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The expression f(x) = (x ^ 2 - 4)(x ^ 2 + 4x + 3 is a polynomial function

The factored form of f(x) = (x ^ 2 - 4)(x ^ 2 + 4x + 3) is f(x) = (x - 2)(x + 2)(x + 3)(x + 1)

The expression is given as:

f(x) = (x ^ 2 - 4)(x ^ 2 + 4x + 3)

Express as difference of two squares

f(x) = (x - 2)(x + 2)(x ^ 2 + 4x + 3)

Expand

f(x) = (x - 2)(x + 2)(x ^ 2 + x + 3x + 3)

Factorize the expression

f(x) = (x - 2)(x + 2)(x(x + 1) + 3(x + 1))

Factor out x + 1

f(x) = (x - 2)(x + 2)(x + 3)(x + 1)

Hence, the factored form of f(x) = (x ^ 2 - 4)(x ^ 2 + 4x + 3) is f(x) = (x - 2)(x + 2)(x + 3)(x + 1)

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Answer:

C. 12/5 kilograms of apples

Step-by-step explanation:

If 5ppl =12kg of apples

then 1 person= ?kg of apples

If more less divides and if less more divides

Therefore

1×12

5

= 12

5

Answer:

7

Step-by-step explanation:

As you can see, each time (let's say n) increases by 1, it divides by 1/2. So from a1 to a2, you get 28/2 or 14, then from a2 to a3, 14/2 or 7.

7 being your answer.

Answer:

Step-by-step explanation:

Given the recursive formula.

Use it to determine the value of te third term.

Answer:

[tex]\fbox{height \: of \: prism = 19 \: mm}[/tex]

Step-by-step explanation:

Given:

Shape of object is pentagonal prism

Side of pentagon= 12mm

Apothem of pentagon= 5 mm

Volume of pentagonal prism= 2,850 cubic mm.

To find:

Hieght of pentagon prism= ?

Solution:

To find height of prism it's necessary to calculate the surface area of base,

[tex]Area \: of \: regular\: pentagon = \frac{5}{2} \times side \: of \: pentagon \: \times apothem \\ Area \: of \: regular\: pentagon = \frac{5}{2} \times 12 \times 5 \\ Area \: of \: regular\: pentagon= \frac{5}{ \not2} \times \not12^{6} \times 5 \\ Area \: of \: regular\: pentagon= 5 \times 6 \times 5 \\ Area \: of \: regular\: pentagon= 150 \: {mm}^{2} [/tex]

[tex]Volume \: of \: prism = surface \: area \: of \: base \: \times height (h) \\ 2850 = 150 \times h \\ h = \frac{2850}{150} \cdot \frac{ {mm}^{3} }{ {mm}^{2} } \\ h = \frac{\not{ {2850}^{19} }} {\not150} \cdot \frac{ {mm}^{\not {3}^{1} } }{ {mm}^{\not2} } \\ \fbox{h = 19 \: mm}[/tex]

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The required height of the pentagonal prism is 19 cm                              

Given that,
A figure of a pentagon prism is shown with
The volume of the prism = 2850 cubic cm
Side of pentagon base = 12 mm.
And the perpendicular distance from the center to the side = 5 mm.

Volume is defined as the ratio of the mass of an object to its density.
Or in mathematics volume can be calculated as the area of the base multiplied by the height.

In order to get the height of the prism first, we have to calculate the area of the base and then divide the volume by its base area to get its height.

The base area = 5/2 * side * perpendicular height to side from center.
                         = 5 / 2 * 12 * 5
                         = 150
The volume of the prism = base area * height
                              2850 = 150 * height
                             height = 2850/15
                                         =  19 cm

Thus, the required height of the pentagonal prism is 19 cm                              

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Answer:

D

Step-by-step explanation:

Answer:

sqrt(2593)

Step-by-step explanation:

17^2+48^2 = 2593^2

Answer:

( 1, 35 )

Step-by-step explanation:

y=mx+c

c= y-intercept ( where the graph line crosses the cross line)

c=0

mx = gradient ( rise/run, up/across )

mx = 175/5 ( you could have picked any point in the graph )

mx = 35

the m is useless now so we discard it

y= 35x+0

if x = 1

then y = 35(1)+0

y= 35

at the coordinate x=1 y is 35

Answer:

where's question.....

