An initial amount of $3500 is invested in an account at an interest rate of 6% per year, compounded continuously. Assuming that no withdrawals aremade, find the amount in the account after two years.Do not round any intermediate computations, and round your answer to the nearest cent.

The Solution:

Given the graph below:

We are required to find the perimeter of the triangle LMN rounded to the nearest unit.

Step 1:

Find the distance LM, where L(-3,2) and M(3,5)

By the formula for distance between two points, we have

Where,

Substituting, we get

Step 2:

Find the distance LN:

Step 3:

Find the distance MN, where M(3,5) and N(9,2)

Step 4:

The perimeter is:

Therefore, the correct answer is 28 units.

Transformation of a Function

We are given the function:

And it's required to find another function g(x) according to the transformation:

g(x) = -f(x) - 2

First, we calculate the negative of f(x):

And now we subtract 2 to find g(x):

The equation above is in the slope-intercept form where the slope is m=-2/3 and the y-intercept = -10

Answer:

The result of the function f(p) = [tex]p^2[/tex] + 3p + 1  for p = -2 is -1

The function is

f(p) = [tex]p^2[/tex] + 3p + 1  

The function is the expression that represents the relationship between the one variable and another variable. If one variable is dependent variable then the another variable will be independent variable.

The values of p = -2

Substitute the value of p in the function and find the solution

f(p) = [tex]p^2[/tex] + 3p + 1  

f(-2) = [tex](-2)^2[/tex] + 3×-2 + 1

f(-2) = 4 - 6 + 1

f(-2) = -1

Hence, the result of the function f(p) = [tex]p^2[/tex] + 3p + 1  for p = -2 is -1

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• Chord: ,a line segment connecting ,any two points, in a curve (circle).

• Diameter: ,a chord passing ,through the center ,of the figure.

• Radius: ,a line segment going ,from the center, to any point in the circumference.

The difference between them is that the chord is any two points touching the circumference, the diameter has to go through the center to any two points, and the radius goes from the center to just one point in the circumference.

Then, the line segment that meets the requirements of being the diameter in circle F is segment CD as it passes through the center.

The radius could be CF, DF, and EF. While a chord could be AB.

Answer: CD

We are told that a 7% tax is applied to the original sales price, in order to determine the tax amount we just have to multiply the original price ($46.85) by the tax percentage (0.07 as 7% in decimal form), then we get:

Tax amount = 0.07×46.85 ≈ 3.28

By adding the tax amount to the original price we should get the final price, like this:

Total purchase price = 46.85 + 3.28 = 50.13

Then, the total purchase price after tax is $50.13

Given:

Amount of chocolate chips needed = 1 1/2 times as much floor.

Amount of floor used = 3 1/2 cups.

Let's find the quantity of chocolate chips that would be needed according to the recipe.

To find the amount of chocolate chips used, we have:

Amount of chocolate chips

SOLUTION

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the growing rate of the first tree

Tree 1 is growing 1.5 inches every week

STEP 2: Calculate the growing rate of the second tree

This implies the slope and is calculated using the formula;

By substitution,

The slope of 1 means that Tree 2 is growing at a rate of 1 inch per week

Hence, the tree that is growing faster is Tree 1 with a rate of 1.5 inches per week

ANSWER:

Tree 1

-1 3/4, 14/8, 1.125 and -0.875 correspond to points 1, 8, 6 and 4 respectively on the number line.

Looking at the number line, there are 8 divisions between two points e.g 0 to 1.  

To know the value of  1 division, we divide the value of the distance between two points by the number of divisions:

= 1/8 = 0.125

To find the locations, we just divide the value of the locations with the value of 1 division:

-1 3/4 / 0.125 = -14  (Count 14 divisions to the left of 0) = point 1

14/8  / 0.125 = 14  (Count 14 divisions to the right of 0) = point 8

1.125/ 0.125 = 9 (Count 9 divisions to the right of 0) = point 6

-0.875 / 0.125 = -7  (Count 7 divisions to the left of 0) = point 4

Therefore, the positions of -1 3/4, 14/8, 1.125 and -0.875 on the number line are points 1, 8, 6 and 4 respectively.

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Compound interest formula:

where:

A is the final amount, here = $250,000

P is the principal amount

i is the interest rate per year (in decimal form), here = 0.085

n is the number of years invested, here = 14

Replacing into the equation and solving for P, we get:

P = $79,785.5

Answer:

Explanation:

Answer:

<A=32°

Explanation:

<BEC = 90° because it has the red half square and we know that <DCE = 42°. <ACB= 2x because <ACD and <DCB both =x. The equation we would set up is

90+(42+x) +2x=180

We get x=16.

Since <ACB = 2x we multiple 16 by 2

16*2=32

So <ACB =32°

We have round of to 100th place means up to 3 places

Now we will reduce the digit from right side upto 3 places

As last digit is 3 which is less than 5 so it will remove directly

Now the last digit is 6 which is greater than 5. So and is even so change we will simply remove this

Answer:

The correct answer is:

The ordered pair (2, 3) is not a solution to the system.

Explanation:

The system given is:

If (2, 3) is a solution of the system, then replacing x = 2 and y = 3 on both equations should give a correct result and the same on both equatiions.

In the first equation;

We can see that this result is not true, as 27 is not equal to 1.

In the second equation:

Once again, a false result.

To see in the system has equations, let's solve for x in the second equation:

Now, we can use substitution in the first equation:

And solve for y:

Now, we can find the value of x:

The solution to the system is (-2, 1)

Thus, the correct option is "The ordered pair (2, 3) is not a solution to the system"

Answer:

400 miles each day

Step-by-step explanation:

You have 1600 miles divided into four days.

1600 / 4

We can use the basic fact that multiplying a number by ten simply means shifting everything to the left, for example 2 x 10 = 20, we just shifted 2 to the left and inserted a 0.

So for this problem, we can do the same. Divide 1600 by 100, or 10 x 10, then divide by 4.

1600/16 = 100

16/4 = 4.

Now, since we divided by ten twice before, we can get the right answer by multiplying by ten twice.

4 x 10 = 40

40 x 10 = 400

The value of S in the expression 5/8-3/8 S = two minus S is 2 1/5.

An expression is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, this is illustrated thus:

5/8 - 3/8S = 2 -S

Collect like terms

-3/8S + S = 2 - 5/8

5/8S = 1 3/8

Divide

S= 1 3/8 ÷ 5/8

S = 11/8 × 8/5

S = 11/5

S = 2 1/5

This illustrates the concept of expression.

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Answer:

Down Here

Step-by-step explanation:

Hello!

Area is measured in units². Here, the units are feet, so the area would be written as feet² (ft²).

Simplifying the expression:

You can't simplify this because the units are not the same, and this can't measure area because all units of the area have to be squared. The term 6ft has non-squared units.

20/6 = p/12

cross-multiply

p x 6 = 20 x 12

6p = 240

divide both-side of the equation by 6

p = 240/6

p = 40

From the given figures in the 2 triangles XYZ and ABC

mXZ = AC

m

Since we have two equal angles and the sides between them are equal, then

The 2 triangles are congruent using ASA postulate

The answer is C

The solution to the inequalities will be,

( 5 ) y ≥ 2

( 6 ) x < 3

( 7 ) No solution.

When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relationship between variables and the numbers.

The given inequalities will be calculated as:-

-4 ≤ 4( 6y - 12 ) - 2y

-4 ≤ 24y - 48 - 2y

-4 ≤ 22 y - 48

22y ≥ 44

y ≥ 2

4x + 3 < 3x + 6

4x - 3x < 6 - 3

x < 3

-5r + 6 ≤ -5( r + 2 )

-5r + 6 ≤ -5r - 10

No solution

Therefore, the inequalities are solved above.

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The rigid transformations of the vertex of the curve are listed below:

(i) (2, 2).

(ii) (2, 3).

In this problem we find the value of a point of a curve f(x), this point (the vertex) must be transformed by using rigid transformations. There are two cases: (i) Vertical translation, (ii) Reflection about the x-axis. The formulas for each case are described below:

Vertical translation

P'(x, y) = P(x, y) + (0, k)

Reflection about the x-axis

P'(x, y) = P(x, y) + (0, - 2 · p)

Where p is the y-coordinate of point P.

If we know that P(x, y) = (2, - 3), then the coordinates for each case are, respectively:

Vertical translation

P'(x, y) = (2, - 3) + (0, 5)

P'(x, y) = (2, 2)

Reflection about the x-axis

P'(x, y) = (2, - 3) + (0, 6)

P'(x, y) = (2, 3)

The transformations of the vertex of the curve are (i) (2, 2) and (ii) (2, 3).

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SOLUTION

The given statement is

"Some politicians are not crooked"

The equivalent statement is

Not all politicians are crooked

And

All politicians are not crooked.

The equivalent statement is

Not all politicians are crooked

And

All politicians are not crooked.

Answer:  Not all politicians are crooked

It is equivalent to saying that  "Some politicians are not crooked". Both are implying that not every politician is crooked and some of them are good.

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I'm drawing now

_______________________

Option C

Answer:

The First one (1.7,3.1)

Step-by-step explanation:

3x-2=-0.5x+4

3.5x=6

x=12/7

x≈1.7

sub x back into to find y

y≈3.1

The answer in polar form:

From the image, we are asked the number of sides a polygon can have to form a regular tesselation.

The first step is to understand what a regular tessellation is;

A regular tessellation is a highly symmetric, edge-to-edge tiling made up of regular polygons, all of the same shape. There are only three regular tessellations: those made up of equilateral triangles, squares, or regular hexagons.

This implies that it could either have 3 sides(triangle), four sides(square), six sides(hexagon).

From the given options we can clearly see that 3 sides is the only available option.

ANSWER: Option B

Answer:

Th

Explanation:

Given the ordered pair (-4, -1), we have that x = -4 and y = -1. Plotting this point, we'll have;

Quadrants are labeled in an anti-clockwise direction with the top right portion of the graph being the 1st quadrant. Looking at the plotted point, we can see that the point is in the 3rd quadrant.

19 in

1 yd

2ft

32 in

First, we have to convert all the length into a unique unit:

For example, inches:

Since

1 ft = 12 inches

2 ft = 2 x12 = 22 inches

1yd = 36 inches

Now, we have to order from least to greatest:

19 in-22in -32in-36in

In the original units:

19 in , 2ft, 32in ,1yd

Okay, here we have a Combination Problem, we need just multiply to get the answer, of this mode:

She can wear 315 outfits.

Answer:

B

Step-by-step explanation:

| x - 4 | + 6 = 13

x - 4 + 6 = 13

x = 11

Or

4 - x + 6 = 13

x = -3

The reflection of a point P over a line as in the P' if the line m is the "perpendicular bisector" of line PP'. Point P' is called the "image" of point P.

For the given question.

Line m is the line along which reflection of point P is taken.

Then, line m is called the "perpendicular bisector" of line PP'.

P is the object and P' will be the image of the point P.

Thus, the complete definition of the reflection is given as-

The reflection of a point P over a line as in the P' if the line m is the "perpendicular bisector" of line PP'. Point P' is called the "image" of point P.

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We were given the equation:

We will proceed to graph this equation as shown below:

We will proceed to plot these ordered pairs on a graph, we have: