PLEASE HELP
Natalie invests $6,680 in a savings account with an interest rate of 2% compounded continuously.
How long will it take for the account balance to reach $8,838.51?

Answer:

Step-by-step explanation:

Solution

17 = a + b

b =  a + 1                    Substitute b into the top equation

17 = a + a+1                Combine

17 = 2a + 1                  Subtract 1 from both sides

17-1 = 2a+1-1               Combine

16 = 2a                       Divide both sides by 2

16/2 = 2a/2

a = 8

b = 8 + 1 = 9

Answer

a = 8

b = 9

Answer:

vector VW= w - v

vector WV= v - w

Step-by-step explanation:

there are no figures to solve the question so i'll just write the formula..

vector VW= w - v

vector WV= v - w

Answer:

1.6

Step-by-step explanation:

4,4-2.8 = 1.6

6-4.4 = 1.6

7.6-6 = 1.6

Then common difference is 1.6

Answer:

First figure out the angle measure of CBA and DBE to find out what Angle measure of ABE is.

Angle CBA and DBE are vertical angles, meaning they are congruent.

so set the equation as:

(2x+21)=(5x)

21=5x-2x

21=3x

x=7

It doesn't matter in which angle you plug 7 you get the same angle measure, so : 5x=5(7)=35 degrees

So to find angle measure of ABE:

We know that ABE and DBE form linear pair, so

180-35=145 degrees

145 degrees is the answer.

Hope it helps!

Answer:

∠ABE = 145°

Step-by-step explanation:

because angle CBA and ABE form a straight line, we know that they must add together to 180 degrees

and because DBE and ABE also form a straight line/angle, they must add together to 180 degrees

we can set this up as a system of equations (I will be writing ABE as "y")

2x + 21 + y = 180

5x + y = 180

We can combine this to beL

2x + 21 + y = 5x + y

 - 2x              -2x

21 + y = 3x + y

   - y       - y

21 = 3x

x = 7

If we plug this back into our original equations (which is set to 180 degrees), we can find y

2(7) + 21 + y = 180

14 + 21 + y = 180

35 + y = 180

- 35       - 35                  

y = 145

(remember, "y" is angle ABE)

we can check this value (ABE = 145) by substituting our second equation

5(x) + ABE = 180

35 + 145 = 180

       180 = 180

(TRUE)

so, the measure of ∠ ABE is 145°

hope this helps!!

Answer:

Two functions which satisfies the H(x) are f(x) = 2x - 4, (x)    = x⁵  and

f(x)  = 2x,  g(x)  = x⁵ - 2

Step-by-step explanation:

The given question is based on the decomposition of a given function into two functions

Decomposition of a function :- functional decomposition is the process of resolving a functional relationship into its constituent parts in such a way that the original function can be reconstructed from those parts by function composition

so the function given in the question is H(x) = 2x⁵ - 4

now by using the concept of decomposition of a function we can find two functions f and g

therefore,

f(x) = 2x - 4

and    g(x)    = x⁵

similarly we can find another pair which satisfies the function H(x)

f(x)  = 2x

and g(x)  = x⁵ - 2

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The area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.

It is defined as the four-sided polygon in geometry having four edges and four corners. It has one pair of opposite congruent angles and the diagonals of a kite are perpendicular.

We have a quadrilateral shown in the picture.

The diagonal divides the quadrilateral into two triangles

The area of the quadrilateral = area of the triangle ADC + area of the

                                                   triangle ADB

= (1/2)3.42×4.39 + (1/2)5.44×3.42

= 7.5069 + 9.3024

= 16.80 square units

Thus, the area of the quadrilateral is 16.80 square units if the diagonal divides the quadrilateral into two triangles.

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Answer:

8x + 100

Step-by-step explanation:

Your answer is correct! But because the equation is already set to "y =", you do not need the "f(x)" in your equation.

The function g(x) is obtained by the transformation of the function f(x) is translated towards left by 1 unit.

A statement, principle, or policy that creates the link between two variables is known as a function.

