f(x) = 4x^4 – 2x^3 – 3x^2 + 6x - 9 Find the Zeros Using Descartes' Rule of Signs

Answer:

Distance travel by Drew = 1,315.21 feet (Approx)

Step-by-step explanation:

Given:

Total block in north = 3

Total block in west = 3

1 block = 310 feet

Find:

Distance travel by Drew

Computation:

Total distance in north = 3 × 310 = 930 feet

Total distance in west = 3 × 310 = 930 feet

Distance travel by Drew = √Total distance in north² + Total distance in west²

Distance travel by Drew = √930² + 930²

Distance travel by Drew = √864,900 + 864,900

Distance travel by Drew = √1,729,800

Distance travel by Drew = 1,315.21 feet (Approx)

Answer:

$45

Step-by-step explanation:

find the hire purchase price: 12 months x $30 = $360 + $35 deposit = $395

difference: 395 - 350 = $45

Answer:

the second one........the shape of the conic section os circle

Step-by-step explanation: A term can be a number, a variable, or a number times one or more variables.

So in this expression, the terms are +2n, +5, -3p, and +4q.

This means that there are 4 terms.

The answer is D - 4 :)

Answer:

D. Decision support systems

Step-by-step explanation:

Operation Support System, sometimes referred to a group of computer programs that is used by the communications service provider for carrying out various operations or functions, such as monitoring, controlling, analyzing and managing a telephone or computer network.

It is often used by professionals such as Network planners, service designers, operations, architects and engineering teams in the service provider.

There are however, types of Operation Support System which are being used for different and specific purpose. They are classified into the following categories:

1. Transaction Processing Systems

2. Process control system

3. Enterprise collaboration system

4. Enterprise Resource

Hence, from the question above, the DECISION SUPPORT SYSTEM is not classified as Operation Support System.

Hi,

Answer:

[tex]Angle=\frac{pi}{4}[/tex] = π/4 = 45°

Have a good day.

Answer:

Please find the attached the required inequality graph

Step-by-step explanation:

Given that inequality is 2.5 ≤ x ≤ 4.5, we have;

The region in the given inequality is the region between 2.5 and 4.5 inclusive

Therefore, to represent 2.5 ≤ x ≤ 4.5 on the number line, we have;

A closed circle (representing the less than or equal to inequality symbol, showing inclusiveness) at 2.5, another closed circle at 4.5 (representing the less than or equal to inequality symbol, showing inclusiveness) and the region between 4.5 and 2.5 shaded.

The equation of line which is perpendicular to the line FG is

y = -2x -3.

The equation of line is an algebraic form of representing the set of points, which together form a line in a coordinate system.

[tex](y -y_{1}) = \frac{y_{2}-y_{1} }{x_{2} -x_{1} } (x-x_{1} )[/tex]

If [tex]m_{1}[/tex] be the slope of one line, then the slope of the perpendicular line is [tex]\frac{-1}{m_{1} }[/tex].

The slope intercept form of the line is given by  y = mx + b

Where, m is the slope of a line.

According to the given question

We have a line FG and the coordinates of points F and G are (-5,1) and (9,8) respectively.

Therefore, the slope of the line FG = [tex]\frac{8-1}{9+5}=\frac{7}{14} =\frac{1}{2}[/tex]

⇒ The slope of the line which is parallel to line FG is -2

Now, from the given option of the equation of line , y = -2x -3 has a slope of -2 .

Hence, the equation of line which is perpendicular to the line FG is

y = -2x -3.

Learn more about the equation of a perpendicular line here:

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Answer:

A

Step-by-step explanation:

The line from the vertex to the base is a perpendicular bisector and divides the isosceles triangle into 2 right triangles.

Using Pythagoras' identity in either of the 2 right triangles, then

([tex]\frac{1}{2}[/tex] x )² + 3² = ([tex]\sqrt{45}[/tex] )²

[tex]\frac{1}{4}[/tex] x² + 9 = 45 ( subtract 9 from both sides )

[tex]\frac{1}{4}[/tex] x² = 36 ( multiply both sides by 4 to clear the fraction )

x² = 144 ( take the square root of both sides )

x = [tex]\sqrt{144}[/tex] = 12 → A

Answer:

49π

Step-by-step explanation:

The formula for the area of a circle is,

[tex]\pi r^2[/tex]

If the radius is 7 inches we need to plug that in for r in the formula.

π(7)^2

7*7 = 49

Thus,

the area in terms of pi is 49π.

Hope this helps :)

Answer:

Step-by-step explanation:

[tex]r = 7\\A = ?\\A =\pi r^2\\A =\pi7^2\\A = 49\pi[/tex]

Answer:

Step-by-step explanation:

5 * 45 = 225

225+75=300

300/500=0.6

The tank will be 60% full.

