X < 2 is the solution to which of the following compound inequalities?

Mathematics

1 answer:

Anna35 [415]2 years ago

7 0

Answer:

see below

Step-by-step explanation:

It works well to think about what these compound inequalities mean. One way to do that is to graph them, or to imagine what the graph of them looks like.

Since the result is a single inequality (x < 2), the compound will be "and" with x < 2 being more restrictive, or will be "or" with x < 2 being the least restrictive of completely overlapping inequalities.

Of the choices offered, C is the one of interest.

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<em>Comment on other choices</em>

A has all real numbers as solutions except in the range 2 ≤ x ≤ 3.

B has no solutions

C simplifies to x < 2 . . . . the one we want

D simplifies to x < 4

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Lines a and b are parallel. What is the measure of angle s?

Arte-miy333 [17]

Answer:

Step-by-step explanation:

t = 158 Corresponding angles

t + s = 180 They are supplementary angles

158 + s = 180 Subtract 158 from both sides

s = 180 - 158

s = 22

As a note, all angles in this situation are either 158 or 22.

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2 years ago

Do even numbers have more factors in odd numbers or do i numbers have more factors than even numbers

Serggg [28]

<span>It is because even numbers always have a factor of two, and therefore, larger composite even numbers will have factors of two and other even numbers based around two, such as 4, 8, 16, 32, and so on. On the other hand, numbers which are odd can have factors of 3, 5, and 7 for example, and their numbers based around them(3, 9, 27; 5, 10, 15; 7, 49, 343; and so on). If we look into it, notice how for odd numbers the space between the numbers based around 3, 5, and 7 are increasingly further apart. This is the reason why less large odd integers to have numerous factors. It is because odd numbers cannot have the prime factor 2, this will reduce their factor number. And is is also because even numbers are already divided by 2, this will give them more factors over the odd numbers.</span>

4 0

2 years ago

An artificial lake is in the shape of a rectangle and has an area of 9/20 square mile the width of the lake is 1/5 the length of

DIA [1.3K]

Answer: The dimensions are:   " 1.5 mi.  × ³⁄₁₀ mi. " .
_______________________________________________
{ length = 1.5 mi. ; width = ³⁄₁₀  mi. } .
________________________________________________
Explanation:
___________________________________________
Area of a rectangle:

A = L * w ;

in which: A = Area = (9/20) mi.² ,
L = Length = ?
w = width = (1/5)*L = (L/5) = ?
________________________________________
A = L * w ; we want to find the dimensions; that is, the values for
"Length (L)" and "width (w)" ;
_______________________________________
Plug in our given values:
_______________________________________
(9/20) mi.² = L * (L/5) ; in which: "w = L/5" ;

→ (9/20) = (L/1) * (L/5) = (L*L)/(1*5) = L² / 5 ;

   ↔ L² / 5 = 9/20 ;

  → (L² * ? / 5 * ?) = 9/20 ?

→ 20÷5 = 4 ; so; L² *4 = 9 ;

    ↔ 4 L² = 9 ;

→ Divide EACH side of the equation by "4" ;

→ (4 L²) / 4 = 9/4 ;
______________________________________
to get: → L² = 9/4 ;
Take the POSITIVE square root of each side of the equation; to isolate "L" on one side of the equation; and to solve for "L" ;
___________________________________________

→   ⁺√(L²) = ⁺√(9/4) ;

→   L = (√9) / (√4) ;

→ L = 3/2 ;

→ w = L/5 = (3/2) ÷ 5 = 3/2 ÷ (5/1) = (3/2) * (1/5) = (3*1)/(2*5) = 3/10;
________________________________________________________
Let us check our answers:
_______________________________________
(3/2 mi.) * (3/10 mi.) =? (9/20) mi.² ??

→ (3/2)mi. * (3/10)mi. = (3*3)/(2*10) mi.² = 9/20 mi.² ! Yes!
______________________________________________________
So the dimensions are:

Length = (3/2) mi. ; write as: 1.5 mi.

width = ³⁄₁₀ mi.
___________________________________________________
or; write as: " 1.5 mi. × ³⁄₁₀ mi. " .
___________________________________________________

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2 years ago

Make g the subject of this relation

zhannawk [14.2K]

Answer:

see explanation

Step-by-step explanation:

Simplify the radical

$\frac{U}{\frac{1}{f}+\frac{1}{g} }$