Jackie buys 3 hot dogs and 1 pretzel from a restaurant for $12.25. Sylvia buys 2 hot dogs and 4 pretzels from the same restaurant for $16.50. Part A

Which system of equations can be used to determine the price of a hot dog, h, and a pretzel, p, at the restaurant?

​​​​​​2h + 1p = 12.25

3h + 4p = 16.50

​​​​​​ 2 h + 1 p = 12.25 , , 3 h + 4 p = 16.50,

2h + 1p = 12.25

3h + 4p = 16.50

2 h + 1 p = 12.25, , 3 h + 4 p = 16.50,

2h + 4p = 12.25

3h + 1p = 16.50

2 h + 4 p = 12.25 , , 3 h + 1 p = 16.50,

3h + 1p = 12.25

2h + 4p = 16.50

the required function is .

step-by-step explanation:

from the given table it is noticed that the graph passing through (-3,7), (0,4), (3,1) and (8,-4).

it is a linear function because the value of y is decrease by one as the value of x increase by 1.

the slope of the function is

the slope of the function is -1 and the y-intercept is 4.

the slope intercept form is

where, m is slope and b is y-intercept.

therefore the required function is . the graph of this function is shown below.

225x²+4=0

225x²=0-4

225x²=-4

x²=-4/225

x=±√-4/225

answer: ratio of volume of cone (with 3 times the height and equal diameter) to volume of cylinder is 2 to 1. the value of π is not used.

step-by-step explanation:

radius is diameter/2 = 4.

area of circle is π r^2.

volume of cylinder is height × area of base = hπr^2 = 3(4^2) π = 48π cubic inches.

not knowing the formula for volume of cone, i calculate it using calculus (which is for calculating things).

volume of cone is integral 0 to h area(y) dy. area(y) is π r(y)^2. r(y) runs r to zero as y runs zero to h, r(0) = r, r(h) = 0.

r(y) = r - r/h y

area(y) = π (r - r/h y)^2 = π (r^2 - 2r^2y/h + r^2y^2/h^2) = π r^2(1-2y/h+y^2/h^2)

antiderivative area(y) = π r^2 (y-y^2/h+y^3/(3h^2))

integral 0 to h = π r^2(h-h^2/h+h^3/(3h^2) - (0)) = π r^2(h - h + h/3) = π r^2(h/3) = π/3 r^2 h

volume of this cone is π/3(4^2)18 cubic inches.

= 6 16 π = 96π cubic inches.

cone has twice the volume, 96/48.

cone height is 6 times the cylinder.

ratio of volume formula: π r^2 cancels.

cone over cylinder ratio is 6h/3 to h, 2 to 1.

7.25

step-by-step explanation:

we know that 7 equals to 7.0. we also know that 1/4=0.25. so we can add the two together and we get 7.25