5. Susan has an income of $10. She buys cherries for $2 a pound and grapes for $4 a pound. Write the equation for her budget line and sketch the line with cherries on the y-axis. What is its slope

2y + 4x = 10

Slope = -2

Step-by-step explanation:

x: quantity of grapes

y: quantity of cherries

2y + 4x = 10

Graph will be a straight line with the following intercepts:

x = 0, 2y + 0 = 10 y = 5 (0,5)

y = 0, 0 + 4x = 10 x = 2.5 (2.5,0)

Sketch: a straight line joining (2.5,0) and (0,5)

2y + 4x = 10

2y = -4x + 10

y = -2x + 2.5

Slope = -2

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.