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Virty [35]
3 years ago
5

Christopher bought 4 pens that cost the same amount of money and a marker that cost $3. He spent a total of $11. Which statement

correctly describes how to find the cost of each pen arithmetically?
Mathematics
1 answer:
Nikolay [14]3 years ago
8 0
The pens cost $2 each.
2*4+3=11
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Show that 2x +1 is a factor of 2x3 +5x2+4x+1 and factories completely
larisa [96]

\text{According to the factor theorem, if f(b) = 0, then x-b is a factor of f(x).}\\\\\text{Given that,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\f\left(-\dfrac 12 \right) = 2\left( - \dfrac 12 \right)^3 +5 \left( - \dfrac 12 \right)^2 +4 \left( - \dfrac 12 \right) +1 \\\\\\~~~~~~~~~~~~=-2 \cdot \dfrac 18 + 5 \cdot \dfrac 14 -2 +1 \\\\\\~~~~~~~~~~~=\dfrac 54 -\dfrac14 -1\\\\\\~~~~~~~~~~~=\dfrac 44 -1 \\\\\\~~~~~~~~~~~=1-1\\\\\\~~~~~~~~~~~=0\\\\\text{So,}~ 2x +1 ~ \text{is a factor of f(x).}

\text{Now,}\\\\f(x) = 2x^3 +5x^2 +4x +1 \\\\~~~~~~=2x^3+x^2 +2x^2 +2x +2x+1\\\\~~~~~~=x^2(2x+1)  +2x(2x+1) +  (2x+1)\\\\~~~~~~=(2x+1)(x^2 +2x +1)\\\\~~~~~~=(2x+1)(x+1)^2

3 0
2 years ago
Solve the combined inequality and describe the graph of the solution.
Vikki [24]
I hope this helps you



4x>-4 x>-1



8x <32 x <4


-1 <x <4
3 0
3 years ago
PLEASE HELP! create an example of a linear system that would best be solved using the substitution method. explain your reasonin
Semenov [28]

Answer:

In your change cup you have 28 coins.  All of which are nickels and quarters.  Together they add up to $4.  How many coins do you have of each.

It is easier to solve by substitution.

3 0
3 years ago
W - 5,129 = 2,329<br><br>A. w = 7,468<br><br>B. w = 7,558<br><br>C. w = 7,458
Shkiper50 [21]
W−5129=2329

Step 1: Add 5129 to both sides.
(5129+2339)

w−5129+5129=2329+5129 =

w=7458

7 0
3 years ago
The general manager of a
sasho [114]

Answer:

18564

Step-by-step explanation:

In the problem Given, we just need to see t any 6, the order of selection does not matter, hence, this is a combination problem :

Using the combination relation :

nCr = 18C6

Recall ;

nCr = n! / (n-r)!r!

18C6 = 18! / (18-6)!6!

18C6 = 18! / 12!6! = (18*17*16*15*14*13) / (6*5*4*3*2*1)

18C6 = 13366080 / 6!

18C6 = 18564

3 0
3 years ago
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