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Marina86 [1]
3 years ago
10

What is the gcf of 16 24 32

Mathematics
2 answers:
miskamm [114]3 years ago
5 0
The gcf out of those three numbers should be 8
MArishka [77]3 years ago
3 0
The Greatest common factor is 8 
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Lines k and n intersect on the y-axis
avanturin [10]

a) The equation of line k is:

y = -\frac{202}{167}x + \frac{598}{167}

b) The equation of line j is:

y = \frac{167}{202}x + \frac{1546}{202}

The equation of a line, in <u>slope-intercept formula</u>, is given by:

y = mx + b

In which:

  • m is the slope, which is the rate of change.
  • b is the y-intercept, which is the value of y when x = 0.

Item a:

  • Line k intersects line m with an angle of 109º, thus:

\tan{109^{\circ}} = \frac{m_2 - m_1}{1 + m_1m_2}

In which m_1 and m_2 are the slopes of <u>k and m.</u>

  • Line k goes through points (-3,-1) and (5,2), thus, it's slope is:

m_1 = \frac{2 - (-1)}{5 - (-3)} = \frac{3}{8}

  • The tangent of 109 degrees is \tan{109^{\circ}} = -\frac{29}{10}
  • Thus, the slope of line m is found solving the following equation:

\tan{109^{\circ}} = \frac{m_2 - m_1}{1 + m_1m_2}

-\frac{29}{10} = \frac{m_2 - \frac{3}{8}}{1 + \frac{3}{8}m_2}

m_2 - \frac{3}{8} = -\frac{29}{10} - \frac{87}{80}m_2

m_2 + \frac{87}{80}m_2 = -\frac{29}{10} + \frac{3}{8}

\frac{167m_2}{80} = \frac{-202}{80}

m_2 = -\frac{202}{167}

Thus:

y = -\frac{202}{167}x + b

It goes through point (-2,6), that is, when x = -2, y = 6, and this is used to find b.

y = -\frac{202}{167}x + b

6 = -\frac{202}{167}(-2) + b

b = 6 - \frac{404}{167}

b = \frac{6(167)-404}{167}

b = \frac{598}{167}

Thus. the equation of line k, in slope-intercept formula, is:

y = -\frac{202}{167}x + \frac{598}{167}

Item b:

  • Lines j and k intersect at an angle of 90º, thus they are perpendicular, which means that the multiplication of their slopes is -1.

Thus, the slope of line j is:

-\frac{202}{167}m = -1

m = \frac{167}{202}

Then

y = \frac{167}{202}x + b

Also goes through point (-2,6), thus:

6 = \frac{167}{202}(-2) + b

b = \frac{(2)167 + 202(6)}{202}

b = \frac{1546}{202}

The equation of line j is:

y = \frac{167}{202}x + \frac{1546}{202}

A similar problem is given at brainly.com/question/16302622

7 0
2 years ago
Convert 7 kilometers into miles
ladessa [460]
4.3496 miles.

HTH (Hope This Helps)
6 0
3 years ago
Please help!! 11 points!!
MariettaO [177]

Answer:3x < 8x - 3

Step-by-step explanation:

5 0
3 years ago
What is the least common multiple of both 9 and 12
Crank
LCM is found by finding the factors of both and making sure that both are inthere
9=3 times 3
12=2 times 2 times 3
common one is 3
so we have to have at least 2 threes and 2 twos
2 times 2 times 3 tiimes 3=36
answer is 36
3 0
3 years ago
Read 2 more answers
What is a histogram? i have a question on it and i dont know how to answer it
o-na [289]
It is <span>a </span>statistical graph<span> that represents the </span>frequency<span> of values of a quantity by </span>verticalrectangles<span> of </span>varying<span> heights and </span>widths<span>. The width of the rectangles is in </span>proportion<span> to the class </span>interval<span> under </span>consideration<span>, and their areas represent the relative frequency of the </span>phenomenon<span> in </span><span>question. And this is one of example of histogram:</span>

5 0
3 years ago
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