Francine currently has $45,000 in her 401k account at work, and plans to contribute $8,000 each year for the next 15 years. How much will she have in the account in 15 years, if the account averages a 4% annual return?

I'm suppose to use a savings annuity formula. Any help would be appreciated!

Answer:

-3

Step-by-step explanation:

My knowledge ;D

x - 6 = - 4

Answer: x = 2

x + 3 = -7

Answer: x = -10

5x = -2

Answer: x = -0.4

0.5x = 5

Answer: x = 10

The solutions to the equations as arranged are 2, -10, -0.4 and 10 respectively

Given the following equations

x − 6 = -4

Add 6 to both sides

x - 6 + 6 = -4 + 6

x = -4 + 6

x = 2

For the equation x + 3 = -7

Subtract 3 from both sides

x + 3 -3 = -7 - 3

x = -10

For the equation 5x = -2

x = -2/5

x = -0.4

For the equation

0.5x = 5

x = 5/0.5

x =10

Hence the solutions to the equations as arranged are 2, -10, -0.4 and 10 respectively

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The simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

To simplify the expression √([2m5z6]/[xy]), we can break it down step by step:

Simplify the numerator:

√(2m5z6) = √(2) * √(m) * √(5) * √(z) * √(6)

= √2m√5z√6

Simplify the denominator:

√(xy) = √(x) * √(y)

Combine the numerator and denominator:

√([2m5z6]/[xy]) = (√2m√5z√6) / (√x√y)

Thus, the simplified form of √([2m5z6]/[xy]) is (√2m√5z√6) / (√x√y).

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Answer:c

Step-by-step explanation is va cuz when your multiply:

Answer:

\(\sqrt[6]{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\sin\left(\frac{3\pi}{4}\right)\right)\)

Step-by-step explanation:

The analysis is as attached below.

Answer:

RP 10.000

Step-by-step explanation:

What it true?

False. The value of 5(1 + 3) ^2 is 80.

If I'm wrong, I apologize.

Answer:

The answer is false

Step-by-step explanation:

\( {5}^{2} + {15}^{2} = 250\)

Answer:

- 1 1/3

Step-by-step explanation:

To solve this, simply divide 4 by -3. 4/-3 = -1 1/3, so that's your answer.

Answer:

a

Step-by-step explanation:

Hence, we know that area of rectangle is equals to the product of length and breadth.

Therefore, the area of rectangle is,

\( = 4 \times( {x}^{2} +3x + 2 ) \\ = 4({x}^{2} + 3x + 2) \\ = \green{ \boxed{4 {x}^{2} + 12x + 8}}\)

Therefore, the answer is 4x² + 12x + 8.

the answer is D: (X,Y)->(x+1,y+4).We can find the mapping formula that translates JKLM to J'K'L'M' by finding the horizontal and vertical distances between the corresponding points.

what is vertical distances  ?

Vertical distance refers to the distance between two points measured in a straight line perpendicular to the horizontal plane. In other words, it is the distance between two points in the up-down direction.

In the given question,

We can find the mapping formula that translates JKLM to J'K'L'M' by finding the horizontal and vertical distances between the corresponding points.

The vector that translates JKLM to J'K'L'M' is given by the difference between the coordinates of J and J', and the difference between the coordinates of K and K'. Let's call these differences "a" and "b", respectively. Then we can write:

a = J' - J = (-1) - 0 = -1

b = K' - K = 3 - (-1) = 4

Therefore, the mapping formula expressed by the vector that translates JKLM to J'K'L'M' is:

(X,Y) -> (X - 1, Y + 4)

So the answer is D: (X,Y)->(x+1,y+4).

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Answer:

\(16a^6x^4y^2\)

Step-by-step explanation:

To simplify this expression, use the exponent rule stating that when an exponent is put to an exponent, the exponent values are multiplied (e.g., \((x^2)^2 = x^{2 \cdot 2} = x^4\))

Using that rule, we get:

\((-4x^2ya^3)^2 = (-4)^2 \cdot x^{(2 \, \cdot \, 2)} \cdot y^2 \cdot a^{(3 \, \cdot \, 2)}\).

This can be simplified to

\(16 \cdot x^4 \cdot y^2 \cdot a^6\),

which can be written as:

\(16a^6x^4y^2\)

using the commutative property of multiplication.

Answer:

Step-by-step

5. D

6. B

7.B

I'm guessing you mean

\(S_{k+1} = S_k + a_{k+1}\)

and that \(S_k\) is the sum

\(S_k = 6 + 12 + 18 + \ldots + 6k = 6 (1 + 2 + 3 + \ldots + k) = 3 k (k+1)\)

using the well-known formula

\(\displaystyle \sum_{i=1}^n i = 1 + 2 + 3 + \cdots + n = \frac{n(n+1)}2\)

Then by substitution,

\(S_{k+1} = 6 (1 + 2 + 3 + \cdots + k + (k+1)) = 3 (k+1) (k+2)\)

and hence

\(a_{k+1} = S_{k+1} - S_k\)

\(a_{k+1} = 3 (k+1) (k+2) - 3k (k+1)\)

\(a_{k+1} = 3 (k+1) \bigg((k+2) - k\bigg)\)

\(\implies \boxed{a_{k+1} = 6 (k + 1)}\)

The selling price of the antique through an online auction website is $680.

