The length and width of a rectangle are consecutive integers. The perimeter of the rectangle is 42 inches. Find the length and width of the rectangle.

The length and width of the rectangle are 21cm and 19cm.

Let the dimensions be represented by x and x+2.

The perimeter of a rectangle is:

= 2(length + width)

= 2(x + x+2) = 80

2x + 2x + 4 = 80

4x + 4 = 80

4x = 80 - 4

4x = 76

Divide

x = 76/4

x = 19

Therefore, the second number will be:

= 19 + 2 = 21

The numbers are 19 and 21.

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The change in the elevation from the bottom of the Ferris is 21.9 feet.

Elevation change refers to the difference in elevation between the beginning and end of your route.

Given that the distance travelled by Vivian just at bottom of the elevation is -9.6 feet.

The distance traveled by Vivian at the top of the elevation is 12.3 feet.

Vivian's shift in elevation would be expressed as the difference between the elevations at the bottom and top.

Let Ei be the initial elevation of -9.6 feet.

Ef = 12.3 feet as the final elevation

Change in elevation;

ΔE = Ef - Ei

ΔE = 12.3 - (-9.6)

ΔE = 12.3 + 9.6

ΔE = 21.9 feet

Therefore, the change in the elevation is found to be 21.9 feet.

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Answer:

y=8/5x-3

Step-by-step explanation:

y-5=8/5(x-5)

y-5=8/5*x-8/5*5

y-5=8/5x-(8*5/5)

y-5=8/5x-(40/5)

y-5=8/5x-8

+5         +5

y=8/5x-3

Hope this helps.

The revolution per minutes of the wheels rotation is 912 rev/ min

Given the parameters;

Convert the velocity

[tex]v = 65mph = 65 mil/h - (1609m/mil0/(3600s/h)[/tex]

v = 29. 1 m/s

Let's find the circumference

Circumference = 2 π r

radius = diameter/ 2 = 0. 6096 meters/ 2 = 0. 30 meters

Circumference= 2 × 3. 142 × 0. 30 = 1. 915

Number of revolutions = 29. 1/ 1. 915 = 15.2 rev/ sec

Let's convert to rev/ min

= 15. 2 × 60

= 912 rev/ min

Thus, the revolution per minutes of the wheels rotation is 912 rev/ min

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Answer: Width= 29 meters & Length= 31 meters

Step-by-step explanation:

Let, width= x and Length= x+2

Perimeter= 120 meters

Now, 2{x+(x+2)}= 120

⇒ x= 29

Width= 29 meters

Length= 31 meters

Answer: 145 minutes ==> 3rd option

Step-by-step explanation:

2*(45-10)+3*(30-5)=

2*35+3*25=

70+75=145 minutes ==> 3rd option

Answer:

145

Step-by-step explanation:

45 × 2 = 90
10 × 2 = 20
90 - 20 = 70

70

30 × 3 = 90
5 × 3 = 15
90 - 15 = 75

75

70 + 75 = 145

145

Using complementary and supplementary angles, we have that:

c. The angles are complementary, hence the equation is 4x - 3 + 2x + 1 = 90 and the solution is x = 15.33.

d. The angles are supplementary, hence the equation is 43x + 16 + 110 = 180 and the solution is x = 18.

When the measures of two angles add to 90º, the angles are complementary.

This is the case in item c, hence:

4x - 3 + 2x + 1 = 90

6x = 92

x = 92/6

x = 15.33.

When the measures of two angles add to 180º, the angles are supplementary.

This is the case in item d, hence:

3x + 16 + 110 = 180.

3x = 54

x = 54/3

x = 18.

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The value of the function f(-8) if f(x) = -x^2 +8x + 4 is f(-8) = -124

The equation of the function is given as

f(x) = -x^2 +8x + 4

The expression f(-8) means that x = -8

So, we have:

f(-8) = -(-8)^2 + 8(-8) + 4

Evaluate the exponent and the product

f(-8) = -64 - 64 + 4

Evaluate the sum and the difference

f(-8) = -124

Hence, the value of the function f(-8) if f(x) = -x^2 +8x + 4 is f(-8) = -124

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Answer:

x = - 2

Step-by-step explanation:

x - 3x = 2(4+x)

-2x = 2*4 + 2x

-2x = 8 + 2x

-2x - 2x = 8

-4x = 8

x = 8/-4

x = -2

Check:

-2 - (3*-2) = 2(4+(-2))

-2 - (-6) = 2(2)

-2 + 6 = 4

The mean and variance of the lengths are 590. 50  and 0. 075 respectively

Given that the lengths are;

590.1,  590. 2, 590. 3, 590. 4, 590. 5, 590. 6, 590. 7 , 590. 8, 590. 9

Mean = sum of terms/ number of terms

Mean = 590.1 +  590. 2 + 590. 3 + 590. 4 + 590. 5 + 590. 6 + 590. 7 + 590. 8 + 590. 9/ 9

Find the sum of the numerator

Mean = 5314. 5/ 9

Mean = 590. 500

Variance = sum of the distances from the mean/ total number - 1

Variance = (590. 1 - 590. 5)² + (590. 2 - 590. 5)² +  (590. 3 - 590. 5)² +  (590. 4 - 590. 5)² +  (590. 5 - 590. 5)² +  (590. 6 - 590. 5)² +  (590. 7 - 590. 5)² +  (590. 8 - 590. 5)² +  (590. 9 - 590. 5)² ÷ 9 - 1

Variance = 0. 16 + 0. 09 + 0. 04 + 0. 01 + 0 + 0. 01 + 0. 04 + 0. 09 + 0. 016 ÷8

Variance = 0. 6/ 8

Variance = 0. 075

Thus, the mean and variance of the lengths are 590. 50  and 0. 075 respectively

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answer:

3/8

explanation:

(m/n)

count units from point a and b vertically, that is m.

count units from point a and b horizontally, that is n.