Answer:

B

Step-by-step explanation:

5 × pi ÷12 = 75 degrees

this is essentially cos75

= cos(30 + 45)

then we use the identities to solve.

the answer will = to 0.2588

Answer:

That would be the second option:  Rotate Figure A 90º about the origin, then dilate it with the center at the origin and a scale factor of 2.

-yOuR nEiGhbOrhOoD cLEaNeR ;)

Answer:

(-2, 17)

Step-by-step explanation:

the first step you can do to find the vertex is to find the axis of symmetry

the equation for that is -b/2a

-(16) / 2(-4)

-16 / 8 = -2

the axis of symmetry is x =-2 so you plug in -2 to the equation

-4(-2)^2 - 16(-2) + 1

-4(4) + 32 + 1

-16 + 33

17

the vertex is (-2, 17)

En un mes el reloj de Alicia se retrasa 1.5 minutos, por otra parte en un año su reloj se retrasa 18 minutos y 15 segundos.

La mayoría de los meses tienen entre 30 y 31 días:

Mes de 30 días:

En general se atrasa 1.5 minutos en un mes.

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Answer:

V = s³

Step-by-step explanation:

You multiply all sides together (L×W×H)

I am not sure but according to my calculation answer of no.1 may be 67. And I am in 8 grade so I couldn't solve others. So sorry !!

Answer:

360°

Step-by-step explanation:

the sum of the exterior angles of any polygon = 360°

Answer:

Each instalment = £27.45

Step-by-step explanation:

Given:

Remaining balance to be paid = Price of work trolley - deposit

                                                   = £59.90 - £5

                                                   = £54.90

If the remaining balance is to be paid in 2 instalments:

Cost of each instalment = remaining balance ÷ 2

                                        = £54.90 ÷ 2

                                        = £27.45

well, he has "x", which oddly enough is 100%, and we also know that 42 is 35% of that, so

[tex]\begin{array}{ccll} amount&\%\\ \cline{1-2} x & 100\\ 42& 35 \end{array} \implies \cfrac{x}{42}=\cfrac{100}{35}\implies \cfrac{x}{42}=\cfrac{20}{7} \\\\\\ 7x=840\implies x=\cfrac{840}{7}\implies x=120[/tex]

Answer:

115

Step-by-step explanation:

41+24=65.

180-65=115

Answer:

Slope Intercept Form: y=3x-10

Step-by-step explanation:

First, we need to solve the slope.

The formula: y2-y1/x2-x1 = m

Coordinate Points:

(2, -4) ; (4,2)

Do 2 - (-4) for the y's and 4-2 for the x's

Formula: 2-(-4)/4-2

2 - (-4) is a positive answer since the negatives cancel to a positive.

That shall be 6.

4-2 = 2

Now we have 6/2 which means 6 divided by 2 which is 3.

Our slope is 3.

Slope-Intercept Formula: y=mx+b

Our "m" is 3

y = 3x + b

Our b which is the y-intercept is undefined.

We need to plug one of the coordinates into the formula to find it.

Plug (2,-4) into the formula.

-4 = 3(2) +b

Do 3 x 2 first

-4 = 6 + b

Now subtract 6 on both sides

-6-4 = b

Our y-intercept is -10 because negative subtracted by negatives is an addition number followed by the greater number's sign.

Formula: y=3x-10

Answer:

y = 3x - 10

Step-by-step explanation:

To determine the line that passes through the points (2, -4) and (4, 2), we need to determine the slope of the line. Then, using the slope of the line and any point, we can determine the equation of the line using point slope form.