Given that,

Kyle sold an antique through an online auction website.

The website host charges Kyle $15, plus 2.5% of the final selling price of the antique.

After selling the antique, Kyle had to pay the website host $32.

Let x be the selling price of the antique.

We get an equation,

15 + (2.5% × x) = 32

15 + 0.025x = 32

0.025x = 17

x = $680

Hence the selling price is $680.

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The completed sequence is: 3/k, 3/k, 3/k, 9/2k.To complete the sequence of numbers with a constant difference between adjacent numbers, we can calculate the common difference by subtracting the first term from the second term.

Let's denote the missing terms as A and B.

The given sequence is: 3/k, A, B, 9/2k.

The common difference can be found by subtracting 3/k from A or B. Therefore:

A - 3/k = B - A = 9/2k - B.

To simplify, we can equate the two expressions for the                     common difference:

A - 3/k = 9/2k - B.

Next, we can solve for A and B using this equation.

Adding 3/k to both sides gives:

A = 3/k + 9/2k - B.

Now, we can substitute the value of A into the equation:

3/k + 9/2k - B - 3/k = 9/2k - B.

Simplifying further, we have:

9/2k - 3/k = 9/2k - B.

Cancelling out the common terms, we find:

-3/k = -B.

Multiplying both sides by -1, we get:

3/k = B.

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The expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2

The sequence is -7, -12, -17, -22, -27...

The first term = -7

The common difference  = The second term - The first term

= -12 - (-7)

= -12+7

= -5

The nth term of the sequence = a+(n-1)d

Where a is the first term

d is the common difference

n is the n terms

Substitute the values in the equation

The nth term of the sequence = -7+(n-1)-5

= -7-5n+5

= -5n-2

Hence, the expression for the nth term of the sequence -7, -12, -17, -22, -27... is -5n-2

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Answer:

x- intercept = - 8 , y- intercept = 4

Step-by-step explanation:

to find the x- intercept let y = 0 in the equation and solve for x

x - 2(0) = - 8

x - 0 = - 8

x = - 8 ← y- intercept

to find the y- intercept let x = 0 in the equation and solve for y

0 - 2y = - 8

- 2y = - 8 ( divide both sides by - 2 )

y = 4 ← y- intercept

In this case, we'll have to carry out several steps to find the solution.

Step 01:

data:

f(x) = x² - 9x - 22

Step 02:

function:

zeros of the quadratic function:

x² - 9x - 22 = 0

(x - 11)(x + 2) = 0

(x - 11) = 0

x = 11

(x + 2) = 0

x = - 2

The answer is:

x = 11

x = - 2

__________________________________________________________
In this question, you are solving the expression by plugging in the value "-3" to all of the "m" variables in the expression.

__________________________________________________________

Solve:

Expression: m + 7m + 1

Plug "-3" into the "m" variables and solve.

-3 + 7(-3) + 1
-3 - 21 + 1

-24 + 1

-23

Your final answer should be: -23

__________________________________________________________

Answer: -23

__________________________________________________________

Answer:

m+7m+1 = -23

Step-by-step explanation:

To solve the given equation we will follow the PEDMAS rule.

PEDMAS stands for :

Substituting the value of m = 3 to evaluate the expression :

\(\begin{gathered} \qquad{\twoheadrightarrow{\sf{m + 7m + 1}}}\\\\\qquad{\twoheadrightarrow{\sf{( - 3) + (7 \times - 3) + 1}}}\\\\\qquad{\twoheadrightarrow{\sf{ - 3 - 21+ 1}}}\\\\\qquad{\twoheadrightarrow{\sf{ - 24+ 1}}}\\\\\qquad{\twoheadrightarrow{\sf{ - 23}}} \\\\\qquad{\star{\underline{\boxed{\sf{\red{ - 23}}}}}}\end{gathered}\)

Hence, the answer is -23.

