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3 years ago

Given the binomials (x + 1), (x + 4), (x - 5), and (x - 2), which one is a factor of f(x) = 3x^3 - 12x^2 - 4x - 55?

1 answer:

4 0

If (x-a) is the factor of f(x) then,
f(a)=0 and vice-versa
or,3x³-12x²-4x-55=0 .. .eqn(1)
Compare (x-a) with the binomials (x + 1), (x + 4), (x - 5), and (x - 2).....then
CHECK f(a)=0 by putting a=-1,-4,5,2 then
we get
f(-1)=3×(-1)³-12×(-1)²-4×(-1)-55=-66
f(-4)=............................,..............=other value than 0
f(5)= 3×(5)³-12×(5)²-4×(5)-55=0 (satisfies eqn1)
f(2)=...............=other value than 0(checkyourself)
Here, only f(5)=0
the factor of f(x)=(x-5)

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A certain number is increased by 5 the result is 8 more than half the number what is the number

sdas [7]

11 would be my best guess, kinda confusing question. I hope I helped!

8 0

3 years ago

You have 600 feet of fencing to enclose a rectangular plot that borders on a river. If you do not fence the side along the river

inn [45]

Answer:

The length and width of plot is $L=300\:ft$ , $W=150\:ft$

Largest area of the plot is $A=45000 ft^{2}$

Step-by-step explanation:

Assume width as x and length as y. Given that length of fencing is 600 feet and fencing is enclosed on 3 sides. So perimeter is given as,

Perimeter = width + length + width

Substituting the value,

$600=x+y+x$

$600= 2x+y$ ….1

Now area of fence of rectangular box is given as follows,

$A=xy$ ….2

Solving equation 1 for y, subtracting 2x from both sides,

$600-2x= y$

Substituting the value in equation 2,

$A=x\left (600-2x \right )$

Simplifying

$A=600x-2x^{2}$

Rewriting,

$A=-2x^{2}+600x$

Above equation looks like quadratic equation $f\left ( x \right )=ax^{2}+bx+c$ whose graph looks like parabola.

Comparing equation f(x) and A values of a, b and c are, $a=-2,b=600$ and $c=0$ .

Now maximum of $f\left ( x \right )$ occurs at vertex.

The x coordinate of the vertex is given as $-\dfrac{b}{2a}$

Substituting the values,

$x=-\dfrac{600}{2\left (-2 \right )}$

Simplifying,

$x=\dfrac{600}{4}$

$x=150$

So width of plot is 150 feet.

Now to calculate value of length by using equation 1,

$600= 2x+y$

Substituting the values,

$600= 2\left (150 \right )+y$

$600= 300+y$

Subtracting 300 from both sides,

$300= y$

So length of plot is 300 ft.

The y coordinate of the vertex is given as $y=f\left ( -\dfrac{b}{2a} \right )$ which also means, $y=f\left ( 150 \right )$

$\therefore A=-2\left (150 \right )^{2}+600\left (150 \right )$

Simplifying,

$\therefore A=-2\left (22500 \right )^{2}+600\left (150 \right )$

$\therefore A=-45000+90000$

$\therefore A=45000$

So, area of the plot will be $A=45000 ft^{2}$

7 0

3 years ago

Y = -(x + 5)(x + 1)

frez [133]

Answer:

dffdfdfdfdfsdewered

Step-by-step explanation:

8 0

2 years ago

The edge length of a cube is 17 cm. Identify the length of its diagonal. Round to the nearest tenth, if necessary. HELP PLEASE!!

lara31 [8.8K]

Answer:

29.4 cm

Step-by-step explanation:

The length of the space diagonal can be found to be the root of the squares of the three orthogonal edge lengths. For a cube, those edge lengths are all the same, so the diagonal length is ...

d = √(17^2 + 17^2 +17^2) = 17√3 ≈ 29.4 . . . . cm

_____

Consider a rectangular prism with edge lengths a, b, c. Then the face diagonal of the face perpendicular to edge "a" has length ...

(face diagonal)^2 = (b^2 +c^2)

and the space diagonal has length ...

(space diagonal)^2 = a^2 + (face diagonal)^2 = a^2 +b^2 +c^2

So, the length of the space diagonal is ...

space diagonal = √(a^2 +b^2 +c^2)

when the prism is a cube, these are all the same (a=b=c). This is the formula we used above.

3 0

3 years ago

Find the measures of EAF DAE and CAD

sdas [7]

You have to build an equation to find the answer,

angles in a straight line add upto 180°
so your equation would be,

12x+30°=180°
-30 -30
=12x=150°
÷12 ÷12
=x=12.5°

now find the measures of the angles by using 12.5 as x.

angle EAF= 2x
=2×12.5
=25° degrees

angle DAE= 4x
=4×12.5
=50°degrees

angle CAD=6x
=6×12.5
=75°degrees

check,
30+25+50+75=180°degrees

hope this helps.......

7 0

3 years ago