The function f(x) = 0.11x + 43 relates how much Derek pays for phone service, f(x), to the number of minutes, x, used for international calls in a month. What is the value and meaning of f(320)?

Answer:

  (9x -2)(9x +2)

Step-by-step explanation:

Each of the terms in the difference is a perfect square, so the "perfect square trick" applies. The factors are the sum and difference of the square roots of the given terms.

  81x² - 4 = (9x +2)(9x -2)

Answer:

The domain would be the set of all whole numbers.

Step-by-step explanation:

Integers are { ......-3, -2, -1, 0, 1, 2, 3....}

Whole numbers are {0, 1, 2, 3, ...... }

Real numbers are all numbers except imaginary number,

Positive integers are {1, 2, 3, 4, ....}

Given,

In the function f(x),

x represents the number of people in line,

We know that number of people can not be negative and it can be 0,

Thus, the possible value of x are 0, 1, 2, 3,......

Also, the domain of a function is the set of all possible value of input,

Since,  x represent the input for the function f(x),

Thus, the domain of f(x) would be the set of all whole number.

Second option is correct.

Answer: The slope is [tex]\frac{2}{3}[/tex]

Step-by-step explanation:

The slope can be calculated with the following formula:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

Then, knowing that the line passes through the points (2,1) and (-1,-1), we can substitute the coordinates into the formula.

In this case:

[tex]y_2=-1\\y_1=1\\x_2=-1\\x_1=2[/tex]

Therefore, the slope of the line that passes through the points (2,1) and (-1,-1) is:

[tex]m=\frac{-1-1}{-1-2}\\\\m=\frac{-2}{-3}\\\\m=\frac{2}{3}[/tex]

Answer:

Step-by-step explanation:

If Thaddeus drives the whole 16 hours, the distance between them is ...

  distance = speed · time

  distance = 20 mi/h · 16 h

  distance = 320 miles.

It is 45 miles more than that. For each hour that Ian drives, their separation distance increases by (25 mph -20 mph)·(1 h) = 5 mi. Then Ian must have driven ...

  (45 mi)/(5 mi/h) = 9 h

The rest of the 16 hours is the time that Thaddeus drove: 7 hours.

___

Let x represent the time Ian drives. Then 16-x is the time Thaddeus drives. Their total distance driven is ...

  distance = speed · time

  365 mi = (25 mi/h)(x) + (20 mi/h)(16 h -x)

  45 mi = (5 mi/h)(x) . . . . . . . . subtract 320 miles, collect terms

  (45 mi)/(5 mi/h) = x = 9 h . . . . . . divide by the coefficient of x

_____

Comment on the solution

You may notice a similarity between the solution of this equation and the verbal discussion above. (That is intentional.) It works well to let a variable represent the amount of the highest contributor. Here, that is Ian's time, since he is driving at the fastest speed.

To solve the problem, we need to set up two equations based on the information given in the problem. Solving the equations simultaneously gives Thaddeus has been driving for 7 hours and Ian has been driving for 9 hours.

First, we'll define the variables. Let's say the time Thaddeus has been driving is T hours, and the time Ian has been driving is I hours. The total distance they covered is the sum of the distances each one traveled, which is 365 miles. Thaddeus travels at a rate of 20 mph, while Ian travels at 25 mph. This is represented by the equation 20T + 25I = 365.

Next, we know that the total time they have been driving is 16 hours, which gives us another equation, T + I = 16. Now we have a system of linear equations that we can solve simultaneously to find the values of T and I. The solution gives T = 7 hours and I = 9 hours. Hence, Thaddeus has been driving for 7 hours and Ian has been driving for 9 hours.

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Answer:

  x = 11°

Step-by-step explanation:

The parallel lines suggest we look to the relationships involving angles and transversals. The angle marked 33° and ∠CAB are alternate interior angles, hence congruent:

  ∠CAB = 33°

5x is the measure of the external angle opposite that internal angle and angle 2x of ΔABC, so it is equal to their sum:

  5x = 2x + 33°

  3x = 33° . . . . . . . . . subtract 2x

  x = 11° . . . . . . . . . . . divide by 3

Answer:

60

Step-by-step explanation:

We have been given the matrix;

[tex]\left[\begin{array}{ccc}5&8\\-5&4\end{array}\right][/tex]

For a 2-by-2 matrix, the determinant is calculated as;

( product of elements in the leading diagonal) - (product of elements in the other diagonal)

determinant = ( 5*4) - (8*-5)

                     = 20 - (-40) = 60

Answer:

c. 60

Step-by-step explanation

math

Hi the answer is 344

Answer:

140

Step-by-step explanation:

54-75=-21

-21+81=60

60-(-27)=87 or 60+27=87

87+53=140

diameter and height i think

Answer:

they describe diameter and height

26-diameter

34-height

Answer:

12 5/8 tons were delivered by the third truck

Step-by-step explanation:

25 = 6 4/8 + 5 7/8 + x

25 = 12 3/8 + x

- 12 3/8

12 5/8 = x

Answer:

6 3/4

Step-by-step explanation:

5 7/8 * 2 +6 1/2 + X = 25

Do the algebra.

x = 6 3/4

Explanation:

It is the average (mean) of the absolute values of the differences between a set of numbers and their mean.

