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2 years ago

Factor 2x^4 + 2x^3 - x^2 - x

Mathematics

1 answer:

MAVERICK [17]2 years ago

8 0

2x^3(x+1)-x(x+1)
(2x^3-x)(x+1)
x(2x^2-1)(x+1)

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Triangle FGH is an equilateral triangle.FH=6x+1,FG=3x+10,and GH=9x-8

Lena [83]

Answer:

Acute triangle

x = 3

GH = 19

Step-by-step explanation:

7 0

2 years ago

Tom has three times as many pencils as pens but has a total of 100 writing utensils. How many pencils does Tom have? How many pe

Genrish500 [490]

Answer:

There are 75 pencils and 25 pens.

Step-by-step explanation:

If Tom has three times as many pencils than pens then,

Pencils = 3(Pens)

If there are a total of 100 writing utensils then,

Pencils + Pens = 100

Substitute the word "pencils" in this equation to 3(Pens),

3(Pens) + Pens = 100

Now remember there is almost a 'hidden' one beside the word "Pens" so,

3Pens + 1Pens = 100

Add the two together,

4Pens = 100

Divide,

Pens = 25

Substitute 25 into the first equation,

Pencils = 3(25)

Pencils = 75

Thus, there are 75 pencils and 25 pens.

3 0

2 years ago

Find a fraction equivalent to 5/7 whose squared terms add up to 1184.

bogdanovich [222]

The system of equations of two unknowns is formulated and solved.

$\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left\{\begin{matrix} \ \ \ \dfrac{x}{y} = \dfrac{5}{7} \\ x^2+y^2 = 1184 \end{matrix}\right. \ \Longrightarrow \ x=\dfrac{5}{7}y } \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf \bf{ \left (\dfrac{5}{7}y \right )^2+y^2=1184\ \Longrightarrow\ 25y^2+49y^2=58016 } \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf \bf{74y^{2}=58016} \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ \ y^{2}=784 } \end{gathered}$}\\\large\displaystyle\text{$\begin{gathered}\sf \bf{ \ \ \ \ \ y=\pm\sqrt{784}=\pm28 } \end{gathered}$}$

$\large\displaystyle\text{$\begin{gathered}\sf \bf{ x=\dfrac{5}{7}(\pm 28)=\pm 20 } \end{gathered}$}$

The fraction that satisfies the request is $\bf{\dfrac{20}{28}}$ , since in $\bf{\dfrac{-20}{-28}}$ the negative signs are canceled and the first fraction is obtained.

3 0

1 year ago

Solve for h in h+6/5=2

Ivenika [448]

Answer:

h=4/5

Step-by-step explanation:

$h + \frac{6}{5} = 2$

Collect like terms and simplify

$h = 2 - \frac{6}{5} \\ h = \frac{4}{5}$

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3 years ago

A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, thi

pickupchik [31]

We are given a rain gutter made from folding a 12 inch wide aluminum sheet to an angle theta. The area of the opening is expressed as A(Θ) = 16 sin Θ (cos Θ + 1) where <span>Θ = 45°. we can just substitute directly the angle in degrees mode in the calculator and the answer is equal to 19.32 inches2.</span>

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2 years ago

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