Use algebra to show that the product of any two terms in the sequence is also a term in the
sequence.

The dimensions of the window that maximize the area of the window is x = 17/(π - 1)(2) and y = 17 - (17/(π - 1)(2)) (1 + π ).

An area is just a surface that is empty. The length and breadth of a form are used to compute its area. The units used to measure length are unidimensional and include feet (ft), yards (yd), inches (in), etc. Nevertheless, a shape's area can only be measured in two dimensions. As a result, it is expressed in square units such as square inches (in2), square feet (ft 2), square yards (yd2), etc. Most forms and things have edges and corners. When determining an object's area, the length and breadth of these edges are taken into account.

Let us suppose the width of the rectangle = x.

The length of the rectangle = y

Thus,

Perimeter = 2 (x + y) + πx

34 = 2x + 2y + πx

2y = 34 - 2x + πx

The area of the window is:

A = (1/2)πx²+ xy

Substitute y = 34 - 2x + πx / 2

To maximize the area we differentiate the area and equate it to 0:

A = (1/2)πx²+ x(34 - 2x + πx / 2)

A =  (1/2)πx²+ 17x - x² + π/2x²

dA/dx = πx + 17 - 2x + πx

2πx + 17 - 2x = 0

2x(π - 1) = - 17

x = 17/(π - 1)(2)

Substitute the value of x in equation:

2y = 34 - 2x + πx

2y = 34 - 2(17/(π - 1)(2)) + π( 17/(π - 1)(2))

y = 17 - (17/(π - 1)(2)) (1 + π )

Hence, the dimensions of the window that maximize the area of the window is x = 17/(π - 1)(2) and y = 17 - (17/(π - 1)(2)) (1 + π ).

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RS is Parallel to PQ and ∠ P has the same size as ∠ QRS. We find the answer by knowing the definition of Rhombus.

Rhombus is a special case of a parallelogram having four equal sides and opposite equal acute and obtuse angles . The term "equilateral quadrilateral" refers to a quadrilateral whose sides all have equal lengths i.e. Rhombus.

In mathematics, a parallelogram is a simple (non-self-intersecting) quadrilateral with two sets of parallel sides.

a. RS is Parallel to PQ

b. ∠ P has the same size as ∠ QRS

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Answer:

When two proper fractions are multiplied together, the product will be smaller than both factors.

Step-by-step explanation:

To understand why this is true, we can consider the concept of fractions as parts of a whole. When we multiply two proper fractions, we are essentially taking a part of a part, which results in a smaller portion overall.For example, if we multiply 1/2 by 2/3, we are taking half of something and then taking two-thirds of that half. The result is 1/3, which is smaller than both 1/2 and 2/3.Therefore, the correct answer is: The product will be smaller than both factors.

Answer:The product will be smaller than both factors.

When two proper fractions are multiplied together The product will be smaller than both factors.Take a look at the equation below.

¾ * ⅔=  3 times 2 is 6 and 4 times 3 is 12. So the equation is 6/12 .

6/12 is simplified to 1/2. 1/2 is less than both 2/3 and 3/4. Which means the product is smaller. Hence, the correct answer is the product will be smaller than both factors.

I hope this helped & Good Luck <3!!!!

The value of cot A is √55/3

Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle. The ratios of sides of a right-angled triangle with respect to any of its acute angles are known as the trigonometric ratios of that particular angle.

cot A = 1/tanA

AC = √ 8²-3²

AC = √64-9

AC = √ 55

tanA = 3/√55

cot A = 1/tanA

cot(A )= 1/(3/√55)

cot( A) = √55/3

therefore the value of cot(A) = √55/3

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The value of x and y in the triangle are 0 and 4 respectively.

The mid segment of a triangle is a line connecting the midpoints between two sides of a triangle. The mid segment theorem states that the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side .

Therefore,

x + 2 = 3 / 2 x + 2

x - 3 / 2 x = 2 - 2

-0.5x = 0

x = 0

Let's find y

2y - 1 = 3y - 5

2y - 3y = -5 + 1

-y = -4

y = 4

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Answer: a) The equation to represent the cost of the car suggested by the son is:

C1 = 250 + 0.22k

where C1 represents the total cost of renting the car, and k represents the number of kilometers driven.

b) The equation to represent the cost of the car suggested by the daughter is:

C2 = 96 + 0.5k

where C2 represents the total cost of renting the car, and k represents the number of kilometers driven.

c) To find when the two cars cost the same, we need to solve the equation:

C1 = C2

Substituting the expressions for C1 and C2 from parts a and b, we get:

250 + 0.22k = 96 + 0.5k

Simplifying this equation, we get:

0.28k = 154

Dividing both sides by 0.28, we get:

k = 550

Therefore, the two cars cost the same when the number of kilometers driven is 550.

d) If the Clarke's plan to drive 500km, we can calculate the total cost for each car by substituting k=500 into the equations from parts a and b:

C1 = 250 + 0.22(500) = 360

C2 = 96 + 0.5(500) = 346

Therefore, the car suggested by the daughter is less expensive for a 500km trip, as it would cost $346 compared to $360 for the car suggested by the son.

