At age 19​, someone sets up an IRA​ (individual retirement​ account) with an APR of7 ​%. At the end of each month he deposits ​$20.00 in the account. How much will the IRA contain when he retires at age​ 65? Compare that amount to the total deposits made over the time period.

The chain rule tells us how to find derivative of a composite function., The following set of equations: R = ln(u² + v² + w²) with u = x + 2y, v = 2x-y, w = 2xy​ ƏR/Əx= 9/7 and ƏR/Əy = 9/7.

The Chain Rule is a mathematical method to differentiate a composition of the functions. From this composition of the functions, we can discern the functions' derivatives and their relationships.

In other words, the derivative of composite function = derivative of the outside function × derivative of the inside function.

The Chain Rule gives:

ƏR/Əx= ƏR/Əu × Əu/Əx + ƏR/Əv × Əv/Əx + ƏR/Əw × Əw/Əx

= [tex]\frac{2u}{u^{2}+v^{2}+w^{2} } *1 + \frac{2v}{u^{2}+v^{2}+w^{2} } *2+ \frac{2w}{u^{2}+ v^{2}+w^{2} } *2y[/tex]

When from given information we have, x = y = 1, we have u = 3, v = 1, and w = 2, so

ƏR/Əx = 6/14 × 1+ 2/14 ×2+ 4/14×2 = 18/17 = 9/7

ƏR/Əy= ƏR/Əu × Əu/Əy + ƏR/Əv × Əv/Əy + ƏR/Əw × Əw/Əy

= [tex]\frac{2u}{u^{2}+v^{2}+w^{2} } *2 + \frac{2v}{u^{2}+v^{2}+w^{2} } *(-1)+ \frac{2w}{u^{2}+ v^{2}+w^{2} } *2x[/tex]

When from given information we have, x = y = 1, we have u = 3, v = 1, and w = 2, so

ƏR/Əy = 6/14 × 2 + 2/14 × (-1) + 1/14 × 2= 18/14 = 9/7

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Quadratic function is  3(x+3)(x-2) given the roots ( -3, 0 ) and ( 2, 0 ) and the point ( 1, -12 ).

In algebra, a polynomial function with one or more variables in which the highest-degree term is of the second degree is known as a quadratic function, a quadratic polynomial, a polynomial of degree 2, or simply a quadratic.

Standard form, vertex form, and intercept form are three alternative ways a quadratic function can be expressed. The basic forms of each of them are as follows:

f(x) = ax² + bx + c in standard form, where a 0.

Vertex form: (h, k) is the vertex of the parabola representing the quadratic function, and f(x) = a(x - h)² + k is the equation.

The quadratic function's x-intercepts are (p, 0) and (q, 0), and its intercept form is f(x) = a(x - p)(x - q), where a 0.

Given Data

Roots (-3,0) and (2,0)

Point (1,-12)

y = a(x-(-3) (x-2)

y = a(x+3)(x-2)

Equating points

-12 = a(1+3)(1-2)

-12 = a(4)(-1)

-12 = -4a

a = 3

f(x) = 3(x+3)(x-2)

Function is  3(x+3)(x-2).

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The dimensions of the given right triangle would be 5.66 inches and 11.31 inches.

A right triangle is defined as a triangle in which one angle is a right angle or two sides are perpendicular.

Let the legs of the triangle be x and y

Using the Pythagorean theorem:

c² = a²+b²

So the hypotenuse will be:

x² + y² = 8²

x² + y² = 64

x² = 64 - y²

So the area of the triangle is:

A = 1/2bh

A = 1/2xy

⇒16 = 1/2xy

32 = xy

x = 32/y

x² = 1024/y²

Substitute the above value in x² = 64 - y² and solving for y we get:

1024/y² = 64 - y²

1024 = 64y²- y⁴

This can be written as:

y⁴ - 64y² + 1024 = 0

Thus y = 4√2 = 5.66

x = 64/(4√2)= 16/√2 = 8√2 = 11.31

Therefore, the dimensions of the given right triangle would be 5.66 inches and 11.31 inches.

