3. Given the recursive equation for each arithmetic sequence, write the explicit equation.
f(n)=f(n-1)-2; f(1)=8
f(n)=5+f(n-1);f(1)=0

Using the Pythagoras theorem, the value of line segment RQ denoted as x is option C: 20 units.

In a right-angled triangle, the square of the hypotenuse side is equal to the sum of the squares of the other two sides, according to Pythagoras's Theorem. These triangle's three sides are known as the Perpendicular, Base, and Hypotenuse.

According to the diagram given -

ST = 9 units and TQ = 16 units.

Δ SRQ and Δ STR are equal and congruent as RT is perpendicular to hypotenuse SQ.

From similar triangles,

Δ SRQ ⩭ Δ STR ------(1)

{∵ RT 丄 Hypotenuse SQ}

Similarly, Δ SRQ and Δ RTQ are equal and congruent Δ SRQ, Δ STR and Δ RTQ  are similar right-angled triangles.

Δ SRQ ⩭ Δ RTQ ------(2)

{∵ Δ SRQ, Δ STR and Δ RTQ are similar triangles}

So, this gives that the sides -

SR/ST = SQ/SR = RQ/TR

SR/9 = 25/SR = x/TR

SR² = 25 × 9

SR = 5 × 3 = 15

Now, applying the Pythagoras theorem -

SR² + RQ² = SQ²

RQ² = SQ² - SR²

RQ² = 25² - 15²

RQ = √(625 - 225)

x = RQ = √400

RQ = 20 units

Therefore, the value of x is obtained as 20 units.

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Answer: If we multiply then I guess it’s 26*3=78 and 78*20=1,560

Step-by-step explanation:

Answer:

$3606.44

Step-by-step explanation:

The question asks us to calculate the principal amount that needs to be invested in order to earn an interest of $6180 in 28 years at an annual interest rate of 6.12%.

To do this, we need to use the formula for simple interest:

\(\boxed{I = \frac{P \times R \times T}{100}}\),

where:

I = interest earned

P = principal invested

R = annual interest rate

T = time

By substituting the known values into the formula above and then solving for P, we can calculate the amount that James needs to invest:

\(6180 = \frac{P \times 6.12 \times 28}{100}\)

⇒ \(6180 \times 100 = P \times 171.36\)     [Multiplying both sides by 100]

⇒ \(P = \frac{6180 \times 100}{171.36}\)    [Dividing both sides of the equation by 171.36]

⇒ \(P = \bf 3606.44\)

Therefore, James needs to invest $3606.44.

Answer:

  see attached

Step-by-step explanation:

You want the graph of the circle defined by the equation ...

  (x-2)^2 + (y-7)^2 = 4.

The equation of a circle with center (h, k) and radius r is ...

  (x -h)² +(y -k)² = r²

Comparing this to the given equation, we see ...

  h = 2, k = 7, r² = 4

Then r = √4 = 2.

The circle will have its center at (2, 7) and will have a radius of 2. It is shown in the attached graph.

<95141404393>

Answer:

d² - 24d + c = (d - 12)² - 144 + c

Answer:

y = \(\sqrt{55}\)

Step-by-step explanation:

using the Altitude- on- Hypotenuse theorem

(altitude)² = product of parts of hypotenuse

then

y² = 11 × 5 = 55 ( take square root of both sides )

y = \(\sqrt{55}\)

The best method would certainly be integration :)

The area is given by the integral,

\(\displaystyle\int_0^2\frac{\mathrm dx}{9-x^2}\)

We can split up the integrand into partial fractions:

\(\dfrac1{9-x^2}=\dfrac16\left(\dfrac1{3-x}+\dfrac1{3+x}\right)\)

Then the area is

\(\displaystyle\frac16\int_0^2\left(\frac1{3-x}+\frac1{3+x}\right)\,\mathrm dx\)

\(=\dfrac16(-\ln|3-x|+\ln|3+x|)\bigg|_0^2\)

\(=\dfrac16\left((\ln5-\ln1)-(\ln3-\ln3)\right)=\boxed{\dfrac{\ln5}6}\)

Answer:

what help you need in this question

Answer:

no solutions

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 )

equation of blue line is y = x + 2 , in slope- intercept form

with slope m = 1

equation of red line is y = x - 3 , in slope- intercept form

with slope m = 1

• Parallel lines have equal slopes

then the blue and red lines are parallel.

the solution to the system is at the point of intersection of the 2 lines

since the lines are parallel then they do not intersect each other.

thus the system shown has no solution.

Answer:

c. 2

Step-by-step explanation:

 2 (3x – y = -2)               6x - 2y = -4

6x - 2y = -4

a) The definition of the composite function is: \((f \circ g)(x) = \frac{6}{12 + 2x}\)

b) The domain of the composite function is: (-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

The composite function of f(x) and g(x) is given by the function rule presented as follows:

(f ∘ g)(x) = f(g(x)).

