Consider the following function.
f(x) = −2x^3 − 6x^2 + 5
(a) Use the Intermediate Value Theorem and a graphing utility to find graphically any intervals of length 1 in which the polynomial function is guaranteed to have a zero. Verify your answers by using the table feature of the graphing utility. (Select all that apply.)

(−4, −3)

(−3, −2)

(−2, −1)

(−1, 0)

(0, 1)

(1, 2)

(2, 3)

(3, 4)

(b) Use the zero or root feature of the graphing utility to approximate the real zeros of the function. (Enter your answers as a comma-separated list. Round your answers to three decimal places.)
x =

Answer:

To fill in the table of values for the equation y = 2x + 1, we can choose different values of x and substitute them into the equation to find the corresponding values of y. For example:

x y

0 1

1 3

2 5

3 7

4 9

To get the value of y, we substitute each value of x into the equation and simplify:

When x = 0:

y = 2(0) + 1 = 1

When x = 1:

y = 2(1) + 1 = 3

When x = 2:

y = 2(2) + 1 = 5

When x = 3:

y = 2(3) + 1 = 7

When x = 4:

y = 2(4) + 1 = 9

Therefore, the table of values for the equation y = 2x + 1 is:

x y

0 1

1 3

2 5

3 7

4 9

Answer:

5

Step-by-step explanation:

S1=R1²=*3²=9 (the outer circle)

S2=R2²=*2²=4 (the inner circle)

S=S1-S2=9-4=5 (the shaded ring)

Answer:

Step-by-step explanation:

0.08*X >= 100000,   i.e.   X >= 100000%2F0.08 = 1,250,000 dollars.

Then each year he will draw 100000, but the bank will return  equal or even greater amount than 0.08*1250000 = 100000,

so his balance will only increase from year to year.

It is a rough estimation.

If we want to consider more realistic case, when he withdraws 100000 at the first day of the year and the bank compounds 8% at the end of the year,

then the unknown starting amount X must satisfy inequality

0.08*(X-100000) >= 100000,   which gives

0.08X - 0.08*100000 >= 100000,

0.08X > (1+0.08)*100000

x >= %28%281%2B0.08%29%2A100000%29%2F0.08 = 1350000.

Answer.  Having  $1,350,000 or more initially on the account provides the sough condition.

Answer:

$26421.76

Step-by-step explanation:

We have to calculate final value i.e. balance to earn $50,000 annually from interest.

[tex]= \dfrac{50,000}{0.08} = \$625,000[/tex]

Now, N = n × y  = 12 × 25 = 300

        I  = 8% =  APR = 0.08

       PV = 0  = PMT = 0

      FV = 625,000 = A

[tex]\text{A}=\dfrac{\text{PMT}\times[(1+\frac{\text{apr}}{\text{n}})^{\text{ny}}-1 }{\frac{\text{apr}}{\text{n}} }[/tex]

[tex]\text{PMT}=\dfrac{\text{A}\times(\frac{\text{APR}}{\text{n}}) }{[(1+\frac{\text{APR}}{\text{n}})^{\text{ny}}-1 }[/tex]

[tex]\text{PMT}=\dfrac{625,000\times(\frac{0.08}{12}) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]

[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+\frac{0.08}{12})^{12\times25}-1] }[/tex]  

[tex]\text{PMT}=\dfrac{625,000\times(0.006667) }{[(1+0.006667)^{300}-1] }[/tex]

[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{[1.006667^{300}-1]}[/tex]

[tex]\text{PMT}=\dfrac{\frac{33335}{8} }{6.34090515}[/tex]

Monthly payment (PMT) = $26421.7591469 ≈ $26421.76

$26421.76 is required monthly payment in order to $50,000 interest.

We can claim that after answering the above question, the As a result, angles the regular polygon has ten sides.

An angle is a shape in Euclidean geometry that is made up of two rays, known as the angle's sides, that meet at a point in the middle known as the angle's vertex. Two rays may combine to generate an angle in the plane in which they are located. An angle is formed when two planes collide. They are known as dihedral angles. In plane geometry, an angle is a potential configuration of two rays or lines that share a termination. The English term "angle" derives from the Latin word "angulus," which means "horn." The vertex is the point at where the two rays, also known as the angle's sides, converge.

The interior angle of a regular polygon with n sides is calculated as follows:

(n-2) * 180° / n = interior angle

The internal angle of the polygon is presented to us as 144°. When we plug this into the formula, we get:

144° = (n - 2) * 180° / n

144° * n = (n - 2) * 180°

144° * n = 180° * n - 360°

144° * n + 360° = 180° * n

360° = 36° * n

n = 10

As a result, the regular polygon has ten sides.

To know more about angles visit:

https://brainly.com/question/14569348

#SPJ1

Answer:

Let x be the cost of 1 kg of mushrooms and y be the cost of 1 kg of turnips.