Step-by-step explanation:

Answer:

x^2 - 9 = 0

Step-by-step explanation:

its right one.......

Answer:

See below.

Step-by-step explanation:

Hello!

The topic we should review for this problem is Order of Operations.

Order of Operations is a rule that identifies which part of an equation should be simplified first.

You might've heard of PEMDAS, where;

P for Parentheses, always first unless there's an exponent inside.

E for Exponent, simplified after the Parentheses.

M or D - Multiplication or Division after the Exponent(s).

A or S - Addition or Subtraction after Multiplication or Division.

[tex](5+3^2)+18[/tex]

First we know that there's an Exponent inside the Parentheses, so we must evaluate that number first.

[tex](5+9)+18[/tex]

Next, evaluate what's in the Parentheses.

[tex]14+18\\32[/tex]

Our correct answer is 32.

We are asked what mistake did Raquel make, and what's the correct simplified version of the expression.

1a.) Raquel's mistake is combining unlike terms. It's impossible to combine together a natural number (5) and an exponential number. (3²)

1b.) The correct simplified version of the expression is represented here;

[tex](5+9)+18\\(First \ Step)[/tex]

Answer:

20cm³

Step-by-step explanation:

Volume = Base x Height

1/2 x 5 x 2 x 4

=20cm³

1) The volume of the first rectangular prism is 175 ft³

2) The volume of the second rectangular prism is 60ft³

3) The volume of the third rectangular prism 140ft³

4) The volume of the Fourth rectangular prism 216ft³

Note that in order to find the volume of area of a complex figure, you must deconstruct it into manageable proportions.

Shape 1 above, we deconstructed the rectangular prism into two 3 dimensional shapes with the following metrics:

a)

Length = 7ft

Height = 2ft

widht = 2ft

Volume = Volume = 7ft x 2ft x 2ft
Volume = 28  ft³

b)

Length = 7ft

Height = 3ft

width = 7ft
Volume = 147 ft³

Total Volume = 28  ft³ + 147 ft³

Volume for Shape 1 = 175 ft³

Shape 2 above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 3ft

Height = 2ft

width = 1ft

Volume = 6 ft³

b) Length = 6ft

Height = 3ft

width = 3ft

Volume = 54 ft³

Thus, total volume for shape 2 is:

Volume = 6 + 54

Volume = 40 ft³

Shape 3, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 7ft

Height = 1ft

width = 2ft
Volume = 14ft³

b)
Length = 7ft

Height = 3ft

width = 6ft
Volume = 126ft³

Thus, the total volume fior shape 3, =

Volume = 14ft³ + 126ft³

Volume = 140ft³


Shape 4, above, we deconstructed the rectangular prism into two 3-dimensional shapes with the following metrics:

a) Length = 4ft

Height = 3ft

width = 2ft
Volume = 24 ft³


b) Length = 4ft

Height = 12ft

width = 4ft
Volume = 192 ft³

Thus, the total volume for Shape 4:

Volume =  24 ft³+ 192 ft³
Volume = 216ft³

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The slope of a line parallel to the line whose equation is 5x - 3y = 18 is equal to 5/3.

In Mathematics, the slope-intercept form of an equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Making y the subject of formula, we have the following:

5x - 3y = 18

3y = 5x - 18

y = 5x/3 - 6

In Geometry and Mathematics, two (2) lines are said to be parallel under the following conditions:

m₁ = m₂ ⇒ 5/3 = 5/3

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Answer:[tex]m[/tex] = [tex]d[/tex]/[tex]25[/tex]

Step-by-step explanation:I don't know if this is correct but i think it is:

Solve D=25m

Evaluate powers D = 25m

Subtract D from both sides D= 25m[tex]1[/tex] - D

Add D to both sides D=25m1

Evaluate powers D=25m

Divide both sides by 25 D/25 =m

Solution m = D/25

It should be noted that AP'Q'R' a 180° rotation about the origin of APQR.

