Which is equivalent to 80
√80*
√80
80*2
[80]*
4

Answer:

  a. 31 months

  b. $818.32

  c. $168.32 interest

Step-by-step explanation:

Given that Joe makes a minimum payment of $21.45 on his credit card purchase of $650 with an APR of 19.85%, you want to know ...

If the balance is reduced by $21.45 per month, it will take ...

  $650/($21.45/mo) ≈ 30.3 months

to pay off the balance.

Joe will be making payments for 31 months.

The total amount Joe pays for his sound system is the sum of its initial cost and the total of interest payments. That sum is ...

  cost + interest = total paid

  $650 +168.32 = $818.32

Joe will pay a total of $818.32.

The total amount of interest Joe pays is $168.32.

__

Additional comment

If the total payment each month is $21.45, then it will take 43 months to pay off the system, for a total cost of $909.61, of which $259.61 is the cost of the credit. (The finance charge is paid first from this payment amount, so the amount that goes to reduce the balance is less.)

The proof that  Δ SVW ≅ Δ UTW is given by ASA congruence criterion.

Two triangles are said to be congruent if all three corresponding sides are equal and all the three corresponding angles are equal in measure. These triangles can be slides, rotated, flipped and turned to be looked identical. If repositioned, they coincide with each other.

The symbol of congruence is’ ≅’.

Given:W is the midpoint of SU

⇒ SW = WUTU ⊥ SU and SU ⊥ SV

To prove:Δ SVW ≅ Δ UTW

Proof:In Δ SVW and Δ UTWSW = UW (given)

∠S ≅ ∠U (given)

∠ SVW ≅ ∠ UTW (vertically opposite angle)

Therefore, Δ SVW ≅ Δ UTW (by ASA congruence criterion)

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A widely used security technology called Transport Layer Protection, or TLS, enables privacy and data security for communications over the Internet. Encrypting communication between online applications and servers, such as when web browsers load a webpage, is one of the main applications of TLS.

When a user accesses a website through HTTPS and the browser initially starts to enquire about the website's origin server, a TLS handshake occurs

Together, the client and server will perform the following during a TLS handshake:

Indicate the TLS version (TLS 1.0, 1.2, 1.3, etc.) they'll be using.

Select the cipher suites they'll employ (see list below).

Using the server's public key and the SSL certificate authority's digital signature, confirm the server's identity.

After the handshake, generate session keys to enable symmetric encryption.

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The value will be 13.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

According to the given graph of

⇒ f(x) = 3ˣ

The point for f(x) = 12

We can see that such x is situated between 2.2 and 2.3

Thus the solution for this be;

⇒ (2.2 + 2.3)/2

⇒ 2.25

As above the solution of 3ˣ = 12

Is x = 2.25 which is about 2

Now, put x = 2.3

Therefore;

3²°³  = 12.51 ≈ 13

Thus it is about 13.

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Answer:

I was willing to pay $20 more for the toy than I actually paid.

Step-by-step explanation:

Let us take the maximum bid be y

So,

(y × 60) ÷ 100 = 30

60y/100 = 30

60y/100 × 100 = 30 × 100

60y = 3000

60y/60 = 3000/60

y = 50

60% of $50 is $30

So,

50 - 30 = 20

Thus, I was willing to pay $20 more for the toy than I actually paid.

The correct option that describes the vertical asymptote is; B: There is a vertical asymptote at x = 4 because Limit of g (x) as x approaches 4 minus = infinity and limit of g (x) as x approaches 4 plus = infinity

A vertical asymptote of a graph is defined as a vertical line x = a where the graph tends toward positive or negative infinity as the inputs approach a.

A vertical asymptote is a value of x for which the function is not defined, that is, it is a point which is outside the domain of a function;

In a graph, these vertical asymptotes are given by dashed vertical lines.

An example is a value of x for which the denominator of the function is 0, and the function approaches infinity for these values of x.

We are given the function;

g(x) = 2(x + 4)²/(x² - 16)

Simplifying the denominator gives;

(x² - 16) = (x + 4)(x - 4)

Thus, our function is;

g(x) = 2(x + 4)²/[(x + 4)(x - 4)]

(x + 4 ) will cancel out to give;

g(x) = 2(x + 4)/(x - 4)

Vertical asymptote:

Point in which the denominator is 0, so:

(x - 4) = 0

x = 4

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The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.

Given that,

Give the equation for the parabola's axis of symmetry by sketching the graph of each quadratic function using its vertex and intercepts.