From the given information, we can form two equations:

2x + 2.5y = 8.55 (Equation 1)

3x + 4y = 13.10 (Equation 2)

To solve for x and y, we can use the method of elimination. Multiplying Equation 1 by 4 and Equation 2 by -2, we get:

8x + 10y = 34.20 (Equation 3)

-6x - 8y = -26.20 (Equation 4)

Adding Equation 3 and Equation 4, we get:

2x + 2y = 8

Simplifying this equation, we get:

x + y = 4 (Equation 5)

Now we have two equations: Equation 2 and Equation 5. We can solve for x and y using substitution or elimination. Here, we will use substitution.

From Equation 5, we can express x in terms of y as:

x = 4 - y

Substituting this expression for x into Equation 2, we get:

3(4 - y) + 4y = 13.10

Simplifying and solving for y, we get:

y = £1.50

Substituting this value for y into Equation 5, we can solve for x:

x + £1.50 = 4

x = £2.50

Therefore, the cost of 1 kg of mushrooms is £2.50 and the cost of 1 kg of turnips is £1.50.

a) The cost of 1 kg of turnips is £1.50.

b) The cost of 1 kg of mushrooms is £2.50.

Two equivalent expressions to  3x + 3(x+y) are:

Two expressions are equivalent if we can rewrite one into the other, in such a way that  we only use algebra to do so.

Here we start with the expression:

3x + 3(x + y)

If we take 3 as a common factor, then we can write:

3x + 3(x + y) = 3*(x + (x + y)) = 3*(x + x + y)

That is an equivalent expression, now if we simplify this:

3*(x + x + y) = 3*(2x + y)

Distribute that product.

3*(2x + y) = 6x + 3y

These is other equivalent expression.

Learn more about equivalent expressions at:

https://brainly.com/question/2972832

#SPJ1

Answer:

[tex]k = - 3[/tex]

Step-by-step explanation:

[tex]y = kx[/tex]

[tex]k \times ( - 1) = 3[/tex]

[tex] - k = 3[/tex]

[tex]k = - 3[/tex]

Answer:

[tex]k = -3[/tex]

Step-by-step explanation:

Step 1: Substitute

To solve this problem you are going to need to substitute the values of y and x into the problem y=kx.  Which would give you the problem of 3=-1k or 3 = -k to make things easier.

Step 2: Using properties of equality

In order to isolate the value of k you would need to divide both sides by -1 because division cancels out multiplication. You would get [tex]\frac{3}{-1} = \frac{-k}{-1}[/tex] or [tex]-3 = k[/tex]

Step 3: Check

In order to check this problem you would need to insert the values back into the original equation and solve. So that would be 3= -1*-3 which does equal 3. So the answer is correct

The intercepts of the line are:

x-intercept: (3, 0)

y-intercept: (0, 1)

What are the intercepts?

To find the x-intercept, we need to find the point where the line intersects the x-axis. This occurs when the y-coordinate of the point is zero. From the given information, we know that the line passes through the point (3, 0), so this point must be the x-intercept.

Therefore, the x-intercept is (3, 0).

To find the y-intercept, we need to find the point where the line intersects the y-axis. This occurs when the x-coordinate of the point is zero. We can find the equation of the line using the two given points (0, y) and (3, 0):

Slope of the line = (y2 - y1) / (x2 - x1)

= (0 - y) / (3 - 0)

= -y / 3

Using the point-slope form of the equation of a line, y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line, we can write:

y - 0 = (-y/3)(x - 3)

Simplifying this equation, we get:

y = (-y/3)x + 1

Multiplying both sides by 3, we get:

3y = -yx + 3

Adding yx to both sides, we get:

yx + 3y = 3

This is the equation of the line in standard form. To find the y-intercept, we set x = 0:

0 + 3y = 3

Solving for y, we get:

y = 1

Therefore, the y-intercept is (0, 1).

Hence, the intercepts of the line are:

x-intercept: (3, 0)

y-intercept: (0, 1)

To know more about the intercepts, visit:

https://brainly.com/question/29113022

#SPJ1

As a result, the cylinder's capacity is roughly 11,088 cubic metres.

The diameter of a circular is the distance measured through its middle. The radius of a circle is the distance to the middle to any spot on the edge. Diameter divided by radius equals two, or 2r=d. 2 r = d .

First, we need to find the radius of the cylinder. We know that the diameter is 28 meters, so the radius is half of that, which is 14 meters.

Using the formula for the volume of a cylinder, V = πr²h, we can now substitute the given values:

V = (22/7) x 14² x 4.5

Simplifying this expression:

V = (22/7) x 196 x 4.5

V = 11,088 cubic meters

Therefore, the volume of the cylinder is approximately 11,088 cubic meters.

