Question 3.13R:
Which of the following are equivalent exponential function(s) to f(x)=(4/7)^−x

The equation of the parabola is y = -x² + 12x - 27

Parabola is the locus of a point such that the same distance from a fixed line, called the directrix, and a fixed point (the focus) is the same.

The equation of a parabola is in quadratic form. Hence it is given as:

y = ax² + bx + c

At point (-5, 0):

0 = a(-5²) + b(-5) + c

25a - 5b + c = 0      (1)

At point (9, 0):

0 = a(9²) + b(9) + c

81a + 9b + c = 0      (2)

At point (10, 30):

30 = a(10²) + b(10) + c

100a + 10b + c = 30     (3)

Solving equations 1, 2, 3 gives: a = -1, b = 12, c = -27

The equation of the parabola is hence y = -x² + 12x - 27

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Answer: 3(6+2), 3(5+3)

Step-by-step explanation:

Since 18+6 equals 24, you need to find the answers that are equivalent to 24.

3(6+2)

If you do order of operations, it would look like this

3(6+2)

3(8) or 3x8

24

3(5+3)

5+3 equals 8, so this is the same as the first answer.

Answer:There are 75 birds in each section.

Step-by-step explanation:450 birds divided by 18 enclosures is 25 birds in each enclosure. 25 birds times 3 enclosures is 75 birds in each section.

The system of equations representing the amount invested are;

(a) x + y + z = 460,000

(b) 0.065·x + 0.07·y + 0.09·z = 36,350

(c) z = x + y

(d) There is one solution. The man invested $90,000 at 6.5%, $140,000 at 7% and $230,000 at 9%

A system of equations are two or more equations that have variables that are common to the equations in the system.

The questions in the parts (a) to (d) obtained from a similar question are;

(a) An equation stating the sum of the three investments

(b) The equation that states that of the sum of the return is 36,350

(c) The equation that states that the amount invested at 9% equals the sum of the other two investments

(d) Solve the derived system of equations

(a) The amount the man invests in the three rental properties = $460,000

Amount invested in the property that earns 6.5% = x

Amount invested in the property that earns 7% = y

The amount invested in the property that earns 9% = z

The equation that represents the sum of the three investments is therefore;

x + y + z = 460,000...(1)

(b) The equation that represents the sum of the returns from the three investment is found as follows;

6.5% = 0.065, 7% = 0.07, 9% = 0.09

(c) The equation stating the amount invested at 9% equals the sum of the other two investment is; z = x + y...(3)

(d) The system of equations is solved as follows;

From equation (1) and (2), we get;

x + y + z = 460,000

z + z = 460,000

2·z = 460000

· = 460,000 ÷ 2 = 230,000

The amount invested in the property that earns 9% per year is $230,000

Equation (3) indicates;

0.65·x + 0.07·y + 0.09 × 230,000 = 36,350

0.65·x + 0.07·y = 36,350 - 0.09 × 230,000 = 15650

The interest earned in the properties that earn 6.5% and 7% = $15650

0.65·x + 0.07·y = 15650...(4)

x + y = 230000...(5)

Equation (4) and (5) indicates;

y = 230,000 - x

0.065·x + 0.07×(230,000 - x) = 15650

16100 - 0.005·x = 15650

0.005·x = 16,100 - 15,650 = 450

x = 450 ÷ 0.005 = 90,000

The amount invested in the property that yields 6.5% per year = $90,000

Therefore;

The amount invested in the property that earns 7% per year = $230,000 - $90,000 = $140,000

There is one solution, the man invested $90,000 at 6.5%, $230,000 at 7%, and $230,000 at 9%

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Answer:

[4] Function

[5] Not a function

[6] Function

Step-by-step explanation:

    The vertical line test is a test to determine if the line graphed is a function. Taking a vertical line, you move it left and right through the graph. If, at any point, there are two or more intersections in the vertical line, the graph is not a function.

     4 and 6 pass the test meaning they are functions, 5 does not.

Answer:

(0,2)

(3,0)

Step-by-step explanation:

(a) the future value after 9 years is  $7254.76  .

(b) the effective rate of interest is  3.769% .

(c) the time required to reach $10000 is  1.77  years  .

The Continuous Compounding formula for the principal P , rate of interest r , and time t is

A = P×[tex]e^{rt}[/tex]

In the question ,

it is given that

Part(a)  

the amount deposited (P) = $5200

rate percent (r) = 3.7% = 3.7/100 = 0.037

time = 9 years

Amount = 5200×[tex]e^{0.037\times9}[/tex]

= 7254.76

the future value after 9 years is $7254.76   .