How to determine the slope of the line?

The slope of the line can be determined by using the formula (y₂ - y₁)/(x₂ - x₁), where x₂ and y₂ are the coordinates of the second point; x₁ and y₁ are the coordinates of the first point.

[tex]\implies\large\text{Slope} = \dfrac{y_{2} - y_{1} }{x_{2} - x_{1} }[/tex]

In this case, our first point and second point are (2, -4) and (4, 2) repectively as stated in the question. Therefore,

When we substitute the following into the formula, we obtain;

[tex]\implies\large\text{Slope} = \dfrac{2- (-4)}{4 - 2 }[/tex]

When we perform subtraction, we obtain;

[tex]\implies\large\text{Slope} = \dfrac{2- (-4)}{4 - 2 } = \dfrac{2 + 4}{2 } = \dfrac{6}{2}[/tex]

Which when simplified, we get;

[tex]\implies\large\text{Slope} = \dfrac{6}{2} = 3[/tex]

As said above, to determine the equation of the line with the slope and a point given, we can use point slope form. The chosen point must be on the line. The question states that "the line that passes through the points (2,-4) and (4, 2)". Therefore, we can tell that (2,-4) and (4, 2) are points that are on the line. Let's choose (4, 2) as our chosen point.

Now, let's substitute the slope of the line and the coordinates of the chosen point in the point slope form equation.

Finally, let's simplify the point slope equation and convert it into slope intercept form (as stated in question).

The slope intercept form states that;

We can see that the "y" variable is isolated on one side of the equation [y = (m)x + (b), Slope intercept form equation]. Thus, we need to isolate the y-variable in y - 2 = 3x - 12 to obtain our equation in slope intercept form. This can be done by adding 2 to both sides of the equation.

Therefore, the equation in slope intercept form is y = 3x - 10.

The total liabilities is $180,338

The total assets is  $1,233,000

The net worth is $1,052,662

Net worth is total assets less liabilities. Assets is the sum of liquid assets and non liquid assets. Liabilities is the sum of car loan and mortgage loan.

Assets = 178,000 + 1,055,000 = $1,233,000

Liabilities = 145,908 + 34,430 = $180,338

Net worth =  $1,233,000 - $180,338 = $1,052,662

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The bond's time to maturity for the Ford bond based on the present date and the maturity date is 77 years 6 months.

The time to maturity for a bond is the length of time that a bondholder would receive interest payments on the bonds held. It is the difference between the present date and the matuity date of the bond.

Time to maturity = May 15 2097 - November 16, 2020 = 77 years 6 months

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Answer:

b

Step-by-step explanation:

the x has been cubed meaning

X * X *X = x^3

X^3 has been added to 5

C is saying they multiplied three to x therefore being

B

Answer:

See below ↓↓↓↓

Step-by-step explanation:

4.

5.

6.

7.

Answer:

x > -10

Step-by-step explanation:

5 - 3x > 35

-5           -5

-3x > 30

[tex]\frac{-3x > 30}{-3}[/tex]= x > -10

we should find perimeter.

45+40+50=135m.

then, we should multiply 135 and rate of per meter.

135×60=8100Rs.

Answer:

-9<2

-1>-3

3>-7

-8<-4

Explanation:

< = less than

> = more than

Answer:

2 -1 3 -4 and its always positive if you do the negitives it would be the lowst

Answer:

height of the tower: 165.8 ft

use tan rule:

[tex]\sf \sf tan(x)= \dfrac{opposite}{adjacent}[/tex]

Here:                            [ your calculator should be in degree mode [D] ]

Solve:

[tex]\hookrightarrow \sf \sf tan(37)= \dfrac{t}{220}[/tex]

[tex]\hookrightarrow \sf t = \sf tan(37)*220[/tex]

[tex]\hookrightarrow \sf t = 165.8 \ ft[/tex]

Answer:  the answer is D, if you just graph it in the Desmos graphing calculator you can solve it easily