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3 years ago

Write the slope-intercept form of the equation of the line that is parallel to AB and passes through Point X. Show all

Mathematics

1 answer:

DanielleElmas [232]3 years ago

7 0

find y=mx+b for line parallel to AB.

The line that is parallel will have the same slope as line AB:

the slope of line AB is

m=(8-3)/(-10-2)

=5/-12

=-5/12

Since the line going through X is parallel the vertical distance of the new line to AB is the same for all values of the domain(x-axis).

at x=-5 the point X has the y value of 10 which is 4 more than the y value for AB based on the graph.

To find the intercept b of the line going through X that is parallel to AB we just add 4 to the intercept of AB, which is 4 so

4+4=8

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Step-by-step explanation:

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Answer:

x = 20

Step-by-step explanation:

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4 years ago

Diagram shows the composite solid formed by a cuboid and a right prism. Trapezium LMNP is the uniform cross section of the prism

kherson [118]

Answer:

MN = 7 cm

Step-by-step explanation:

Well the volume we can separate into pieces

first the ABCDEFGH (? you know this cuboid)

which has a volume of

$V = AB\cdot BC\cdot CH\\\\V = 3*6*(3+JY+4)$

if you ask where does the 4 come from

it comes from LP = KB = YC and JY + YC =JC

$V = 18(7+MX)$

this is because JY = MX

the other volume is of BCNPKLXY (hope you understand which one)

and the volume is

$V = BP*PN*NX\\\\V=8*6*4\\\\V = 192$

and the last one is KYXLMJ (the top "triangle")

the volume is

$V = \frac{LX*XM}{2}*LK\\\\V = \frac{6*MX}{2}*8\\\\V= 6*4*MX\\\\V=24MX$

so now add them up

and has to equal 444

$V_T = 18(7+MX)+192+24MX\\\\V_T = 126+18MX+192+24MX\\\\V_T = 318+42MX\\\\444=318+42MX\\\\444-318=42MX\\\\126=42MX\\\\MX = 3$

and finally we know that MN = MX + XN = 3+4 = 7

so here is our answer MN = 7 cm

a couple of notes

$1.\:\angle LXM = 90\\\\2.\:\angle KYX = 90$

3. the units don't matter due to the fact that everything is in cm

4. see the picture below to get a better idea of which prism I am talking of

5. tell me if you have questions :D

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