3 years ago

Find the quotient of x-8 over x-10 by inspection.

Mathematics

1 answer:

Andru [333]3 years ago

7 0

$\frac{x-8}{x-10}$

$\frac{x-10+2}{x-10}$

$\frac{x-10}{x-10}+\frac{2}{x-10}$

$1 + \frac{2}{x-10}$

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He difference of two numbers is 50. twice one number equals three times the other. find the numbers.

Juli2301 [7.4K]

X-y=50 and 2x=3y
x=y+50 so 2(y+50) = 3y

2y+100=3y
y=100

x-100=50
x=150

so our numbers are 150 and 100

150-100=50 and 150 is 3*50 and 100 is 2*50 so fits all requirements!

hope this helps you! thank you!

6 0

3 years ago

What is the product of a,b, and c?

Yuri [45]

Answer:

$abc = - \frac{16}{3}$

Step-by-step explanation:

${x}^{ - 2} {y}^{3} \sqrt[3]{ 64{x}^{5} {y}^{3} } = a {x}^{b} {y}^{c} \\ \\ {x}^{ - 2} {y}^{3} \times 4 \times {x}^{ \frac{5}{3} } \times y= a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{5}{3} - 2 } {y}^{3 + 1} = a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{5 - 6}{3} } {y}^{4} = a {x}^{b} {y}^{c} \\ \\ 4 {x}^{ \frac{ - 1}{3} } {y}^{4} = a {x}^{b} {y}^{c} \\ \\ equating \: like \: terms \: on \: both \: sides \\ \\ a = 4 \\ \\ b = - \frac{1}{3} \\ \\ c = 4 \\ \\ abc = 4 \times ( - \frac{1}{3} ) \times 4 \\ \\ = 16 \times ( - \frac{1}{3} ) \\ \\ abc = - \frac{16}{3}$