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A) The probability that the Aerospace Company wins both contracts is 29.04%.

B) The probability that the Aerospace Company loses both contracts is 70.96%.

C) The probability that the Aerospace Company wins only one contract is 23.76%.

Probability describes the chance or likelihood of an expected event occurring out of many outcomes.

Probability is a ratio of an outcome versus many possible events.

Probability is represented as a percentage, fraction, or decimal, like a ratio.

The probability of winning the first contract = 44%

The probability of losing the first contract = 56% (1 - 44%)

The probability of winning the first and the second contract = 66%

The probability of losing the first and the second contract = 34% (1 - 66%)

The probability of losing the first contract and winning the second = 54%

A) The probability that they win both contracts = the probability of winning the first contract multiplied by the probability of winning the second contract.

= 29.04% (44% x 66%)

B) The probability that they lose both contracts = 1 minus the probability of winning both contracts.

= 70.96% (1 - 29.04%)

C) The probability that they win only one contract = the probability of winning the first contract multiplied by the probability of winning only the second contract.

= 23.76% (44% x 54%)

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we have the equations

equate both equations

First iteration

For x=1

For x=2

For x=1.5

the answer must be less than 1.5 and greater than 1

so

Verify each option

A ----> 13/8=1.625 -----> is not a solution

B ----> 23/16=1.4375 ---> could be an approximate solution

C ---> 25/16=1.5625 ----> is not a solution

D ---> 7/4=1.75 ----> is not a solution

therefore

The maximum height reached by the ball in discuss as described is; 96 while the time spent by the ball in the air is; 0 seconds.

It follows from the task content that the maximum height of the ball in the air is to be determined and so.is the time spent by the ball in the air.

Therefore, since the correct form of the function given is;

h(t) = -16t² + 96

By expressing the function above in vertex form; it follows that we have;

h(t) = -16 (t - 0)² + 96.

This vertex form function above therefore translates to the fact that the point, (0, 96) represents the vertex of the balls motion curve.

Ultimately, the maximum height reached by the ball is; 96 and the time it takes to reach this height is; 0 seconds.

PS; The scenario above in real life situation would translate to dropping a ball from the top.

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Answer:

Explanation:

iven the function:

Answer: y = 2x² + 2x - 60

Step-by-step explanation:

        We will write this in factored form since we are given the roots and leading coefficient. This will be written in the form y = c(x - a)(x - b) where c is the coefficient and a & b are the roots.

        y = c(x - a)(x - b)

        y = 2(x + 6)(x - 5)

        Now, we will distribute so we end up with the standard quadratic equation form.

        y = 2(x + 6)(x - 5)

        y = 2x² + 2x - 60

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ANSWER

EXPLANATION

addox has $100.

He plans to spend $20 each time he goes to the movies.

To find out how many times he can go to the movies,

Answer:

(-7,6)

Step-by-step explanation:

Midpoints

x = (x1 + x2)/2

y = (y1 + y2)/2

-6 = (-5 + x2)/2

x2 - 5 = -12

x2 = -7

2 = (-2 + y2)/2

y2 - 2 = 4

y2 = 6

If each of the 4 sloping side ahs length 10 cm

This implies they have length 40 cm altogether

To find the base length, simply subract the 40 cm from the total length of 68cm

68 - 40 = 28

each base length = 28/4 = 7cm

Area of the square base is = l x l = 7 x 7 = 49 cm²

The positive integer represents an addition to the income while.a negative integer represents a subtraction.

Positive integers are used to represent income since they indicate an increase rather than a decrease in the financial value of the company. In other words, cash is coming in rather than leaving. A positive number 10 is used as an example to illustrate an increase in operating revenue when there is profit on items sold, say $10.

When you express an expense with a negative number, you're actually subtracting money value rather than adding it. In other words, money is leaving the company rather than being brought in. For instance, when a transportation expense is incurred to deliver items to the customer, it is recorded as an expense deducted from, let's say, the business' revenue sales. Since they are already identified and recognized as expenses and deducted nonetheless, they are typically shown in brackets in accounting to signify negative worth.

