Answer:3x^3(3x^3+2x+5)
Step-by-step explanation:by looking at the polynomial, you can see that all three shares the variable x. Since 9,6, and 25 all share the GCF of 3, you can factor it out. Since the smallest x value of the polynomial is x^3, that is the x value you want to factor out. Since if you factor out x^3 then 15x^3 would not have a variable anymore.
Answer: x log[5] = log[125]
Explanation:
The original expression is 125 = 5^x
To express that as a logarithmic equation take logarithms on both sides:
log [125] = [log 5^x]
By the properties of the logartims of powers that is:
log [125] = x log[5]
And that is the equation required.
If you want to solve it, you can do 125 = 5^2, and apply the same property (logarithm of a power) to the left side, yielding to:
log [5^2 ]= x log[5]
=> 2 log[5] = x log[5]
=> 2 = x
The answer is 32.5 aka 32 1/2.
Let's assume two variables x and y which represent the local and international calls respectively.
x + y = 852 = total number of minutes which were consumed by the company (equation 1)
0.06*x+ 0.15 y =69.84 = total price which was charged for the phone calls (Equation 2)
from equation 1:-
x=852 -y (sub in equation 2)
0.06 (852 - y) + 0.15 y =69.84
51.12 -0.06 y +0.15 y =69.84 (subtracting both sides by 51.12)
0.09 y =18.74
y= 208 minutes = international minutes (sub in 1)
208+x=852 (By subtracting both sides by 208)
x = 852-208 = 644 minutes = local minutes
9514 1404 393
Answer:
20 miles
Step-by-step explanation:
The north and east distances form the legs of a right triangle. The straight-line distance between the trains is the hypotenuse of that triangle. The Pythagorean theorem can be used to find the length of the hypotenuse (d).
d² = 12² +16²
d² = 144 +256 = 400
d = √400 = 20
The two trains are 20 miles apart.
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<em>Additional comment</em>
You may recognize the given distances are in the ratio 3 : 4. You may recall that side ratios of 3 : 4 : 5 make a right triangle. If so, you recognize that the straight-line distance is (4 miles)×5 = 20 miles. (3:4:5 right triangles show up often in algebra and geometry problems, so might be something you want to look for.)