The function f(x) is given below.

f(x) = 2ˣ

Then the function g(x) is given as

[tex]\rm g(x) = 2^{x + 1}[/tex]

The function g(x) is obtained by the transformation of the function f(x) is translated towards left by 1 unit.

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A function assigns the values. The correct option is C, x=-6.

A function assigns the value of each element of one set to the other specific element of another set.

A.) When the value of x is -12,

f(-12) = 2/3(-12) + 7 = -1

g(-12) = 2(-12) + 15 = -9

B.) When the value of x is -9,

f(-9) = 2/3(-9) + 7 = 1

g(-9) = 2(-9) + 15 = -3

C.) When the value of x is -6,

f(-6) = 2/3(-6) + 7 = 3

g(-6) = 2(-6) + 15 = 3

D.) When the value of x is -3,

f(-9) = 2/3(-3) + 7 = 5

g(-9) = 2(-2) + 15 = 11

Hence, the correct option is C, x=-6.

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Answer:

[tex]\text{B}) \text{ } -3 < x < -1\\\text{D}) \text{ } 2 < x < \infty[/tex]

Step-by-step explanation:

The graph lies below the x-axis.

Answer: Figure QRTS is congruent to figure Q'R'T'S'.

Step-by-step explanation:

A reflection is a rigid motion, and rigid motions preserve congruency.

Answer: 72

Step-by-step explanation:

[tex]\sum^{3}_{t=0} (6t^{2}-3)=(6(0)^{2}-3)+(6(1)^{2}-3)+(6(2)^{2}-3)+(6(3)^{2}-3)=\boxed{72}[/tex]

Answer:

y = -7x

Explanation:

Take two points from table: (-4, 28), (-3, 21)

Find slope:

[tex]\sf slope: \dfrac{y_2 - y_1}{x_2- x_1} \ \ where \ (x_1 , \ y_1), ( x_2 , \ y_2) \ are \ points[/tex]

[tex]\rightarrow \sf slope\ (m): \dfrac{21-28}{-3-(-4)} = -7[/tex]

Now find equation:

[tex]\sf y - y_1 = m (x - x_1)[/tex]

[tex]\rightarrow \sf y - 21 = -7(x - (-3))[/tex]

[tex]\rightarrow \sf y = -7(x +3) + 21[/tex]

[tex]\rightarrow \sf y = -7x -21 + 21[/tex]

[tex]\rightarrow \sf y = -7x[/tex]

Slope

Equation of line

Answer:

first option

Step-by-step explanation:

[tex]\frac{(2g^5)^3}{(4h^2)^3}\\= \frac{8g^1^5}{64h^6} \\= \frac{g^1^5}{8h^6}[/tex]

To simplify the equation, we have y = [tex]\frac{3}{4x^2 + 24x} + 8[/tex]

Given the expression

y-8 = 3/4x [x-(-6)]

First, expand the bracket

[tex]y - 8[/tex]= [tex]\frac{3}{4x^2 + 24x}[/tex]

Make 'y' the subject of formula

y = [tex]\frac{3}{4x^2 + 24x} + 8[/tex]

Thus, to simplify the equation, we have y = [tex]\frac{3}{4x^2 + 24x} + 8[/tex]

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Part 1: Finding [tex](g\circ h)(x)[/tex]

Note that [tex](g\circ h)(x)=g(h(x))[/tex]

In this case, it is [tex]g(\sqrt{x+4})=(\sqrt{x+4})^{2}-3=x+4-3=\boxed{x+1}[/tex]

Part 2: Domain

For the domain, we need to make sure the radicand of h(x) is greater than or equal to 0, so we get [tex]x+4 \geq 0 \longrightarrow \boxed{x \geq -4}[/tex]

The composition (g ο h) = x+ 1 and the domain of the composition (g ο h) is = (-∞ , ∞).

The composition (g ο h) means that the function g(x) composes of h(x) that is g(h(x)). So we have to put the the values of h(x) in the function g(x).