Example: consider the set {1, 2, 4}. The mean is computed in the usual way: the sum divided by the number of contributors —

mean = (1 + 2 + 4)/3 = 7/3 = 2 1/3

Then the deviations are ...

1 -2 1/3 = -1 1/3 . . . . the absolute value of this is 1 1/3

2 -2 1/3 = -1/3 . . . . . the absolute value of this is 1/3

4 -2 1/3 = 1 2/3 . . . . the absolute value of this is 1 2/3

The mean of these absolute values is their sum divided by the number of them:

(1 1/3 +1/3 +1 2/3)/3 = (3 1/3)/3 = 1 1/9

The MAD of {1, 2, 4} is 1 1/9.

_____

Your graphing calculator or spreadsheet program may have a function that will calculate this for you.

[tex]S[/tex] is a closed surface with interior [tex]R[/tex], so you can use the divergence theorem.

[tex]\vec F(x,y,z)=x\,\vec\imath+y\,\vec\jmath+9\,\vec k\implies\nabla\cdot\vec F(x,y,z)=\dfrac{\partial(x)}{\partial x}+\dfrac{\partial(y)}{\partial y}+\dfrac{\partial(9)}{\partial z}=2[/tex]

By the divergence theorem, the flux of [tex]\vec F[/tex] across [tex]S[/tex] is given by the integral of [tex]\nabla\cdot\vec F[/tex] over [tex]R[/tex]:

[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV[/tex]

Convert to cylindrical coordinates, setting

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

[tex]y=y[/tex]

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

The integral is then

[tex]\displaystyle2\int_{v=0}^{v=2\pi}\int_{u=0}^{u=1}\int_{y=0}^{y=8-u\cos v}u\,\mathrm dy\,\mathrm du\,\mathrm dv=\boxed{16\pi}[/tex]

The flux of a vector field across a surface is calculated using a surface integral, which involves integrating the dot product of the vector field and the differential area element over the surface. For closed surfaces, the outward orientation is used. Electric flux, the flux of the electric field across a surface, is mentioned as an example.

The flux of a vector field across a surface can be calculated using a surface integral. For the given vector field F(x, y, z) = x i + y j + 9 k and the surface S defined as the boundary of the region enclosed by the cylinder x2 + z2 = 1 and the planes y = 0 and x + y = 8, the flux is evaluated by integrating F·dS over the surface S.

The orientation of the surface is important in this process. For a closed surface, the positive (outward) orientation is used. The normal vector at any point on the surface points from the inside to the outside, and this outward normal is used to compute the flux through a closed surface.

Conceptually, this is like breaking the surface up into infinitesimally small patches dA and summing up the contributions of the vector field F (in this case, x i + y j + 9 k) through each patch - this is referred to as electric flux in the context of electric fields. This calculation embodies the concept of electric flux, which is defined as the scalar product of the electric field and the area vector.

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Answer:

2.9%

Step-by-step explanation:

The problem says the stations are 260 feet apart.  Assuming that this is the horizontal distance between them, then the grade is:

7.5 / 260 × 100% = 2.9%

This is less than the maximum of 3.5%, so it meets the standards.

Answer:

Equation 1:  r = 4 +( 3 * cos theta  )

Equation 2: r = sqrt ( 5² * sin(2 theta) )

Step-by-step explanation:

GRAPH 1:  

The first graph is a dimpled limacon.

General equation for dimpled limacon:

r = a + b cos theta                     ∴ if dimple is along the x- axis

r = a + b sin theta                      ∴ if dimple is along the y-axis

y-intercept : { a, -a }  = { 4, -4 }   ∴ the points at which limacon intersects y-axis

Negative side of x-axis = ( a – b ) ⇒ 1

Positive side of x-axis = ( a + b ) ⇒ 7

Subtract the value of a from sum of a and b to find b:

b = 7 – 4 ⇒ 3

Equation1:  r = 4 +( 3 * cos theta  )

GRAPH 2:  

The second graph is a lemniscates.  