\(\rule{300}{2.5}\)

Factory A sent 14 loads of rice to Store 1

Factory A sent no loads of rice to Store 2

Factory B sent 6 loads of rice to Store 1

Factory B sent 16 loads of rice to Store 2

Let

    A1 = Loads sent from Factory A to Store 1

    A2 = Loads sent from Factory A to Store 2

    B1 = Loads sent from Factory B to Store 1

    B2 = Loads sent from Factory B to Store 2

Then, the equations describing the scenario are;

    \(A1+A2=14\)

    \(B1+B2=22\)

    \(A1+B1=20\)

    \(A2+B2=16\)

    \(200A1+350A2+300B1+250B2=8600\)

The simultaneous equations can be expressed in matrix form thus:

\(\left[\begin{array}{ccccc}{A1}&{A2}&{B1}&{B2}&{}\\1&1&0&0&14\\0&0&1&1&22\\1&0&1&0&20\\0&1&0&1&16\\200&350&300&250&8600\end{array}\right]\)

Reducing the matrix:

Step 1:

\(R_3 \leftarrow R_3 - R_1\\R_5 \leftarrow R_5 - 200R_1\)

\(\left[\begin{array}{ccccc}{A1}&{A2}&{B1}&{B2}&{}\\1&1&0&0&14\\0&0&1&1&22\\0&-1&1&0&6\\0&1&0&1&16\\0&150&300&250&5800\end{array}\right]\)

Step 2:

Switch \(R_4\) and \(R_2\)

\(\left[\begin{array}{ccccc}{A1}&{A2}&{B1}&{B2}&{}\\1&1&0&0&14\\0&1&0&1&16\\0&-1&1&0&6\\0&0&1&1&22\\0&150&300&250&5800\end{array}\right]\)

Step 3:

\(R_3\leftarrow R_3+R_2\\R_5 \leftarrow R_5-150R_2\)

\(\left[\begin{array}{ccccc}{A1}&{A2}&{B1}&{B2}&{}\\1&1&0&0&14\\0&1&0&1&16\\0&0&1&1&22\\0&0&1&1&22\\0&0&300&100&3400\end{array}\right]\)

Step 4:

\(R_4\leftarrow R_4+R_3\\R_5 \leftarrow R_5-300R_3\)

\(\left[\begin{array}{ccccc}{A1}&{A2}&{B1}&{B2}&{}\\1&1&0&0&14\\0&1&0&1&16\\0&0&1&1&22\\0&0&0&0&0\\0&0&0&-200&-3200\end{array}\right]\)

Step 5:

Switch \(R_4\) and \(R_5\)

\(R_4\leftarrow R_4 \times \frac{1}{-200}\\R_1 \leftarrow R_1-R_2\)

\(\left[\begin{array}{ccccc}{A1}&{A2}&{B1}&{B2}&{}\\1&0&0&-1&-2\\0&1&0&1&16\\0&0&1&1&22\\0&0&0&1&16\\0&0&0&0&0\end{array}\right]\)

Step 6:

\(R_1 \leftarrow R_1 + R_4\\R_2\leftarrow R_2 - R_4\\R_3 \leftarrow R_3-R_4\)

\(\left[\begin{array}{ccccc}{A1}&{A2}&{B1}&{B2}&{}\\1&0&0&0&14\\0&1&0&0&0\\0&0&1&0&6\\0&0&0&1&16\\0&0&0&0&0\end{array}\right]\)

So,

\(A1=14\\A2=0\\B1=6\\B2=16\)

From the above calculations, we see that

Factory A sent 14 loads of rice to Store 1

Factory A sent no loads of rice to Store 2

Factory B sent 6 loads of rice to Store 1

Factory B sent 16 loads of rice to Store 2

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The steps which you would take to determine if these figures are similar include the following:

2. Multiply the vertices of polygon ABCD by 1/2.

5. Reflect the intermediate image.

In Mathematics and Geometry, a dilation is a type of transformation which typically transforms the dimension (size) or side lengths of a geometric object, without affecting its shape.

Therefore, the dimension or side lengths of the dilated geometric object would be stretched or compressed (shrunk) depending on the scale factor that is applied.

By critically observing the graph representing polygon ABCD, we can logically deduce that a sequence of transformations that would polygon ABCD (pre-image) onto polygon A"B"C"D" (image) is a dilation by a scale factor of 1/2 and a reflection of intermediate image.

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

Answer:

(1+2V3)^2=13+4V3

<=> 1 +4V3 +12 = 13+4V3

<=> 1 +12 = 13

<=> 13=13

sorry if i wrong :(

Answer:

Angle A = tan^-1(11/5)
Angle C = 90 - tan^-1(11/5)
AC = sqrt(146)

Step-by-step explanation:

As this is a right triangle, we can apply the Pythagorean theorem a^2 + b^2 = c^2, where c is the hypotenuse while a and b are the legs, to solve for AC.

11^2 + 5^2 = AC^2

121 + 25 = AC^2

146 = AC^2

sqrt(146) = AC^2

Next, to find angle A, we can use one of the trigonometric functions. Let’s use tangent for simplicity. Tangent of an angle is “opposite divided by adjacent”. If we set the angle to A, opposite is side BC and the adjacent is side AB. Thus, tan(A) = 11/5 and tan^-1(11/5) = A.
Since the sum of angles in a triangle is 180, we can find angle C by setting up this equation: C = 180 - 90 - tan^-1(11/5), which is 90 - tan^-1(11/5)

Answer:

Answer is 30 m

Step-by-step explanation:

First calculate the cricumfrance of the circle, then divide it by 4 and thats the edge of the shaded area and the radius is the other edjes im pretty sure