The polynomial equation x^4 + x^3 + x^2 + x + 1 = 0 has zero positive real roots. Please select the best answer from the choices provided T F

To start calculating the volume of the cone, we obtain the following data:

To calculate the volume of a cone, we apply the following formula:

[tex]\boldsymbol{\sf{V=\dfrac{\pi r^{2}h }{3} }}[/tex], where

We solve, substituting our data in the formula:

taking the square root

Multiplying

Dividing

Therefore the volume of the cone is 144 cm³.

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\textbf{What is the formula for finding the}\\\\\huge\textbf{the volume of a cone?}[/tex]

[tex]\large\boxed{\mathsf{\dfrac{\pi \times r^2\times h}{3} = volume}}[/tex]

[tex]\bullet\large\textsf{ Whereas, \boxed{r} is your \underline{radius}, \boxed{h} is your \underline{height}, \& \boxed{\pi} is your pi.}[/tex]

[tex]\bullet\large\textsf{The pi }\boxed{(\pi)}\large\textsf{ is approximately equal to 3.14.}[/tex]

[tex]\huge\textbf{What are the labels in your equation?}[/tex]

[tex]\star\ \large\boxed{{Radius}}\rightarrow \textsf{\underline{4\ centimeters}}}}}[/tex]

[tex]\star\ \large\boxed{{Height}}\rightarrow \textsf{\underline{9\ centimeters}}}}}[/tex]

[tex]\star\ \large\boxed{{\pi}}\rightarrow \textsf{\underline{3}}}}}[/tex]

[tex]\huge\textbf{What does should the equation look}\\\\\huge\textbf{like?}[/tex]

[tex]\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}[/tex]

[tex]\huge\textbf{What are the steps to solve for the}\\\\\huge\textbf{question to get the result?}[/tex]

[tex]\large\boxed{\mathsf{\dfrac{3 \times 4^2 \times9}{3}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{3\times4\times4\times9}{3}}}[/tex]

[tex]\large\boxed{= \mathsf{\dfrac{3\times16\times9}{3}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{48\times9}{9}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{432}{3}}}[/tex]

[tex]\large\boxed{\mathsf{= \dfrac{432 \div 3}{3\div3}}}[/tex]

[tex]\large\boxed{= \mathsf{\dfrac{144}{1}}}[/tex]

[tex]\large\boxed{\mathsf{= 144\div1}}[/tex]

[tex]\large\boxed{= \textsf{144}}[/tex]

[tex]\huge\textbf{What is the result to this question?}[/tex]

[tex]\huge\boxed{\frak{144\ cm^3}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer:

410 Miles

Step-by-step explanation:

Please refer to the photo attached. (Apologies for the legitimately terrible drawing)

The Shortest Distance between any 2 points is the distance thats connects the 2 points directly.

In this case, we can use Pythgoras's Theorem to find AB which is the shortest distance between A and B.

By Pythagoras's Theorem,

[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {ab}^{2} = {ac}^{2} + {cb}^{2} \\ {ab}^{2} = {90}^{2} + {400}^{2} \\ab = \sqrt{ {90}^{2} + {400}^{2} } \\ = 410 \: miles[/tex]

Answer:

240π cm³ (exact)

754 cm³ (approximate)

Step-by-step explanation:

I assume the shape of the cup is a cylinder. The height of the cylinder is 15 cm.

Think of a vertical rectangle that contains the vertical axes of the cylinder.

Two sides of the rectangle are diameters of the bases of the cylinder. The other two side are heights of the cylinder. The pencil is 17 cm long and is a diagonal of this rectangle. We can find the diameter of the base of the cylinder using the Pythagorean theorem.

In a rectangle that is 15 cm long, the diagonal measures 17 cm.

a² + b² = c²

15² + b² = 17²

b = 8

The diameter of the cup is 8 cm.

radius = 8 cm/2 = 4 cm

V = πr²h

V = π(4 cm)²(15 cm) = 240π cm³ (exact)

V = 754 cm³ (approximate)

Using the concept of an one-to-one function, it will be one-to-one for c = 13.

A function is said to be one-to-one if each output is mapped to only one input.

In this problem, outputs 2, 5 and 11 have already been matched to inputs 1, 3 and 5, respectively, hence the output for input 6 has to be c = 13 for a one-to-one function.

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Answer: -8

Step-by-step explanation:

When x = 5, f(x) = -8.

The value of the function f(5) = -8.

We have,

The concept used to find the value of f(5) is function evaluation.

In this case, we are given a function represented by a table with x and f(x) values.

To evaluate the function at a specific value, such as f(5), we look for the corresponding x-value in the table and determine the corresponding f(x) value.

In this example, we found that when x = 5, f(x) is -8 by looking at the table provided.

