Determine the period of the function g(x) = (cos ;)

The give quadratic function is dilated by the given coefficient, and shifted

horizontally to the left.

(a) The transformation of the common function f(x) are;

Please find attached the required graph created with MS Excel

(b) Where t = 0, represent the year 2,000 we have;

(c) The mortgage debt in the year 2014 is M ≈ $5.622 trillion

Reasons:

The given function is f(t) = 0.0037·(t + 14.979)²

Year 1990 is t = 0

(a) The given common function is; f(x) = x²

The transformation of the quadratic function are;

The coefficient 0.0037 widens the common function such that f(t) is wider

than f(x).

The constant, 14.979 added to the variable, t, shifts the graph of the

common function horizontally to the left.

Therefore;

Please find attached the required graph over the interval 0 ≤ t ≤ 19 created with MS Excel.

(b) The amount of mortgage debt in 2,000 is given as follows;

With t' = 0 represent the year 2,000, we have;

At year 1990, t' = -10

Which gives, t' = t + 10

From which we have;

f(t) = 0.0037·(t + 14.979)² = 0.0037·(t' + 10 + 14.979)²  = 0.0037·(t' + 24.979)²

Therefore;

The function with t = 0 representing the year 2,000 is presented as follows;

f(t) = 0.0037·(t + 24.979)²

(c) In the year 2014, we have;

t = 2014 - 2000 = 14

Which gives;

f(14) = 0.0037·(14 + 24.979)² ≈ 5.622

The mortgage debt in the year 2014 is M ≈ $5.622 trillion dollars

Learn more about transformation of quadratic functions here:

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Answer:

i think the answer would be 20

Answer:

y = x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Here m = 1 , then

y = x + c ← is the partial equation

To find c substitute (- 2, - 3 ) into the partial equation

- 3 = - 2 + c ⇒ c = - 3 + 2 = - 1

y = x - 1 ← equation of line

Answer:

She sells them six years later for$23.25 per share, and pays a $30 flat fee. ... 1 of 4. Purchase price of 400 shares = 400*23 =9200. total purchase costStep-by-step explanation:

Answer:

$4.35

Step-by-step explanation:

The expected value of a random variable X, often denoted as E(X), indicates the probability-weighted average of all possible values/events. The general formula of expected value is

[tex]\mathrm{E(\textit X \mathrm)} = \displaystyle\sum_{\mathclap{i=1}}^{k} \ X \times P(X) \\ \\ \\ = X_{1} \times P(X_{1}) \ + \ X_{2} \times P(X_{2}) \ + \ X_{3} \times P(X_{3}) + \ \cdots \ + X_{k} \times P(X_{k})[/tex].

Therefore, the expected value of the winnings from a game is

[tex]\mathrm{E(\textit X \mathrm)} \ = \ 1 \times 0.35 \ + \ 2 \times 0.2 \ + \ 5 \times 0.1 + \ 8 \times 0.2 \ + 10 \times 0.15 \\ \\ = \ 4.35 \ \ (\mathrm{nearest \ hundredth})[/tex].

Answer:

<N=<T

<P=<Q

<O=<R

<M=<S

Step-by-step explanation:

they are in order since (N) is the first letter in one triangle then (T) has to be the corresponding angle.

Answer:

62/100 but simplified is 32/50

Answer:

X= - ¾ X= - 0.75

Step-by-step explanation:

thats all i can do hope it help :D

Answer: 3y = 9x -12

Step-by-step explanation:

Answer:

Option D : $153

This is how I got that:

9:30 AM to 1:15 PM = 3 hours and 45 minutes

The first hour charges $15 and for the remaining 2 hours and 45 minutes

Mr. Anand is charged 36$. Remember it says that each additional hour or part thereof, so the 2 hours and 45 minutes is considered 3 hours.

So our total for one paddle boat is $51

But Mr. Anand hired three boats so we simply times 51 by 3 and get our solution to the problem:

Mr. Anand must pay $153 or Option D

~That's All Folks~

-Siascon

Answer:

D. The wait time will be about 2 mins.

Step-by-step explanation:

You have to substitute the x into the equation as we know it is 10.

So, y = (-1.62 × 10) + 18.

Thus, y = -16.2 + 18.

Then, y would equal 1.8.

Therefore you would round to the nearest minute which would be 2.

Hope this helps :)

Answer:

x = 80 degrees

Step-by-step explanation:

Draw a line through DG and name the intersection of that line and line AB as K.

By the same side interior angle theorem, GKC is 40 degrees.

By the sum of interior angles of triangle theorem, CGK is 180-70=110 degrees.

By supplementary angle theorem, x = 80 degrees.

Δ PQR has: PM is a median

so: MR = QM = 3 cm

ANSWER: MR = 3 cm

Ok done. Thank to me :>

Answer:

11/14

Step-by-step explanation:

Have a nice day !!!

Answer:

its B, its 11/14

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

66

Answer:

108 ft²

Step-by-step explanation:

For the polygon on the left, we are given the length of one side (3 ft) and the total area (27 ft²). With this information, we can determine the length of the other side - 9 ft. I found this by dividing 27 ft² by 3 ft, giving me the final result of 9 ft.

Next, we have to find the other side of the polygon on the right so we can ultimately determine its area. It looks like there is a scale factor of 2 between the two polygons, since 3 × 2 = 6. We know that the bottom side of the left polygon is 9, so multiplying 9 by 2 should give us the bottom side of the polygon on the right. 9 × 2 = 18.

