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

Hey there! I'm happy to help!

The surface area is just the area of this net. If you fold up the net it will give you a hollow 3-d shape.

On this net we have three congruent rectangles and two congruent triangles.

We see that each rectangle has a short side of 10 cm and a long side of 15 cm. The area of a rectangle is found by multiplying the long side by the short side.

15×10=150

So, each rectangle has an area of 150 cm².

Now, for the triangles. To find the area of a triangle you multiply the base by the height and then divide by two.

Each triangle has a base of 10 cm and a height 8 2/3 cm.

We multiply them.

10×8 2/3=86 2/3

And we divide by two.

86 2/3 ÷ 2 = 43 1/3

So, each triangle has an area of 43 1/3.  

Now, we add together the areas of our three rectangles and two triangles.

150+150+150+43 1/3+43 1/3=536 2/3

Therefore, the surface area is 536 2/3 cm².

Have a wonderful day!

Answer:

If it walks like a duck and it talks like a duck, then it is a duck.

and

Either it does not walk like a duck or it does not talk like a duck, or it is a duck.

are logically equivalent to each other.

but neither of the two is logically equivalent to

If it does not walk like a duck and it does not talk like a duck, then it is not a duck.

Step-by-step explanation:

Given statements:

Statemen 1:

If it walks like a duck and it talks like a duck, then it is a duck.

Statement 2:

Either it does not walk like a duck or it does not talk like a duck, or it is a duck.  

Statement 3:

If it does not walk like a duck and it does not talk like a duck, then it is not a duck.

Let

Using p = it walks like a duck , q =it talks like a duck, r = it is a duck  the given statements can be written in symbolic form as:

Statement 1:  

p ∧ q → r

The ∧ symbol shows that if both p and q are true then, they imply r. This means both p and q together imply r

Statement 2:

~p ∨ ~q ∨ r

Here the statement p and q are negated and joined using or. So either negation p or negation of q or r (alternative)  

Statement 3:

~p ∧ ~q → ~r

The ∧ symbol shows that if both negation of p and negation of q are true then, they imply r. This means both negated p and negated q together imply negated r

Statement 1:

p ∧ q → r ≡ ~(p∨q) ∨ r               Using conditional equivalence p→q ≡ ~p ∨ q

              ≡ (~p ∧ ~q ) ∨ r          

You can see it is  equivalent to Statement 2 i.e. ~p ∧ ~q → ~r

Hence Statement 1 and Statement 2 are logically equivalent.

Now Statement 3:

~p ∧ ~q → ~r ≡ ~(~p ∧ ~q ) ∨ ~r   Using conditional equivalence p→q ≡ ~p ∨ q

                     ≡ ~(~p ) ∨ ~(~q ) ∨ ~r Using De Morgan's Law ~(p∧q) ≡ ~p ∨~q

                     ≡  p ∨ q ∨ ~r Using Double Negation Law ~(~p)≡p

This shows that Statement 3 is neither logically equivalent to Statement 1 nor logically equivalent to Statement 2.

Proof by truth table is attached. The table shows that the columns for Statement 1 and Statement 2 have same truth values.

Hence

"If it walks like a duck, and it talks like a duck, then it is a duck,"

and

"If it does not walk like a duck, and does not talk like a duck, then it is not a duck,"

are logically equivalent.

The table also shows that column for Statement 3 does not match with either of the columns for Statement 1 and Statement 2. So

If it does not walk like a duck and it does not talk like a duck, then it is not a duck.

is not logically equivalent to Statement 1 and Statement 2.

Answer:

duck walk

Step-by-step explanation:

Answer:

52 students

Step-by-step explanation:

From the question above, we have the following information:

a) Vidya ranks 7th from the top.

Mathematically,

Vidya = 7th student

b) Divya 3 ranks behind Vidya.

Divya = Vidya + 3

Hence, Mathematically:

Divya = 7 + 3 = 10

Divya = 10th student

c) Also, Divya is 7 ranks ahead of Medha.

Mathematically,

Medha = 10 + 7= 17

Medha= 17th student

d)Sushma is 32 ranks behind Medha

Mathematically,

Sushma = Medha + 32

= 17 + 32 = 49

Sushma is the 49th student

Therefore, since, Sushma is 4th from the bottom, total number of students is:

49 + 3 = 52 students

Answer:

18.5

Step-by-step explanation:

In the above question, we are given the following values

Cumulative probability ( confidence interval) = 0.95 = 95%

Mean = 10.5

Standard deviation = 4.10

We are asked to find the value of x.