Part(b)

the effective rate is calculated using the formula

effective rate = [tex]e^{r}[/tex] - 1

effective rate = [tex]e^{0.037}[/tex] - 1

= 1.03769 - 1

= 0.03769

= 3.769%

Part(c)

the time to reach $10000 is calculated using the formula

10000 = 5200[tex]e^{0.037\times t}[/tex]

[tex]e^{0.037\times t}[/tex] = 10000/5200

[tex]e^{0.037\times t}[/tex] = 100/52

taking ㏑both the sides , we get

0.037×t×㏑(e) = ㏑(100/52)

0.037t = 0.65392

t = 0.65392/0.037

t = 1.76735

t ≈ 1.77 years

Therefore , (a) the future value after 9 years is  $7254.76  .

(b) the effective rate of interest is  3.769% .

(c) the time required to reach $10000 is  1.77  years  .

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The common ratio of the resulting sequence is 1.4.

Given that, the three terms are 60, 100 and 180.

A geometric sequence is a special type of sequence where the ratio of every two successive terms is a constant. This ratio is known as a common ratio of the geometric sequence.

Let the same constant is added to the given number is x.

60+x, 100+x and 180+x

Now, the common ratio is

(100+x)/(60+x) = (180+x)/(100+x)

⇒ (100+x)(100+x)=(180+x)(60+x)

⇒ (100+x)²=10800+180x+60x+x²

⇒ 10000+200x+x²=10800+180x+60x+x²

⇒ 10000+200x=10800+180x

⇒ 20x=800

⇒ x=40

The three number are 100, 140 and 220

The common ratio is 140/100 =1.4

Therefore, the common ratio of the resulting sequence is 1.4.

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There are no extraneous solutions when plugging -7 into x-5=2(x+1).

So extraneous solutions means the solutions that you get by solving an equation, but after you try plugging it back into your original equation, the solution does not work.

Now we have our solutions of x=7, and we just need to check whether it is extraneous or not. We can do this by taking x=1 and plugging it back into your original equation  x - 5 = 2(x + 1)

x - 5 = 2(x + 1)

-7 - 5 = 2(-7 + 1)

-12 = -14 + 2

-14 + 14

0 = 0

We end up getting that 0 = 0 which is correct,

Thus, there are no extraneous solutions.when plugging -7 into x-5=2(x+1).

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Answer:

-6 3/4

Step-by-step explanation:

Take the reciprocal of the second fraction by flipping the numerator and denominator and changing the operation to multiplication. Then the equation becomes

−34×91=?

For fraction multiplication, multiply the numerators and then multiply the denominators to get

−3×94×1 = −274

This fraction cannot be reduced.

The fraction

−274

is the same as

−27÷4

Convert to a mixed number using

long division for -27 ÷ 4 = -6R3, so

−274 = −6 3/4

Therefore:

−34÷19 = −6 3/4

Answer: 7 hours

Step-by-step explanation:

525 x 4.5= 2362.5

2362.5 / 6= 393.75

393.75 / 60= 6.5625

Answer:

-188

Step-by-step explanation:

The circumference of ΔAOC, ΔAOB and ΔABC are  4√2(1+√2), 2(√5+3) and 2(3+√5+2√2) units respectively and area of ΔAOC, ΔAOB and ΔABC are 8,4 and 12 square units respectively.

The perimeter of a triangle can be calculated by simply adding the length of all the sides.

The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.

There are three triangle in the given diagram namely ΔAOC, ΔAOB and ΔABC.

We will find the area and circumference of each of the triangle.

First we find area of each triangle.

Area of ΔAOC = 1/2*CO*AO = 1/2*4*4 = 8 square units.

Area of ΔAOB = 1/2*BO*AO = 1/2*2*4 = 4 square units.

Area of ΔABC = 1/2*BC*AO = 1/2*6*4 = 12 square units.

Now, we will find circumference of each triangle.

Since,  ΔAOC, ΔAOB are right angled triangle

⇒    AC = [tex]\sqrt{AO^{2}+OC^{2} }[/tex] = [tex]\sqrt{4^{2}+(-4)^{2} }[/tex] = [tex]\sqrt{32}[/tex] = 4√2 units.

and AB = [tex]\sqrt{AO^{2}+OB^{2} }[/tex] = [tex]\sqrt{4^{2}+2^{2} }[/tex] = [tex]\sqrt{20}[/tex] =2√5 units.

