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Jlenok [28]
3 years ago
7

Solve the inequality 2x2 + 10x < –8

Mathematics
1 answer:
BigorU [14]3 years ago
5 0

Answer:

-4<x<-1

Step-by-step explanation:

To solve the problem, we divide the whole expression by 2:

2x^2 + 10x < –8 → x^2 + 5x < –4

→  x^2 + 5x + 4 < 0

Factorizing

→ (x+4)(x+1) < 0

The expression is ONLY negative when:

x>-4 and x<-1

Therefore, the solution is:

-4<x<-1

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3 years ago
Read 2 more answers
The sum of three numbers is 8. The third is 9
Ierofanga [76]

Answer:

→<u> </u><u>First</u><u> </u><u>value</u><u> </u><u>is</u><u> </u><u>1</u>

→<u> </u><u>Second</u><u> </u><u>value</u><u> </u><u>is</u><u> </u><u>2</u>

→<u> </u><u>Third</u><u> </u><u>value</u><u> </u><u>is</u><u> </u><u>5</u>

Step-by-step explanation:

• let numbers be x, y and z

{ \tt{z = 8y - 9 -  -  - (eqn \: 1)}} \\  \\ { \tt{10x = 8y - 7 -  -  - (eqn \: 2)}} \\  \\ { \tt{x + y + z = 8 -  -  - (eqn \: 3)}}

• from eqn 2, make x the subject:

{ \tt{x =  \frac{8y - 7}{10} }} \\

• substitute all variables in eqn 3:

{ \tt{ \frac{8y - 7}{10}  + y + 8y - 9 = 8}} \\  \\ { \tt{8y - 7 + 10y + 80y - 90 = 80}} \\  \\ { \tt{98y = 177}} \\  \\ { \boxed{ \tt{ \: y = 1.8}}}

• find z

{ \tt{z = 8y - 9}} \\  \\ { \tt{z = 8(1.8) - 9}} \\  \\ { \tt{z = 14.4 - 9}} \\  \\ { \boxed{ \tt{ \: z = 5.4 \: }}}

• find x:

{ \tt{x =  \frac{8(1.8) - 7}{10} }} \\  \\ { \tt{x =  \frac{7.4}{10} }} \\  \\ { \boxed{ \tt{ \: x = 0.74 \: }}}

Rounding to nearest value:

{ \boxed{ \rm{x = 1}}} \\ { \boxed{ \rm{y =2 }}} \\ { \boxed{  \rm{z = 5}}}

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Answer:

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Archaea because it can survive in the diverse environments and is distinctly different from Bacteria which can also survive.

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