To solve for x , we would be using the z score formula.

z score = (x-μ)/σ,

where x is the raw score,

μ is the population mean

σ is the population standard deviation

z score was not given in the question, but we have our cumulative probability as 95%(0.95).

Using the appropriate table,

the z score for 95% confidence is z = 1.96.

Therefore,

z score = (x-μ)/σ,

1.96 = x - 10.5/4.10

Cross multiply

1.96×4.10 = x - 10.5

x = (1.96 × 4.10) + 10.5

x = 8.036 + 10.5

x = 18.536

Approximately to 1 decimal place

x = 18.5

Answer:

Here,

initial price (p)=$6500

Time from 2007 to 2020 (t)= 13yrs.

rate (r)=14.3%

now,

[tex]present \: price \: (pt) = p(1 - \frac{r}{100} )[/tex]

or, pt = $6500(1-14.3/100)

by simplifying it we get,

The, present price is $5570.5.

now, if you are searching for depreciated amount only then,

depreciated amount =$6500-$5570.5

=$929.5.

Hope it helps...

Answer:

Rate of growth he will need to achieve his goal is 9.8%

Step-by-step explanation:

Principal=$5,000

Time(t)=70-30=40 years

Period (n)=12 months

Interest rate (r)=?

A=$250,000

r=n{(A/P)^1/nt - 1}

=12{(250,000/5000)^1/12*40 - 1}

=12{(50)^1/480 - 1}

=12{(50)^0.0021 - 1}

=12(1.0083 - 1)

=12(0.0082)

=0.0984

r=0.0984*100

=9.84%

To the nearest tenth=9.8%

Answer:

8 i'm pretty sure

Step-by-step explanation:

Answer:

y = 9 1/3 or 8 if the first equation is 1/3x + 1/4y = 1.

Step-by-step explanation:

1/3x + 1/4y = 2

    2x - 3y = -30

Multiply the first equation by -6:

- 2x - 3/2y = -12  

Adding the last 2 equations:

-9/2 y = -42

y = -42 * -2/9

y = 9 1/3.

If the first equation is 1/3x + 1/4 y = 1

then y = -36 * -2/9

= 8.

Answer:

Given,

Volume of a cone = 1540 cm[tex] {}^{3} [/tex]

Radius ( r ) = 7 cm

π ( pi ) = [tex] \frac{22}{7} [/tex]

Height of cone ( h ) = ?

Now, let's find the height of cone:

Volume of cone = [tex]\pi \: {r}^{2} \frac{h}{3} [/tex]

plug the values

[tex]1540 = \frac{22}{7} \times {(7)}^{2} \times \frac{h}{3} [/tex]

Evaluate

[tex]1540 = \frac{22}{7} \times 49 \times \frac{h}{3} [/tex]

Calculate

[tex]1540 = \frac{154 \: h}{3} [/tex]

Apply cross product property

[tex]154 \: h = 1540 \times 3[/tex]

Calculate the product

[tex]154 \: h = 4620[/tex]

Divide both sides of the equation by 154

[tex] \frac{154 \: h}{154} = \frac{4620}{154} [/tex]

Calculate

[tex]h \: = 30 \: cm[/tex]

Hope this helps...

Best regards!!

Step-by-step explanation:

mean is always equal to additon of total no.s by total no.s

2 + 4 + 6 + 8 + 10 + 12

=42

total no.s = 6 no.s

42/6

=7

therefore 7 is the answer which is the mean deviation of the following no.s .

Answer:

B

Step-by-step explanation:

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

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

Explanation:

We have two large red tiles labeled with -x^2 on them. They add to -2x^2 which is found in every answer choice listed. This means that we must have a plus sign between the two parenthesis groups. If we had a subtraction sign, then -x^2 minus -x^2 would turn into 0x^2 or just 0, and the x^2 terms would go away entirely.

Because we must have a plus sign between the parenthesis, this means the answer is between C and D.

Now focus on the x terms. The slash marks mean that all of the x terms pair up and add to 0. They go away as there aren't any x terms that haven't been slashed. That explains why there are no x terms on the right hand side of any of the answer choices.

The question is: which of C or D has the x terms add to 0x? The answer would be choice D since 2x + (-2x) = 2x-2x = 0x. Choice C has 2x+2x = 4x which is what we don't want.