Now here it is given that

g(x) = [tex]x^{2} -3[/tex] and h(x) = [tex]\sqrt[2]{x + 4}[/tex]

so to get (g ο h) we have to replace the x with the value of h(x)

That gives :

g(h(x)) = [tex]\sqrt[2]{x+4} ^{2} - 3[/tex]

g(h(x)) = x + 4 - 3 = x +1

So the composition (g ο h) = x+ 1

The domain of the function is the values of x for which the function is defined.

so the domain of the composition (g ο h) is :

g(h(x)) = x+ 1

This function is undefined for no value of x .

So its domain is (-∞ , ∞).

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Answer:

A = { x:x >3 ,where x --> R}

B = { x:x <4, where x --> R}

Y = { x:x is month of year with more than 30 days}

W = { x:x is all days of a week}

Answer: The graph crosses the x-axis at x = 2.

Step-by-step explanation:

The root has a multiplicity of 3, meaning that it crosses the x axis at x=2.

Answer: 2

Step-by-step explanation:

[tex]a_{n}=2(2)^{n-1}\\\\a_{1}=2(2)^{1-1}=2\\\\a_{2}=2(2)^{2-1}=4[/tex]

Average rate of change:

[tex]\frac{4-2}{2-1}=\boxed{2}[/tex]

The ranges of batting averages were least common among the players is 0.320-0.329 and 0.360-0.369 , Option D is the correct answer.

Average is the middle value of a set of data points , calculated by summing all the data points and then dividing by the number of points.

It is given that , 30 best batting averages for a semi-pro baseball league.

The ranges of batting averages were least common among the players

To find this , it has to be observed that which range has the lowest frequency

The range 0.320-0.329 and 0.360-0.369 has frequency of 1 which is the least among all

Hence Option D is the correct answer.

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None of the options is true.

Three Different, Regular tessellation is formed 1. if we join regular polygons of side 3, called equilateral triangle,2. Regular polygon of side 4, called Square, and 3. Regular polygon of side,6 called hexagon,

to form a pattern.

A polygon is said to be regular if all interior angles and all sides are equal.

The regular polygon of side 3, when joined together can be named: 3.3.3.

The regular polygon of side 4, when joined together can be named 4.4.4.

The regular polygon of side 6, when joined together can be named 6.6.6.

So, a regular tessellation is formed, from a regular polygon having,3,4, and 6 Sides.

None of the sides of the polygon, which is given in the option, can be used to form a regular tessellation.

None of the options is true.

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Answer:

3.8918

round the 1 from the 8 to get 2

3.892

Answer:

4 r^3

Step-by-step explanation:

sqrt ( 16 r^6 )    = sqrt ( 4^2 * (r^3)^2  )    =   4 r^3

The cost of goods sold is $10,258 million and the Cash paid to supplier is $10,447 million.

a. Cost of goods sold

Cost of Goods Sold=Beginning Inventories + Purchases – Ending Inventories

Cost of goods sold = $1,997 + $10,392 - $2,131

Cost of goods sold = $10,258

b. Cash paid to supplier

Cash paid=2015 Beginning balance  + Purchases - 2015 Ending balance

Cash paid = $1,181 + $10,392 - $1,126

Cash paid = $10,447

Therefore the cost of goods sold is $10,258 million and the Cash paid to supplier is $10,447 million.

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Answer:

The plots are (0,2) (1,-1)

Step-by-step explanation:

a slanted line starting from top left corner ending in the bottom right

Answer:

width = 10 cm

Step-by-step explanation:

the ratio of width to length is 2 : 5 = 2x : 5x ( x is a multiplier )

the perimeter (P) of a rectangle is calculated as

P = 2 × width + 2 × length

given P = 70 then

2(2x) + 2(5x) = 70

4x + 10x = 70

14x = 70 ( divide both sides by 14 )

x = 5

Then

width = 2x = 2 × 5 = 10 cm and length = 5x = 5 × 5 = 25 cm

The count of patients needing a blood transfusion can be modelled as a continuous distribution.

A continuous distribution is a distribution that can take on an infinite number of possible values. A continuous distribution is not defined at specific values. The number of patients can be 1 or 10 or 50 or even 0.

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Answer:

The answer is C. Hope it helps

should i create the world problem with 12 3 and 9?