Alyssa is preparing her grocery list for the week. she wants to have a smoothie for breakfast every day and plans on a total of 6 cups of smoothies made from frozen fruit puree and yogurt. knowing that fruit puree costs $2.00 per cup and yogurt costs $3 per cup, she budgets $14.00 for the ingredients. which system could alyssa’s roommate marni use to find x, the number of cups of fruit puree, and y, the number of cups of yogurt, alyssa plans to buy? x + y = 6 2x + 3y = 14 x + y = 6 3x + 2y = 14 6x + 2y = 14 2x + 3y = 6 x + y = 14 2x + 3y = 6

x + y = 6

2x + 3y = 14

Step-by-step explanation:

Since x is the number of cups of fruit puree and y is the number of cups of yogurt, it has to be 2x + 3y, since the question stated that fruit puree is $2 per cup and yogurt is $3 per cup. She budgets $14, so both of these have to add up to that, therefore 2x + 3y = 14. x + y = 6 because fruit puree and yogurt combined will make 6 cups of smoothies.

the transverse axis of a hyperbola is the line that contains the two vertices and the two focuses.

in this example (hyperbola of equation x^2/2 - y^2/4 = 1), the transverse axis is the  x-axis  . 

step-by-step explanation:

answer: (-8,4) are the coordinates of a

step-by-step explanation:

let the side of square abcd is x .

thus the area of square abcd is .

now, by the diagram area of triangle ead= 1/2 × ea × ad = 1/2 × ea × x

( because ad is the side of square)

and, according to the question,

the areas of square abcd and right ead are equal.

⇒

⇒ea=2x

thus, ea: ab=2: 1

therefore, point a divides line segment eb into the ratio 2: 1.

⇒ by sectional formula coordinates of a are,

=

=

=(-8, 4)

thus the coordinates of a are (-8,4)