To find the value of f(5), we need to look at the table and find the corresponding value of the function when x = 5.

From the given table, when x = 5, f(x) is -8.

Therefore,

The value of the function f(5) = -8.

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In quadrant IV, [tex]\sin(A)[/tex] is negative. So

[tex]\sin^2(A) + \cos^2(A) = 1 \implies \sin(A) = -\sqrt{1-\cos^2(A)} = -\dfrac35 = \boxed{-0.6000}[/tex]

The probability that the total number of heads in all the coin tosses equals 12 is 0.0273.

Given a fair dice and tossing a fair coin sixteen times.

We have to find the probability that the total number  of heads in all the coin tosses equals 12.

The probability lies between 0 and 1.

Probabiltiy of coming head when the coin is tossed 1 time is 0.5 and probability of coming tails is also 0.5.

Let X shows the sum of heads while tossing.

P(X=12)=?

We can find the probability using binomial theorem.

=[tex]16C_{12} (0.5)^{12} (0.5)^{2}[/tex]

We have to toss sixteen times and out of 16 times we need head 12 times.

=16!/12!4!*0.00024*0.0625

=1820*0.000015

=0.0273

Hence the probability that the total number of heads in all the coin tosses equals 12 is  0.0273.

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Using proportions, it is found that there are 5 cups of milk in each bowl of chocolate pudding.

A proportion is a fraction of a total amount, and the measures are related using a rule of three.

The cafeteria used 10 quarts for 8 bowls, hence the number of quarts per bowl is:

10/8 = 1.25

Each quart has 4 cups, hence the number of cups is:

4 x 1.25 = 5 cups.

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Answer:

167

Hope this helps you out

Answer:

167

Step-by-step explanation:

Break it into steps.

2+2+5 = 9

69 + 9 = 78

78 + 89 = 167

Hope this helps.

Answer:

4 and 1

Step-by-step explanation:

The given system of equations has the solution, x = 0, and y = 2, giving the ordered pair (0, 2). Hence, the first option is the right choice.

In the question, we are asked for the ordered pair, which is the solution to the system of equations:

2x + 3y= 6 ... (i)

–3x + 5y = 10 ... (ii).

To solve for the solution to the system of equations, we use the elimination method.

We multiply (i) by 3, and (ii) by 2, and then add the resultant equations to eliminate x as follows:

 6x + 9y = 18 {(i) * 3}

-6x + 10y = 20 {(ii) * 2}

_____________

19y = 38,

or, y = 38/19 = 2.

Substituting, y = 2, in (i), we get:

2x + 3y = 6,

or, 2x + 3(2) = 6,

or, 2x + 6 = 6,

or, 2x = 6 - 6 = 0,

or, x = 0/2 = 0.

Thus, the given system of equations has the solution, x = 0, and y = 2, giving the ordered pair (0, 2). Hence, the first option is the right choice.

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The complete question is:

"Which ordered pair is a solution to the system of linear equations?

2x + 3y= 6

–3x + 5y = 10

(0,2)

(2,0)

(3,2)

(2,3)"

Answer: Option (1)

Step-by-step explanation:

[tex]\angle DMA[/tex] is another name for angle 3, but not [tex]\angle DME[/tex].

Answer:

-4

Step-by-step explanation:

Slope = y/x

1. y=12 x=-3

  12/-3=-4

2. y=8, x=-2

   8/-2 = -4

3. y=4, x=-1

   4/-1 = -4

4. 0/0 = 0

5. y=-4, x=1

   -4/1 = -4

Hope it helps I had this question last year on Acellus.

Answer:1+1

Step-by-step explanation:

The area of the rectangular patio to be painted is: B. A = (x + 20)(x + 10) - 12.

A rectangle, by definition, is a quadrilateral with two pairs of opposite that have the equal lengths. All four angles of a rectangle are right angles (90 degrees).

The area of a rectangle = (length of rectangle)(width of rectangle).

Given the following parameters for the patio and the bench:

Area to be painted = area of rectangular patio - area of rectangular bench

Area of rectangular patio = (x + 20)(x + 10)

Area of rectangular bench = (6)(2) = 12

Area to be painted = (x + 20)(x + 10) - 12

The answer is: B. A = (x + 20)(x + 10) - 12.

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Question:

A sample of cans of peaches was taken from a warehouse, and the content of each can mearsed for weight. the sample means was 486g with stand deviation 6g. state the weight percentage of cans with weight:

Draw normal curve to help - split into 8 section ( i can't draw it here)

a) 34.13% of cans will be between 480g and 486g.

b) 13.59 + 2.15 + 0.13= 15.87% of cans greater than 492g.

Look at the Stand Dev Graph where the give you the number

Step-by-step explanation:

Let me give you a different question and i will answer it, which you help you answer your question.

