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natulia [17]
3 years ago
14

Write the equations included in the same set of related facts as 6x8=48

Mathematics
1 answer:
Rus_ich [418]3 years ago
6 0
8x6=48, 1x48, 2x24=48, 3x16=48, 4x12, and 6x8
I hope this helps!!!
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PLEASE HELP I WILL GIVE A LOT OF POINTS!
vazorg [7]

9514 1404 393

Answer:

  (2.27, 0.96)

Step-by-step explanation:

The orthocenter is the point of intersection of altitudes of the triangle. The equation for an altitude is the equation of a line through a vertex that is perpendicular to the opposite side.

For example, the line perpendicular to side AC can be found as ...

  (∆x, ∆y) = C-A = (3, -1) -(-4, 2) = (7, -3)

  ∆x(x -h) +∆y(y -k) = 0 . . . . perpendicular through point (h, k)

For side AC, we want the point to be B(4, 5), so the equation is ...

  7(x -4) -3(y -5) = 0

  7x -3y -13 = 0

Similarly, the altitude to side AB can be written as ...

  (∆x, ∆y) = B -A = (4, 5) -(-4, 2) = (8, 3)

  8(x -3) +3(y +1) = 0

  8x +3y -21 = 0

__

By the "cross multiplication method", the solution to these equations is ...

  x = (-3(-21) -(3(-13))/(7(3) -8(-3)) = (63+39)/(21+24) = 102/45 = 2 4/15 ≈ 2.27

  y = (-13(8) -(-21)(7))/45 = 43/45 ≈ 0.96

The orthocenter is near (2.27, 0.96).

__

A graphing application confirms this result.

_____

<em>Additional information about the cross multiplication method</em>

For the general form equations ...

  • ax +by +c = 0
  • dx +ey +g = 0

The "cross multiplication method" has you write the array ...

  \begin{array}{cccc}a&b&c&a\\d&e&g&d\end{array}

and form the "cross products" in groups of four coefficients:

  D = ae -db, X = bg -ec, Y = cd -ga

Then the solution to the set of equations is ...

  1/D = x/X = y/Y   ⇒   x = X/D, y = Y/D

__

<em>Additional note</em>

Videos of this method show you writing the array as bcab/egde and using the final equation x/X=y/Y=1/D. The above gets the same result in a more straightforward manner.

3 0
2 years ago
Which of the following represents 4x^5/6 in radical form
mash [69]
Remember, order of operations
exponent before multiply

so 4x^5/6=4 times x^5/6
simplify the x^5/6 first

remember
x^\frac{m}{n}=\sqrt[n]{s^m}

so
x^\frac{5}{6}=\sqrt[6]{x^5}

so
4x^\frac{5}{6}=4\sqrt[6]{x^5}
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6 0
3 years ago
What is the weight of a square if a triangle weighs 4 grams? Explain your reasoning
stellarik [79]

Answer:

8 grams

Step-by-step explanation:

The balance is in equilibrium, so the weights of the two sides are equal.

Let the weight of a square be s.

Left side: 2s + 4

Right side: s + 3(4) = s + 12

The weights are equal, so we set the two expressions equal.

2s + 4 = s + 12

s = 8

Answer: The weight of a square is 8 grams.

8 0
3 years ago
Dari data berikut tentuka median ( nilai tengah):
Andrej [43]
First, put the numbers in order
A. 1,2,3,4,5,7,8,8,9.....median (middle number) is 5..when there is an odd number of data values, there will only be one median.
B. 14,14,15,16,17,18,19,20....if there is an even number of data points, there will be 2 middle numbers. In that case, u add the 2 middle numbers and divide by 2 to find the median. (16 + 17) / 2 = 33/2 = 16.5 is ur median.
7 0
3 years ago
You randomly choose one of the tiles. Without replacing the first tile, you randomly choose a second tile. Find the probability
scoray [572]
I think it's 1/2 or 1/4
8 0
3 years ago
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