If this helped, make sure to mark it as brainliest :D

Answer:

C.60%

Step-by-step explanation:

45 x 5 = 225  225 + 75 = 300

300 / 500 = 0.6 = 60%

Answer:

see explanation

Step-by-step explanation:

If Dan earns $x then Bob earns $3x ( 3 times as much as Dan ), then

x + 3x = 72 , that is

4x = 72 ( divide both sides by 4 )

x = 18

Thus

Dan earns $18 and Bob earns 3 × $18 = $54

The earning of Bob will be 54 dollars and the earning of Dan will be 18 dollars.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Let the earning by Bob be x and the earning by Dan be y.

Bob and Dan earned a total of $72 shoveling snow. Then the equation will be

x + y = 72 ...1

If Bob earned 3 times as much as Dan. Then the equation will be

x = 3y   ...2

Substitute the value of x in equation 1, then the equation will be

3y + y = 72

     4y = 72

       y = $18

Then the money earned by Bob will be

x = 3y

x = 3(18)

x = $54

Thus, the earning of Bob will be 54 dollars and the earning of Dan will be 18 dollars.

More about the linear system link is given below.

https://brainly.com/question/20379472

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Answer:

First option is the correct option.

Step-by-step explanation:

[tex] \frac{2x + 5}{ {x}^{2} - 3x } - \frac{3x + 5}{ {x}^{3} - 9x } - \frac{x + 1}{ {x}^{2} - 9 } [/tex]

Factor out X from the expression

[tex] \frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x( {x}^{2} - 9)} - \frac{x + 1}{ {x}^{2} - 9} [/tex]

Using [tex] {a}^{2} - {b}^{2} = (a - b)(a + b)[/tex] , factor the expression

[tex] \frac{2x + 5}{x(x - 3)} - \frac{3x + 5}{x(x - 3)(x + 3) } - \frac{x + 1}{(x - 3)(x + 3)} [/tex]

Write all numerators above the Least Common Denominators x ( x - 3 ) ( x + 3 )

[tex] \frac{(x + 3) \times (2x - 5) - (3x + 5) - x \times (x + 1)}{x(x - 3)(x + 3)} [/tex]

Multiply the parentheses

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - (3x + 5) - x(x + 1)}{x(x - 3)(x + 3)} [/tex]

When there is a (-) in front of an expression in parentheses, change the sign of each term in the expression

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - x \times (x + 1)}{x(x - 3)(x + 3)} [/tex]

Distribute -x through the parentheses

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x }{x(x - 3)(x + 3)} [/tex]

Using [tex] {a}^{2} - {b}^{2} = (a + b)(a - b)[/tex] , simplify the product

[tex] \frac{2 {x}^{2} + 5x + 6x + 15 - 3x - 5 - {x}^{2} - x}{x( {x}^{2} - 9)} [/tex]

Collect like terms

[tex] \frac{ {x}^{2} + 7x + 15 - 5}{x( {x}^{2} - 9)} [/tex]

Subtract the numbers

[tex] \frac{ {x}^{2} + 7x + 10}{ x({x}^{2} - 9)} [/tex]

Distribute x through the parentheses

[tex] \frac{ {x}^{2} + 7x + 10}{ {x}^{3} - 9x} [/tex]

Write 7x as a sum

[tex] \frac{ {x}^{2} + 5x +2x + 10 }{ {x}^{3} - 9x } [/tex]

Factor out X from the expression

[tex] \frac{x(x + 5) + 2x + 10}{ {x}^{3} - 9x} [/tex]

Factor out 2 from the expression

[tex] \frac{x( x + 5) + 2(x + 5)}{ {x}^{3} - 9x } [/tex]

Factor out x + 5 from the expression

[tex] \frac{(x + 5)(x + 2)}{ {x}^{3} - 9x } [/tex]

Hope this helps...

Best regards!!