Lastly, choice D is further proven correct by noticing that the constants 3 and -1 add to 3+(-1) = 3-1 = 2. We have two small blue squares that add to 2 after the cancellations have happened.

Answer:

k = -18.

But See below.

Step-by-step explanation:

f(x) =  x^4 - 3x^3 - 6x^2 + kx - 16

If  x^2 + 3x + 2 is a factor then so is (x + 1) and (x + 2) as

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

So by the Factor Theorem f(-1) = 0:

f(-1) = (-1)^4 - 3(-1)^3 - 6(-1)^2 - 1k - 16 = 0

1 + 3 - 6 - k - 16 = 0

-18 - k = 0

k =  -18.

Checking:

f(-2) =   (-2)^4 - 3(-2)^3 - 6(-2)^2 - 18(-2) - 16

=  16 + 24 - 24 + 36 - 16 = 36   (NOT 0).

Answer:

k=11

explaination:

Answer:

Step-by-step explanation:

[tex]tan^{-1} (\frac{\sqrt{3} }{3} )=x\\tan x=\frac{\sqrt{3} }{3} =tan (\frac{\pi}{6} )\\x=\frac{\pi}{6}[/tex]

Answer:

Step-by-step explanation:

eliminate either vraible, here it is easy to eleimate y, by just subtacting, then solve for x. When you get the value of x, plug in one of the equation and find y. ther you go

Answer:

x= 3.8

y= -29.3

Step-by-step explanation:

Answer:

x=6

Step-by-step explanation:

Take -2 and add it to 10 and get 12. So then the equation is 2x=12. Divide 2 by 12 and get x=6.

Answer:

∠A=123°.

Step-by-step explanation:

From the given figure it is clear the CD and CE are two tangent lines on circle with center A.

Radius is perpendicular to the tangent at the point of tangency.

[tex]\angle ADC=90^{\circ}[/tex]

[tex]\angle AEC=90^{\circ}[/tex]

Smaller arc DE = (5x-2)°

It means central angle DAE is (5x-2)°.

[tex]\angle DAE=(5x-2)^{\circ}[/tex]

Now, ADCE is a quadrilateral and sum of all angles of a quadrilateral is 360 degrees.

[tex]\angle ADC+\angle DCE+\angle AEC+\angle DAE=360^{\circ}[/tex]

[tex]90^{\circ}+(2x+7)^{\circ}+90^{\circ}+(5x-2)^{\circ}=360^{\circ}[/tex]

[tex](7x+5)^{\circ}+180^{\circ}=360^{\circ}[/tex]

[tex](7x+5)^{\circ}=360^{\circ}-180^{\circ}[/tex]

[tex](7x+5)^{\circ}=180^{\circ}[/tex]

[tex]7x+5=180[/tex]

[tex]7x=175[/tex]

[tex]x=25[/tex]

The value of x is 25.

[tex]\angle A=5x-2=5(25)-2=125-2=123^{\circ}[/tex]

Therefore, the measure of ∠A is 123°.

Answer:

d- Mode

Step-by-step explanation:

Mean is 7

Range is 11

Median is 2.5

Mode is the most repeated no... which is 5

Answer:

D. all of the above

Step-by-step explanation:

All the letters from the options have a line of symmetry.

Answer:

10x^2 + 8x

Step-by-step explanation:

Area of the outer rectangle = 5x(3x + 2) = 15x^2 + 10x

Area of the inner rectangle = x(5x - 2) = 5x^2 - 2x

Area of the shaded region = (15x^2 + 10x) - (5x^2 - 2x)

= 10x^2 + 8x

5x(3x + 2) - x(5x - 2) required expression.

Step-by-step explanation:

I get there are 2 rectangles in figure.

How can I get the area of shaded region? What if, I subtract the area of inner rectangle from outer rectangle. Ya It will surely work (⌒o⌒).

Now,

Area of outer rectangle = [tex]\sf length \times breadth[/tex]

[tex]5x \times (3x + 2)[/tex]

[tex]5x(3x + 2)[/tex]

Again,

Area of inner rectangle = [tex]\sf length \times breadth[/tex]

[tex]=x \times (5x - 2)[/tex]

[tex]=x(5x - 2)[/tex]

[tex] \sf Area \:of \:Shaded\: region = \: Area_{\:outer}-Area_{\:inner}[/tex]

[tex] \sf \: 5x(3x + 2) - x(5x - 2)[/tex]

If We simplify further then,

= 15x² + 10x - 5x² + 2x

= 10x² + 12x

Area of shaded region is 10x² + 12x in a simple way.

