Answer:
![(a)\ 4 < 5x - 1 < 10](https://tex.z-dn.net/?f=%28a%29%5C%204%20%3C%205x%20-%201%20%3C%2010)
![(b)\ 4 < 5x - 3 < 10](https://tex.z-dn.net/?f=%28b%29%5C%204%20%3C%205x%20-%203%20%3C%2010)
![(d)\ 4 < 2x + 1 < 10](https://tex.z-dn.net/?f=%28d%29%5C%204%20%3C%202x%20%2B%201%20%3C%2010)
![(e)\ 4 < 2x + 3 < 10](https://tex.z-dn.net/?f=%28e%29%5C%204%20%3C%202x%20%2B%203%20%3C%2010)
Step-by-step explanation:
Required
Whose solution is ![x = 2](https://tex.z-dn.net/?f=x%20%3D%202)
![(a)\ 4 < 5x - 1 < 10](https://tex.z-dn.net/?f=%28a%29%5C%204%20%3C%205x%20-%201%20%3C%2010)
Add 1 to both parts
![4 +1< 5x < 10+1](https://tex.z-dn.net/?f=4%20%2B1%3C%205x%20%20%3C%2010%2B1)
![5< 5x < 11](https://tex.z-dn.net/?f=5%3C%205x%20%20%3C%2011)
Divide through by 5
![1< x](https://tex.z-dn.net/?f=1%3C%20x%3C2.2)
Substitute 2 for x
--- this is true
![(b)\ 4 < 5x - 3 < 10](https://tex.z-dn.net/?f=%28b%29%5C%204%20%3C%205x%20-%203%20%3C%2010)
Add 3 to both parts
![4 +3< 5x < 10+3](https://tex.z-dn.net/?f=4%20%2B3%3C%205x%20%20%3C%2010%2B3)
![7< 5x < 13](https://tex.z-dn.net/?f=7%3C%205x%20%20%3C%2013)
Divide by 5
![1.4< x < 2.6](https://tex.z-dn.net/?f=1.4%3C%20x%20%20%3C%202.6)
Substitute 2 for x
--- this is true
![(c)\ 4 < 5x - 7 < 10](https://tex.z-dn.net/?f=%28c%29%5C%204%20%3C%205x%20-%207%20%3C%2010)
Add 7 to both parts
![4 +7< 5x < 10+7](https://tex.z-dn.net/?f=4%20%2B7%3C%205x%20%3C%2010%2B7)
![12< 5x < 17](https://tex.z-dn.net/?f=12%3C%205x%20%3C%2017)
Divide by 5
![2.4< x < 3.4](https://tex.z-dn.net/?f=2.4%3C%20x%20%3C%203.4)
Substitute 2 for x
--- this is false because 2.4 > 2
![(d)\ 4 < 2x + 1 < 10](https://tex.z-dn.net/?f=%28d%29%5C%204%20%3C%202x%20%2B%201%20%3C%2010)
Subtract 1 from all parts
![4 - 1](https://tex.z-dn.net/?f=4%20-%201%20%3C2x%3C10-1)
![3](https://tex.z-dn.net/?f=3%20%3C2x%3C9%5C%5C)
Divide by 2
![1.5 < x < 4.5](https://tex.z-dn.net/?f=1.5%20%3C%20x%20%3C%204.5)
Substitute 2 for x
--- this is true
![(e)\ 4 < 2x + 3 < 10](https://tex.z-dn.net/?f=%28e%29%5C%204%20%3C%202x%20%2B%203%20%3C%2010)
Subtract 3 from all parts
![4 -3< 2x < 10-3](https://tex.z-dn.net/?f=4%20-3%3C%202x%20%3C%2010-3)
![1 < 2x < 7](https://tex.z-dn.net/?f=1%20%3C%202x%20%3C%207)
Divide by 2
![0.5 < x < 3.5](https://tex.z-dn.net/?f=0.5%20%3C%20x%20%3C%203.5)
Substitute 2 for x
----- this is true
![(f)\ 4 < 2x + 6 < 10](https://tex.z-dn.net/?f=%28f%29%5C%204%20%3C%202x%20%2B%206%20%3C%2010)
Subtract 6 from all parts
![4 -6< 2x< 10-6](https://tex.z-dn.net/?f=4%20-6%3C%202x%3C%2010-6)
![-2< 2x< 4](https://tex.z-dn.net/?f=-2%3C%202x%3C%204)
Divide by 2
![-1< x< 2](https://tex.z-dn.net/?f=-1%3C%20x%3C%202)
Substitute 2 for x
--- this is false because 2 = 2; not 2 < 2
Answer:
x = 3/2
Step-by-step explanation:
7/3 = (x + 2)/x
7x = 3(x + 2)
7x = 3x + 6
4x = 6
x = 6/4 = 3/2
There, someone helped you. Now could you do it alone next time?
1) x² + 8x + 15 = 0
Now what multiples to 15 and adds to 8? 5 and 3, 5x3=15, 5+3=8
so its
(x+5)(x+3)=0
now solve
x+5=0 x+3 =0
x = -5 x = -3
so the solution is -5, -3
4) x² - 11x + 28 = 0
what multiples to 28 and adds to -11? -7 and -4
(x-7)(x-4) =0
x= 7, 4
10) x² = 17x - 72 (okay ill do 3 of them)
first get numbers on same side where x² is positive
x² -17x + 72 = 0
what multiples to 72 and adds to -17? -9 and -8
(x-9)(x-8)=0
x= 9, 8
Answer:
It's 1,000
Step-by-step explanation:
exponential form is f(x)= a × b^2
(a=initial amount)
(b=growth rate)
you would replace a for 1000 and b for .06 (+1)
v(t)=1000(1.06)^2t
therefore the initial amount is 1000
if this didnt help sorry lol
Answer:
127
Step-by-step explanation:
m<PQR and m<RQS are supplementary angles so their sum is 180
3x - 5 + x + 1 = 180 add like terms
4x - 4 = 180 subtract 4 from both sides
4x = 176 divide both sides by 4
x = 44
m<PQR is 3x - 5 replace x with 44
3*44 - 5 = 127