For the composition of two functions, we have that the output of the inner function, which in this example is given by g(x), serves as the input of the outer function, which in this example is given by f(x).

The functions for this problem are given as follows:

Hence the composite function is obtained as follows:

\((f \circ g)(x) = f(\left\frac{6}{x}\right)\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{6}{x} + 2}\)

\((f \circ g)(x) = \frac{\frac{6}{x}}{\frac{12 + 2x}{x}}\)

\((f \circ g)(x) = \frac{6}{12 + 2x}\)

The domain is all real values except x = 0, x = -2 and x = -6, as f(x) is not defined at x = -2 and g(x) is not defined at x = 0 and the composite function is not defined at x = -6, hence the interval notation is:

(-∞, -6) U (-6, -2) U (-2,0) U (0, ∞).

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The Area of Square is 81 cm².

let the side of the square which is length for both rectangles be a.

let the width of rectangle be x and y.

So, x+ y= a

sum of perimeters= 54

2 (a +x ) + 2 (a+ y) = 54

2a+ 2x + 2a+ 2y = 54

2a + 2a + 2(x+ y) = 54

4a + 2 (a) = 54

4a + 2a = 54

6a = 54

a= 54/6

a= 9

So, area of square

= 9 x 9

= 81 cm²

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Answer:

b and c

Step-by-step explanation:

Amy's forth  account is the most over drawn of all the four accounts

What is the total balance of all accounts?

The total balance of all 4 accounts can be determined as the sum of all account balances, bearing in mind that a positive is added whereas an overdrawn balance is deducted

Total balance=$250-$45+$100+$x

The total balance=$130

the balance in the forth account=$x

Let us substitute $130 for the total balance

$130==$250-$45+$100+$x

$130=$305+$x

$x=$130-$305

$x=-$175

The fact that the forth account has  a balance of negative $175 means that it is also overdrawn, in essence, the correct option out of the 4 options is A, the forth account is most overdrawn because it is more overdrawn that the second account with a negative balance of $45.

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The solution to the algebraic expression is y =3

This algebraic expression contain variable and constant along with unknow variables.

y^(3)-27=9y^(2)-27y

Add 27y  to both sides

y^(3)-27 +27y =9y^(2)-27y +27y

Simplify

y^3-27 +27y =9y^2

Subtract 9y^2 from both sides

y^3-27 +27y-9y^2 =9y^2- 9y^2

y^3-27 +27y-9y^2= 0

Simplify

y^3 - 9y^2 + 27y - 27 =0

Factor by grouping y^3 - 9y^2 + 27y - 27 ; (y-3)^3

(y -3) (-y^2 + 6y -9) = 0

(y-3)^3 =0

Using the zero factor principle if ab = then a = 0 or b= 0

y-3= 0

Add 3 to both sides

y =3

Therefore, solution to the algebraic expression is y =3

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If the brain volumes (cm³) of 20 brains have a mean of 1085.2 cm³ and a standard deviation of 125.6 cm³. For such data: it is significantly low for a brain because 1386.4 cm³ is less than the upper limit.

Mean = 1085.2 cm³

Standard deviation = 125.6 cm³

Hence,

Lower limit = Mean - 2 x Standard deviation

Lower limit  =1085.2 - 2 x 125.6

Lower limit =1161.2 - 251.2

Lower limit  =910

Upper Limit = Mean + 2 x Standard deviation

Upper Limit = 1161.2 +  2 x 125.6

Upper Limit =1161.2 +251.2

Upper Limit =1412.4

The limit of values is from 910 to 1412.4.

A value below 910 will be is considered low and a value above 1412.4  will be considered high

Therefore 1386.4 cm³ is less than the upper limit. Thus it is significantly low for a brain.

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Step-by-step explanation:

3x × 8x- 3x×16

24x -48x

-24x

A: The linear equations are x + y = 125 and x = y + 45.

B: Everyday Angela spends 40 minutes in playing golf.

C: No, it is not possible for Angela to spend 80 minutes playing soccer every day.

What is a linear equation?

A linear equation is one that has a degree of 1 as its maximum value. No variable in a linear equation, thus, has an exponent greater than 1. A linear equation's graph will always be a straight line.

Part A:

Let x be the number of minutes Angela plays soccer every day

Let y be the number of minutes Angela plays golf every day

According to the problem statement the linear equations are -

x + y = 125 (total time playing both sports is 125 minutes)

x = y + 45 (Angela plays 45 more minutes of soccer than golf)

Part B:

Substitute x = y + 45 into the first equation -

(y + 45) + y = 125

Use the addition operation -

2y + 45 = 125

2y = 80

y = 40

Angela spends 40 minutes playing golf every day.

