Answer:
a) x = 26
b) (3 units right, 1 unit down)
Step-by-step explanation:
(a)
![12\sqrt[3]{x+1} =36](https://tex.z-dn.net/?f=12%5Csqrt%5B3%5D%7Bx%2B1%7D%20%3D36)
Divide both sides by 12:
![\implies \sqrt[3]{x+1} =3](https://tex.z-dn.net/?f=%5Cimplies%20%5Csqrt%5B3%5D%7Bx%2B1%7D%20%3D3)
Cube both sides:
![\implies x+1 =3^3](https://tex.z-dn.net/?f=%5Cimplies%20x%2B1%20%3D3%5E3)
![\implies x+1 =27](https://tex.z-dn.net/?f=%5Cimplies%20x%2B1%20%3D27)
Subtract 1 from both sides:
![\implies x=26](https://tex.z-dn.net/?f=%5Cimplies%20x%3D26)
(b)
![h(x)=g(x-3)+1](https://tex.z-dn.net/?f=h%28x%29%3Dg%28x-3%29%2B1)
translation of ![\left(\begin{array}{ccc}3\\1\end{array}\right)](https://tex.z-dn.net/?f=%5Cleft%28%5Cbegin%7Barray%7D%7Bccc%7D3%5C%5C1%5Cend%7Barray%7D%5Cright%29)
(3 units right, 1 unit down)
Answer:
6+8x
Step-by-step explanation:
If he pays with a £5 note and gets 30p change, that means the total cost was £4.70
All the items prices have to add up to £4.70
£1.18 + 94p = £2.12 so the two jars of jam together must cost £2.58 (£4.70 - £2.12).
If two jars cost £2.58 then one jar must cost half of that: £1.29
One jar = £1.29
Answer:
3,432 m²
Step-by-step explanation:
The amount of aluminum in square meters needed to make the mailboxes = 1863(surface area of each mailbox)
Surface area of each mail box = ½(surface area of cylinder) + (Surface area of rectangular prism/box - area of the surface of the box that joins the half-cylinder)
✔️Surface area of ½-cylinder = ½[2πr(h + r)]
r = ½(0.4) = 0.2 m
h = 0.6 m
π = 3.14
Surface area of ½-cylinder = ½[2*3.14*0.2(0.6 + 0.2]
= 0.628(0.8)
Surface area of ½-cylinder = 0.5024 m²
✔️Surface area of the rectangular box/prism = 2(LW + LH + WH)
L = 0.6 m
W = 0.4 m
H = 0.55 m
Surface area = 2(0.6*0.4 + 0.6*0.55 + 0.4*0.55)
Surface area of rectangular box = 1.58 m²
✔️Area of the surface joining the half cylinder and the box = L*W = 0.6*0.4 = 0.24 m²
✅Surface area of 1 mailbox = (0.5024) + (1.58 - 0.24)
= 0.5024 + 1.34
= 1.8424
Amount of aluminum needed to make 1863 mailboxes = 1863 × 1.8424 = 3,432.3912
= 3,432 m²