Use the formula A=P[1+r/n]nt to solve the compound interest problem.
Find how long it takes for $900 to double if it is invested at 6% interest comp
The money will double in value in approximately $\square$ years.
(Do not round until the final answer. Then round to the nearest tenth as need.
The money will double in value in approximately years.
(Do not round until the final answer. Then round to the nearest tenth as need

The answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.

A sequence is defined as an arrangement of numbers in a particular order.

A sequence is given ; -1/5, 2/6, -3/7, 4/8.....

Part A

From inspection of the sequence, the pattern is:

i) Add 1 to the numerator of the previous term.

ii) Add 1 to the denominator of the previous term.

iii) Make every other term negative.

Therefore, The next four terms are -5/9, 6/10, -7/11, 8/12

Part B

From inspection of the sequence, we can see that the numerator is the position of the term (n) in the sequence.  So when n = 1 the numerator is 1, when n = 2 the numerator is 2, etc.

The denominator is 5 more than the position of the term in the sequence.  So when n = 2 the denominator is 2 + 4 = 6, and when n = 4 the denominator is 4 + 4= 8.

Hence, the rule can be,

f(n) = n/(n+4)

If n is even, then f(n) is positive.

If n is odd, then f(n) is negative.

Part C

56 is an even number.

As the function f(n) is positive when n is even, the sign of f(56) is positive.

Therefore, the answers are ; a) -5/9, 6/10, -7/11, 8/12, b) f(n) = n/(n+4) and c) f(56) is positive.

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The equivalent expression to (36 - y²) is (6 - y) (6 + y).

The correct answer option is option C

(36 - y²)

Check all options

A. (36 + 12y + y²)

No

B. (36 - 12y + y²)

No

C. (6 - y) (6 + y)

open parenthesis

= 36 + 6y - 6y - y²

= 36 - y²

Yes

D. (6 - y) (6 - y)

= 36 - 6y - 6y + y²

= 36 - 12y + y²

No

In conclusion, the expression (6 - y) (6 + y) is equivalent to (36 - y²)

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The equation in the standard form of a parabola is y = -3x² - 7x - 2

What is the standard form of a parabola?

Another equation that, when graphed, produces a parabola is one written in standard form. Like the letters in the vertex form equation, each letter in the standard form equation provides a nugget of knowledge about the parabola.

Here, we have

The standard equation of a parabola is

y = ax² + bx + c

Substitute the given values in this equation

When x = - 3 and y = -8

-8 = a (-3)² + b (-3) + c

-8 = 9a - 3b + c …. (1)

When x = 0 and y = - 2

-2 = a (0)² + b (0) + c

c = -2....(2)

When x = 2 and y = -28

-28 = a (2)² + b (2) + c

-28 = 4a + 2b + c …. (3)

Equations (1) and (3) can be written as

9a - 3b + c = -8 …. (4)

4a + 2b + c = -28 …. (5)

Multiply equation (4) by 2 and equation (5) by 3 to eliminate 'b'

18a - 6b + 2c = -16

12a + 6b + 3c = -84

Subtracting these equations

30a + 5c = -100

Substitute the value of 'c' here

30a + 5(-2) = -100

30a = -100 + 10

30a = -90

a = -3

Substitute the value of a and c in equation (1)

-8 = 9a - 3b + c

-8 = -27 - 3b -2

-6 = -27 - 3b

3b = -21

b = -7

Here the value of a = -3, b = -7, and c = -2.

Hence, the equation in the standard form of a parabola is y = -3x² - 7x - 2

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Answer: Sonya's heart rate increased by 75% after running a mile on the treadmill.

Step-by-step explanation:

To find the percent increase in Sonya's heart rate, we can use the following formula:

Percent increase = (New value - Old value) / Old value * 100

Substituting the given values into the formula, we get:

Percent increase = (133 beats per minute - 76 beats per minute) / 76 beats per minute * 100

Calculating the result, we get:

Percent increase = 57 beats per minute / 76 beats per minute * 100

= 0.75 * 100

= 75%

Therefore, Sonya's heart rate increased by 75% after running a mile on the treadmill.

Step-by-step explanation:

[tex]2x + 3y = 5[/tex]

[tex]2x = 5 - 3y[/tex]

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

Answer: Add 3y to both sides of the equation. 2x=5+3y Divide each term in 2x=5+3y by 2 and simplify.

the percent of change in the average cost of a gallon from year one to year two is 5.8%

The term "average cost" refers to the production cost per unit, which is determined by dividing the overall production cost by the overall number of units produced.

The overall cost of production can also be divided into fixed and variable costs. Since total fixed costs often remain constant, changes in total variable costs are the main cause of changes in average costs.

The average cost of a gallon of gas in year one was $2.95

The average cost of a gallon of gas in year two was $2.78

The change in the average cost of a gallon from year one to year two is

$2.95 - $ 2.78

⇒$0.17

So percent of change in the average cost of a gallon from year one to year two is

($0.17/$2.95) * 100%

⇒ 0.0576 * 100%

⇒ 5.76%

⇒ 5.8%

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Answer: centimeters 3

By using compound interest, it can be calculated that-

A) Deposit is $45544.69

B) Interest = $84455.31

What is compound interest?

If the interest on a certain principal at a certain rate over a certain period of time increases exponentially rather than linearly, the interest earned is called compound interest.

If p is the principal, r is the rate and n is the time in years, then amount is calculated by

[tex]A = p(1 + \frac{r}{100})^n[/tex]

The difference between the amount and the principal is the compound interest

A)Here,

Let the principal be $p

Rate = 6%

Time = 18 years

Amount = $130000

[tex]130000 = p(1 + \frac{6}{100})^{18}[/tex]

[tex]130000 = p(1 + \frac{3}{50})^{18}[/tex]

[tex]130000 = p(\frac{53}{50})^{18}[/tex]

[tex]130000 = p(1.06)^{18}[/tex]

[tex]p = \frac{130000}{1.06^{18}}[/tex]

p = $45544.69

B) Interest = $(130000 - 45544.69)

                  = $84455.31

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Answer: 28 inches

Hope this helps!!! :)

Answer:

  C.  4² +8² ≠ 10²

Step-by-step explanation:

You want to know why it is not possible for the lengths 4, 8, and 10 to form a right triangle.

The side lengths of a right triangle must satisfy the Pythagorean relation:

  a² +b² = c²

These numbers do not:

  4² +8² = 16 +64 = 80 ≠ 10² = 100

A right triangle is not formed because ...

  4² +8² ≠ 10²

__

Additional comment

The smallest Pythagorean Triple is {3, 4, 5}. Doubling these numbers gives {6, 8, 10}. If the two longest sides are 8 and 10, the shortest must be 6 for a right triangle to be formed.

When the side lengths are reduced to a mutually prime set of numbers, their sum must be even.

   4:8:10 reduces to 2:4:5 which has an odd sum.

On solving the question, we that when focus is (0,4) and a directrix y is -4 coordinate is (0,0).

Parabola is the name of the graph of the quadratic function. Another way to think of this is the collection of all points whose distance from the focal point is equal to the distance from the line.

Focus (0,4) ,

the directrix y is (-4)

The vertex (h ,k) - halfway between the,

directrix and focus.

y = [y coordinate of focus + directrix] / 2.

The x coordinate will be the same as the x coordinate of the focus.

[tex]\frac{(0, 4-4)}{2} \\(0,0)[/tex]

Focus of (3,0),

a directrix of x = -3

The vertex (h , k) is halfway

between the directrix

and focus.

x = [x coordinate of focus + directrix] / 2.

The x coordinate will be the same as the y coordinate of the focus.

[tex]\frac{3-3,0}{3} \\(0,0)[/tex]

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The equation that represents the total cost you pay for cable television after x months is y = 35 + 29.95x.

What is an equation?

The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.

Given that a cable operator offers that buy a television at $29.95 per month plus a one-time installation fee.

The total cost that need to pay after 6 months is  $214.70.

Assume that a be the cost one-time installation fee.

Then total cost that need to pay after 6 months is  (6 × 29.95) + a = 179.7 + a

Therefore,

179.7 + a = $214.70

a = 35.

After x month, he needs to pay 35 + 29.95x.

Assume that y represents total cost after x months.

y = 35 + 29.95x

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Answer:

x= 1/3rd and 5/3rds

Step-by-step explanation:

9x^2 + 5 = 18x

9x^2-18x+5=0

a=9 b=-18 c=6

x=-b+- the Square root of b^2-4ac all over 2a

so x= 18+- the Square root of -18^2 -4x9x5 all divided by 18

x= 18+- the square root of 144 all over 18

so 18+12 over 18 and 18-12 over 18

this simplifies down to x= 5/3 and 1/3

Answer:

Center: (2,-1)

Radius: 4

Step-by-step explanation:

Circle equation: (x-h)^2 + (y-k)^2 = r^2

Finding the center:

Set to equaling 0 and solve for x and y

(x - 2)^2=0

(y + 1)^2=0

Finding the radius:

In the equation, because it's set to r^2, you would undo the square.