We have to determine the function domain and range using the graph is f(x) = (x-1)²+2

We know that,

Its vertex A quadratic function's form is provided by

f(x) = a(x-h)²+k

So, (h,k) is the vertex of the parabola

Take

f(x) = (x-1)²+2

(1,2) is the vertex of the parabola.

Therefore, The vertex of the parabola is (1,2) when the function is f(x) = (x-1)²+2 when the equation for the parabola's axis of symmetry.

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The values on a number line that are less than -2 include -3, -4 etc

A number line is a diagram of a graduated straight line used to represent real numbers in elementary mathematics. It is assumed that each real number and each point on a number line correspond to one another.

The horizontal straight lines known as number lines are where integers are arranged in equal intervals. A number line can be used to represent every number in a sequence. This line continues forever at both ends.

It should be noted that -3, and above are less than -2.

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Answer:

13/2

Step-by-step explanation:

check the attached file

Answer:

  6.5

Step-by-step explanation:

You want the definite integral of |2x-3| from -1 to 2 using geometric area formulas.

The attached figure shows the integral to be the sum of the areas of two triangles. The left one has a base of 2.5 and a height of 5; the right one has a base of 0.5 and a height of 1. The areas can be found using the triangle area formula:

  A = 1/2bh

  A = 1/2(2.5)(5) = 6.25 . . . . . area of left triangle

  A = 1/2(0.5)(1) = 0.25 . . . . . area of right triangle

Then the integral is ...

  [tex]\displaystyle \int_{-1}^2{|2x-3|}\,dx=6.25+0.25=\boxed{6.50}[/tex]

Answer:

The answer is 2x + 6 or 2(x + 3)

Step-by-step explanation:

2/3 (9x + 6) -1/2(8x - 4)

(18x + 12)/3 - (8x + 4)/2

6x + 4 - 4x + 2

Rearrange it

6x - 4x + 4 + 2

Combine like terms

2x + 6

Take 2 as common

2(x + 3)

Thus, The answer is 2x + 6 or 2(x + 3)

(a) The critical points of the given system of equations are (0,0), (2,2), and (-2,-2).

(b) Near the critical point (0,0), the linear system is: [tex]\frac{dx}{dt} = 2y, \frac{dy}{dt} = -2x[/tex]. Near the critical point (2,2), the linear system is: [tex]\frac{dx}{dt} = -2y, \frac{dy}{dt} = 2x[/tex] Near the critical point (-2,-2), the linear system is: [tex]\frac{dx}{dt} = 2y, \frac{dy}{dt} = -2x[/tex]

(c) The eigenvalues of the linear system near (0,0) are: ±2i. The eigenvalues of the linear system near (2,2) are: ±2i. The eigenvalues of the linear system near (-2,-2) are: ±2i. These eigenvalues indicate that the nonlinear system is stable near each of the critical points.

(d) The phase portrait of the nonlinear system will be a series of circles centered at each of the critical points and will show that the system is stable near each of the critical points.

A critical point of a system of equations is a point at which the derivative of the system is equal to zero.

To find the critical points of the given system, we can set the derivative of each equation equal to zero and solve for x and y. For the first equation, this gives us:

[tex]\frac{dx}{dt}[/tex] = (2 + x)(y - x) = 0

If we set the derivative equal to zero, then either (2 + x) = 0 or (y - x) = 0. If (2 + x) = 0, then x = -2. If (y - x) = 0, then y = x.

For the second equation, setting the derivative equal to zero gives us:

dy/dt = (4 - x)(y + x) = 0

If we set the derivative equal to zero, then either (4 - x) = 0 or (y + x) = 0. If (4 - x) = 0, then x = 4. If (y + x) = 0, then y = -x.

Therefore, the critical points of the given system are (-2,0), (4,0), and (0,0).

Next, we can find the corresponding linear system near each critical point by finding the Jacobian matrix of the given system at each critical point. The Jacobian matrix is a matrix of the partial derivatives of the system with respect to x and y.

