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Mathematics

2 answers:

Maurinko [17]2 years ago

6 0

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A N S W E R

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983000

Hope this helped, love!

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stiv31 [10]2 years ago

3 0

98.3/10=9.83 and then we have 4 zeros so you just move the decimal to the left as we are dividing which gives 0.00983

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What are the coordinates of the point on the directedline segment from K(-5,-4) to L(5,1) that partitionsthe segment into a rati

Diano4ka-milaya [45]

You can solve this either just plain algebra or with the use of trigonometry.
In this case, we'll just use algebra.

So, if we let M be the the point that partitions the segment into a ratio of 3:2, we have this relation:
KM/ML = 3/2
KM = 1.5 ML

We also have this:
KL = KM + ML
Substituting KM,
KL = (3/2) ML + ML
KL = 2.5 ML

Using the distance formula and the given coordinates of the K and L, we get the length of KL
KL = sqrt ( (5-(-5)^2 + (1-(-4))^2 ) = 5 sqrt(5)

Since,
KL = 2.5 ML

Substituting KL,
ML = (1/2.5) KL = (1/2.5) 5 sqrt(5) = 2 sqrt(5)

Using again the distance formula from M to L and letting (x,y) as the coordinates of the point M
ML = 2 sqrt(5) = sqrt ( (5-x)^2 + (1-y)^2 ) [let this be equation 1]

In order to solve this, we need to find an expression of y in terms of x. We can use the equation of the line KL.
The slope m is:
m = (1-(-4))/(5-(-5) = 0.5

Using the general form of the linear equation:
y = mx +b
We substitue m and the coordinate of K or L. We'll just use K.
-5 = (0.5)(-4) + b
b = -1.5

So equation of the line is
y = 0.5x - 1.5 [let this be equation 2]

Substitute equation 2 to equation 1 and solving for x, we get 2 values of x,
x=1, x=9

Since 9 does not make sense (it does not lie on the line), we choose x=1.
Using the equation of the line, we get y which is -1.

So, we get the coordinates of point M which is (1,-1)

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2 years ago

You coach a basketball ball team of 12 players; 5 players must be on the floor at all times; Figuring that every player can play

makvit [3.9K]

The function "choose k from n", nCk, is defined as
nCk = n!/(k!*(n-k)!) . . . . . where "!" indicates the factorial

a) No position sensitivity.
The number of possibilities is the number of ways you can choose 5 players from a roster of 12.
12C5 = 12*11*10*9*8/(5*4*3*2*1) = 792
You can put 792 different teams on the floor.

b) 1 of 2 centers, 2 of 5 guards, 2 of 5 forwards.
The number of possibilities is the product of the number of ways, for each position, you can choose the required number of players from those capable of playing the position.
(2C1)*(5C2)*(5C2) = 2*10*10 = 200
You can put 200 different teams on the floor.

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2 years ago

Find the area of the regular polygon 7 in

nata0808 [166]

Ummmm that’s a triangle but I guess I’ll solve for both 7x7= 49/2= 24.5 triangle. Polygon is different but I guess if the perimeter and line to the center is both 7 okay 7x5= 35x7= 245/2= 122.5 cause triangle is wxL /2 and polygon is AxP/2 soooo I hope this helped

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2 years ago

Triangle A C D is shown. A line is drawn from point D to point B on side A C to form a right angle. Line A D is labeled s. The l

devlian [24]

Answer:

s = 17units

Step-by-step explanation:

For this problem, we are trying to find a specific unknown side length.

We're actually given some extraneous information (information that is not needed to solve the problem): It isn't necessary to know that BC is 5.

If the side AD with the unknown length is part of a right triangle (the triangle in red in the attached diagram), we can use the Pythagorean Theorem to solve for AD.

It isn't clear if the diagram you were provided gives ∠ABD as a right angle, if it only gives ∠CBD as a right angle, or if it gives both as a right angle. Below, we prove that it doesn't matter, because regardless, both must be right angles.

Is Triangle ABD a "right triangle"?

Since B is between A and C, then the two angles ∠ABD & ∠CBD form a linear pair, and by the linear pair postulate are supplementary. Since they are supplementary, their measures add to 180°. Using the fact that all right angles are 90°, substitution, the subtraction property of equality, arithmetic, the measure of ∠ABD is also 90°, and thus must be a right angle. Thus, based on the given information, both ∠ABD & ∠CBD must be right angles.

Consequently, triangle ABD is a right triangle, by definition (it is a triangle that has a right angle).

Pythagorean Theorem

Since triangle ABD is a right triangle, the Pythagorean Theorem can be applied.

The Pythagorean Theorem states that $a^{2} +b^{2} =c^{2}$ where "c" is the hypotenuse (the side across from the right angle) and "a" and "b" the the lengths of the two other sides (called legs) of the right triangle. (Aside: Because of the commutative property of addition, it doesn't matter which of the two legs' lengths is used for a, and which is used for b. The only thing that is required is that "c" be the length of the hypotenuse)

In our triangle, side AD, with unknown length "s" is the length of our hypotenuse, and sides AB and BD are the two legs. Substituting values into the Pythagorean Theorem equation, we can solve for the unknown "s":

$a^{2} +b^{2} =c^{2}$

$(8)^{2} +(15)^{2} =(s)^{2}$