Circumference of ΔAOC = AC+CO+AO = 4√2+4+4 =4√2+8 = 4√2(1+√2) units.

Circumference of ΔAOB = AB+BO+AO = 2√5+2+4 =2√5+6=  2(√5+3)units.

Circumference of ΔABC = AB+BC+AC = 2√5+6+4√2 = 2(3+√5+2√2)units.

Therefore, circumference of ΔAOC, ΔAOB and ΔABC are  4√2(1+√2), 2(√5+3) and 2(3+√5+2√2) units respectively and area of ΔAOC, ΔAOB and ΔABC are 8,4 and 12 square units respectively.

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The component  describes a country of capitalism is All economic decisions made by government.

According to a common understanding, capitalism is an economic system in which individual actors own and control property according to their interests and where supply and demand freely set market prices in a way that benefits society. The fundamental quality of capitalism is the desire to make a profit.

Capital, which developed from capitale, a late Latin term based on caput, meaning "head," is where the word "capitalism" originates. Chattel and cattle, both of which allude to moveable property, also have their roots in capital (only much later to refer only to livestock).

A capitalist economy allows for the private ownership and control of capital assets like mines, railroads, and factories. It also allows for the purchase of labor for monetary wages, the accrual of capital gains to private owners, and the allocation of prices.

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Frodo ran 132/35 miles in one hour.

Given, that Frodo ran 2(1/5) miles in 7/12 of an hour.

Now, 2(1/5) miles = 7/12 hour

11/5 miles = 7/12 hour

7/12 hour = 11/5 miles

1 hour = (11/5)×(12/7)

1 hour = 132/35 miles

So, Frodo ran 132/35 miles in one hour.

Hence, Frodo ran 132/35 miles in one hour.

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Answer:

Step-by-step explanation:

0.2

Answer:

0.2

Step-by-step explanation:

i did it :)

Answer:

first solve for y and simplify

y+5=[tex]\frac{2}{3} x[/tex]+4/3

y=[tex]\frac{2}{3} x[/tex]+4/3-5

y=[tex]\frac{2}{3} x[/tex]-11/3

Now graph this

y intercept=(0,-11/3)

use the slope to find another point

(3,-1.667)

draw a line using both points

Hello..!

¿What is consumidores terciarios?

They are the ones that feed on carnivores and their parasites.

An example:

When we see a dead bird, a week goes by and then there are only the bones, since as it says they feed on dead birds, that is, they eat everything without leaving anything, whether they are birds, cows or people.

Answer:

I'm not sure if to answer is Spanish or English so here's both:

Spanish: Los organismos que comen consumidores secundarios se llaman consumidores terciarios y son carnívoros que comen carnívoro.

English: Tertiary consumers are organisms that eat secondary consumers

An expression for the area of △KNM is = 1/2 x 2b x a

Given,

In the question:

In triangle KNM ;

The length of the base (MK) = 2b

and, height of the triangle is= a

To write an expression  for the area of △KNM .

Now, According to the question:

We know that :

Area of triangle is = 1/2 x base x height

The length of the base (MK) = 2b

and, height of the triangle is= a

Plug all the values in the area of triangle :

Here, Area of triangle is = 1/2 x 2b x a

Hence, An expression for the area of △KNM is = 1/2 x 2b x a.

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1584 hands(combination) contains two 3s and two 5s.

The query serves as an example of combination (also known as selections).

Two 3s are to be selected from 4 = 4C2

                                                        = 6

Two 5s are to be selected from 4 = 4C2

                                                        = 6

No. of cards in standard deck = 52

No. of remaining cards = 52 - 4 - 4

                            = 44

No. of remaining cards to be selected = 5 - 2 - 2

                                                                = 1

No. of last selection = 44C1

                                 = 44

Total selection = 44 * 6 * 6

                        = 1584

Hence, total hands is 1584.

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Answer:

140 bows

Step-by-step explanation:

hope this helps :)

The simplest ratio of blue eyes to green eyes expresses as 2:1.

The ratio is defined as a relationship between two quantities, it is expressed as one divided by the other.

The table shows how many students had each eye color.

Brown: 21

Blue: 6

Green: 3

In order to calculate the ratio of two quantities, we can use the following steps

First, we have to find the quantities of both scenarios for which we are determining the ratio. In this case, it is 6 blue eyes and 3 green eyes.

Write it in the fraction form a/b. So, we write it as 6/3.