The rewritten equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁ is [tex]R_2 = \frac{R_TR_1}{R_1-R_T}[/tex].

Hence, the 3rd option is the right choice.

To rewrite any equation, in terms of the other variable, we just need to change the isolation of the variable by rearranging it.

In the question, we are given the equation for the total resistance [tex]R_T[/tex] for a circuit with two resistance R₁ and R₂ connected in parallel as:

[tex]R_T = \frac{R_1R_2}{R_1+R_2}[/tex]

We are asked to rewrite the equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁.

To rewrite the equation, we do as follows:

[tex]R_T = \frac{R_1R_2}{R_1+R_2}\\\Rightarrow R_T(R_1 + R_2) = R_1R_2\\\Rightarrow R_TR_1 + R_TR_2 = R_1R_2\\\Rightarrow R_1R_2 - R_TR_2 = R_TR_1\\\Rightarrow R_2(R_1-R_T) = R_TR_1\\\Rightarrow R_2 = \frac{R_TR_1}{R_1-R_T}[/tex]

Thus, the rewritten equation to represent the resistance of resistor 2, R₂, in terms of [tex]R_T[/tex] and R₁ is [tex]R_2 = \frac{R_TR_1}{R_1-R_T}[/tex].

Hence, the 3rd option is the right choice.

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For the complete question, refer to the attachment.

x<3

Step-by-step explanation:

–2(5 – 4x) < 6x – 4

(–10 + 8x) < 6x – 4

8x –6x < –4 + 10

2x < 6

x < 3

Answer:

2

Step-by-step explanation:

• Multiplying two numbers with same bases is the same as adding their powers:

∴ [tex](\frac{4^{\frac{5}{4} } \cdot 4^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒ [tex](\frac{4^{\frac{5}{4} } ^ + ^{\frac{1}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒ [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

• Dividing two numbers with same bases is the same as subtracting their powers:

∴  [tex](\frac{4^{\frac{6}{4} }}{4^{\frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒ [tex](4^{{\frac{6}{4} - \frac{1}{2} }})^{\frac{1}{2} }[/tex]

⇒  [tex](4^{1})^{\frac{1}{2} }[/tex]

⇒  [tex]4^{\frac{1}{2}[/tex]

• Raising anything to the power of  [tex]\frac{1}{2}[/tex] is the same as square-rooting it:

∴  [tex]4^{\frac{1}{2}[/tex]

⇒ [tex]\sqrt{4}[/tex]

⇒ 2

Since there are same number of either side, hence the solution has infinite number of solution

System of equations are equation that consist of two or more equations with unknown variables.

Given the equations

2x - y = 7

2y = 4x - 14

This can also be written as

2x - y = 7

y = 2x - 7

Substitute equation 2 into 1

2x - (2x - 7) = 7

2x-2x+7= 7

7 = 7

Since there are same number of either side, hence the solution has infinite number of solution

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Graph is in the attached image.

Answer:

1/36

Step-by-step explanation:

The probability for showing a three the first time is 1/6, and then again is another 1/6, multiply and you get 1/36

Check the picture below.

part A

since the base of the triangular base is 16, and the altitude "h" splits the base in two equal halves, half that is just 8, so we're looking at a right triangle with a hypotenuse of 17 and a side of 8, thus

[tex]\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - a^2}=b \qquad \begin{cases} c=\stackrel{hypotenuse}{17}\\ a=\stackrel{adjacent}{8}\\ b=\stackrel{opposite}{h}\\ \end{cases} \\\\\\ \sqrt{17^2-8^2}=h\implies \sqrt{225}=h\implies \boxed{15=h}[/tex]

part B

well, the prism is simply two triangles and 3 rectangles, le's simply add their areas.

[tex]\stackrel{two~triangles}{2\left[ \cfrac{1}{2}(\stackrel{base}{16})(\stackrel{height}{15}) \right]}~~ + ~~\stackrel{two~rectangles}{2(20)(17)}~~ + ~~\stackrel{one~rectangle}{(20)(16)} \\\\\\ 240~~ + ~~680~~ + ~~320\implies \text{\LARGE 1240}[/tex]

The function with the greatest rate of change over the interval [0, 2] is: D. a.

In Mathematics, the rate of change of a function over a given interval can be determined by calculating the slope of the straight line which connect its end points.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

For line a, we have:

Points (x, y) = (0, 1) and (2, 4)

Slope = (4 - 1)/(2 - 0)

Slope = 3/2 or 1.5.

For line b, we have:

Points (x, y) = (0, 0) and (2, 2)

Slope = (2 - 0)/(2 - 0)

Slope = 2/2 or 1.0.

For line c, we have:

Points (x, y) = (0, -1) and (2, 0)

Slope = (0 + 1)/(2 - 0)

Slope = 1/2 or 0.5.

