Table of Values Luisa is baking a cake. For every \frac{3}{4}
4
3
​
cup of sugar she uses 1\frac{1}{2}
2
1
​
cups of flour. Complete the table shown below, which shows a proportional relationship for the number of cups of sugar to the number of cups of flour.

Cups of SugarCups of Flour
\frac{1}{8}
8
1
​
A
\frac{3}{4}
4
3
​
1\frac{1}{2}
2
1
​

5\frac{1}{4}
4
1
​
B
10\frac{1}{5}
5
1
​
C

We know that for every (3/4) cups of sugar, she uses (1/2) cups of flour.

Now let's find how much flour she needs to use for each case:

If she uses (1/8) cups of sugar, how much flour she uses?

First, we need to count how many times we have (3/4) cups of sugar in (1/8) cups of sugar, which is the quotient:

(1/8)/(3/4) = 4/(3*8) = 4/24 = 1/6

This means that we need to use (1/6) times (1/2) cups of flour.

this is:

(1/6)*(1/2) cups of flour = (1/12) cups of flour.

If she uses (4/3) cups of sugar, we need to count how many times we have (3/4) cups of flour in that amount, this is:

(4/3)/(3/4) = (4*4)/(3*3) = 16/9

Then we need to se (16/9) times (1/2) cups of flour, this is:

(16/9)*(1/2) cups of flour = (16/18) cups of flour = (8/9) cups of flour

If she uses (1/2) cups of sugar, we need to count how many times we have (3/4) cups of sugar in that amount, this is:

(1/2)/(3/4) = 4/(2*3) = 4/6

Then she needs to use (4/6) times (1/2) cups of flour

this is:

(4/6)*(1/2) cups of flour = 4/(6*2) cups of flour = (1/3) cups of flour.

If she uses (1/4) cups of sugar, we need to count how many times we have (3/4) cups of sugar in that amount, this is:

(1/4)/(3/4) = 4/(4*3) = 4/12

Then she needs to use (4/12) times (1/2) cups of flour

this is:

(4/12)*(1/2) cups of flour = 4/(12*2) cups of flour = (1/6) cups of flour.

If she uses (1/5) cups of sugar, we need to count how many times we have (3/4) cups of sugar in that amount, this is:

(1/5)/(3/4) = 4/(5*3) = 4/15

Then she needs to use (4/15) times (1/2) cups of flour

this is:

(4/15)*(1/2) cups of flour = 4/(15*2) cups of flour = (2/15) cups of flour.

  5.   y=6; de=7; fg=8

  6.   x=4.2; jl=14.2; mn=13

step-by-step explanation:

when chords cross inside a circle, the product of the segment lengths is a constant.

5. dh×eh = fh×gh

  y = gh = dh×eh/fh = 3×4/2 . . . divide by the coefficient of gh

  y = 6

of course, the total chord length is the sum of the lengths of its segments.

  de = dh +eh = 3+4 = 7

  fg = fh +gh = 2+6 = 8

6. this problem works the same way as the previous one.

  x = lk = mk×nk/jk = 6×7/10 = 4.2

  jl = jk +lk = 10 +4.2 = 14.2

  mn = mk +nk = 6 +7 = 13

comment on chords and secants

you can think of the points h (problem 5) and k (problem 6) as points where the chords meet. a chord is part of a secant line, a line that intersects the circle in two points. one can also consider these points (h or k) to be the points where the respective secant lines meet.

then, the product that is a constant is the product of the distance from the meeting point (h or k) to one circle intersection with the distance from that meeting point to the other circle intersection. for problem 5, the constant is the product hd×he = hf×hg.

it turns out that this rule regarding the products of lengths to points of intersection is also true when the secants intersect outside the circle.

that is, you only need to remember one rule to work both kinds of problems.

answer: get jesus in your life

step-by-step explanation: