First you multiply 3 times x and 3 times 2
4(3(x + 2) -1) =50
and get
4( 3x +6 -1) =50
then you add 6 plus -1
4 ( 3x +5) = 50
then multiply 4 times 3x and 4 times 5
12x +20 = 50 and subtract 20 from both sides
-20 -20
and you will get
12x = 30
divided both sides by 12
12x/12 = 30/12
then you find the ones that are the same amount in decimals but are smaller
and that's your answer: x= 5/2
hope you get it!!!
Ok so
parabola standard form is
y=ax^2+bx+c
if you have the points
(-2,18)
(0,4)
(4,24)
sub points to find a,b and c
(-2,18)
sub -2 for x and sub 18 for y
18=a(-2)^2+b(-2)+c
18=4a-2b+c
(0,4)
sub 0 for x, nice a, an b cancel
4=a(0)^2+b(0)+c
4=0+0+c
4=c
we can sub that back later
(4,24)
24=a(4)^2+b(4)+c
24=16a+4b+c
we have
18=4a-2b+c
c=4
24=16a+4b+c
sub 4 for c
18=4a-2b+4
24=16a+4b+4
minus 4 from both sides
14=4a-2b
20=16a+4b
simlify all equations
7=2a-b
5=4a+b
add to solve for 6a
12=6a+0b
12=6a
divide both sides by 6
2=a
sub back
7=2a-b
7=2(2)-b
7=4-b
-3=b
equation is
y=2x^2-3x+4
Since we know this is an arithmetic sequence, to find the number of terms, it will be helpful to find the distance d between every term.
d = 1616 - 1313
d = 303
now let's think about how to generate the nth term of an arithmetic sequence given the first term 1313 and distance d.
second term = d + 1313
third term = second term + d
third term = 1313 + 2d
fourth term = third term + d
fourth term = 1313 + 3d
we are starting to see a pattern:
nth term = 1313 + (n-1)d
we know this pattern will continue because we are simply adding d to the previous term to get the next term so if the previous term n - 1 was 1313 + d(n - 2), then the next term n will be 1313 + d(n-1). to put i simply, since the first term was 1313, we know the 2nd term must be 1313 + d and since the 2nd term is 1313 + d, we know the third term must be 1313 + 2d and so on until the nth term which is 1313 + (n-1)d. we know the nth term of this sequence is 7373 and we know that d is 303 so:
7373 = 1313 + 303(n-1) and we just have to solve for n.
doing so gives:
n = 21 terms
let me know if you have any questions!
Answer:
7, 14, 10, 10 inches
Step-by-step explanation:
x = short side
2x = longest side
x + 3 = side 3
x + 3 = side 4
x + (2x) + (x+3) + (x+3) = 41
5x + 6 = 41
5x = 35
x = 7
sides are 7, 14, 10, 10
Variable varies or changes
constatant term doesn't change
examples
variables can change so example
x>10
x can be 11 or 33 or anythign bigger than 10
constants are no fun
they don't change an are boring, like
3 or 8, it just stays that way