When the mortgage is completely paid off for Mark and Lynne’s house, it will be 4 times as old as it is now. If they have 15 years left on the mortgage, how old is the house right now?

The variable 'c' in the given expression has No Solution.

Given, that

2/3c - 1 = 1 + 2/3c

Now, as we have same coefficient of the variable c i.e. 2/3

So, On subtracting 2/3c from both the sides, we get

2/3c - 2/3c - 1 = 1 +2/3c - 2/3c

-1 ≠ 1

Hence, we got no solutions that can satisfy the given expression.

So, the variable 'c' in the given expression has No Solution.

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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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Answer:

-188

Step-by-step explanation:

The correct options are:

Given,

In the question:

Which statements are true about exponential decay functions?

Now, According to the question;

We know that the exponential function is given by:

[tex]f(x) = ab^x[/tex]

where a>0 and b are constants.

Also, it represents a growth function if b>1

and a decay function if 0<b<1

where b is the base.

Hence, the domain of the function is all the real numbers )

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The standard deviation of death in an army corps each year is 0.78

From the question, we have the following parameters that can be used in our computation:

Distribution type = Poisson distribution

Average of the distribution = 0.61

The standard deviation of the distribution is calculated as:

Standard deviation = √Average of the distribution

Substitute the known values in the above equation, so, we have the following representation

Standard deviation = √0.61

Evaluate the square root expression

So, we have

Standard deviation = 0.78

Hence, the standard deviation is 0.78

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Answer: 48in

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

(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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Answer: 7 hours

Step-by-step explanation:

525 x 4.5= 2362.5

2362.5 / 6= 393.75

393.75 / 60= 6.5625

According to the given percentage, the shipping and handling fee that Elizabeth will pay is $16.6

Percentage:

Percentage refers one-hundredth (1/100) of something. And it refers to the rate or proportion of that one hundred.

Given,

Elizabeth buys a microscope priced at $83. Shipping and handling are an additional 20% of the price.

Here we need to find the shipping and handling will Elizabeth paid.

We know that, the price of the product is $83.

And the charges for the shipping and handling is 20%.

So, it can be written as the following form,

=> Additional charges = 20% of 83

=> Additional charges =  20/100 x 83

=> Additional charges = 20 x 0.83

=> Additional charges = 16.6

Therefore, the shipping and handling charges is $16.6

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The equation of the parabola from the vertex is f(x) = -3(x - 5)² + 9

The equation of the function is given as

f(x) = 3x²

Also, we have

Vertex = (5, 9)

The form of the equation is given as

f(x) = a(x - h)² + k

Where

Vertex = (h, k)

This means that

Vertex = (h, k) = (5, 9)

Substitute (h, k) = (5, 9) in the equation f(x) = a(x - h)² + k

So, we have

f(x) = a(x - 5)² + 9

This also means that

f(x) = -3(x - 5)² + 9

The -3 is gotten from f(x) = -3x²

Hence, the equation of the parabola is f(x) = -3(x - 5)² + 9

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Bank A grants a shorter payment period and is the least costly, so the Ruffins should take the loan from Bank A.

In finance literature and practice, the loan interest (cost) increases with a more extended payment period.

In other words, a shorter payment period reduces the interest cost of a loan.  The loan cost is also influenced by the amount of the principal and the interest rate.

Down payment = 25%

Interest rate = 11%

Mortgage period = 25 years

2 points at closing

N (# of periods) = 300 months (25 years x 12)

I/Y (Interest per year) = 11%

PV (Present Value) = $142,500 ($190,000 - $47,500)

FV (Future Value) = $0

Results:

Period Payments (PMT) = $1,396.66

Sum of all periodic payments = $418,998

Total Interest = $276,498

Down payment = $47,500 ($190,000 x 25%)

2 points = $2,850 ($142,500 x 2%)

Sum of periodic payments = $418,998

Total costs = $469,348 ($47,500 + $2,850 + $418,998)

Down payment = 15%

Interest rate = 10%

Mortgage period = 30 years

N (# of periods) = 360 months (30 years x 12)

I/Y (Interest per year) = 10%

PV (Present Value) = $161,500

FV (Future Value) = $0

Results:

Period Payments (PMT) = $1,417.28

Sum of all periodic payments = $510,220.08

Total Interest = $348,720.08

Down payment = $28,500 ($190,000 x 15%)

Sum of periodic payments = $510,220.80

Total costs = $538,720.80 ($28,500 + $510,220.80)

Thus, we can recommend the Ruffins should go for a Bank A loan that costs less than Bank B's.

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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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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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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: 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:

x=3

Step-by-step explanation:

I’m pretty sure these 2 angles are equivalent

64-4x=58-2x

6-4x=-2x

6=2x

3=x

Hopes this helps please mark brainliest

The factoring of the polynomial f(x) = x^4 + 3x³ - 2x² + 48x - 288 is given as follows:

f(x) = (x - 4i)(x + 4i)(x + 6)(x - 3).

The polynomial is factored by it's linear factors, given as follows:

f(x) = (x - x')(x - x'')(x - x''')(x - x'''').

In which x', x'', x''' and x'''' are the roots of the polynomial f(x).

In this problem, we have that -4i is a root, hence, by the Conjugate Roots Theorem, 4i is also a root and hence:

f(x) = (x - 4i)(x + 4i)(x - x''')(x - x'''').

f(x) = (x² + 16)(x - x''')(x - x'''').

As a fourth order polynomial can be the product of two second order polynomials, hence:

x^4 + 3x³ - 2x² + 48x - 288 = (x² + 16)(ax² + bx + c)

x^4 + 3x³ - 2x² + 48x - 288 = ax^4 + bx³ + (c + 16)x² + 16bx + 16c.

Hence the coefficients are given as follows:

Then the equation for the final two factors is:

x² + 3x - 18 = 0.

Which is simplified as follows:

x² + 3x - 18 = (x + 6)(x - 3).

Hence the simplified polynomial is:

f(x) = (x - 4i)(x + 4i)(x + 6)(x - 3).

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Answer:

x=-1/13

Step-by-step explanation:

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: 63

Step-by-step explanation:

When there are two lines intercepting the two angles opposite each other are the same

and GHK and IHF are opposite of each other so there for are equal

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

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:

this is Ture

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

By changing both equations to slope-intercept, it is easier to determine whether two lines are perpendicular.

Since [tex]y = \frac{5}{2} x+ 5[/tex] is already in slope-intercept form, we just need to change the first given equation.

2x + 5y + 3 = 0

2x + 5y = -3

5y = -2x -3

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

Two lines are perpendicular when the slope of the lines (coefficient of x) are negative reciprocals (opposite sign of the inverse of a number).

Comparing the two slopes [tex]\frac{5}{2}[/tex]  and [tex]\frac{-2}{5}[/tex], we can see they they both fit the criteria of being opposite signs and inverses of each other.

So  2x + 5y + 3 = 0 is perpendicular to y = (5/2)x+ 5.

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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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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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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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