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Andru [333]
3 years ago
11

Solve the following inequality. 4x-1> -9

Mathematics
1 answer:
pychu [463]3 years ago
3 0
Solve inequalities the way you would solve an equation except for this rule-
If you multiply or divide a negative, the sign must be switched.

Do the inverse of everything like in an equation-
4x-1> -9
+1      +1 (Add 1)
4x>-8
/4    /4     (Divide 4)
You are not dividing a negative number from another number.  So keep the sign.
x>-2
Your answer is C.


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How many sets of three consecutive integers are there in which the sum of the three integers equals their product?
skad [1K]

Answer:

3

Step-by-step explanation:

since the 3 integers are consecutive, we are dealing with x, x+1, x+2.

and their sum is the same as their product :

x + (x + 1) + (x + 2) = x(x + 1)(x + 2)

3x + 3 = x(x² + 3x + 2) = x³ + 3x² + 2x

x³ + 3x² - x - 3 = 0

this is a polynomial of third degree.

and as such it has 3 solutions.

of course, it could be that some of them are the same or are even in the realm of complex numbers (i = sqrt(-1)), but usually these 3 solutions are different real numbers.

I tried x=1 just to see, and, hey, it is a solution for this equation.

x = 1 means that the other 2 consecutive integers are 2 and 3.

and indeed, 1+2+3 = 1×2×3 = 6.

now it is easier to find the other 2 solutions, as a zero solution can be expressed as a factor of the whole expression.

for x = 1 the factor term is (x - 1), as this term is then turning 0, when x = 1.

I can divide the main expression by this factor and then analyze the quotient about the other 2 solutions.

x³ + 3x² - x - 3 : x - 1 = x² + 4x + 3

- x³ - x²

----------------

0 4x² - x

- 4x² - 4x

-----------------------

0 + 3x - 3

- 3x - 3

---------------------------

0 0

so, the original expression can be written as

(x² + 4x + 3)(x - 1).

now we need to find the 2 zero solutions for x²+4x+3

the general solution to a quadratic equation is

x = (-b ± sqrt(b² - 4ac))/(2a)

in our case

a = 1

b = 4

c = 3

so,

x = (-4 ± sqrt(4² - 4×1×3))/(2×1) =

= (-4 ± sqrt(16 - 12))/2 = (-4 ± sqrt(4))/2 =

= (-4 ± 2)/2 = -2 ± 1

x1 = -2 + 1 = -1

x2 = -2 - 1 = -3

so, we have the additional solutions :

-1 0 1

-3 -2 -1

-1 + 0 + 1 = -1×0×1 = 0

-3 + -2 + -1 = -3×-2×-1 = -6

and there we have it fully proven :

there are 3 different sets of 3 consecutive integers with the same sum as product.

4 0
2 years ago
PLS HELP BRAINLIEST AND EXTRA POINTS !
Svetlanka [38]

Answer:

D

Step-by-step explanation:

4 + 12 + 18 + 68=  102/2 51

40 + 28 + 52 + 76= 196/2 98

51:98

5 0
3 years ago
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(–2) + 6 + 1 = 1 + 6 + (–2) =
Fudgin [204]

Answer:

5=5

Step-by-step explanation:

6 0
3 years ago
Amanda plans to have 20 friends over to Watch NCAA Basketball on Saturday. She plans to serve pizza, wings, soda, and brownies.
poizon [28]
<h2><u>In total, she will need $98.34 to pay all of the foods she plans to serve at the party.</u></h2>

All of the work:

<em>How to solve the amount of pizza she needs:</em>

20 x 3 = 60

60 divided by 10 = 6

<em>How to solve the amount of soda bottled needed:</em>

20 x 16 = 320

320 divided by 64 = 5

<em>How to solve the number of pans she needs:</em>

20(2 x 3) = 40 x 60

40 x 60 divided by 8 x 12 = 5

<h2>THE COST CAN BE FOUND BY MULTIPLYING THE NUMBER OF THE ITEM NEEDED AND THE PRICE FOR EACH OF THE ITEM.</h2>

<em>Number of pizza she needs:6 pizza, costs $77.94</em>

<em>Number of soda bottles she needs:5 bottles, costs $8.45</em>

<em>Number of pans she needs:5 pans, costs $11.95</em>

<em>Add 77.94, 8.45, and 11.95 and get 98.34</em>

7 0
3 years ago
Define perpendicular bisector
Maksim231197 [3]
My guess would be A, but I may be wrong
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