It should be noted that to perform a 180° rotation about the origin, one has to draw the original figure and label its coordinates and draw the origin and label it O.

One can also use the following formula to find the coordinates of the image of a point (x,y) after a 180° rotation about the origin:

(x', y') = (-x, -y)

Here, P'Q'R' represents the coordinates of the image of the point PQR. We simply take the negative of the original x and y coordinates to find the new coordinates after the rotation.

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Answer:

x = -4/3

Step-by-step explanation:

hope this helps^^

The value of y, given that Triangle FEG is similar to Triangle IHJ is 10.

Seeing as Triangle FEG is similar to Triangle IHJ, we can assume that angle EGF is the same as angle HJ1.

This means that 5 y + 8 is equal to 58 degrees.

The value of y is therefore :

5 y + 8 = 58

5 y = 50 - 8

y = ( 50 - 8 ) / 5

y = 50 / 5

y = 10

In conclusion, given the two similar triangles and the angles EGF and HJI, the value of y can be found to be 10.

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The set using Roster method is, D = {76, 90, 92, 94, 96}

The roster technique is defined as a method for displaying the elements of a set by listing the elements within brackets.

A roster method example is to write the set of numbers from 1 to 10 as

{1, 2, 3, 4, 5, 6, 7, 8, 9, and 10}.

Given:

Set D is the set of positive two-digit even numbers greater than 74

that do not contain the digit 8

First, Even numbers greater than 74 are

76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98.

Now, Even Number doe not contain 8 are 76, 90, 92, 94, 96.

Using Roster method the set is

D= {76, 90, 92, 94, 96}

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Answer:

500 words per minute.

Step-by-step explanation:

Answer:

16yd

Step-by-step explanation:

I am from Michigan thank me this is really easy you nerd

This is funny helping you big people as a kid.

$68/10 is better to buy as price of one ticket will be $6.8 which is less than that of $7.5 for other ticket.

The appraisal of a single item or part within one group is known as unit value.

So,

$68/10 tickets = 68/10

$68/10 tickets = $6.8 for each ticket.

Now,

$15/2 tickets = 15/2

$15/2 tickets = $7.5 for each ticket.

Thus, $68/10 is better to buy as price of one ticket will be $6.8 which is less than that of $7.5 for other ticket.

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Answer:

x = 9/4 y = 15/4

Step-by-step explanation:

The ordered pair representing the point where both companies would charge the same amount is (25, 136.25).

From the given table, we can form the following equation for monthly cost of each company.

Company 1, the function for the monthly cost is;

(5, $55.25 ) and (10, $75.5). Let the monthly cost = y₁

(y₁ - 55.25 )/(x - 5) = ( 75.5 - 55.25 )/ (10 - 5)

y₁ = 4.05x + 35

Company 2, the function for the monthly cost is;

(5, $31.25 ) and (10, $57.5). Let the monthly cost = y₂

(y₂- 31.25 )/(x - 5) = ( 57.5 - 31.25 )/ (10 - 5)

y₂ = 5.25x + 5

To find the point where both companies charge the same amount, we need to set their costs equal to each other and solve for the number of garments, x:

y₁ = y₂

4.05x + 35 = 5.25x + 5

Subtracting 4.05x and 5 from both sides:

30 = 1.2x

Dividing both sides by 1.2:

x = 25

So both companies would charge the same amount when 25 garments are laundered. T

To find the cost, we can plug x = 25 into either equation:

y₁ = 4.05(25) + 35 = 136.25

y₂ = 5.25(25) + 5 = 136.25

Ordered pair = (25, 136.25)

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The complete question is below:

Two dry cleaning companies offer a home pick-up and delivery service. The monthly cost depends on the number of garments laundered, and is shown in the following table.

Number of Garments      Company 1       Company 2

5                                         $55.25              $31.25

10                                        $75.50             $57.50

15                                        $95.75              $83.75

Determine when both companies would charge the same amount and what that cost would be. Write your answer as an ordered with x representing the number of garments and y representing the cost.

it will take approximately 1.30 loads of trash from the garbage truck to fill the 40-foot by 9-foot by an 8-foot storage container. However, since you can't have a partial load, you would need to round up to 2 loads to completely fill the container.

what is an algebraic expression?

An algebraic expression is a combination of numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, and division) that can be simplified and evaluated.

