Consider the following function. f(x) = 9 − x2/3 Find f(−27) and f(27). f(−27) = f(27) = Find all values c in (−27, 27) such that f '(c) = 0. (Enter your answers as a comma-separated list. If an answer does not exist, enter DNE.) c = Based off of this information, what conclusions can be made about Rolle's Theorem? This contradicts Rolle's Theorem, since f is differentiable, f(−27) = f(27), and f '(c) = 0 exists, but c is not in (−27, 27). This does not contradict Rolle's Theorem, since f '(0) = 0, and 0 is in the interval (−27, 27). This contradicts Rolle's Theorem, since f(−27) = f(27), there should exist a number c in (−27, 27) such that f '(c) = 0. This does not contradict Rolle's Theorem, since f '(0) does not exist, and so f is not differentiable on (−27, 27). Nothing can be concluded.

Answer:

y = -x+7

Step-by-step explanation:

We need to get x+y=4 in slope intercept from to determine the slope

x+t=4

Subtract x from each side

x-xy = -x+4

y= -x+4

The slope is -1

Parallel lines have the same slope

We have the slope and a point of the new line.

We can use the point slope form

y-y1 = m(x-x1)

y-8 = -1(x--1)

y-8 = -1(x+1)

Distribute the negative sign

y-8 = -x-1

Add 8 to each side

y-8+8 = -x-1+8

y = -x+7

The divergence of the vector field [tex]\vec F[/tex] is

[tex]\nabla\cdot\vec F=y^2+0+x^2=x^2+y^2[/tex]

By the divergence theorem,

[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_V(x^2+y^2)\,\mathrm dV[/tex]

where [tex]V[/tex] denotes the region with boundary [tex]S[/tex]. Convert to cylindrical coordinates:

[tex]x=u\cos v[/tex]

[tex]y=u\sin v[/tex]

[tex]z=z[/tex]

The integral is then

[tex]\displaystyle\int_0^{2\pi}\int_0^2\int_{u^2}^4u^3\,\mathrm du\,\mathrm dv=\frac{32\pi}3[/tex]

Using the Divergence Theorem, the flux of the vector field F across the surface S can be calculated by finding the dot product of F and the outward-pointing unit normal vector to the surface. This concept is similar to that of a Gaussian surface in physics, which is used to analyze the flux of electric fields.

In this problem, you are required to use the Divergence Theorem in order to calculate a surface integral, specifically the flux of the vector field F across a defined surface S. At a basic level, the Divergence Theorem states that the flux of a vector field through a closed surface is equal to the triple integral of the divergence of the field over the volume enclosed by the surface.

In this specific scenario, we have the vector field F(x, y, z) = (cos(z) + xy²) i + xe⁻ᶻ j + (sin(y) + x²z) k, and the surface S is bounded by the paraboloid z = x² + y² and the plane z = 4. To calculate the surface integral, you would first express these surfaces parametrically and then find the outward pointing unit normal vector to the surface. The dot product of F and this normal vector will give the amount of F flowing across an infinitesimal element of the surface, which when integrated over the entire surface, yields the flux of F across S.

This process is similar to the concept of Gaussian surface, which is used to calculate the flux of an electric field. In both cases, we're examining how a field interacts with a defined space or volume.

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Answer:

14 m^2

Step-by-step explanation:

The method used to find the area of this trapezoid is to put the given numbers into the formula for the area of a trapezoid. That formula is ...

A = (1/2)(b1 +b2)h

where b1 and b2 are the lengths of the parallel bases, and h is the perpendicular distance between them.

The figure shows you that b1 and b2 are 5 m and 2 m (in no particular order) and h is 4 m. Putting these numbers into the formula gives ...