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Answer:

1 and 403    13 and 31   13 and 31

Step-by-step explanation:

Solution

From the given graph

The zeros of the given graph are

Converting the zeros to roots gives

The factorized form of the equation of the given graph is

Hence, the answer is option B

The element would remain 515 grams after 17 years.

Isotopes are two or more different atom types that share the same atomic number and place in the periodic table but have different quantities of neutrons in their nuclei, resulting in various nucleon numbers.

Given Data

the initial mass of a sample of Element X is 610 grams

Element X is a radioactive isotope such that every 70 years, its mass decreases by half.

Since the half-life, or the number of years after which an isotope decays to half its original level, is stated to be 70 years.

k = [tex]\frac{2}{70}[/tex]

k= 0.0099

Equation-

N = 610e⁻⁰°⁰⁰⁹⁹ˣ

x = time

time = 17

N = 610 e⁻⁰°⁰⁰⁹⁹⁽¹⁷⁾

N = 610(0.845)

N = 515.49

The element would remain 515 grams after 17 years.

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Answer:

see explanation

Step-by-step explanation:

(a)

the angles shown are alternate interior angles and are congruent

(c)

since they are congruent , then

- 1 + 8x = 7x + 11 ( subtract 7x from both sides )

- 1 + x = 11 ( add 1 to both sides )

x = 12

(d)

then

7x + 11 = 7(12) + 11 = 84 + 11 = 95

- 1 + 8x = - 1 + 8(12) = - 1 + 96 = 95

Solution

For this case we know that the distance covered by the plane is 1350 mi and the velocity 400 mph

We also know that the distance is given by:

D= vt

Let D= Distance travelled by the car and airplane

Vp= Vc+ 400 (Velocity of the plane)

1350 = (Vc +400)*t

150 = Vc * t

We can solve for t and we got:

t= 150/Vc

Replacing in the first equation we got:

1350= (Vc+400)* (150/Vc)

Solving for Vc we got:

1350= 150 + 60000/Vc

1200 = 60000/Vc

Vc= 60000/1200= 50 mph

Then the velocity of the car is Vc= 50mph and for the plane

Vp= 50+ 400= 450 mph

Using a linear function, the constraints for the values of x and of y, respectively, are given as follows:

A linear function, in slope-intercept format, is modeled according to the following rule:

y = mx + b

In which:

In the context of this problem, we have that:

Thus the linear function that models the depth of the submarine after x seconds is given by:

f(x) = -50 - 10.5x.

This rate is for 5 seconds, hence the constraint for x is 0 ≤ x ≤ 5, and the minimum depth attained by the submarine is:

f(5) = -50 - 10.5(5) = -102.5 ft.

Hence the constraint for y is given as follows:

-102.5 ≤ y ≤ -50.

The complete problem is given by the image at the end of the answer.

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[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$3000\\ r=rate\to 6\%\to \frac{6}{100}\dotfill &0.06\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &20 \end{cases} \\\\\\ A=3000\left(1+\frac{0.06}{12}\right)^{12\cdot 20} \implies A=3000(1.005)^{240}\implies A \approx 9930.61[/tex]

ANSWER:

STEP-BY-STEP EXPLANATION:

We have that the given expression is the following:

The other expression is the following:

We simplify in each case:

This means that the expressions are equal

Answer: sqrt{3} over 2, this also equivalent to 0.866025

Answer:

  y = 1/2cos(x/2 -5π/4) -1

Step-by-step explanation:

You want the equation of the shifted and scaled cosine function shown in the graph.

A point on a function f(x) will be translated (right, up) = (h, k) by the transformation ...

  g(x) = f(x -h) +k

A function will be vertically expanded by a factor of p and horizontally expanded by a factor of q by the transformation ...

  g(x) = p·f(x/q)

The graph shows a cosine function with a peak-to-peak amplitude of 1, which is 1/2 the parent function's amplitude, so p=1/2.

