Answer:
Step-by-step explanation:
![3\log_5(x-10)-\dfrac{1}{2}\log_54=5\log_52\\\\\text{Domain:}\ x-10>0\to x>10\\\\\text{use}\\\\\log_ab^n=n\log_ab\\\\\log_ab-\log_ac=\log_a\left(\dfrac{b}{c}\right)\\========================\\\\\log_5(x-10)^3-\log_54^\frac{1}{2}=\log_52^5\qquad\text{use}\ a^\frac{1}{2}=\sqrt{a}\\\\\log_5(x-10)^3-\log_5\sqrt4=\log_532\\\\\log_5(x-10)^3-\log_52=\log_532\\\\\log_5\dfrac{(x-10)^3}{2}=\log_532\iff\dfrac{(x-10)^3}{2}=32\qquad\text{multiply both sides by 2}\\\\(x-10)^3=64\to x-10=\sqrt[3]{64}\\\\x-10=4\qquad\text{add 10 to both sides}\\\\x=14\in D](https://tex.z-dn.net/?f=3%5Clog_5%28x-10%29-%5Cdfrac%7B1%7D%7B2%7D%5Clog_54%3D5%5Clog_52%5C%5C%5C%5C%5Ctext%7BDomain%3A%7D%5C%20x-10%3E0%5Cto%20x%3E10%5C%5C%5C%5C%5Ctext%7Buse%7D%5C%5C%5C%5C%5Clog_ab%5En%3Dn%5Clog_ab%5C%5C%5C%5C%5Clog_ab-%5Clog_ac%3D%5Clog_a%5Cleft%28%5Cdfrac%7Bb%7D%7Bc%7D%5Cright%29%5C%5C%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%3D%5C%5C%5C%5C%5Clog_5%28x-10%29%5E3-%5Clog_54%5E%5Cfrac%7B1%7D%7B2%7D%3D%5Clog_52%5E5%5Cqquad%5Ctext%7Buse%7D%5C%20a%5E%5Cfrac%7B1%7D%7B2%7D%3D%5Csqrt%7Ba%7D%5C%5C%5C%5C%5Clog_5%28x-10%29%5E3-%5Clog_5%5Csqrt4%3D%5Clog_532%5C%5C%5C%5C%5Clog_5%28x-10%29%5E3-%5Clog_52%3D%5Clog_532%5C%5C%5C%5C%5Clog_5%5Cdfrac%7B%28x-10%29%5E3%7D%7B2%7D%3D%5Clog_532%5Ciff%5Cdfrac%7B%28x-10%29%5E3%7D%7B2%7D%3D32%5Cqquad%5Ctext%7Bmultiply%20both%20sides%20by%202%7D%5C%5C%5C%5C%28x-10%29%5E3%3D64%5Cto%20x-10%3D%5Csqrt%5B3%5D%7B64%7D%5C%5C%5C%5Cx-10%3D4%5Cqquad%5Ctext%7Badd%2010%20to%20both%20sides%7D%5C%5C%5C%5Cx%3D14%5Cin%20D)
Answer:
The constant of variation is the number that relates two variables that are directly proportional or inversely proportional to one another.
Step-by-step explanation:
The total interest earned is 40.75 and the final balance is 65.75
<u>Solution:</u>
Given, principle amount P = 25
Interest rate 
Times compounded per year n = 12
Time in years t = 30
On substituting the values we get
![A = 25 [ 1+ \frac{0.0325}{12}]^{12\times30}= 25 [2.63]= 65.75](https://tex.z-dn.net/?f=A%20%3D%2025%20%5B%201%2B%20%5Cfrac%7B0.0325%7D%7B12%7D%5D%5E%7B12%5Ctimes30%7D%3D%2025%20%5B2.63%5D%3D%2065.75)
Interest I = A - P [since, A = P+I]
Answer:
D
Step-by-step explanation:
y = -0.2 x²
This has a negative sign, as opposed to y = x², so it will point in the opposite direction.
The leading coefficient (0.2) is less than 1. This means the parabola is shrunk vertically, or stretched horizontally. So the parabola is wider than y = x².
Complete question :
Gary has (20x + 7) dollars. Gary decides to buy two pairs of jeans. Each pair of jeans costs (2x - 3) dollars. write an expression that represents how much money gary will have left over after the purchase then simplify your expression
Answer:
$(16x - 1)
Step-by-step explanation:
Given that:
Amount Gary has = $(20x + 7)
Price per pair of jeans = $(2x - 3)
Number of pairs = 2
Cost of 2 Jean pairs = 2 * $(2x - 3) = $(4x - 6)
Amount left after purchase :
$(20x - 7) - $(4x - 6)
20x - 7 - 4x + 6
20x - 4x - 7 + 6
$(16x - 1)
