Find the interest earned on a $50,000 deposited for six years at 4 1/8% interest, compounded continuously.

The equation of a line that passes through the point (8, -4) and is parallel to the line 6x + 2y = 9 is 3x+y-20=0.

6x + 2y - 9 = 0

2y = -6x + 9

divide by 2 on both sides

y = -3x + 9/2

slope m = -3 and c = 9/2.

Line equation through point(8, -4) is y-y1 = m(x-x1)

y - (-4) = -3(x-8)

y+4=-3x+24

3x+y-20=0.

Therefore the equation of a line that passes through the point (8, -4) and is parallel to the line 6x + 2y = 9 is 3x+y-20=0.

Learn more about the equation and parallel here:

https://brainly.com/question/402319

#SPJ1

Solution

The given function is

With given interval

The function is differentiable on the open interval (1,2) and it is continuous on the closed interval [1,2]

Therefore mean value theorem can be used

Calculating the c value iit follows:

This gives

Differentiating the given function gives:

Equate f'(c) and f'(x)

This gives

Solve the equation for x

Therefore the values of c are

B

1) Firstly, we need to orderly write this sequence of numbers:

2) Then we need to calculate the Range of this Data Set, by subtracting from the highest values the least one:

2.2) The Midrange is the average between the Highest Value and the Least value on this Data Set:

3) Thus the answer is B

The graph of the equation can be given as

What is an equation of the line how to graph the equation?

An equation is an expression between two variables With an equality sign. Usually an equation of the line can be given as y= mx + c, Where x is independent and y is dependent and c is y-intercept. as the value of x changes the value of y also changes.

We are given an equation y-12 = 4(x-(-3))

We first simplify the equation

we get y -12 = 4(x+3)

Multiplying 4 inside the bracket we get,

y-12= 4x+12

Adding 12 on both sides to get slope intercept form.

y=4x+24

The slope of the line is 4 and y-intercept is 24.

Now we can plot the given equation.

To learn more about graphing an equation please refer the following link

https://brainly.com/question/24696306

#SPJ13

Vertex of a parabola

The point where the parabola intersects its axis of symmetry is called the "vertex" and is the point where the parabola is most sharply curved.

The given function is,

We will apply graphical method to obtain the solution to the vertex of the parabola

From the graph above, the vertex of the parabola is (- 3.5, - 13.5) which can also be represented into fraction as

And finally, the parabola opens upward.

Hence, the correct option is Option 2.

Letter B is the correct answer.

2 Al 2

3 Ni 3

6 Br 6

The other equatins are unbalanced

In the graph, there are 2 zeros, one for each type.

The zero where the graph crosses the x axis is 1. When x=1, the function intercepts the x axis and crosses it.

The zero where the graph touches but does not cross the x axis is -1. When x=-1, the function touches x axis but goes back to the quadrant.

Answer:

-6 2/9

Explanation:

Given the expression:

First, open the brackets:

Next, change the fractions to improper fractions:

Then, take the lowest common multiple of 9 and 3 to combine the fractions:

The result is -6 2/9.

The slope-intercept form is:

So first we will find the gradient:

Parallel lines have the same gradient:

So now that we know the gradient of the line as -2, we will then find the equation of the line using the formula below as it passes through (7,4):

Answer:

Given to Step 1: Lin calculated 4 - 17 incorrectly; should be -13.

Step 3 to Step 4: Lin should have subtracted 8x from each side; should be 18x.

Lin's answer should be x = 1/2

Explanation:

The initial expression is:

8(x - 3) + 7 = 2x(4 - 17)

So, the first error is in step 1, because 4 - 17 = - 13, then step 1 should be:

8(x - 3) + 7 = 2x(-13)

Then, we can apply the distributive property as:

8x - 8(3) + 7 = -26x

8x - 24 + 7 = -26x

We need to add similar terms:

8x - 17 = - 26x

Then, we can subtract 8x from both sides as follows:

8x - 17 - 8x = - 26x - 8x

-17 = -34x

Finally, we can divide by -34 as follows:

-17/(-34) = -34x/(-34)

1/2 = x

Therefore, the answers are:

Given to Step 1: Lin calculated 4 - 17 incorrectly; should be -13.

Step 3 to Step 4: Lin should have subtracted 8x from each side; should be 18x.

Lin's answer should be x = 1/2

The standard form of a quadratic function presents the function in the form

where (h, k) is the vertex.

The standard form is useful for determining how the graph is transformed from the graph of y = x^2. The figure below is the graph of this basic function.

You can represent a horizontal (left, right) shift of the graph of

by adding or subtracting a constant, h, to the variable x, before squaring. Here h = -3

The magnitude of a indicates the stretch of the graph. a = 2

Answer:

Explanation:

Here, we want to drop the appropriate symbols

When we add the given number 22 to p, it would give a number which is at most 100

That means the number must be less than or equal to 100

mathematically, we have that as:

Answer:

1, 3, 9, 27, 81

Step-by-step explanation:

using the recursive rule

[tex]t_{n}[/tex] = 3 [tex]t_{n-1}[/tex] with t₁ = 1 , then

t₂ = 3 × t₁ = 3 × 1 = 3

t₃ = 3 × t₂ = 3 × 3 = 9

t₄ = 3 × t₃ = 3 × 9 = 27

t₅ = 3 × t₄ = 3 × 27 = 81

the first 5 terms are 1, 3, 9, 27, 81

Step 1: sketch out the right angled triangle

Step 2: calculate the value BC

To calculate the value of BC we will use the trigonometric ratio

By substituting the values, we will have

Hence,

The value of BC =3.3cm

Total  number of cakes left is 1.25 i.e. 1 and quarter.

Given,

Number of cakes = 8

Number of  pieces of each cake =12

Number of slices sold = 81

Then,

Total number of slices of cake = [tex]12*8=96[/tex]

Now,

number of remaining slices =[tex]96-81=15[/tex]

To find number of remaining cake left, divide number of remaining slices to the pieces of each cake.

Number of remaining cake = [tex]\frac{15}{12} =1.25[/tex]

Thus, total number of cakes left is 1.25 i.e. 1 and quarter.

To learn more about fractions refer here

brainly.com/question/25415062

#SPJ9

Step 1

A rectangle is a quadrilateral with the parallel opposite two sides being equal and with each vertex being 90°. The sum of angles in a rectangle is 360°. It has 2 diagonals.

Step 2

Derive an answer from the statement in step 1

The consecutive sides are perpendicular is the only right option.

Hence option D

The normal price is $25, we need to find the 40% of $25.

40% = 0.4

So if we multiply $25 by 0.4

Let's have an example of a seller that sells phones.

His salary have a fixed part of $50, and it increases by $2 by each phone he sells.

We want to find out how much will be his salary if he sells 5, 10 and 15 phones.

If we use the variable x to represent the number of phones sold, his salary (variable y) will be defined by the equation:

Now, using the values of x we want to calculate, we have that:

We can plot these points to see how much his salary increases for each phone sold, and also we can have an idea of any point we want to find out:

We must describe the local and end behaviour of the function:

First, we rewrite the polynomials in numerator and denominator in terms of their roots:

Local behaviour

We see that f(x) has a zero in the denominator for x = -1 and x = 5. The function f(x) has vertical asymptotes at these values. To analyze the local behaviour, we must compute the lateral limits for x → -1 and x → 5.

Limit x → - 1 from the left

Computing the limit from the left when x → -1, is equivalent to replacing x by -1 - ε and computing the limit when ε → 0:

In the last step, we can't throw the ε in the parenthesis different to zero.

Limit x → - 1 from the right

Computing the limit from the left when x → -1, is equivalent to replacing x by -1 + ε and computing the limit when ε → 0:

In the last step, we can't throw the ε in the parenthesis different to zero.

Limit x → 5 from the left

Computing the limit from the left when x → 5, is equivalent to replacing x by 5 - ε and computing the limit when ε → 0:

In the last step, we can't throw the ε in the parenthesis different to zero.

Limit x → 5 from the right

Computing the limit from the left when x → 5, is equivalent to replacing x by 5 + ε and computing the limit when ε → 0:

In the last step, we can't throw the ε in the parenthesis different to zero.

End behaviour

To describe the end behaviour of the function, we must compute the limits of the function when x → -∞ and x → +∞.

Limit x → -∞

To compute the limit we have divided numerator and denominator by x² and distributed the limit. The result of each limit is given by the leading term, which has the highest power of x.

Limit x → +∞

To compute the limit we have divided numerator and denominator by x² and distributed the limit. The result of each limit is given by the leading term, which has the highest power of x.

Local behaviour

The function f(x) has vertical asymptotes at x = -1 and x = 5.

End behaviour

Let's start in the first information:

This can be verified, because, AC, AB, AD and AE are all congruent, because they are the radius of A and, since BC and DE are congruent, triangles ABC and ADE are also congruent.

Thus, the angles mBAC and mDAE are congruent. The measure of thesee angles are the same as the arcs BC and DE, so we verified this alternative.

In the explanation above, we also verified the second alternative:

And we verified the third alternative:

We are left with the last alternative:

This can't be verified. One way of seeing that is that we can rotate triangle ABC around the circle without changing any of the given information, however this changes mCAD.

So the only statement that cannot be verified from the given information is the last one:

Given:

it is given that common ration of a geometric sequence is r = 5 and 7th term is - 43.

Find:

we have to find the value of 9th term.

Explanation:

we know the formula for nth term of a geometric sequence is

since, 7the term is - 43,

Therefore, we have

The 9the term of the geometric sequence is

Therefore, 9th term of given geometric sequence is -1075.

Answer:

2029.2 ft

Step-by-step explanation:

If x represents the number of minutes, then all you have to do is plug in 170 ( the number of minutes ) into the equation.

y = 7.96 (170) + 676

y = 1353.2 + 676

y = 2029.2

y represents the hiker's elevation in feet, so the answer would be 2029.2 ft.

let me know if anything is confusing :-))

1/3 cup of carrot juice ---------------------------------->2/3 cup of apple juice

x cups of carrot juice ----------------------------------->1 cup of apple juice

Using cross multiplication:

solve for x:

She uses 1/2 cups of carrot juice for 1 cup of apple juice

Explanation

We are given the following function:

We are required to determine the instantaneous rate of change at x = 2π.

This is achieved thus:

Hence, the answer is:

The best variable to solve is x=3-2v, after dividing the first equation by 3.

x=4, and v=-1/2

1) Solving that system by Substitution

2) Making then

x=3-2v

2x-10v=13

3) Plugging into the 2nd equation

2(3-2v)-10v=13

6-4v -10v=13

6-14v=13

-14v=13-6

-14v=7

v=-1/2

Plugging into the first equation

x=3-2v

x=3-2(-1/2)

x=3+1

x=4

Let a be the number of bacteria after one hour.

From the table, we get a=33.

The difference between 57 and 33 is 57-33= 24.

The difference between 81 and 57 is 81-57=24

Hence we get the common difference d=24.

The given data is in the arithmetic progression.

The formula for the nth term in the arithmetic progression is

Substitute a=33 and d=24, we get

Hence the required recursive equation is

Option A is correct.

Explanation

Step 1

the graph to the right represents the cost of a taxi where X is the distance in miles and y is the cost.

if the cost is $10m it means,exist a x, that satisfies

look for the y value = 10 in the graph

Step 2

down vertically for to find the x value

Given:

a.) Area of circle = 300 m²

Let's determine its radius,

Therefore, the radius of the circle is approximately 9.77 m