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Studentka2010 [4]
2 years ago
6

Write the equation of the line parallel to 4x-5y=2 and passing through point (0,0)

Mathematics
1 answer:
kotykmax [81]2 years ago
8 0

k:y=m_1x+b_1;\ l:y=m_2x+b_2\\\\k\ \perp\ l\iff m_1\cdot m_2=-1\\\\k\ ||\ l\iff m_1=m_2

We have:

4x-5y=2\ \ \ \ |-4x\\\\-5y=-4x+2\ \ \ \ |:(-5)\\\\y=\dfrac{4}{5}x-\dfrac{2}{5}\to m_1=\dfrac{4}{5}\\\\l:y=m_2x+b\\\\k\ \prep\ l\Rightarrow\dfrac{4}{5}m_2=-1\ \ \ \ |\cdot\dfrac{5}{4}\\\\m_2=-\dfrac{5}{4}

l:y=-\dfrac{5}{4}x+b

The line l is passing through point (0, 0). Substitute the coordinates of the point to the equation of a line l:

0=-\dfrac{5}{4}\cdot0+b\to b=0

y=-\dfrac{5}{4}x\ \ \ \ |\cdot4\\\\4y=-5x\ \ \ \ |+5x\\\\5x+4y=0

<h2>Answer: 5x + 4y = 0</h2>
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Find the product (4x-5y)^2
sleet_krkn [62]
To find the product of (4x-5y)^2,
we can rewrite the problem as:
(4x-5y)(4x-5y) (two times because it is squared)

Now, time to use that old method we learned in middle school:
FOIL. (Firsts, Outers, Inners, and Lasts)

FOIL can help us greatly in this scenario.
Let's start by multiplying the 'Firsts' together:
4x * 4x = <em>16x^2</em>

Now, lets to the 'Outers':
4x * -5y = <em>-20xy</em> 

Next, we can multiply the 'Inners':
-5y * 4x = <em>-20xy</em>

Finally, let's do the 'Lasts':
-5y * -5y = <em>25y</em>^2

Now, we can take the products of these equations from FOIL and combine like terms. We have: 16x^2, -20xy, -20xy, and 25y^2.
-20xy and -20xy make -40xy.

The final equation (product of (4x-5y)^2) is:
16x^2 - 40xy + 25y^2

Hope I helped! If any of my math is wrong, please report and let me know!
Have a good one.
4 0
3 years ago
A delivery truck is stocked with boxes of leather footballs. The graph shows the relationship between the number of footballs an
pashok25 [27]

Answer:

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Step-by-step explanation:

To find the answer, you'd have to continue tracing the diagonal line until it intersects with the vertical line that corresponds to the number 3.

If you do that, you'll see that in3 boxes, there are 21 footbals.


You can also calculate it mathematically:

If you have 7 balls per box as shown in the graph, you just have to multiply 7 by 3 to know how many balls you'll find in 3 boxes. 7 * 3 = 21.



Hope it helped,



BioTeacher101

6 0
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Step-by-step explanation:

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