Answer:
log(x^7·y^2)
Step-by-step explanation:
The applicable rules are ...
... log(a^b) = b·log(a)
... log(ab) = log(a) +log(b)
_____
The first term, 7log(x) can be rewritten as log(x^7). Note that an exponentiation operator is needed when this is written as text.
The second term 2log(y) can be rewritten as log(y^2). These two rewrites make use of the first rule above.
Now, you have the sum ...
... log(x^7) +log(y^2)
The second rule tells you this can be rewritten as ...
... log(x^7·y^2) . . . . . seems to match the intent of the 3rd selection
Let x = no. of 10 oz cups sold
Let y = no. of 14 oz cups sold
Let z = no. of 20 oz cups sold
:
Equation 1: total number of cups sold:
x + y + z = 24
:
Equation 2: amt of coffee consumed:
10x + 14y + 20z = 384
:
Equation 3: total revenue from cups sold
.95x + 1.15y + 1.50z = 30.60
:
Mult the 1st equation by 20 and subtract the 2nd equation from it:
20x + 20y + 20z = 480
10x + 14y + 20z = 384
------------------------ subtracting eliminates z
10x + 6y = 96; (eq 4)
Mult the 1st equation by 1.5 and subtract the 3rd equation from it:
1.5x + 1.5y + 1.5z = 36.00
.95x + 1.15y+ 1.5z = 30.60
---------------------------subtracting eliminates z again
.55x + .35y = 5.40; (eq 5)
Multiply eq 4 by .055 and subtract from eq 5:
.55x + .35y = 5.40
.55x + .33y = 5.28
--------------------eliminates x
0x + .02y = .12
y = .12/.02
y = 6 ea 14 oz cups sold
Substitute 6 for y for in eq 4
10x + 6(6) = 96
10x = 96 - 36
x = 60/10
x = 6 ea 10 oz cups
That would leave 12 ea 20 oz cups (24 - 6 - 6 = 12)
Check our solutions in eq 2:
10(6) + 14(6) + 20(12) =
60 + 84 + 240 = 384 oz
A lot steps, hope it made some sense! I hope this helps!! ;D
Answer:
2x-6+2=14
Step-by-step explanation:
2x-6+2=14
2x-4=14
2x=14-4
2x=10
x=5
Answer:
XZ = 26.7
ZY = 11.7
Area = 140.4 sq inches
Step-by-step explanation:
m∠Z = 180-(26+90) = 64°
to get XZ you can use the law of sines:
sin 90°/XZ = sin 64°/24
1/XZ = sin(64°)
cross-multiply to get:
XZ·sin(64°) = 24
XZ = 24/sin(64°)
XZ = 26.7
to get ZY you can use the law of sines again:
sin 64°/24 = sin 26°/ZY
cross-multiply to get:
ZY·sin(64°) = 24·sin(26°)
ZY = 24·sin(26°) ÷ sin(64°)
ZY = 11.7
Area = 1/2(11.7)(24)
= 12(11.7)
= 140.4 sq inches
Answer:
Step-by-step explanation:
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<u><em>Cancelling (x-1)</em></u>
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