Simplify the fraction further, if possible. The simplified fraction will give the final ratio.

Here, 6/3 can be simplified to 2/1.

Therefore, the simplest ratio of blue eyes to green eyes expresses as 2:1.

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After the subtraction, the simplified value is 16 hours : 9 minutes : 22 seconds

Subtraction

Subtraction means the process of finding the difference between two or more numbers.

Given,

Here we have the timings.

9h 24min 13s

-6h 45min 9s

Now, we have to perform the subtraction on it and also write it in the simplified form.

In order to perform the subtraction, we have to convert the given timings into decimal form, then we get,

=> 9h 24min 13s = 9.4036

Similarly, the second one is converted as decimal form, like

=> - 6h 45min 9s = -6.7525

Now, we have to perform the subtraction on it,

=> 9.4036 - (-6.7525)

=> 16.1561

Now, we have to convert this into time format, then we get,

=> 16 hours : 9 minutes : 22 seconds

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The domain of the inverse function is, x ≥ 8, x is greater than equal to 8.

What is domain and range?

A function's range is the set of all values that the function accepts, and its domain is the set of all values for which the function is defined.

Given: A square root function has a domain of x≥2 and a range of y≥8.

We have to find the domain of it's inverse.

Since, The range of the inverse function's original function, f, is its domain. This also implies that the domain of the inverse function of the original function f is the range of that function.

Therefore, y [tex]\geq[/tex] 8 is the domain of inverse function.

Replace y with x.

Hence, the domain of the inverse function is  x ≥ 8.

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Answer:

r=65° S=66° t=81°

Step-by-step explanation:

R=180-(99+16)° triangle has 180° R=65° to find S 180-(65+33+16)=S S=66

T=180-(33+66) T=81°

Answer: 48in

Step-by-step explanation: 4 seasons per year, 4 x 2 is 8, so you would do 6 x 8 = 48.

The first derivative of the function f'(x) = 2 · [√(x + x²) + 3 · sin 3x]² · [(1 + 2 · x) / [2 · √(x + x²)] + 9 · cos 3x], whose value at x = 1 is - 35.909.

Herein we find a function whose first derivative has to be found. This can be done by using the following derivative rules:

Derivative of a power

f(x) = c · xⁿ → f'(x) = n · c · xⁿ ⁻ ¹

Chain rule

f[g(x)] = (df / dg) · (dg / dx)

Derivative of a sum of functions

d / dx [f(x) + g(x)] = df / dx + dg /dx

Derivative of the sine

d / dx [sin x] = cos x

Now we proceed to find the derivative of the function:

f'(x) = 2 · [√(x + x²) + 3 · sin 3x]² · [(1 + 2 · x) / [2 · √(x + x²)] + 9 · cos 3x]

And we evaluate the derivative at x = 1:

f'(1) = 2 · [√(1 + 1²) + 3 · sin 3]² · [(1 + 2) / [2 · √(1 + 1²)] + 9 · cos 3]

f'(1) = 2 · (√2 + 0.423)² · (3 / 2 - 8.910)

f'(1) = - 35.909

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777.6 cubic ft is the volume of the shed that Lorie ordered to hold her gardening supplies.

The volume of a rectangular prism is expressed as;

V = w × h × l

Where w is the width, h is height and l is length

Given the data in the question;

To determine the volume of the shed, plug the given values into the above formula and simplify.

V = w × h × l

V = 12 ft × 3 1/5 ft × 20.25 ft

V = 12 ft × 3.2 ft × 20.25 ft

V = 12 ft × 64.8 ft²

V = 777.6 ft³

Therefore, the volume of the shed is 777.6 ft³.

Option B is the correct answer.

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Pennington's rate of change is; 80 miles per hour.

William's rate of change is; 60 miles per hour.

The family which is travelling faster is; Pennington's family.

It follows from the task content that the rate of change, otherwise termed slope is to be determined for each of Pennington and Williams.

For Pennington;

As evident in the given graphs; the distance travelled and time of travel are proportional.

Hence, by observation; Pennington's family travelled 40 miles in 0.5 hours and hence;

the rate of change = Distance / time is;

= 40/0.5

= 80 miles per hour.

For Williams;

As evident in the given graphs; the distance travelled and time of travel are proportional.

Hence, by observation; William's family travelled 180 miles in 3 hours and hence;

the rate of change = Distance / time is;

= 180/3

= 60 miles per hour.

On this note, the Pennington's family are traveling faster as their rate of change is greater.

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