[tex]\sqrt{16}[/tex]=4

The function f(x) = 14(0.87) has is a constant function has no growth or decay.

A function can be defined as the outputs for a given set of inputs.

The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.

Given a function f(x) = 14(0.87) Now it is a constant function as for every different values of x the function f(x) has same value and has no growth or decay.

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Answer:

second option or B

And to mark brainliest on answers when 2 people answer a crown button will appear on the bottom right and you click that

Step-by-step explanation:

-7+4x>-3

+7.     +7

4x>4
/4.  /4

x>1
So second option is correct

Hopes this helps sorry for late response I was eating

The value of the given fraction in mixed numbers is 6, or 36/6.

A fraction is a portion of a whole or, more broadly, any number of equal pieces. In ordinary English, a fraction represents the number of pieces of a specific size, such as one-half, eight-fifths, or three-quarters. In mathematics, a fraction is used to represent a piece or part of a whole. It symbolizes the equal pieces of the whole. A fraction is made up of two parts: the numerator and the denominator. The top number is known as the numerator, while the bottom number is known as the denominator.

Here,

=81/6-45/6

=(81-45)/6

=36/6

=6

The value for given fraction in mixed number will be 6 that is 36/6.

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Answer:

√64 = 8

8i

Step-by-step explanation:

i = √-1

but √64 is a positive number which will produce 8i

Answer: y-3 = -4/5(x+0)

Step-by-step explanation:

formula

y-y1=m(x-x1)

y = y coordinate of the second point

y1 = y coordinate of point one

m = slope

x = x coordinate of the second point

x1 = x coordinate of point one

slope formula

y2-y1/x2-x1

-1-3/5-0

slope = -4/5

the 2 points on the graph are (0,3) (5,-1)

substitute and solve

y-3 = -4/5(x+0)

y-3=-4/5x

Answer: Gwen's breakfast in total was $8. Max's Breakfast in total is $8 as well. so their breakfast together is $16 in total

Answer:

their breakfast cost 16 dollars

Step-by-step explanation:

because you would do 2 times 2 which is 4 and 1 times 4 which is also 4 add those two together to get 8 and the double it because max got the same thing

The Cramer rule can be applied to solve the system of equations and the value of x₂ is x₂ = 12.

For a given system of equations ax + by = c ; px + qy =r, if the determinant of the coefficient matrix [tex]A = \begin{bmatrix}a&b\\p&q\end{bmatrix}[/tex] is non-zero, then as per the Cramer rule, the solution to the system of equations is:

[tex]x=\frac{ \begin{vmatrix}c&b\\r&q\end{vmatrix}}{\begin{vmatrix}a&b\\p&q\end{vmatrix}}\quad\text{and}\quad y=\frac{ \begin{vmatrix}a&c\\p&r\end{vmatrix}}{\begin{vmatrix}a&b\\p&q\end{vmatrix}}[/tex]

The given system of equations is:

-2x₁ - x₂ = 2

-3x₁ - 2x₂ = -3

The coefficient matrix of the system of equations is:

[tex]A = \begin{bmatrix}-2&-1\\-3&-2\end{bmatrix}[/tex]

Now, find the determinant of the coefficient matrix:
[tex]A = \begin{vmatrix}-2&-1\\-3&-2\end{vmatrix}\\A = 4-3\\A =1[/tex]

Since the determinant of the coefficient matrix is non-zero, the Cramer rule can be applied.

According to the Cramer rule, it follows:

[tex]x_2=\frac{\begin{vmatrix}-2&2\\-3&-3\end{vmatrix}}{\begin{vmatrix}-2&-1\\-3&-2\end{vmatrix}}\\\\x_2=\frac{6-(-6)}{1}\\\\x_{2}=12[/tex]

Hence, the Cramer rule can be applied to solve the system of equations and the value of x₂ is x₂ = 12.

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Answer:88 i think

Step-by-step explanation:

The value of a number in the number line is always positive thus, the value of -8 will be 8 and it will be the largest among all.

In mathematics, a number line is a straight line containing numbers arranged at equal segments or periods throughout its duration.

In another word, a number line is basically a line in which infinite numbers have been written in ascending order or increasing order.