The difference of the expression [tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex] is [tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]

The expression is given as:

[tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex]

Factorize the denominators

[tex]\frac{2x + 5}{x(x -3)} - \frac{3x + 5}{x(x^2 - 9)} - \frac{x + 1}{x^2 - 9}[/tex]

Apply the difference of two squares to the denominators

[tex]\frac{2x + 5}{x(x -3)} - \frac{3x + 5}{x(x - 3)(x + 3)} - \frac{x + 1}{(x - 3)(x + 3)}[/tex]

Take LCM

[tex]\frac{(2x + 5)(x + 3) - 3x - 5 -x(x + 1) }{x(x - 3)(x + 3)}[/tex]

Expand the numerator

[tex]\frac{2x^2 +6x + 5x + 15 - 3x - 5 -x^2 - x }{x(x - 3)(x + 3)}[/tex]

Collect like terms

[tex]\frac{2x^2 -x^2 - x +6x + 5x - 3x+ 15 - 5 }{x(x - 3)(x + 3)}[/tex]

Simplify

[tex]\frac{x^2+7x+ 10 }{x(x - 3)(x + 3)}[/tex]

Factorize the numerator

[tex]\frac{(x+5)(x+ 2) }{x(x - 3)(x + 3)}[/tex]

Expand the denominator

[tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]

Hence, the difference of the expression [tex]\frac{2x + 5}{x^2 -3x} - \frac{3x + 5}{x^3 - 9x} - \frac{x + 1}{x^2 - 9}[/tex] is [tex]\frac{(x+5)(x+ 2) }{x^3- 9x}[/tex]

Read more about equivalent expressions at:

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First find the area of the sector.

For that, use this equation:

area = [tex]\frac{x }{360} * \pi r^{2}[/tex]

where 'x' is the angle and 'r' is the radius

Sub the values in

area = [tex]\frac{56}{360} * \pi15^2[/tex]

Solve:

area = [tex]35\pi[/tex]

It is easier to keep it in terms of pi until the end

Now, calculate the area of the triangle within the sector

area = 1/2 ab x sinC

where 'a' and 'b' are the radius (side lengths) and C is the angle

thus,

area = 1/2(15 x 15) x sin(56)

area = 93.27 (to 2 d.p)

Now subtract the area of the triangle from the area of the sector

[tex]35\pi[/tex] - 93.27 = 16.6857

This would give you a final answer of 16.69 units^2

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Answer:

1,325

Step-by-step explanation:

30 /2

= 155,000 - 245(15)

= 5,000 - 3,675

= 1,325

Answer:

1,325

Step-by-step explanation:

Answer:

(E) including reminders to watch the endorsement, compare signatures, and view

Step-by-step explanation:

The principle features that will help the company to confirms checks authenticity. It include endorsements and compare the signatures with the designated signatories. If the signatures are matched correctly with the assigned signatories the check is hold in light to view the watermark on it.

Hey Mate !

Your Answer is given in the snip below !!

Please do mark me as brainliest !!!

(ANSWER=  (D)   [tex]\frac{1}{6}[/tex] )

Explanation

Answer:

You have a standard number cube.

What is the probability of rolling a number less than 3, and then rolling a prime number?

D. 1/6

Answer:

Its the last option. On the bottom.

Step-by-step explanation:

You need to Solve for x to find the zeroes of the equation.

x-1=0 So one x is at 1.

x+4=0 So the other x is at -4.

This graph is also not negative so it does not get flipped across the x-axis

The graph of the function [tex]f(x) = (x - 1)(x + 4)[/tex] is graph (d)

The equation of the function is given as:

[tex]f(x) = (x - 1)(x + 4)[/tex]

From the above function, we have the zeros of the function to be:

1 and -4

This means that:

Hence, the graph is graph (d)

Read more about quadratic functions at:

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Answer:

a) Median: 9

b) Range: 5

c) Mode: 7

Step-by-step explanation:

The median is the number in the middle.

First, you put the numbers in order: 7, 7, 7, 8, 10, 11, 12, 12

The middle of this is 8 and 10, so you plus them and divide by to 2, then it gives 9, so the median is 9.

To find the range, you minus the highest number and the lowest number, 12-7=5.

Mode is the most occurring and repetitive number, in this case, 7, because it is written 3 times.

Hope this helps!!!

Answer:

[tex]\boxed{\mathrm {Median = 9}}[/tex]

[tex]\boxed{\mathrm{Range = 5}}[/tex]

[tex]\boxed{\mathrm{Mode = 7}}[/tex]

Step-by-step explanation:

The observations are:

8,7,12,7,11,10,7,12

In ascending order:

=> 7,7,7,8,10,11,12,12

A) Median => Middlemost no.

Median = 8,10

=> [tex]\frac{8+10}{2}[/tex]

=> [tex]\frac{18}{2}[/tex]

Median = 9

B) Range = Highest No. = Lowest No.

RANGE = 12-7

Range = 5

C) Mode => frequently occurring number

Mode = 7

Answer:

The triangle inequality states that the sum of the lengths of the two shortest sides of a triangle must be greater than the length of the largest side. Because 4 + 12 > 17 is not a true statement, the answer is "This triangle does not exist because the sum of 4 and 12 is less than 17."

