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3 years ago

What is the solution of mc016-1.jpg? \frac{x^2-1}{x^2+5x+4}<0

Mathematics

2 answers:

Alinara [238K]3 years ago

6 0

Answer:

C 5 over 4

Step-by-step explanation:

lions [1.4K]3 years ago

5 0

( x² - 1 ) / ( x² + 5 x + 4 ) < 0
x² + 5 x + 4 = x² + 4 x + x + 4 = x ( x + 4 ) + ( x + 4 ) = ( x + 4 ) ( x + 1 )
Therefore:
( x - 1 ) ( x + 1 ) / ( x + 4 ) ( x + 1 ) < 0
( x -1 ) / ( x + 4 ) < 0
1.
x - 1 > 0 and x + 4 < 0
x > 1 and x < - 4 ( not possible )
2.
x - 1 < 0 and x + 4 > 0
x < 1 and x > - 4
Answer: x ∈ ( - 4, 1 ).

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3 years ago

You sell your bicycle to your friend for 65$ your friend gives you x five dollar bills and y ten dollar bills. There are a total

jeka94

Answer:

There are $5$ five dollar bills and $4$ ten dollar bills.

Step-by-step explanation:

Given:

Selling price of bicycle $=\$65$ .

The friend gave $x$ five dollar bills and $y$ ten dollar bills.

Total number of bills $=9$ .

To find: Number of five dollar bills and ten dollar bills the friend gave.

Solution:

The friend gave $x$ five dollar bills and $y$ ten dollar bills and the friend gave $9$ bills in all.

So, $x+y=9$ .

$\Rightarrow x=9-y ...(i)$

Selling price of bicycle $=\$65$ .

So, $5x+10y=65...(ii)$

Putting the value of $x$ from equation $(i)$ in equation $(ii)$ .

$\Rightarrow 5(9-y)+10y=65$

$\Rightarrow 45-5y+10y=65$

$\Rightarrow 45+5y=65$

$\Rightarrow 5y=65-45$

$\Rightarrow 5y=20$

$\Rightarrow y=\frac{20}{5}$

$\Rightarrow y=4$

Now, putting the value of $y$ in equation $(i)$ .

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Hence, there are $5$ five dollar bills and $4$ ten dollar bills.

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3 years ago

Write the equation of a vertical ellipse with a major axis of 20, a minor axis of 12, and a center of (6, 3)

maksim [4K]

Answer:

The equation of a vertical ellipse is $\frac{(x-6)^2}{100} + \frac{(y-3)^2}{36} = 1\\$

Step-by-step explanation:

Here, given:

Length of major axis: 20

⇒ 2 a = 20 , or , a = 10

Length of minor axis: 12

⇒ 2 b = 12 , or , b = 6

Also, center (h,k) = (6,3)

Now, STANDARD EQUATION OF ELLIPSE :

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\\$

Now, substituting the values, a, b , h and k in above expression, we get:

$\frac{(x-6)^2}{10^2} + \frac{(y-3)^2}{6^2} = 1\\$

or, $\frac{(x-6)^2}{100} + \frac{(y-3)^2}{36} = 1\\$

Hence, the equation of a vertical ellipse is $\frac{(x-6)^2}{100} + \frac{(y-3)^2}{36} = 1\\$

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3 years ago

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Aleks [24]

Answer:

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3 years ago

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Serga [27]

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3 years ago

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