Answer:
(-162)/7 or -23 1/7 as mixed fraction
Step-by-step explanation:
Simplify the following:
(-36)/14 (-18) (-3)/6
Hint: | Express (-36)/14 (-18) (-3)/6 as a single fraction.
(-36)/14 (-18) (-3)/6 = (-36 (-18) (-3))/(14×6):
(-36 (-18) (-3))/(14×6)
Hint: | In (-36 (-18) (-3))/(14×6), divide -18 in the numerator by 6 in the denominator.
(-18)/6 = (6 (-3))/6 = -3:
(-36-3 (-3))/14
Hint: | In (-36 (-3) (-3))/14, the numbers -36 in the numerator and 14 in the denominator have gcd greater than one.
The gcd of -36 and 14 is 2, so (-36 (-3) (-3))/14 = ((2 (-18)) (-3) (-3))/(2×7) = 2/2×(-18 (-3) (-3))/7 = (-18 (-3) (-3))/7:
(-18 (-3) (-3))/7
Hint: | Multiply -18 and -3 together.
-18 (-3) = 54:
(54 (-3))/7
Hint: | Multiply 54 and -3 together.
54 (-3) = -162:
Answer: (-162)/7
Answer:
The number of liters of 25% acid solution = x = 160 liters
The number of liters of 40% acid solution = y = 80 liters
Step-by-step explanation:
Let us represent:
The number of liters of 25% acid solution = x
The number of liters of 40% acid solution = y
Our system of Equations =
x + y = 240 liters....... Equation 1
x = 240 - y
A 25% acid solution must be added to a 40% solution to get 240 liters of 30% acid solution.
25% × x + 40% × y = 240 liters × 30%
0.25x+ 0.4y = 72...... Equation 2
We substitute 240 - y for x in Equation 2
0.25(240 - y)+ 0.4y = 72
60 - 0.25y + 0.4y = 72
Collect like terms
- 0.25y + 0.4y = 72 - 60
0.15y = 12
y = 12/0.15
y = 80 Liters
Solving for x
x = 240 - y
x = 240 liters - 80 Liters
x = 160 liters
Therefore,
The number of liters of 25% acid solution = x = 160 liters
The number of liters of 40% acid solution = y = 80 liters
Answer:
2.05 inches
Step-by-step explanation:
V = 4/3 x πr³
36=4πr³/3
36x3= 4πr³
108= 4πr³
108/4 = πr³
27= πr^3
27/π =r³
r=
![\sqrt[3]{27 \div \pi}](https://tex.z-dn.net/?f=%20%5Csqrt%5B3%5D%7B27%20%5Cdiv%20%5Cpi%7D%20)
r= 2.048in
round off to 2.05in
<u>PROOF</u>
V = 4÷3 x πr³
V= 4/3 x π(2.05)³
V=4/3 x π8.6
V=4×π×8.6/3
V=108/3
V=36in³
Therefore: radius= <u>2.05 inches</u>
Easy
y=2x-7
sub 2x-7 for every y you se inother equation
x+2(2x-7)=1
x+4x-14=1
5x-14=1
add 14 both sides
5x=15
divide 5
x=3
sub back
y=2x-7
y=2(3)-7
y=6-7
y=-1
(3,-1) is solution
Answer:
14.16 miles further.
Step-by-step explanation:
Campbell to Summerfield
9.52mi + 4.62 mi + 10.08 mi = 24.24 mi
Princeton to summerfield
is 10.08 mi
Therefore difference is 24.24mi - 10.08mi = 14.16 mi
Hope this helps.