A = (1/2)(5 m + 2m)(4 m) = (1/2)(28 m^2) = 14 m^2

Notice you can factorize

[tex]x^5+5x^4-5x^3-25x^2+4x+20[/tex]

by grouping the terms as

[tex](x^5-5x^3+4x)+(5x^4-25x^2+20)=x(x^4-5x^2+4)+5(x^4-5x^2+4)[/tex]

[tex]\implies f(x)=(x+5)(x^4-5x^2+4)[/tex]

Then you know right away that [tex]x=-5[/tex] is a (real) root, so we eliminate C and D.

The remaining quartic can be factored easily:

[tex]x^4-5x^2+4=(x^2)^2-5x^2+4=(x^2-4)(x^2-1)=(x-2)(x+2)(x-1)(x+1)[/tex]

which admits four more (also real) roots, [tex]x=\pm2[/tex] and [tex]x=\pm1[/tex], so the answer is B.

Answer:

$25.20

Step-by-step explanation:

Cost of the meal = $21

Total cost

= c + 0.20c

= 21 + 0.20(21)

= $25.20

For this case we have the following function, to calculate the total cost of the meal, including 20% of the tip:

[tex]f (c) = c + 0.20c[/tex]

They tell us that a meal costs $ 21.00. That is,[tex]c = 21[/tex]

[tex]f (21) = 21 + 0.20 (21)\\f (21) = 21 + 4.2\\f (21) = 25.2[/tex]

Thus, the total cost of the meal is 25.2

Answer:

$ 25.2

Answer:

  104°

Step-by-step explanation:

Even a crude diagram can be helpful. Half of angle ACD is the complement of the 64° angle made with diagonal BD. Since that complement, 26°, is half the bisected angle, which is half the measure of ∠BAD, the measure of ∠BAD must be 4×26° = 104°.

___

Opposite angles of a rhombus are congruent, and each diagonal is a bisector of the angles at its endpoints. The diagonals bisect each other and meet at right angles.

Answer:

there are solutions for all values of k

Step-by-step explanation:

In order for there to be no real solutions, the value of the discriminant must be negative. For this equation, the discriminant is ...

(-(k+2))^2 -4(3)(k-1)

We want to find values of k for which this is negative:

(k^2 +4k +4) -12k +12 < 0

k^2 -8k +16 < 0

(k -4)^2 < 0

A square is never negative, so there are no values of k that result in the equation having no solutions.

The domain is the input values, which would also be X values.

{ x |x= -5, -3, 1, 2,6}

For this case we have by definition that the domain of a function y = f (x) is the set of all the values that the variable x takes, for which the function is defined. They are also represented by the starting set.

It is observed in the figure, that the domain is:

[tex]{x | x = -3,2, -5,1,6}\\{x | x = -5, -3,1,2,6}[/tex]

Answer:

Option A

[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{a}x^2\stackrel{\stackrel{b}{\downarrow }}{+b}x\stackrel{\stackrel{c}{\downarrow }}{+c} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ \stackrel{-16}{negative}&\textit{no solution}~~\checkmark \end{cases}[/tex]

Answer:

A quadratic equation of the form 0 = ax² + bx + c with a discriminant value of –16 has no real solution

Step-by-step explanation:

A quadratic equation ax²+bx+c=0 with discriminant D=b²-4ac has

2 unequal real solutions if D is positive i.e. D>0

2 equal real roots if D=0

no real root if D is negative i.e. D<0

Here, we are given value of D= -16 which is less than zero

Hence, a quadratic equation of the form 0 = ax² + bx + c with a discriminant value of –16 has no real solution

Answer:

3x⁴ + x³ + 3 x² - 18 x + 4  

Step-by-step explanation:

Answer:

Step-by-step explanation:

3x^4+x^3+3x^2-18+4

Answer:

  The first two tables show y as a function of x.

Step-by-step explanation:

A relation is not a function if the same x-value shows up more than once in the table. That will be the case for the last two tables, each of which has x=2 show up twice.