Part C:

If Angela spends 80 minutes playing soccer every day, then

x = 80

y + 45 = 80 (using the equation x = y + 45)

y = 35

But this would mean that she plays golf for 35 minutes and soccer for 80 minutes, which adds up to a total of 115 minutes.

This is not possible since the problem states that Angela plays both sports for a total of 125 minutes every day.

Therefore, it is not possible for Angela to have spent 80 minutes playing soccer every day.

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True statement are:

A. This graph is not a function because the value x = 3 is assigned to

more than one y-value.

D. This graph is a function because the value of x is the same for

every value of y.

Given,

In the question:

To see the graph :

Mark all the statement that are true.

Now, According to the question:

From the graph,

Equations are expressions of two mathematical expressions t such as two numbers, functions. An equality between quantities and operations, usually with an equal sign "=".

Functions is a correspondences between two sets that are not empty each element in the set of input values can corresponds to a element in a set of output values that is unique.

Hence, True statement are:

A. This graph is not a function because the value x = 3 is assigned to

more than one y-value.

D. This graph is a function because the value of x is the same for

every value of y.

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The area of the composite figure is 122.24 units².

The composite figure consist of a rectangle and two semi circles. Therefore, the area of the composite figure is the sum of the area of the individua shapes.

Hence,

area of the composite figure = area of the rectangle + 2(area of semi circle)

Therefore,

area of the composite figure = 9 × 8 + 2(1 / 2 πr²)

area of the composite figure = 72 + πr²

where

r = 8 / 2 = 4 units

Therefore,

area of the composite figure = 72 + 3.14 × 4²

area of the composite figure = 72 + 3.14 × 16

area of the composite figure = 72 + 50.24

area of the composite figure = 122.24 units²

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The higher R-squared value of the multiple regression model with the higher order independent variable implies that the linear model is not the best fit and that a more complex model is needed to better explain the data

1. Multiple regression models involve fitting a model that includes one or more independent variables to predict a dependent variable.

2.A value of X to a higher power, such as X squared, for an independent variable in a multiple regression model indicates that the relationship between the independent and dependent variables is not linear.

3. If this model produces a higher value of R-squared than a linear model, it means that it is a better fit for the data.

4. However, it does not necessarily imply that the linear model's residual plot is not randomly distributed around the zero line.

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The surface area of the given composite figure is; 528 ft²

To get the surface area of the attached composite shape, we will have to break the object down into smaller shapes to get;

Surface area 1 = 2(15 * 4) = 120 ft²

Surface area 2 = 2(9 * 4) = 72 ft²

Surface area 3 = 2(6 * 4) = 48 ft²

Surface area 4 = 2((15 * 15) - (9 * 9)) = 288 ft²

Thus;

Total surface area = 120 + 72 + 48 + 288

Total surface area = 528 ft²

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If Group 1 trees produce 25 percent more coconuts than Group 2, proportionately, Group 2 trees produce 120 coconuts.

Proportion refers to the two ratios equated to each other.

Proportion shows how much quantity or value is contained in another.

We depict proportions using fractional values, such as fractions, decimals, and percentages.

The number of coconuts produced by Group 1 trees = 150

The percentage by which Group 1 trees produce more than Group 2 = 25%

Let Group 1's production compared to Group 2's = 1.25 (100% + 25%)

Let Group 2's production = 100% = 150/125 x 100

= 120 coconuts

Thus, Group 2 trees would produce 120 coconuts compared to Group 1 trees that produced 150, which was proportionately, 25% more.

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Answer:

Step-by-step explanation:

sp = 504

gain = 12%

in this case

sp =100%+12%=504

112%=504

1%=504/112 =4.5

100%=450

so cost =$450

Hope im correct, if i am im glad to be of service.

The shape of the resultant matrix of the multiplication of a "2 by 4" matrix and a "4 by 3" matrix will be a "2 by 3" matrix, the correct option is (d).

We know that the general rule for matrix multiplication, which is If matrix A is "m by n" matrix (it has m rows and n columns) and the matrix B is "n by k" matrix (it has n rows and k columns),

Then the product AB is an "m by k" matrix, which means, that the resulting matrix will have "m" rows and "k" columns.

In this case, the "2 by 4" matrix means that matrix has 2-rows and 4-columns, and

The "4 by 3" matrix means the matrix has 4-rows and 3-columns.

Since the number of columns in the first matrix (4) matches the number of rows in the second matrix (4), we can perform the multiplication.

The resulting matrix will have 2 rows and 3 columns,

Therefore, the shape of the resultant matrix is (d) 2 by 3.

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The given question is incomplete, the complete question is

Please identify from the following choices which has the shape of the resultant matrix of multiplication of a "2 by 4" and "4 by 3" matrices.

(a) 3 by 2

(b) 2 by 4

(c) 4 by 4

(d) 2 by 3

Answer:

R=20cents

B=75cents

G=75 cents

$1.70