General equation for lemniscates is:

r² = a² cos(2theta)                        ∴ if petals of graph are on coordinate axis

r² = a² sin(2 theta)                ∴ if petals of graph are not on coordinate axis

now, according to the graph:

a = 5 ⇒ a² = 25

angle of graph:  cos2θ, simply divide 360° by 2:

[tex]\frac{360}{2}[/tex] ⇒ 180°

The petals cannot be on coordinate axis, we start from 45° and then the next petal will be on:

45° + 180° = 225°

Since the graph is not on the coordinate axis, so

r² = 5² sin(2 theta)   ⇒    r = sqrt ( 5² * sin(2 theta) )      

Equation 2: r = sqrt ( 5² * sin(2 theta) )      

Answer:

  KM = 20

Step-by-step explanation:

Point V is the midpoint of KM, so ...

  KV = VM

  2.5z = 5z -10

  10 + 2.5z = 5z . . . . . add 10

  10 = 2.5z . . . . . . . . . subtract 2.5z

This is sufficient to answer the question:

  KV = VM = 2.5z = 10

  KM = KV + VM = 10 + 10

  KM = 20

_____

In this case, it is not necessary to find the value of z. If you wanted to, you could divide by the coefficient of z in the last equation:

  10/2.5 = z = 4

-288/5 or - 57.6 I used a calculator so I cannot solve step by step

Answer:

  2 cm and 6 cm

Step-by-step explanation:

The product of the dimensions must be 12 cm². (All answer choices meet that requirement.)

Opposite sides of a rectangle are the same length, so the sum of the two dimensions must be half the perimeter, 8 cm. The sums of the answer choices are ...

Only the first answer choice meets the requirement for a perimeter of 16 cm. The dimensions could be 2 cm and 6 cm.

6

×

2

Explanation:

For the rectangle

Length

=

ℓ

Breadth

=

b

Area is  

12

cm

2

ℓ

b

=

12

Perimeter is  

16

cm

2

(

ℓ

+

b

)

=

16

ℓ

+

b

=

8

Substitute  

b

=

12

ℓ

from first equation

ℓ

+

12

ℓ

=

8

ℓ

2

+

12

=

8

ℓ

ℓ

2

−

8

ℓ

+

12

=

0

Use quadratic formula (

x

=

−

b

±

√

b

2

−

4

a

c

2

a

) to find  

ℓ

ℓ

=

−

(

−

8

)

±

√

(

−

8

)

2

−

(

4

×

1

×

12

)

2

×

1

ℓ

=

8

±

√

16

2

ℓ

=

8

±

4

2

ℓ

1

=

8

+

4

2

=

6

ℓ

2

=

8

−

4

2

=

2

If  

ℓ

1

is taken as length then  

ℓ

2

is the breadth of the rectangle.

The compound inequality representing the range of possible values for 'x' (side length BC) in the triangle ABC, given that side lengths AB=13 and AC=21, is 8 < x < 34.

In the triangle ABC with side lengths, AB=13, AC=21, and BC=x, we use the triangle inequality theorem which states that the length of a side of a triangle is less than the sum of the lengths of the other two sides and more than the absolute difference between them. Applying this theorem to your specific situation, we get the compound inequality 8 < x < 34. This inequality represents the range of possible values for the side length x is BC.

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For triangle ABC with sides AB = 13, AC = 21, and BC = x, the range of possible values for x is[tex]\( 8 < x < 34 \)[/tex] based on the triangle inequality theorem.

In triangle ABC, the relationship among its side lengths is governed by the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the remaining side.

For the given triangle with side lengths AB = 13, AC = 21, and BC = x, we can express this relationship as a compound inequality. Let \[tex]( a \), \( b \), and \( c \)[/tex]  represent the lengths of the sides of the triangle. According to the triangle inequality theorem, we have:

[tex]\[ a + b > c \][/tex]

Substitute the given values:

[tex]\[ 13 + x > 21 \][/tex]

Now, solve for[tex]\( x \)[/tex]

[tex]\[ x > 8 \][/tex]

Similarly, for the other pair of sides:

[tex]\[ 21 + x > 13 \][/tex]

Solving for \( x \):

[tex]\[ x > -8 \][/tex]

However, since side lengths cannot be negative, we disregard the second inequality. Therefore, the compound inequality representing the range of possible values for [tex]\( x \) is \( 8 < x < 34 \).[/tex] This means that any value of [tex]\( x \)[/tex] between 8 and 34 (exclusive) will satisfy the conditions for the given triangle.

Answer:

B

Step-by-step explanation:

In the equation for interest compounding continuously, the A stands for the amount after the compounding is done, the P is the initial amount invested, the e is Euler's number, the r is the rate in decimal form, and the t is the time in years that the money is invested.  Setting up our equation with the given values looks like this:

[tex]A=22,000e^{(.0385)(11)}[/tex]

Multiply the rate with the time to simplify a bit to

[tex]A=22,000e^{.4235}[/tex]

Raise e to the power of .4235 on your calculator (hit 2nd then the ln button to get your e) and get

[tex]A=22,000(1.527297754)[/tex]

Multiply out to get $33600.55, but rounding up gives you B as your answer.