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

Work Shown:

f ''' (x) = cos(x) .... third derivative

f '' (x) = sin(x)+C ... integrate both sides to get second derivative. Don't forget the +C at the end

We are given f '' (0) = 9, so we'll make use of this to find C

f '' (x) = sin(x)+C

f '' (0) = sin(0)+C

9 = sin(0) + C

9 = 0 + C

9 = C

C = 9

Therefore, f '' (x) = sin(x)+C turns into f '' (x) = sin(x)+9

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

Integrate both sides of the second derivative to get the first derivative function

f '' (x) = sin(x)+9

f ' (x) = -cos(x)+9x+D ... D is some constant

Make use of f ' (0) = 4 to find D

f ' (x) = -cos(x)+9x+D

f ' (0) = -cos(0)+9(0)+D

4 = -1 + 0 + D

D = 5

So we have f ' (x) = -cos(x)+9x+D turn into f ' (x) = -cos(x)+9x+5

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

Lastly, apply another round of integrals and substitutions to find the f(x) function. We'll use f(0) = 8.

f ' (x) = -cos(x)+9x+5

f(x) = -sin(x) + (9/2)x^2 + 5x + E .... E is some constant

f(0) = -sin(0) + (9/2)(0)^2 + 5(0) + E

8 = 0 + 0 + 0 = E

E = 8

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

We have

f(x) = -sin(x) + (9/2)x^2 + 5x + E

turn into

f(x) = -sin(x) + (9/2)x^2 + 5x + 8

Assuming both vertical lines are parallel and assuming I'm supposed to find all the unmarked angles...

Angle C:

Supplementary Angles.

x+36=180

180-36=x

x=144

Angle B:

Corresponding Angles.

Angle B ≅ Angle C

144

Angle A:

360 degrees in a quadrilateral

36+144+81+x=360

261+x=360

x = 99

Hope it helps <3

Answer:

Step-by-step explanation:

[x/2-2/1] × [2x^2 + x -3]

we can solve this very simply by multiplication

Answer: while solving an equation involving fractions we eliminate the fraction by multiplying the LCD of all the denominators present in the equation . LCD means Least common Denominator so for this question when we try to eliminate the denominator we first try to find the LCM (2,4,6) because that will give us the LCD.

2=2

4=2·2

6=2·3

LCM = 2·2·3

LCM = 12

It means we need to multiply the 12 to each term of equation to eliminate the fractions before solving.

12

To eliminate the fractions, multiply the equation by the 12

A equation is an expression that shows the relationship between two or more variables and numbers.

Given the equation:

[tex]x-\frac{5}{4}+2x=\frac{5}{6}+x[/tex]

To eliminate the fractions, multiply by the L.C.M of the denominator of the fraction i.e. 12 to get:

12x - 15 + 24x = 10 + 12x

Find out more on Equation at: https://brainly.com/question/2972832

Answer:

Hey there!

6x+6=7x-6

6=x-6

12=x

x=12

Hope this helps :)

Answer:512

Step-by-step explanation:

Let's solve your equation step-by-step.

3√x=3√512

3√x=67.882251

Step 1: Divide both sides by 3.

3√x

3

=

67.882251

3

√x=22.627417

Step 2: Solve Square Root.

√x=22.627417

x=22.6274172(Square both sides)

x=512

Check answers. (Plug them in to make sure they work.)

x=512(Works in original equation)

Answer:

x=512

Answer:

1/4

Step-by-step explanation:

-1 1/6 ÷ (-4 2/3)

Change to improper fractions

- ( 6*1 +1)/6 ÷ -(3*4 +2)/3

-7/6÷ -14/3

Copy dot flip

-7/6 * -3/14

Rewriting

-7/14 * -3/6

-1/2 * -1/2

1/4

Answer:

C = 35 + 0.08t

Step-by-step explanation:

The equation is:

35 + 0.08t = C

C = Cost by month

t = cost for each additional message

Answer:

The rise is -6.

Step-by-step explanation:

For this problem, the direction of the vector gives the indication of a negative slope.  We know that the equation to find slope = rise/run meaning y/x values.  So for this, we can see the y-value of the blue triangle (the rise) to be 6, and the x-value of the blue triangle (the run) to be 3.  And as stated before, this is a negative slope, in the y-direction.  Hence, the rise is -6 for the blue triangle.