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3 years ago

E/P 14)The equation 2x²+ 4kx - 5k = 0, where k is a constant, has no real roots.

Mathematics

1 answer:

aalyn [17]3 years ago

4 0

Step-by-step explanation:

Discriminant = 16k² - 4(2)(-5k)

Since 16k² + 40k < 0, 2k² + 5k < 0, k(2k + 5) < 0.

Therefore -5/2 < k < 0.

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A hotel offers two activity packages. One costs $192 and includes 3 h

matrenka [14]

Answer:

Cost of 1 hour of horseback riding is $30 and cost of 1 hour of parasailing is $51.

Step-by-step explanation:

Let cost of horseback riding be $h$

Let cost of parasailing be $p$

"First Package costs $192 and includes 3 h of horseback riding and 2 h of parasailing. "

We can write $3h+2p=192$

"Second Package costs $192 and includes 3 h of horseback riding and 2 h of parasailing. "

We can write $2h+3p=213$

Solving these 2 equations simultaneously will give us cost of horseback riding for 1 hours [h] and cost of parasailing for 1 hours [p].

Solving for $h$ in Equation 1 and substituting that in Equation 2, we can solve for $p$ :

$3h+2p=192\\3h=192-2p\\h=\frac{192-2p}{3}$

$2(\frac{192-2p}{3})+3p=213\\\frac{384-4p}{3}+3p=213\\\frac{384-4p+9p}{3}=213\\384+5p=639\\5p=639-384\\5p=255\\p=51$

Now, taking the value $p=51$ and putting it in either equation and solving for $h$ will give us the value of $h$ . Let's substitute it into Equation 1:

$3h+2(51)=192\\3h+102=192\\3h=192-102\\3h=90\\h=30$

Hence, cost of 1 hour of horseback riding is $30 and cost of 1 hour of parasailing is $51.

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