Answer:
Area of the other polygon = 4 in.²
Step-by-step explanation:
Area of the bigger polygon : Area of the smaller polygon = square of the side length of the bigger polygon : square of the corresponding side length of the smaller polygon
Let "x" represent the area of the smaller polygon
Thus, we have:
100/x = 20²/4²
100/x = 400/16
100/x = 25
Cross multiply
25x = 100
Divide both sides by 25
25x/25 = 100/25
x = 4
Area of the other polygon = 4 in.²
The system is:
i) <span>2x – 3y – 2z = 4
ii) </span><span>x + 3y + 2z = –7
</span>iii) <span>–4x – 4y – 2z = 10
the last equation can be simplified, by dividing by -2,
thus we have:
</span>i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
iii) 2x +2y +z = -5
The procedure to solve the system is as follows:
first use any pairs of 2 equations (for example i and ii, i and iii) and equalize them by using one of the variables:
i) 2x – 3y – 2z = 4
iii) 2x +2y +z = -5
2x can be written as 3y+2z+4 from the first equation, and -2y-z-5 from the third equation.
Equalize:
3y+2z+4=-2y-z-5, group common terms:
5y+3z=-9
similarly, using i and ii, eliminate x:
i) 2x – 3y – 2z = 4
ii) x + 3y + 2z = –7
multiply the second equation by 2:
i) 2x – 3y – 2z = 4
ii) 2x + 6y + 4z = –14
thus 2x=3y+2z+4 from i and 2x=-6y-4z-14 from ii:
3y+2z+4=-6y-4z-14
9y+6z=-18
So we get 2 equations with variables y and z:
a) 5y+3z=-9
b) 9y+6z=-18
now the aim of the method is clear: We eliminate one of the variables, creating a system of 2 linear equations with 2 variables, which we can solve by any of the standard methods.
Let's use elimination method, multiply the equation a by -2:
a) -10y-6z=18
b) 9y+6z=-18
------------------------ add the equations:
-10y+9y-6z+6z=18-18
-y=0
y=0,
thus :
9y+6z=-18
0+6z=-18
z=-3
Finally to find x, use any of the equations i, ii or iii:
<span>2x – 3y – 2z = 4
</span>
<span>2x – 3*0 – 2(-3) = 4
2x+6=4
2x=-2
x=-1
Solution: (x, y, z) = (-1, 0, -3 )
Remark: it is always a good attitude to check the answer, because often calculations mistakes can be made:
check by substituting x=-1, y=0, z=-3 in each of the 3 equations and see that for these numbers the equalities hold.</span>
Firstly, I noticed that there are fractions, decimals, and percents. I will change everything to percents, so it’s more easy for me to compare each of them.
List 1. 140%, 25%, 14%. This is from greatest to least, not least to greatest.
List 2. 25%, 14%, 14%. This is not from least to greatest, either.
List 3. 14%, 25%, 140%. This is from least to greatest.
List 4. 140%, 14%, 25%. This is not from least to greatest.
List 3 is from least to greatest. I got this answer by converting all of the fractions and decimals to percentages.
Answer:
16.25% was spent on food
Step-by-step explanation:
Step one
given data
A family spends $520 every month on food
The family's income is $3200 Monthly
Required
We want to find the percentage of the income spent on food only
Step two
percentage spent on food= amount spent on food/income*100
percentage spent on food= 520/3200*100
percentage spent on food= 0.1625*100
percentage spent on food= 16.25%
=16.25%
Answer:
100
Step-by-step explanation:
Because if 50 percent of x is 50 than x = 100
