Answer:
and ![y = -5\cdot t +21](https://tex.z-dn.net/?f=y%20%3D%20-5%5Ccdot%20t%20%2B21)
Step-by-step explanation:
Given that
and
, the parametric equations are obtained by algebraic means:
1)
Given
2)
Given
3)
Associative and modulative properties
4)
Existence of multiplicative inverse/Commutative property
5)
Associative property
6)
/ ![(-1)\cdot a = -a](https://tex.z-dn.net/?f=%28-1%29%5Ccdot%20a%20%3D%20-a)
7)
Modulative property
8)
Existence of additive inverse
9)
Associative and commutative properties
10)
Distributive property
11)
![(-a)\cdot (-b) = a\cdot b](https://tex.z-dn.net/?f=%28-a%29%5Ccdot%20%28-b%29%20%3D%20a%5Ccdot%20b)
12)
By 1)
13)
/Result
14)
Compatibility with addition
15)
Compatibility with addition
16)
Associative property
17)
Associative property
18)
Associative and commutative properties/Definition of subtraction/Result
In consequence, the right answer is
and
.
Answer:
4(x+2) = 4x + 8
Step-by-step explanation:
because if they are multiplied out it would be 4x+8 = 4x + 8 which means it is infinite because both sides are equal
Answer:
-0.6309
Step-by-step explanation:
Using the change of base formula,
Log 1/2 to base 3 = Log1/2 ÷ Log 3 = Log 0.5 ÷ Log 3
Log 0.5 = -0.3010
Log3 = 0.4771
Log 0.5 ÷ Log 3 = -0.3010 ÷ 0.4771 = -0.6309
Answer:
5 inches
Step-by-step explanation:
A cone's volume can be found using the formula
. If the cone has a diameter of 3 inches then its radius is half r= 1.5 inches. Substitute r = 1.5 and V = 12 cubic inches.
![V = \frac{1}{3} \pi r^2 h \\12 = \frac{1}{3} \pi (1.5)^2 h \\12 = \frac{1}{3} \pi (2.25) h\\12 = 2.355h\\5.10 = h](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20r%5E2%20h%20%5C%5C12%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%281.5%29%5E2%20h%20%5C%5C12%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%282.25%29%20h%5C%5C12%20%3D%202.355h%5C%5C5.10%20%3D%20h)
This means the height of the cone is 5.10 inches or to the nearest inch 5 inches.