To know more about Radius visit:

https://brainly.com/question/27696929

#SPJ1

Answer:

85 degrees.

Step-by-step explanation:

These are parallelograms, meaning the opposite sides are parallel. Since they are parallel, that the line EA becomes a transversal and a bisector for the angle CEK. That means the angle 8 and 3 are equivalent and 7 and 4 are equivalent. This is due to Same Side Interior Angles. These are two halves of the big angle. If the halves are equal, so are the angles. Therefore, CEK = CAK.

The variable term can be added to both sides to solve an inequality with a positive coefficient when it is solved with a negative coefficient.

In mathematics, inequalities specify the connection between two non-equal values. Equal does not imply inequality. Typically, we use the "not equal symbol (≠)" to indicate that two values are not equivalent. But various inequalities are used to compare the values, whether it is less than or larger than.

A coefficient in mathematics is a multiplicative component in a polynomial term, a series term, or an expression. It is typically a number, but it can also be any expression. When the coefficients are themselves variables, they may also be termed parameters.

Recognize that the variable term can be added to both sides to solve an inequality with a positive coefficient when it is solved with a negative coefficient; in this instance, the relationship between the variable and the inequality symbol has flipped.

To know more about Inequality, visit

https://brainly.com/question/30231190

#SPJ1

Answer:

The answer would be 14 miles!

According to the solution we have come to find that, 48% of the teas served were caffeinated.

A percentage is a way of expressing a proportion or a fraction as a number out of 100. The symbol used for percentage is the "%" sign. For example, if you have 10 apples and you want to express how many of them are red, you can say that 20% (or 2 out of 10) of the apples are red.

To find the percentage of caffeinated teas served, we need to divide the number of caffeinated teas by the total number of teas served, and then multiply by 100 to get the answer as a percentage.

Total number of teas served = 36 + 39 = 75

Percentage of caffeinated teas served = (36/75) x 100%

                                                                = 48%

Therefore, 48% of the teas served were caffeinated.

To learn more about percentage, visit the link:

https://brainly.com/question/24877689

#SPJ9

To determine the profit earned from selling 250 shares worth $4.50 each with a 7% fee charged by the stock broker, we need to calculate the total revenue earned and the total cost incurred.

Total revenue earned from selling 250 shares at $4.50 per share:

Revenue = 250 x $4.50 = $1,125

Total cost incurred for buying and selling the shares, including the 7% fee charged by the broker:

Cost = 2 x 250 x $4.50 x 0.07 = $157.50

Here, we are multiplying the number of shares (250) by the price per share ($4.50) to get the total value of the shares. Then we multiply this by 2, since we need to account for both the buying and selling transactions, and then multiply by the broker fee rate of 7% (0.07) to get the total cost incurred.

Therefore, the profit earned from the sale of 250 shares is:

Profit = Revenue - Cost

Profit = $1,125 - $157.50

Profit = $967.50

Hence, the profit earned from selling 250 shares worth $4.50 each with a 7% fee charged by the stock broker is $967.50.

To know more about profit:

https://brainly.com/question/30091032

#SPJ9

Answer:

Option (C)

-0.46 brother

Answer:

Option (C)

-0.46

Step-by-step explanation:

The measure of the angle A in the given right angled triangle is found as: A = 64.82°

Applying the sin function in the given right angled triangle.

Sin A = 77/85

Sin A = 0.905

A = Sin⁻¹ (0.905)

A = 64.82°

Thus, the measure of the angle A in the given right angled triangle is found as: A = 64.82°

Know more about the trigonometric functions

https://brainly.com/question/1143565

#SPJ1

Answer: James' age now is 12 years old.

Fionna and Anuar each had 349 cards, bringing the total to 417. Fionna alone had 145 cards.

A mathematical concept known as the unitary approach entails calculating the value of a single unit in order to calculate the value of a given quantity. Finding the value of one unit and utilising that value to determine the value of a given quantity is an approach for solving problems. For instance, you can use the unitary technique to determine the price of 10 apples if you know that 5 apples cost $10. Now, divide $10 by 5, which equals $2, to determine the price of one apple. The cost of 10 apples is then determined by multiplying the price of one apple ($2) by 10, giving you a final cost of $20.

given

145 total cards with Fionna

349 total cards with Fionna and Aura

Card count with Anuar: 349 - 145

= 204

Rizza's number of cards equals 1/3 of 204.

= 204 / 3

= 68

Total number of cards: 68, 204, and 145

= 417

Fionna and Anuar each had 349 cards, bringing the total to 417. Fionna alone had 145 cards.

To know more about unitary method visit:

https://brainly.com/question/28276953

#SPJ1

Up to 180 degrees

Your Welcome

By adding all the numbers in the line plot, we conclude that she will have enough olive oil.

To check this, we just need to add the 13 numbers and see if it is more than 16.

