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Igoryamba
3 years ago
9

Nia has number cards for 2 3 8 9 and 5 what are the different ways Nia can arrange the cards to show only even numbers with the

2 in the ten thousands place
Mathematics
1 answer:
PIT_PIT [208]3 years ago
5 0

Answer:

23958, 23598, 25938, 25398, 29358, 29538....

Step-by-step explanation:

We have given the number cards for for 2 3 8 9 and 5. We have to find the different  ways Nia can arrange the cards to show only even numbers with the 2 in the ten thousands place.

The number should be even numbers with two in the ten-thousand places.

Only 8 is left as an even number. So 8 would be at the one's place.

In the ten-thousand places, arrange the three digits 3,9 and 5 in the middle.

So there are 3*2=6 ways to arrange the  middle three digits in the ten-thousand places.  

23958, 23598, 25938, 25398, 29358, 29538....

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Find the equation of the line that is parallel to the given line and passes through the given point
Sati [7]

Answer:

\huge\boxed{y=-\dfrac{1}{4}x-1\to x+4y=-4}

Step-by-step explanation:

\text{Let}\ k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\l\ ||\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\==========================\\\\\text{We have}\ x+4y=-6.\\\text{Convert to the slope-intercept form:}\\\\x+4y=-6\qquad\text{subtract}\ x\ \text{from both sides}\\\\4y=-x-6\qquad\text{divide both sides by 4}\\\\y=\dfrac{-x}{4}-\dfrac{6}{4}\\\\y=-\dfrac{1}{4}x-\dfrac{3}{2}\to m_1=-\dfrac{1}{4}

\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (9,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}\\\\x=9,\ y=-3\\\\-3=-\dfrac{1}{4}(9)+b\\\\-3=-\dfrac{9}{4}+b\qquad\text{add}\ \dfrac{9}{4}\ \text{to both sides}\\\\-\dfrac{12}{4}+\dfrac{9}{4}=b\to b=-\dfrac{3}{4}

\text{Lines are to be parallel. Therefore}\ m_2=-\dfrac{1}{4}.\\\\\text{We initially have the form equation}\ y=-\dfrac{1}{4}x+b.\\\\\text{The line passes through the point}\ (8,\ -3).\\\\\text{Substitute the coordinates of the point to the equation of a line:}

x=8,\ y=-3\\\\-3=-\dfrac{1}{4}(8)+b\\\\-3=-2+b\qquad\text{add 2 to both sides}\\\\-1=b\to b=-1

\text{Therefore the equation is:}\ y=-\dfrac{1}{4}x-1.\\\\\text{Convert to the standard form}\ Ax+By=C:\\\\y=-\dfrac{1}{4}x-1\qquad\text{multiply both sides by 4}\\\\4y=-x-4\qquad\text{add}\ x\ \text{to both sides}\\\\x+4y=-4

5 0
3 years ago
The drawing below is of a regular pentagon. The measure for each interior angle in a regular pentagon is 108°. Angle A is supple
myrzilka [38]

Answer:

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Step-by-step explanation:

<u>The interior and exterior angles are supplementary:</u>

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6 0
2 years ago
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Step-by-step explanation:

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Convenient: Sample drawn from a conveniently available pool.

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Situation d:

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Situation e:

People chosen at random, so Random sampling.

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