At the critical point (-2,0), the Jacobian matrix is:

[(2 + x)(y - x) (2 + x)(y - x)]

[(4 - x)(y + x) (4 - x)(y + x)]

Evaluating this matrix at the point (-2,0) gives us:

[(-2)(0 - (-2)) (-2)(0 - (-2))]

[(-2)(0 + (-2)) (-2)(0 + (-2))]

= [4 4]

[-4 -4]

At the critical point (4,0), the Jacobian matrix is:

[(2 + x)(y - x) (2 + x)(y - x)]

[(4 - x)(y + x) (4 - x)(y + x)]

Evaluating this matrix at the point (4,0) gives us:

[(4)(0 - 4) (4)(0 - 4)]

[(4 - 4)(0 + 4) (4 - 4)(0 + 4)]

= [-8 -8]

[0 0]

At the critical point (0,0), the Jacobian matrix is:

[(2 + x)(y - x) (2 + x)(y - x)]

[(4 - x)(y + x) (4 - x)(y + x)]

Evaluating this matrix at the point (0,0) gives us:

[(2)(0 - 0) (2)(0 - 0)]

[(4 - 0)(0 + 0) (4 - 0)(0 + 0)]

= [0 0]

[0 0]

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Answer:

Your answer is x = 47.

Step-by-step explanation:

First, you need to move the constant to the right-hand side and change its sign.

4x = 180 + 8

Now, you need to add the numbers.

4x = 188

Last but not least, you need to divide both sides of the equation by 4, which gets you to:

x = 47

Ф {0, [3√3/2(3√3-π)]}

The poster above has good diagrams ; so , I will just go through the calculations .

The region of integration is with in the circle x ^2+y^2=2y but outside the circle   x^2+y^2=1.

I would convert to polar . With polar , we have  x^2+y^2=r^2 ,x=rcosФ and        y=rsinФ
We thus have the first circle becomes x^2+y^2=2y ⇒r^2=2rsinФ Divide through by r,  and you get r=2sinФ(1).  
This is the upper circle in the previous posters diagrams .

The other equation of a circle becomes :
x^2 + y^2 =  1  ⇒ r^2 = 1 ⇒ r =  1   (2)      
These two curves intersect at :
r= 2sinФ =1 ⇒     sinФ=1/2  ⇒Ф= [tex]\alpha[/tex]/6 or 5[tex]\pi[/tex]/6    
From the previous poster's diagrams , we can see that there is as much mass on either side of the positive. y axis or
Ф=[tex]\pi[/tex]/2 axis in polar ; so , the X  coordinate of the center of mass is zero  
X=0 We can also see from his diagrams that the mass and moment of mass is symmetrical about the Ф=[tex]\pi[/tex]/2
we only need to integrate from Ф=[tex]\pi[/tex]/6 to Ф=[tex]\pi[/tex]/2  ( the answers from to are the same and double )
The differential of area in polar coordinates is
d A=rdrdФ  They say the area mass density is inversely proportional to the distance from the origin .

This can be written as : p=k/r. We can thus say the differential of mass is
d M=PDA=

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Answer:

$8 per person

Step-by-step explanation:

32 divided by 4 is 8

32 : 4 = 8 : 1

Answer:

x = 58, y = 61

Step-by-step explanation:

We can use two properties of a parallelogram to solve this

1. The opposite angles of a parallelogram are equal

2. The sum of the 4 interior angles of a parallelogram equal 360

Using property 1,

Using property 2
(2x - 3) + y + (y + x) + y = 360

3x + 3y + 3 = 360

3x + 3y = 360 - 3 = 357

Divide both sides by 3 to get
x + y = 357/3
x + y = 119  [2]

Add [1] and [2] together to eliminate y and get

x - y + x + y = -3 + 119

2x = 116

x = 116/2 = 58

Use equation [2]

x + y = 119
58 + y = 119

y = 119 - 58

y = 61

As per the expenses, the planning technique that is suitable for Alice is  strategic planning

The term expenses in math refers the cost that businesses incur in running their operations.

Here we have given that allice is interested in making deductible charitable contributions, but she does not want to incur the expense of drafting a private trust agreement.

And we need to find planning techniques will meet her needs

While we looking into the given question, we have identified that  she does not want to incur the expense of drafting a private trust agreement.

Based on these one, she would prefer strategic planning includes a high-level overview of the entire business and it is the foundational basis of the organization and will dictate long-term decisions.

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The average grade received on two tests and the final exam is 78.67%

What is average?

The ratio of the sum of the values in a particular set to all the values in the set is the mean value, which is the definition of the average.

The average formula has numerous practical uses. If we were asked to determine the average male height in India or the average age of the men and women in a group, we would add up all the data and divide it by the total number of data points.

Given, the grades in tests are 74% and 82%. Also, the grade on final exam is 80%.

Now, considering that we have to find the average grade in tests and final exams combined, we put the average formula.

Average grade = Sum of percentages of each exam/Total exams

Thus, average is

= (74+82+80)%/3

= 236%/3

= 78.67%

The average grade received on two tests and the final exam is 78.67%.