The period is (9π/2 -π/2) = 4π, which is twice the period of the parent cosine function, so q=2.

The first peak of the graphed waveform is at x=5π/2, and the midline of the graphed waveform is y=-1, so we have (h, k) = (5π/2, -1).

Putting these transformations together, we find the equation of the graph to be ...

  y = 1/2cos((x - 5π/2)/2) -1 . . . . . . scaling applied before translation

  y = 1/2cos(x/2 -5π/4) -1

The solution for the inequality 3(x + 2) > x is given by:

B. {x | x > -3}.

An inequality is solved similarly to an equality, in which we isolate the desired variable.

The biggest difference is the fact that the solution for the inequality won't be a single value like the solution for the equality, it will be a range containing infinity real values.

For this problem, the inequality is given as follows:

3(x + 2) > x.

Applying the distributive property, we have that:

3x + 6 > x.

Now we move x to the left side and 6 to the right side, both with inverse signals, hence:

3x - x > -6.

2x > -6

x > -6/2

x > -3.

Hence the correct option for the inequality in this problem is given by option B.

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The product of (b-na)(4b+9na) is 4b² + 5abn - 9a²n².

Algebraic expressions can be multiplied using the following procedures. You can start by calculating the algebraic sum of the like and unlike terms, multiplying the term coefficients, and adding the variable powers with the same base.

Given:

To find the product of (b-na)(4b+9na).

To determine the product, multiply each term of the first expression by each term of the second expression.

(b-na)(4b+9na)

= 4b² + 9abn - 4abn - 9a²n²

= 4b² + 5abn - 9a²n²

Therefore the product of (b-na)(4b+9na) is 4b² + 5abn - 9a²n².

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A graph which represents the number of outfits and shoes that Alejandra can pack while staying under the weight limit is shown in the image attached below.

A graph can be defined as a type of chart that's commonly used to graphically represent data on both the horizontal and vertical lines of a cartesian coordinate, which are the x-axis and y-axis.

In this scenario, the x-axis represents the number of outfits while the y-axis represents the number of shoes. Additionally, since one pair of shoes weighs three (3) pounds and one outfit weighs two (2) pounds, the x and y coordinates would be given by this inequality:

2x + 3y < 30

Making y the subject of formula, we have:

3y < -2x + 30

Dividing all through by 3, we have:

3y/3 < -2x/3 + 30/3

y < -2x/3 + 10

Note: For 30 pounds, there would be 10 shoes (0, 10) while for 30 pounds, there would be 15 outfits (15, 0).

In conclusion, the boundary line is dashed or dotted to indicate that the boundary is not part of the solution because the inequality symbol is less than (<).

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1. Remember

Means

Therefore,

2. Remember that we have to solve what's inside the parenthesis first. Therefore,

The length of JK is 42.

JL is a line and K is the mid-point of that line.

   J____________.___________L

                              K

From this we get:

JK = KL

JL = JK + KL

JL= 2JK = 2KL

Here it is given that,

JK = 6x and JL = 13x - 7

JL = 2JK

13x - 7 = 2× 6x

13x - 7 = 12x

x = 7

We have to find the length of JK

JK = 6x

    =6× 7

    = 42

Therefore the length of JK is 42.

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Answer:

they all are correct asu know first expression is multiple by other one so u can check

The length of the shadow of fence will be equal to 6 feet.

Proportionality may be defined as the term which can be used to describe or denote a relationship between two entities which are always in the same ratio. For example, the number of bananas is proportional to the number of trees with the proportionality being average number of bananas per number of trees. Here, we are given the height of house = 16 feet and length of its shadow = 24 feet and also the height of fence = 4 feet. Since, both house and fence lie in the same area they both are proportional. Let the length of shadow be x. Since, they are proportional

16/24 = 4/x

2/3 = 4/x

=> x = 12/2

=> x = 6 feet.

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He should have divided both sides by -10.