For line d, we have:

Points (x, y) = (0, 0.5) and (2, 2.5)

Slope = (2.5 - 0.5)/(2 - 0)

Slope = 2/2 or 1.

In conclusion, we can logically deduce that "function a" has the greatest rate of change over the interval [0, 2].

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The explicit function that defines the sequence is 15/2 - 9n/2

The sequence is given as:

3, -3/2, -6, -21/2

The above sequence is an arithmetic sequence, with the following parameters

The explicit formula is then calculated as:

T(n) = a + (n -1) * d

This gives

T(n) = 3 +(n -1) * -9/2

Expand

T(n) = 3 + 9/2 - 9n/2

Evaluate

T(n) = 15/2 - 9n/2

Hence, the explicit function that defines the sequence is 15/2 - 9n/2

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Answer:

First, transform the given equation into the slope-intercept form, y = mx + b.

2x - 3y < 12

3y > 2x - 12

y > [tex]\frac{2}{3}[/tex]x - 4

Since the equation is y > [tex]\frac{2}{3}[/tex]x - 4, first draw the graph of y = [tex]\frac{2}{3}[/tex]x - 4 with a dotted line (because it is >, not ≥) and shade the area above the dotted line.

Answer:

5.4 ft to nearest tenth.

Step-by-step explanation:

We know the adjacent side  of the right triangle  and we need the hypotenuse so we use the cosine:

cos 50 = 3.5/x

x = 3.5 / cos 50

  = 5.445 ft.

The upper quartile for NFC is 3 points higher than that of AFC.

A box plot is used to study the distribution and level of a set of scores. The scores are distributed into 4 groups. Each group has a value of 25%

On the box, the third line on the box represents the upper quartile. 75% of the scores represents the upper quartile.

Upper quartile for AFC : 26

Upper quartile for NFC : 23

Difference = 26 - 23 = 3

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Answer:

y = - [tex]\frac{1}{6}[/tex] x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x - 2 ← is in slope- intercept form

with slope m = 6

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex] , then

y = - [tex]\frac{1}{6}[/tex] x + c ← is the partial equation

to find c substitute (6, - 2 ) into the partial equation

- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1

y = - [tex]\frac{1}{6}[/tex] x - 1 ← equation of perpendicular line

Answer:

a ≈ 16.5 cm , b ≈ 23.8 cm

Step-by-step explanation:

using the Law of Sines in Δ ABC

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex]

we require to calculate ∠ C

∠ C = 180° - (42 + 75)° = 180° - 117° = 63°

Then to find a

[tex]\frac{a}{sinA}[/tex] = [tex]\frac{c}{sinC}[/tex] ( substitute values )

[tex]\frac{a}{sin42}[/tex] = [tex]\frac{22}{sin63}[/tex] ( cross- multiply )

a × sin63° = 22 × sin42° ( divide both sides by sin63° )

a = [tex]\frac{22sin42}{sin63}[/tex] ≈ 16.5 cm ( to the nearest tenth )

similarly to find b

[tex]\frac{b}{sinB}[/tex] = [tex]\frac{c}{sinC}[/tex] ( substitute values )

[tex]\frac{b}{sin75}[/tex] = [tex]\frac{22}{sin63}[/tex] ( cross- multiply )

b × sin63° = 22 × sin75° ( divide both sides by sin63° )

b = [tex]\frac{22sin75}{sin63}[/tex] ≈ 23.8 cm ( to the nearest tenth )

Answer:

Step-by-step explanation:

    [tex]\sf \boxed{\bf\dfrac{a}{Sin \ A}=\dfrac{b}{Sin \ B}=\dfrac{c}{Sin \ C}}[/tex]

Side 'a' faces ∠A.

Side 'b' faces ∠B.

Side 'c' faces ∠C.

We have to find ∠C using angle sum property of triangle.

  ∠C + 75 + 42 = 180

         ∠C +117   = 180

                  ∠C  = 180 - 117

                 ∠C = 63°

[tex]\sf \dfrac{a}{Sin \ 42}= \dfrac{22}{Sin \ 63}\\\\ \dfrac{a}{0.67}=\dfrac{22}{0.89}\\\\[/tex]

   [tex]\sf a = \dfrac{22}{0.89}*0.67\\\\ \boxed{a = 16.56 \ cm }[/tex]

                        [tex]\sf \dfrac{b}{Sin \ B} = \dfrac{c}{Sin \ C}\\\\ \dfrac{b}{Sin \ 75}=\dfrac{22}{Sin 63}\\\\ \dfrac{b}{0.97} =\dfrac{22}{0.89}\\\\[/tex]

                             [tex]\sf b = \dfrac{22}{0.89}*0.97\\\\ \boxed{b =23.98 \ cm }[/tex]