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Answer:lol

Step-by-step explanation:lol

Answer:

(-2, 1.5)

Step-by-step explanation:

When graphed their solution is (the point where both the line intercept/touch) (-2,1.5)

I graphed this equations online**

c is the answer. jdjsisiao

With all this information, and reading our question carefully, we can decipher the following:

9(n-3) = 3 + (9n + 3n)

9n - 27 = 3 + (9n +3n) (Step 1. Distributive Property)

9n - 27 = 3 + 12n       (Step 2. Combine like terms; 9n + 3n = 12n)

-9n                  -9n    (Step 3. Subtract 9n from both sides to isolate the variable)

______________

  -27 = 3 + 3n            

     -3      -3               (Step 4. Subtract 3 from both sides)

________________

-30 =       3n                        

 -----         ----

  3            3              (Step 5. Divide 3 from both sides)

________________

 -10 = n

Therefore, n = -10

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Using the slope, the required value of k is 48.

In mathematics, the steeper direction of a line is overall processed by the slope or gradient of the line.

A line's slope can be used to determine how steep it is.

Theoretically, the gradient is calculated as "rise over run" (change in y divided by change in x).

Given is a line that crosses through the origin:

y = mx

Let,s take x = -12 and y = -2.

y = mx

-2 = -12m

m = -2/12

m = -1/6

m is the slope.

The equation now:

y = mx

y = -1/6x

Now, insert:
x = k and y = 8

y = mx

8 = -1/6x

x = 6*8

x = 48

Therefore, using the slope, the required value of k is 48.

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The fraction in simplest form is  [tex]\frac{8}{125}[/tex].

What is a fraction?

The components of a whole or group of items are represented by fractions. A fraction consists of two components. The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection. The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.

Given, [tex](\frac{2}{5})^{3}[/tex]

= [tex]\frac{2}{5} *\frac{2}{5} *\frac{2}{5}[/tex]

= [tex]\frac{8}{125}[/tex]

Hence, the fraction in simplest form is  [tex]\frac{8}{125}[/tex].

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(x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.

What is polynomial?

In arithmetic, a polynomial is an expression consisting of indeterminates and coefficients, that involves solely the operations of addition, subtraction, multiplication, and positive-integer powers of variables.

Main body:

as the polynomial with rational coefficients that has zeros x=2 and x=3i

(x-2) and (x-3i) are factors of third-degree polynomial.

so ,

⇒(x-2)(x-3i)

solving (x-3i)

x = 3i

squaring both sides,

x² = -9

so , (x²+9) is a factor.

hence , (x-2)(x²+9) is set of factors corresponds to a third-degree polynomial with rational coefficients.

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A function that will match the given graph is; f(x) = 2(x - 5)²(x + 2)

In polynomial graphs, we know that the roots are the points where the graph crosses or touches the x-axis.

In this given graph, we see that the graph touches the x-axis at x = 5 and then crosses the x-axis at x = -2. Thus;

The roots of the equation are -2 and 5.

However, when the graph changes sign at a point on the x-axis, it means that point represents double roots. Thus, we will now have three roots which are -2, 5 and 5. The factors of the polynomial are;

(x + 2), (x - 5)²

Now, we see that when x = 0, y = 100 from the graph. Thus;

a(0 + 2)(0 - 5)² = 100

a(50) = 100

a = 100/50

a = 2

Thus, the equation would now be;

f(x) = 2(x - 5)²(x + 2)

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Answer:

307.50

Step-by-step explanation:

277.50 + .1(300)

277.50 + 30

307.50

The distance of the boat on the right to the finish line is 297.29 m and the distance of the boat on the left to the finish is 294.11 m, so the boat on the left will reach the finish line faster.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The left boat is a little closer to the finish line (100m instead of 110m). On the other hand, the right boat has an advantage, because it is moving more directly toward the finish line (22° instead of 20°).

And, The speed of each boat is 10 m/s.

Now,

Let the hypotenuse = h

So, We can formulate;

For left boat,

⇒ sin 20° = 100 / h

⇒ h = 100 /sin 20°

⇒ h = 100 / 0.34

⇒ h = 294.11 m

For right boat;

⇒ sin 22° = 110 / h

⇒ h = 110 /sin 22°

⇒ h = 110 / 0.37

⇒ h = 297.29 m

Thus, According to the above, the distance of the left boat is less, so it can be inferred that this boat will reach the finish line faster.

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