Now, we have the side lengths for the polygon on the right and can determine its area. What is 6 ft × 18 ft? Well, the answer is 107 ft², and this is the answer to the question.

Hopefully that's helpful! :)

Answer:

x=-19

Step-by-step explanation:

3x-9=2(x-14)

3x-9=2x-28

x-9=-28

x=-19

Standard form = ax+by+c=0

= Writing the given eq. in standard form =

= y+7=-3x-3

= 3x+y+7+3=0

= 3x+y+10=0

Mathematical processes are the steps used to determine the result of operations

The dimension of the rectangle is given as:

[tex]Length = 5x^2 - 8x + 9[/tex]

[tex]Width = x + 5[/tex]

(1) The perimeter of the triangle

This is the sum of the side lengths of the rectangle.

So, we have:

[tex]Perimeter = 2 \times (Length + Width)[/tex]

This gives

[tex]Perimeter = 2 \times (5x^2 - 8x + 9 + x + 5)[/tex]

Collect like terms

[tex]Perimeter = 2 \times (5x^2 - 7x + 14)[/tex]

Open brackets

[tex]Perimeter = 10x^2 - 14x + 28[/tex]

Hence, the perimeter of the rectangle is [tex]10x^2 - 14x + 28[/tex]

(2) The area of the triangle

This is the product of the dimensions of the rectangle.

So, we have:

[tex]Area = Length \times Width[/tex]

This gives

[tex]Area = (5x^2 - 8x + 9) \times (x + 5)[/tex]

Open brackets

[tex]Area = 5x^3 - 8x^2 + 9x +25x^2 - 40x + 45[/tex]

Collect like terms

[tex]Area = 5x^3 - 8x^2 +25x^2+ 9x - 40x + 45[/tex]

[tex]Area = 5x^3 +17x^2 -31x + 45[/tex]

Hence, the area of the rectangle is [tex]5x^3 +17x^2 -31x + 45[/tex]

Read more about areas and perimeters at:

https://brainly.com/question/15656646

The sum of the interior angles of a quadrilateral is 360°.

The ratio of 2 angles is 2 : 13. Take them as 2x° & 13x°.

Now, solve for x.

[tex]\mathfrak{215+70+2x+13x=360} [/tex]

[tex]\mathfrak{285+15x=360} [/tex]

[tex]\mathfrak{15x=360-285} [/tex]

[tex]\mathfrak{15x=75} [/tex]

[tex]\mathfrak{x=\dfrac{75}{15}} [/tex]

[tex]\underline{\mathfrak{x=5}} [/tex]

So,

2x = 2(5) = [tex]\boxed{\mathfrak{10^{\circ}}} [/tex]

13x = 13(5) = [tex]\boxed{\mathfrak{65^{\circ}}} [/tex]

[tex]\mathbb{MIREU} [/tex]

Answer:

Idea one, if you want to memorize words fast and better, you can put part of it in your password of something and then try to log in to whatever you set the password on everyday. Idea two, if you want to study fast and quicker you need to spend big half of the day learning what you need to learn and reading books.

Hope this helps!

The best way I could explain this is that everyone has there own pace at doing things. Like me I learn very fast but I have to read over something to memorize them.

The only way I could say is that maybe take more notes and go over them everyday. It helped me a lot when I wanted to learn more and get better grades. Also another way is taking you time at first and when you get use to it you'll be able to read faster learn quicker but you have to go slow first to go fast.

The value of n in the equation (3√7)^5 = 7^n is 5.32288

In the given equation (3√7)^5=7^n, n is solved as follows

(3√7)^5 = 7^n

= (3√7)^5 = 7^n

7.937253933^5 = 7^n

31502.96087 = 7^n

take ㏑ of both sides

㏑ 31502.96087 = n ㏑ 7

divide through by ㏑ 7

n = ㏑ 31502.96087 / ㏑ 7

n = 5.32287517

the value of n is 5.32288

Learn more about logarithm at:

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#SPJ1

Answer:

Differentiation is used to break down the function into parts, and integration is used to unite those parts to form the original function. Geometrically the differentiation and integration formula is used to find the slope of a curve, and the area under the curve respectively.

Answer:

integration is the opposite of differentiation

Step-by-step explanation:

integration requires addition of 1 to the power and then division by the value eg

the integral of

[tex]{x}^{2} = \frac{ {x}^{2 + 1} }{2 + 1} \\ = \frac{ {x}^{3} }{3} [/tex]

while in differentiation, u subtract one and multiply by the value. eg

the differential of

[tex] \frac{ {x}^{3} }{3} = 3( \frac{ {x}^{3 - 1} }{3} ) \\ = 3( \frac{ {x}^{2} }{3} ) \\ = {x}^{2} [/tex]

Answer:

Here is your answer

Step-by-step explanation:

A cubic spline is a spline constructed of piecewise third order polynomials which pass through a set of control points. The second derivative of each polynomial is commonly set to zero at the endpoints since this provides a boundary condition that completes the system of equations.

Answer:

A cubic spline is a spline constructed of piecewise third-order polynomials in which pass through a set of control points. __________________________________________________________

Hope this helps!!

If I am wrong, please tell me, I enjoy learning from my mistakes:)

Answer:

20 inches

Step-by-step explanation:

Use the Pythagorean Theorem.

[tex]a^2 + b^2 = c^2\\15^2 + b^2 = 25^2\\225 + b^2 = 625\\b^2 = 400\\b = \sqrt{400} \\b = 20[/tex]