To determine the number of loads of trash from the garbage truck that will fill a 40-foot by 9-foot by 8-foot storage container, we need to compare the volume of the container to the volume of the garbage truck's back.

The volume of the garbage truck's back is:

V_garbage_truck = length x width x height

V_garbage_truck = 23 ft x 8 ft x 12 ft

V_garbage_truck = 2,208 cubic feet

The volume of the storage container is:

V_container = length x width x height

V_container = 40 ft x 9 ft x 8 ft

V_container = 2,880 cubic feet

To find out how many loads of trash from the garbage truck will fill the storage container, we need to divide the volume of the container by the volume of the garbage truck's back:

Number of loads = V_container / V_garbage_truck

Number of loads = 2,880 cubic feet / 2,208 cubic feet

Number of loads ≈ 1.30 loads

Therefore, it will take approximately 1.30 loads of trash from the garbage truck to fill the 40-foot by 9-foot by an 8-foot storage container. However, since you can't have a partial load, you would need to round up to 2 loads to completely fill the container.

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By answering the above question, we may state that The range of -3 x 2 inequality is the answer to the compound inequality.

A connection between two expressions or values that is not equal in mathematics is referred to as an inequality. Hence, inequity results from imbalance. In mathematics, an inequality establishes the connection between two non-equal numbers. Egality and inequality are not the same. Use the not equal symbol most frequently when two values are not equal (). Values of any size can be contrasted using a variety of inequalities. By changing the two sides until just the variables are left, many straightforward inequalities may be solved. Nonetheless, a variety of factors support inequality: Both sides' negative values are split or added. Exchange the left and the right.

We must first remove 6 from each of the three elements of the compound inequality -6 4x + 6 14 in order to arrive at the following result:

-6 - 6 ≤ 4x < 14 - 6

If we simplify, we get:

-12 ≤ 4x < 8

Then, we divide each of the three inequality components by 4, keeping in mind that we don't need to reverse the inequality's signs because 4 is positive, to arrive at:

-3 ≤ x < 2

The range of -3 x 2 is the answer to the compound inequality.

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Answer:

a. 480       Then 384

b. 845       Then 591.5
c. 1,189      Then 653.95
d. 153.75   Then 149.90625
e. 315        Then 299.25

f. 430.5     Then 419.7375

The best represent graph of the function is option a.

What is a function?

It is an expression which contains one independent variable and another is dependent variable.

The given function is

   f(x)= [tex]4^{x[/tex] - 4

As it is an exponential function so it must have a horizontal asymptote. Here the horizontal asymptote is f(x)= -4

For x intercept we need to take f(x)=0 and for y intercept substitute 0 for x and solve for y. [Here y can be treated as f(x).]

Here x intercept(s)= None

y intercept(s) = (0,-3)[ putting x=0 in   f(x) so 1-4= -3]

Hence the graph is given below.

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Answer:

25

Step-by-step explanation:

let the no of days food avl for eat be X .

according to question...

100/80=X/20

=X × 80 = 100×20

=80x =2000

= x =2000/80

x=25 days

The price οf the ticket when the number οf stοps is 13, fοund using the given expressiοn, is $6.55.

Mathematical expressiοns cοnsist οf at least twο numbers οr variables, at least οne maths οperatiοn, and a statement. It's pοssible tο multiply, divide, add, οr subtract with this mathematical οperatiοn. A finite cοmbinatiοn οf symbοls that are well-fοrmed in accοrdance with cοntext-dependent principles is referred tο as an expressiοn οr mathematical expressiοn. There are twο sοrts οf expressiοns in mathematics: numerical expressiοns, which οnly cοntain numbers, and algebraic expressiοns, which alsο include variables. Expressiοns can be categοrised as arithmetic/numerical expressiοns, fractiοnal expressiοns, οr algebraic expressiοns depending οn the terms they cοntain.

Given the expressiοn as:

1.35 + 0.40(s)

This is used tο calculate the price οf a ticket οn the lοcal cοmmuter train.

s = number οf stοps

Nοw the cοmplete questiοn is tο calculate the price οf the ticket fοr 13 stοps.

Sο s = 13

Substitute in the expressiοn,

1.35 + 0.40(s) = 1.35 + 0.40 * 13 = 1.35 + 5.2 = $6.55

Therefοre the price οf the ticket when the number οf stοps is 13, fοund using the given expressiοn, is $6.55.

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PLEASE GIVE BRAINLIEST <3

Answer:

I'm pretty sure it's bumper cars ( B ).

Hope this helped! <3