As per the given numbers in the number line has been drawn below,

The value of a number in the number line is the absolute value without considering the sign.

For example value of -2 is the distance from zero to -2 so it will be 2.

The largest value is 8 among all numbers.

Hence "The value of a number in the number line is always positive thus, the value of -8 will be 8 and it will be the largest among all".

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Answer:

16.13

Step-by-step explanation:

multiply 10.75 and 1.5 which equals 16.125 so you would round up to 16.13 so your final answer would be $16.13 per hour

The value of the given expression 6 3/5-2 7/10 is 39/10.

What is an expression?

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

Here, we have

Given: 6 3/5-2 7/10

We have to solve this expression and find the value of the given expression.

6 3/5-2 7/10 = 33/5 - 27/10

6 3/5-2 7/10 = (66-27)/10

6 3/5-2 7/10 = 39/10

Hence, the value of the given expression is 39/10.

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The length of the major arc AB is 15.44 units

Given:  line x + 2y = −5 and circle of radius 5 centered at the origin

The equation of a circle of radius r whose center is the origin O (0, 0) is given by x²+y² = r². Thus:

x²+y² = 5²

x²+y² = 25

To find the points where the line intersects the circle, we can substitute the equation of the circle into the equation of the line.

Substituting this into the equation of the line, we have;

x + 2y = -5

x²+y² = 25

Solving for x, we have

x = (-5 ±√(33))/2

Since the circle is centered at the origin, both of these points are on the circle. Thus, the coordinates of the points A and B are

A: (-5 +√(33))/2, (-5 - √(33))/4

B: (-5 - √(33))/2, (5 - √(33))/4

To find the length of the major arc AB, we can use the formula

length = θ/360 × 2πr

where r is the radius of the circle, and θ is the central angle formed by points A and B. The central angle can be found using the formula

θ= 180 - 2cos⁻¹((AB² + r² - AC²)/(2 × AB × r))

where AB is the distance between the points A and B, and AC is the distance between point A and the center of the circle (which is the origin)

We can use the Pythagorean Theorem to find AB and AC:

AB = √(((-5 + √(33))/2 - (-5 - √(33))/2)² + ((-5 - √(33))/4 - (5 - √(33))/4)²)

     = √(66)

AC = √(((-5 + √(33))/2)² + ((-5 - √(33))/4)²)

    = √(25 + 33)/2

    = √(58)/2

Substituting these values into the formula for θ, we have

θ = 180 - 2cos⁻¹((√(66)² + 5² - (√(58)/2)²)/(2 × √(66) ×5))

  = 180 - 2cos⁻¹((66 + 25 - 29)/(20))

  = 180 -2cos⁻¹(62/20)

  = 180 - 2cos⁻¹(3.1)

  = 180 - 2 × 1.43

  = 180 - 2.86

  = 177.14

Finally, substituting this value into the formula for the length of the major arc, we have

length = 2 × π × 5 × (177.14/360)

           = 2  × π  5 ×  (0.4925)

           = 2 ×  3.14 ×  5 ×  (0.4925)

           = 6.28 × 5 ×  (0.4925)

           = 31.4 ×  (0.4925)

           = 15.44 units

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The compound inequality solved are:

x ≤ 2 and x > -5

x > 4 or x < -5.3

The graph of the number line is given above.

It shows a relationship between two numbers or two expressions.

There are commonly used four inequalities:

Less than = <

Greater than = >

Less than and equal = ≤

Greater than and equal = ≥

We have,

-2 x ≤ 4 and 10 > -2x

x ≤ 4/-2 and 10/2 > -x

x ≤ -2 and 5 > -x

x ≤ 2 and x > -5

This means.

-5 < x ≤ 2

The number line can be graphed as,

<----__-5__-4__-3__-2__-1__0__1__2__3__4__5----->

             o---------------------------------------- o

10 < 3x - 2 or -3x - 2 > 14

10 + 2 < 3x or -3x > 14 + 2

12 < 3x or -3x > 16

x > 4 or -x > 16/3

x > 4 or x < -16/3

x > 4 or x < -5.3

x > 4 can be represented on a line graph as,

__-1__0__1__2__3__4__5__6__7--------->

                                     o----------------------->

x < -5.3 can be represented on a number graph as,

<---------8__-7__-6__-5__-4__-3__-2__-1__0__1__2__3__4---------->

<--------------------------o

Thus,

The compound inequality solved are:

x ≤ 2 and x > -5

x > 4 or x < -5.3

The graph of the number line is given above.

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