terms in brackets.

If the term outside the bracket is negative, then when distributing/opening the brackets, the signs of the terms changes.

So in this prob. -x would multiply to both +5x and +2

-x*5x+-x*2

∴-5x^2-2x

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4 years ago

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A ladder 16 feet long is leaning against the wall of a tall building. The base of the ladder is moving away from the wall at a r

svet-max [94.6K]

Answer:

a. 0.588

b. 0.0722

c. 4.576 sqft/sec

Step-by-step explanation:

Let b and h denote the base and height as indicated in the diagram. By pythagoras theorem, $h^2 + b^2 = 16^2 = 256 \dotsc\;(1)$ because it is a right angle triangle.

It is given that $\frac{db}{dt} = 1$

Now differentiate (1) with respect to t (time) :

$\displaystyle{2h\frac{dh}{dt} + 2b\frac{db}{dt} = 0 \implies \frac{dh}{dt} = -\frac{b}{h} \frac{db}{dt}}$

$\displaystyle{=-\frac{b}{\sqrt{256 - b^2}} \frac{db}{dt} = -\frac{8}{13.856} \times 1 = -0.588}$

The minus sign indicates that the value of h is actually decreasing. The required answer is 0.588.

b. From the diagram, infer that $16 \sin{\theta} = b$ . When b = 8, then $\theta = \arcsin{0.5} = \ang{30}$ .

Differentiate the above equation w.r.t t

$\displaystyle{16 \cos{\theta} \frac{d\theta}{dt} = \frac{db}{dt} \implies \frac{d\theta}{dt} = \frac{1}{16 \cos{\theta}} = \frac{1}{13.856} = \mathbf{0.0722}}$