Each point above the line plot means how many times that number will apear in our sum, then the sum will be:

(2*0 + 4*(4/8) + 3*(6/8) + 3*1 + (1 + 2/8))

Now we need to solve that:

(2*0 + 4*(4/8) + 3*(6/8) + 3*1 + (1 + 2/8))

= 2 + 9/4 + 3 + 1 + 1/4

= 2 + 3 + 1 + 9/4 + 1/4

= 6 + 10/4

= 6 + 8/4 + 2/4

= 6 + 2 + 1/2

= 8 + 1/2

That is the amount of ounces of oil that she needs for the 13 recipes, it is less than 16 ounces, so she will have enough oil.

Learn more about sums at:

https://brainly.com/question/17695139

#SPJ1

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

A value or combination of values that satisfy an equation, inequality, system of equations, or system of inequalities are known as solutions in mathematics. Take the equation x2 - 3x + 2 = 0, for instance. This equation has a solution in the form of an x value that makes the equation true. The quadratic formula allows us to determine that this equation has two solutions, x = 1 and x = 2. According to this, a solution for a system of equations is a set of values that simultaneously satisfy every equation in the system. Mathematical problem-solving, which has many applications in areas like engineering, physics, economics, and more, is a crucial component of the subject.

given

We must identify the point(s) at where the two lines intersect in order to obtain the solution(s) to the system of equations depicted by the graph. The graph demonstrates that the lines cross at the location (-3, 3).

Hence, there is only one answer, which is (-3, 3) as the two lines intersect in order to obtain the solution(s) to the system of equations.

To know more about solution visit :-

https://brainly.com/question/16989201

#SPJ1

Answer:

28 people

Step-by-step explanation:

21 / 3 = 25

7 = 25%

25 x 4 = 100%

so

7 x 4 = 28

28 people are in the class

Answer: 9x^2y

the gcf of -63 , 9 and 90 is 9

And the gcf of the variables is x^2 and y

So, 9x^2y

Frequency Distribution Table is down below.

Class Count Cumulative Frequency Table

160 - 180 3 3

181 - 201 5 8

202 - 222 14 22

223 - 243 14 36

244 - 264 10 46

265 - 285 2 48

286 - 306 1 49

307 - 327 1 50

Total 50     100

Here its peak is in between 202 to 243 frequency range. There are three extreme values that are 270, 295 and 325 pounds weight.

Median lies in the interval 223-243 and mean also lies in that interval. Maximum values lies in between 200 - 225 interval.

The distribution is left skewed.

Learn more about frequency distribution on;

https://brainly.com/question/17114842

#SPJ1

By answering the question using the information provided, we can conclude that in order to arrive at the general solution, we must take into account the scenario in which [tex]y-1\neq 0 , y \neq 1[/tex], by constructing equations.

Two equations are said to be equivalent when their bases and solutions line up. To create an equivalent equation, the same quantity, symbol, or expression must be added to or removed from both of the equation's two sides.

We can also create an analogous equation by multiplying or dividing both sides of an equation by a nonzero integer.

Solving differntial calculus

[tex](1+x)y'=( x+2) (y-1)[/tex]

We will first employ varying separation. The variables y and x will be placed on the opposite sides of the equation, and both sides will be integrated.

[tex](1+x)y'/(y-1) = (x+2)dx[/tex]

We will integrate both sides using the substitution[tex]u= y-1,\frac{du}{dy} =y'[/tex]

∫[tex](x+2)dx[/tex] =∫[tex](1+x)\frac{du}{u}[/tex]

㏑l[tex]u[/tex]l +[tex]x[/tex]㏑l[tex]u[/tex]l= [tex]\frac{1}{2} x^{2}+2x+c[/tex]

Substituting [tex]u= y-1[/tex]

㏑l[tex]y-1[/tex]l+ [tex]x[/tex]㏑l[tex]y-1[/tex]l= [tex]\frac{1}{2x^{2} } +2x+c[/tex]

Learn more about equations

brainly.com/question/2972832

#SPJ1

The complete question is: Find the general solution to the differential equation (1+x)y' = (x + 2)(y − 1).

Step-by-step explanation:

The volume of a cone can be calculated using the formula:

V = (1/3)πr^2h

where r is the radius of the base, h is the height of the cone, and π is a constant approximately equal to 3.14.

In this case, the diameter of the base of the cone is 8 cm, which means the radius is half of that, or 4 cm. The height of the cone is given as 10 cm. Substituting these values into the formula, we get:

V = (1/3)π(4 cm)^2(10 cm)

V ≈ 167.55 cubic centimeters

Therefore, the volume of the paper drinking cone is closest to 167.55 cubic centimeters.

Answer:

3n + 5n = 8n = 95

n = 11

$95 - $88 = $7

(11 paint brushes, 11 boxes of colored pencils)