For this case we have that the equation of a straight line in the form of an intersection is given by:

[tex]y = mx + b[/tex]

Where:

m: It's the slope

b: It is the cutoff point with the y axis

We found the slope:

[tex]m = \frac {y2-y1} {x2-x1} = \frac {8-6} {4-5} = \frac {2} {- 1} = - 2[/tex]

So, the line is:

[tex]y = -2x + b[/tex]

We find the cut point by substituting a point:

[tex]8 = -2 (4) + b\\8 = -8 + b\\b = 8 + 8\\b = 16[/tex]

Finally, the equation is:

[tex]y = -2x + 16[/tex]

We can also have the equation of the point-slope form:

[tex]y-y_ {0} = m (x-x_ {0})[/tex]

Where:

[tex](x_ {0}, y_ {0}) = (4,8)[/tex]represents a point:

So:

[tex]y-8 = -2 (x-4)[/tex]

ANswer:

[tex]y-8 = -2 (x-4)\\y = -2x + 16[/tex]

Answer:

Final answer is x=4, y=7.

Step-by-step explanation:

Questions says to use the graph to determine the number of solutions the system has. where system of equations are x=4 and y=x+3

any equation of the form x=k is a vertical line crossing x-axis at k.

So x=4 is a vertical line crossing x-axis at 4.

y=x+3 has slope m=1 and y-intercept b=3

So it passes through point (0,3) and for slope m=1, rise 1 up then 1 right to get new point.

Then final graph is given as shown in the picture.

We can see that both lines intersect at point (4,7).

Hence final answer is x=4, y=7.

Answer:

24 ˚

Step-by-step explanation:

Exterior angle of a regular    -sided polygon:

360 ˚/ n ⇒ 360 ˚/15 = 24 ˚

Answer:

A) 24

Step-by-step explanation:

Since the sum of the exterior angles is always 360 degrees, if you divide 360 degrees by 24 degrees you get 15 which is the number of equal exterior angles and therefore 15 vertices and sides to the polygon.

Answer:

  36, 32, 28, 24

Step-by-step explanation:

Fill in the values of n and do the arithmetic.

  a1 = 36 -4(1 -1) = 36

  a2 = 36 -4(2 -1) = 32

  a3 = 36 -4(3 -1) = 28

  a4 = 36 -4(4 -1) = 24

_____

You could recognize the formula as the specific case of the explicit formula for an arithmetic sequence with first term 36 and common difference -4. That tells you the second term is 36 -4 = 32, and each successive term is 4 less than the one before.

Answer:

x = ±(√2)/3

Step-by-step explanation:

For the quadratic ...

ax^2 +bx +c = 0

the quadratic formula gives solutions as ...

x = (-b ±√(b^2-4ac))/(2a)

Comparing your quadratic to the general form above, we find ...

a = 9; b = 0, c = -2

Filling these values into the formula gives ...

x = (-0 ±√(0^2 -4(9)(-2)))/(2·9)

x = ±(√72)/18 = ±(6√2)/18

x = ±(√2)/3

Answer:

1. Yes

2. No

3. Yes

4. No

Step-by-step explanation:

When you say a random sample, this means that every member of the population will have a chance to be part of the sample. If you consider the scenarios, only the 1st and 3rd option will come up with a random sample because the respondents of the sample is not predetermined. If you take the other options into consideration, you can see that not everyone would have had a chance to be part of the sample.

Answer: 144$

Step-by-step explanation: multiply 5 by 12 and then multiply that answer by 2.40

Answer:

1/4

Step-by-step explanation:

The are 8 different sections that the spinner can land on

2 of them are labeled blue

P(blue) = spots labeled blue/ total spots

            = 2/8

            = 1/4

Answer:

  11.7%

Step-by-step explanation:

The account balance (A) for a principal amount P and monthly interest rate r will be ...

  A = P(1 +r)^8

Then we can divide by P and take the 8th root to find r:

  A/P = (1+r)^8

  (A/P)^(1/8) = 1 +r

  (A/P)^(1/8) - 1 = r

Since this is the monthly rate, we need to multiply this value by 12 to find the annual interest rate on the account:

  annual rate = 12((A/P)^(1/8) -1) = 12((9779/9047)^(1/8) -1) ≈ 0.11728 ≈ 11.7%

Answer:  [tex]\frac{15}{35}[/tex]

Step-by-step explanation:

Equivalent fractions are defined as those fractions that represent the same value but their numerators and denominators are different.

For a fraction in the form [tex]\frac{a}{b}[/tex] you can find an equivalent fraction by multiplying the numerator and the denominator by the same number "c":

[tex]\frac{a}{b}=\frac{a*c}{b*c}[/tex]

Then, for the fraction [tex]\frac{3}{7}[/tex] you have an equivalent fraction with denominator 35. This is obtained by multiplying the denominato 7 by 5.

Then, the numerator will be:

[tex]3*5=15[/tex]

So:

[tex]\frac{3*5}{7*5}=\frac{15}{35}[/tex]

Answer:

The equivalent fraction of 3/7 is 15/35

Step-by-step explanation:

It is given that, a fraction 3/7

To find the equivalent fraction

We have 3/7

some of equivalent fraction of 3/7 are

3/7 * 2/2 = 6/14

3/7 * 3/3 = 9/21

3/7 * 4/4 = 12/28

3/7 * 5/5 =15/35

3/7 * 6/6 =  18/42  ....

We need denominator 35

Therefore the correct answer is 15/35

I think these two are the right answer.

Answer:

Im pretty sure its 13 for Tracy and 26 for Simon

Answer:

I believe Simon is currently 24 and Tracy is 12

Step-by-step explanation:

24+12=36

12+12=24

you add 12 to each to see in 12 YEARS

Then you can see if it is 1.5 times as much by dividing by 1.5 or multiplying by 1.5

Like:

24*1.5=36

36/1.5=24

And that's how you do it

hope this halps :)

pls mark me brainliest as well

Answer: 7

Explanation:

x^2-4x=21

x^2-4x-21=0

(x+3)(x-7)=0

x=-3

x=7

*** if you need to find the positive # only, the ANSWER is 7****

The correct equation for the problem is x² - 4x = 21. By using the quadratic formula, we find that the number can be either 7 or -3.

The student provided a mistaken equation for the problem which is x² + 4x = 21, not x² + 4x 21 = 0. The correct equation that represents the problem 'The square of a number decreased by 4 times the number equals 21' is x² - 4x = 21. To solve this equation, we first bring the constants to one side to set the equation equal to zero:

x² - 4x - 21 = 0

Now we have a quadratic equation of the form ax² + bx + c = 0, where a = 1, b = -4, and c = -21. We will use the quadratic formula, which is:

x = (-b ± √(b² - 4ac)) / (2a)

Substituting the values of a, b, and c into the formula gives us:

x = (4 ± √((-4)² - 4(1)(-21))) / (2*1)

x = (4 ± √(16 + 84)) / 2

x = (4 ± √100) / 2

x = (4 ± 10) / 2

Thus, the solutions are x = (4 + 10) / 2 = 7 and x = (4 - 10) / 2 = -3.

Therefore, the numbers that satisfy the equation are 7 and -3.

Answer:

The measure of the angle is [tex]68.79\°[/tex]

Step-by-step explanation:

step 1

Find the radius of the circle

The area of the circle is equal to

[tex]A=\pi r^{2}[/tex]

we have

[tex]A=78.5\ cm^{2}[/tex]

[tex]\pi =3.14[/tex]

substitute and solve for r

[tex]78.5=(3.14)r^{2}[/tex]

[tex]r^{2}=78.5/(3.14)[/tex]

[tex]r=5\ cm[/tex]

step 2

Find the circumference of the circle

The circumference of the circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]r=5\ cm[/tex]

[tex]\pi =3.14[/tex]

Substitute

[tex]C=2(3.14)(5)[/tex]

[tex]C=31.4\ cm[/tex]

step 3

Find the measure of the angle by an arc length of 6 cm

we know that

The circumference of a circle subtends a central angle of 360 degrees

So

by proportion

[tex]\frac{31.4}{360}=\frac{6}{x}\\ \\x=360*6/31.4\\ \\x=68.79\°[/tex]

Answer:

The measure of the angle subtended by the arc is 68.8°

Step-by-step explanation:

Formula for calculating length of an arc is expressed as:

Length of an arc = theta/360×2πr

Where theta is the angle subtended by the arc

r is the radius of the circle

To get the radius r;

Given Area of the circle to be 78.5cm²

Since area = πr²

78.5 = πr²

78.5 = 3.14r²

r² = 78.5/3.14

r² = 25

r =√25

r = 5cm

This radius of the circle is 5cm

Remember that

Length of an arc = theta/360° × 2πr

6 = theta/360 × 2(3.14)(5)

6 = 31.4theta/360

2160 = 31.4theta

theta = 2160/31.4

theta = 68.8°

Answer:

-4x=-3

3= 4x

Step-by-step explanation:

The equation –4x = –3 fulfills the condition of variable isolation. Options C and D are correct

Given that,
To determine the expression consist of the isolation of the variable and constant.

The equation is the relationship between variables and represented as y = ax + b is an example of a polynomial equation.

Here,
-6 + 2x = 6x - 9
-4x = -3 or 4x = 3

Thus, the equation –4x = –3 fulfills the condition of variable isolation. Options C and D are correct.

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Answer:

1. EF≅HG

2. EF║HG

3. Definition of parallelogram

4. when two parallel lines are cut by a transversal, alternate interior angles are congruent

5. EK≅GK

   FK≅HK

Step-by-step explanation:

1. As per the properties of a parallelogram, the opposite sides are congruent.

hence in given parallelogram EFGH the two sides EF≅HG

2. As per the properties of a parallelogram, the opposite sides are parallel.

hence in given parallelogram EFGH the two sides EF║HG

3.  Definition of parallelogram: A quadrilateral is called a parallelogram if two of its opposite sides are parallel.

4. As per the properties of transversal lines, when two parallel lines are cut by a transversal, alternate interior angles are congruent.

5. As proven in given question ΔEKF≅ΔGKH, so as per the CPCTC

                      EK≅GK and FK≅HK

!

There are different properties that are ascribed to a shape. The statement or reason to fill each box are;

A parallelogram is known to be a shape that is said to be composed of four sides. Where the sides opposite each other are regarded as parallel. The Examples of parallelograms are; squares, rhombuses, etc.

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The equation of a line is:

y = mx + c

The m is the gradient of the line, and the c is the y-intercept of the line

That means that the y-intercept of [y = -4x + 3]  is 3

and the y-intercept of [y = -4x + 4] is 4

So the distance between the two y-intercepts is:

4 - 3 = 1

Answer:

a. 0.169x+69.11 > 0.126x+76.74

Step-by-step explanation:

So, there's a lot of talk in the question statement.  Of course, it presents some important data... but it's also meant to confuse you.

We can boil it down to the following life expectancies :

Men =  0.169x+69.11

Women = 0.126x+76.74

Then they ask you to write with that men have a greater life expectancy than woman using the models above.

Start by writing the goal:

men > women

Then replace "men" by the model and "women" by the model:

0.169x+69.11 > 0.126x+76.74

And you have your answer.

Answer:

A

Step-by-step explanation:

maybe, maybe not

Answer:

  see below

Step-by-step explanation:

Of your remaining answer choices, the only one that shows a reflection (not a translation) is the one below. It has the orientation of the figure reversed (side lengths shortest-to-longest are CCW instead of CW).

The reflection over y=x reverses the coordinates: (x, y) ⇒ (y, x), so the vertices become ...