The balance in the account after 11 years is $33,600.6. Thus, the correct option is B.

Theoretically, long-term average interest means that interest is continuously earned on a current account as well as reinvested into the balance to increase future interest earnings.

The equation is given as,

[tex]\rm P=P_o \times e^{rt}[/tex]

The balance in the account after 11 years is calculated as,

[tex]\rm P = \$22,000 \times e^{0.0385\times 11}[/tex]

Simplify the equation, then we have

P = $22,000 x 1.52729

P = $33,600.6

Thus, the correct option is B.

More about the continuous compounding link is given below.

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Answer:

  17.8 hours

Step-by-step explanation:

Serena's bonus on $1200 sales is 15%×$1200 = $180. In order to make $500 for the week, then she must have at least ...

  $500 - 180 = $320

in hourly pay.

At $18 per hour, that requires she work $320/($18/h) = 17.77_7 h.

Serena must work a minimum of about 17.8 hours to make $500.

_____

Comment on the answer

The exact result of the computation is 17 7/9 hours. Many payroll departments record hours to the nearest 1/4 or 1/10 hour. For Serena's pay to be at least $500, she must work 17.8 (rounded to tenths) or 18.0 (rounded to quarters) hours.

Answer:

Cortex layer

Step-by-step explanation:

The fibrous protein core of the hair, formed by elongated cells containing melanin pigment, is the cortex layer

Answer:

The fibrous protein core formed by elongated cells that contains melanin pigment is the cortex.

I hope this helps with you

The answer is g(x) = (1/4 x)^2

It has a horizontal stretch of 4. Since it is horizontal it goes inside the parentheses and becomes the reciprocal of 4  which is  1/4

Hope this helped!

~Just a girl in love with Shawn Mendes

The answer is c. This is the ONLY possible answer.

Answer:

B. 0.12

Step-by-step explanation:

To obtain this probability, you need to multiply the two probabilities.. since it's comprised of two events: one that he's in the brass section, one that he plays trombone.  The probably of him playing trombone only happens if he's in the brass section.

So, you have the possibility he's in the brass section: 0.50

The possibility he's playing trombone, if he's in the brass section: 0.24

P = 0.5 * 0.24 = 0.12

Answer:

B: 0.12

Step-by-step explanation:

ap3x

[tex]\bf \textit{Pythagorean Identities} \\\\ sin^2(\theta)+cos^2(\theta)=1 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ sin^2(x)+sin^2(x)cot^2(x)\implies sin^2(x)+\underline{sin^2(x)}\cdot \cfrac{cos^2(x)}{\underline{sin^2(x)}} \\\\\\ sin^2(x)+cos^2(x)\implies 1[/tex]

Check the picture below.

By Green's theorem,

[tex]\displaystyle\int_C\cos y\,\mathrm dx+x^2\sin y\,\mathrm dy=\iint_D\left(\frac{\partial(x^2\sin y)}{\partial x}-\frac{\partial(\cos y)}{\partial y}\right)\,\mathrm dx\,\mathrm dy[/tex]

where [tex]D[/tex] is the region with boundary [tex]C[/tex], so we have

[tex]\displaystyle\iint_D(2x+1)\sin y\,\mathrm dx\,\mathrm dy=\int_0^5\int_0^4(2x+1)\sin y\,\mathrm dy\,\mathrm dx=\boxed{60\sin^22}[/tex]

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you ...

  Sin = Opposite/Hypotenuse

Side DF is opposite the marked angle, and the hypotenuse is EF, so ...

  sin(60°) = (√3)/2 = DF/(14√3) . . . . . to solve, multiply by the denominator

  DF = (√3)/2·(14√3) = 7·3 = 21

__

Likewise,

  Cos = Adjacent/Hypotenuse

Side DE is adjacent to the marked angle, so ...

  cos(60°) = 1/2 = DE/(14√3) . . . . . to solve, multiply by the denominator

  DE = (1/2)(14√3) = 7√3

Answer: the answer is 6

Step-by-step explanation: 3 times 2 is 6 then 6 times 1 is still 6

Answer: [tex]3!=6[/tex]

Step-by-step explanation:

The factorial function has the following symbol: "!" (As you can observe, it is an exclamation mark).

 The factorial functions are applied to the numbers greater than zero. Then, the factorial of a positive integer "n" is representend as:

[tex]n![/tex]

Since you need to simplify 3!, you has to multiply all the positive  integer numbers that are between the number 3 and and the number 1.

Therefore, for 3! you get the following result:

[tex]3!=3*2*1\\3!=6[/tex]