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Alisiya [41]
3 years ago
10

Find all real numbers z for which the equation (z-5)x^2-zx+5=0 only has one real solution. If you find more than one, then list

the values separated by commas.
Mathematics
1 answer:
Nataliya [291]3 years ago
7 0

Step-by-step explanation:

For the quadratic equation to have 1 repeated real solution, the discriminant b² - 4ac must be zero.

=> (-z)² - 4(z - 5)(5) = 0

=> z² - 20(z - 5) = 0

=> z² - 20z + 100 = 0

=> (z - 10)² = 0

Therefore z = 10.

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Dennis_Churaev [7]
\bf -\cfrac{16}{21}-\left( -\cfrac{13}{15} \right)\implies -\cfrac{16}{21}+\cfrac{13}{15}\impliedby \textit{we'll use the LCD of 105}
\\\\\\
\cfrac{(-16\cdot 5)~+~(13\cdot 7)}{105}\implies \cfrac{-80~+~91}{105}\implies \cfrac{+11}{105}\implies \cfrac{11}{105}

in case you wonder why we used 105 as LCD,  

21 = 3 * 7

15 = 3 * 5

the "3" is common to both denominators, so we "use it once" and our LCD is then 3 * 7 * 5.
7 0
3 years ago
Cost of an oil change: $18.00; Markup: 3/4 answers
hjlf
I am assuming that the cost of an oil change already includes the mark-up.

So, 18 is 175%.  18 ÷ 1.75 = 10.29 is the original cost.

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Answer:

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