Answer:

This triangle does not exist due to the fact that the sum of 4 and 12 is less than 17

Step-by-step explanation:

The triangle formaction rule states that the 2 smaller sides must be able to combine and be greater than the greatest side.

Triangle

Sides - 3, 4, 5

3+4=7

Meaning the two smaller sides add up to because greater than 5.

Non-Triangle

Sides - 5, 6, 13

5+6=11

This means that this is not a triangle because the smaller sides ‘5 and 6’ do not add up to become greater than 13.

Gemma’s Triangle

Sides - 4, 12, 17

4+12=16

Hence, Gemma‘s figure is not a triangle because the 2 smaller sides ‘4 and 12’ don‘t add up to be greater than 17.

Answer:

18- 14+8=3x

4+8=3x

12=3x

12/3=2x/3

x=4

Answer:

2/3, -8, -1/6, 4.

Step-by-step explanation:

Step-by-step explanation:

The rational root theorem states that if the leading coefficient is taken to be an and the constant coefficient is taken to be a0 the possible roots of the equation can be expressed as :

Now, from the given options, the possible choices can be :

A, B, C and E

D can be there because after taking any pair the rational root can't be 3

F can't be possible because an does't have 4 in its factors so denominator cannot be 4.

Answer:

B 2.5 Gal

Step-by-step explanation:

Answer:

I think the correct answer may be B.

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

For the first triangle which is triangle <KJL

Hypotenuse= 8✓2

Angle=30°

Opposite = ?

Therefore we will use Sine formula

Sin30° = Y/8✓2

Y=4✓2

For the second triangle which is triangle <JML

Hypotenuse= 4✓2

Opposite=X

Angle=45°

Therefore we will use Sine formula again

Sin45°=X/4✓2

X=4

Answer:

Step-by-step explanation:

ΔJKL is half of equilateral triangle and ΔJML is half of square.

We can use properties of these triangles (picture):

m∠KJL=90° and m∠JKL = 30° ⇒  JL = 0.5KL = 0.5•8√2 = 4√2

m∠JML=90° and m∠MJL = 45° ⇒  JL = ML√2

                                                        4√2 = x√2

                                                             x = 4

Answer:

Step-by-step explanation:

To find x we use tan

tan∅ = opposite / adjacent

From the question

The adjacent is x

The opposite is 30

So we have

tan 25° = 30/x

x tan 25 = 30

Divide both sides by tan 25

x = 30/tan 25

x = 64.34

x = 64 to the nearest tenth

Hope this helps you

Answer:

3

Step-by-step explanation:

Answer:

c is the correct answer

Step-by-step explanation:

Answer:

150

Step-by-step explanation:

Answer:

150  =  half of 300

± 180

230

soooo 230 students

Step-by-step explanation:

Answer:

a. 16; b. aₙ = 4ⁿ⁻¹; c. predation and carrying capacity will limit the population

Step-by-step explanation:

a. The first female had 4 pups.

If each of them had 4 pups, there would be 4 × 4 = 4² = 16 pups.

b. 1st generation                        =     1 pup

2nd generation = 4 ×  1 pup      =    4 pups

3rd generation  = 4 ×  4 pups    =  16 pups

4th generation  = 4 × 16 pups    = 64 pups

5th generation  = 4 × 64 pups = 256 pups

The sequence is           1,   4, 16, 64, 256, …

We can also write it as 4⁰, 4¹, 4²,  4³,   4⁴, …

Note that the exponent is one less than the number of the generation.

Thus, the general formula for the nth term, aₙ, is

aₙ = 4ⁿ⁻¹, where

n = the number of the generation

a = the number of pups in that generation.

c. a₂₅ = 4²⁵⁻¹ = 4²⁴ ≈ 281 000 000 000 000 or 281 trillion

The population would not reach that number because there would not be enough food for all those pups. Pups would die of starvation until their numbers equalled the carrying capacity of the ecosystem and would level off at that point.

There would also be increased predation by coyotes, bobcats, etc. This would also keep the population growth in check,

======================================================

Work Shown:

A = area of trapezoid RSTU

A = height*(base1+base2)/2

A = ST*(UT+RS)/2

A = 14*(5+10)/2

A = 105 square cm

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

B = area of rectangle PQWV

B = length*width

B = WV*PV

B = 7*2.5

B = 17.5 square cm

If you're curious how I got PV = 2.5, you basically cut PT = 10 in half twice. So you go from 10 to 5, then from 5 to 2.5; which works because we have a bunch of midpoints.

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

C = total shaded area

C = A + B

C = 105 + 17.5

C = 122.5

Answer: x=one-half y minus

Step-by-step explanation:

Answer:

x=1/2 y-3

Step-by-step explanation: