Logarhythm

Let c = Cheko's toy cars and k = Keddy's toy cars. 

c + k = 370
0.25c = 0.2k + 25

20c = -20k + 7400 
25c = 20k + 2500

------------------------

45c = 9900

c = 220

c + k = 370
(220) + k = 370
k = 150 

220 - 150 = 70

Cheko collected 70 more cars than Keddy. 

Factors of 10 are 1, 2, 5, and 10. 

Only 2 and 5 are 3 apart, meaning the two numbers are -2, and 5. 

Since we want to fill this tank to a depth of 26 inches, and the base of the tank is already given, we just need to multiply the dimensions to find how much water we need:

17 x 21 x 26 = 9282 inch³ of water. 

\(\sum_{k=1}^{6} -3(-4)^{k-1} = -3(-4)^{1-1} -3(-4)^{2-1}-3(-4)^{3-1}-3(-4)^{4-1}-3(-4)^{5-1}\)

                                 \(= -3(-4)^{0} -3(-4)^{1}-3(-4)^{2}-3(-4)^{3}-3(-4)^{4}\)

                                 \(= -3 + 12 - 48 +192 - 768\)

                                 \(= -615\)

let me know if I did anything wrong :)

first let's find the 50th term. 

the "zeroth" term would be 16 - 3 = 13, meaning the 50th term would be 3(50) + 13 = 163. 

\(S_n = \frac{n(a_1 + a_n)}{2}\) where \(a_1\) is the first term and \(a_n\) is the last term of the sum you're finding.

\(S_{50} = \frac{50(16 + 163)}{2}\)

\(S_{50} = 25(179)\)

\(S_{50} = 4475\)

tell me if I did anything wrong :)

You get birthed by your original parents. But something unfortunate happens and they decide to leave you at an orphanage because they can't take care of you, which is where you get adopted. 

1) 8x² - 72 = 0 

    x² - 9 = 0

    x² = 9

    x = ± 3

\(\frac{(\frac{1}{y} - \frac{1}{x})}{\frac{1}{y} + \frac{1}{x}}\)

\(= \frac{\frac{x - y}{xy}}{\frac{x+y}{xy}}\)

\(= \frac{x-y}{x+y}\)

I think this is right..

\(\log_x 4 = \log_3 27\)

\(\log_x 4 = 3\)

\(x^3 = 4\)

\(x = \sqrt[3]{4}\)

\(7(3x + 5)\)

\(= 7(3(\frac{1}{2}) + 5)\)

\(= 7(1\frac{1}{2} + 5)\)

\(= 7 \cdot 6\frac{1}{2}\)

\(= 45 \frac{1}{2}\)