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Ilia_Sergeevich [38]

3 years ago

5

Help please I don't get it

2 answers:

Sonja [21]3 years ago

8 0

A variable is an unknown, so for example Joe has 5 cards but Gordon has 5 times more cards then Joe, our variable is x (whatever letter you want but i)
X=how many cards Gordon has
I hope this helps!

rewona [7]3 years ago

7 0

A variable is a letter that represents unspecified numbers. We use a variable in the same manner as all other numerals.

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What is the center of the circle that has a diameter whose endpoints are (9, 7) and (-3, -5)?

emmasim [6.3K]

Answer: OPTION B.

Step-by-step explanation:

Given the endpoints of the diameter of the circle, we need to find the midpoint, which is the center of the circle.

The following formula is used to calculate the Midpoint:

$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Given the endpoints of the diameter of the circle:

$(9, 7)\ and\ (-3, -5)$

We can identify that:

$x_1=9\\x_2=-3\\y_1=7\\y_2=-5$

Then, we can substitute these values into the formula:

$M=(\frac{9+(-3)}{2},\frac{7+(-5)}{2})\\\\M=(3,1)$

Therefore, the center of the circle is: $(3,1)$

3 0

3 years ago

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:

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

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A scuba instructor wants to know the opinions of scuba divers about online scuba diving tests. She obtains a list of 900 scuba d

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