The teacher should buy 10 gallons of ice cream.

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Answer:

The answer is 10

Step-by-step explanation:

(1) Option A (25 glee club members are randomly selected; 16 plan to go to a 4-year college.) would probably best represent the entire population of seniors.

(2) 416 seniors would be planning to attend a four-year university, by unitary method.

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Now,

(1) Since Option A has a larger fraction ([tex]\frac{16}{25} > \frac{14}{25} > \frac{13}{25}[/tex]), it is probably the only one that best represents the majority of the people.

(2) As seen from Part (1),

Out of 650 seniors, around 416 will go to a 4-year college as, by unitary method:

For every 25 members, 16 plan to go to 4-year college

For every 650 members, [tex]\frac{16}{25}(650)=416[/tex] will plan to go to 4-year college.

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(COMPLETE QUESTION:

Lincoln High wants to estimate the number of seniors who plan to go to a 4-year college. 1) Which of the following surveys probably would best represent the entire population of seniors? a) 25 glee club members are randomly selected; 16 plan to go to a 4-year college. b) 25 honor roll students are randomly selected from the senior class; 14 plan to go to a 4-year college. c) 25 seniors are randomly selected; 13 plan to go to a 4-year college. 2) There are 650 seniors at Lincoln High. Using your answer from part (a), estimate the number of seniors who plan to go to a 4-year college.)

Considering the function for his salary, his gross pay is of $409.13.

His gross pay is modeled by the following function:

P(x,y,z) = 3.75x + 3.75(1.5)y + 0.15z.

In which:

For this problem, the parameters are given as follows:

x = 25, y = 5, z = 1915.

Hence his pay is given by:

P(25,5,1915) = 3.75(25) + 3.75(1.5)(5) + 0.15(1915) = $409.13.

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The cliff is 98.89 feet tall.

In the attached diagram, we can there are two triangles forming. Small triangle involves Juan and tent and larger triangle involves Juan and cliff. As per the known fact, tan theta = perpendicular ÷ base. So, tan theta will be common for both the triangles. Hence, relating the components of tan theta, of both the triangles.

Smaller triangle :

tan theta = 10/45

Larger triangle :

tan theta = h/(400 + 45)

tan theta = h/445

Relating both the triangles as follows -

10/45 = h/445

Performing cross multiplication

10×445 = h×45

h = 4450÷45

h = 98.89 feet

Hence, the cliff is 98.89 feet tall.

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Luke will drive for 9 hours while Priya will drive for 3 hours.

Driving is the controlled operation and movement of a vehicle, including cars, motorbikes, trucks, buses, and bicycles. Drivers must abide by the local traffic and road laws when driving on public roadways, which are only permitted when a number of requirements are met. The word "driving" has an etymology that dates back to the 15th century, and it has evolved as what driving has included has changed over time, from working animals in the 15th century to automobiles in the 1800s. Since the fifteenth century, driving has also demanded more advanced physical, mental, and safety abilities.

Let number of hours Priya travelled be x and number of hours Luke travelled  be 3x.

Now, Total hours travelled by Priya and Luke;

x+3x=12

x=3

Hence number of hours Priya travelled is 3 hours and Luke travelled for 9 hours.

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The answer choice which represents the length to swim diagonally and expressed to the nearest tenth as required in the task content is; Choice D; 14.2 meters.

It follows from the task content that the pool in discuss is rectangular and hence, the diagonal of the rectangle makes a right triangle with two perpendicular sides of the rectangle.

Hence, from Pythagoras theorem; we have;

hyp² = opp² + adj²

Hence,

D² = 9² + 11²

D² = 81 + 121

D² = 202

D = √202

D = 14.2 rounded to the nearest tenth.

Therefore, The answer choice which represents the length to swim diagonally and expressed to the nearest tenth as required in the task content is; 14.2 meters.

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The complete arithmetic sequence is 1, .25, -0.5, -1.25, -2

The arithmetic sequence is given as:

1, .25, blank, -1.25, blank

Replace the blanks in the arithmetic sequence with x and y

So, we have:

1, .25, x, -1.25, y

An arithmetic sequence has a common difference (d)

The common difference is calculated using

d = T2 - T1

So, we have

d = 0.25 - 1

d = x - 0.25

d = y + 1.25

Substitute d = x - 0.25 in d = 0.25 - 1

x - 0.25 = 0.25 - 1

This gives

x = 0.25 + 0.25 - 1

Evaluate the sum

x = -0.5

Substitute d = 0.25 - 1 in d = y + 1.25

0.25 - 1  = y + 1.25

This gives

y = 0.25 - 1 - 1.25

Evaluate

y = -2

Hence, the complete arithmetic sequence is 1, .25, -0.5, -1.25, -2

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Answer:

440

Step-by-step explanation:

To do this problem, you have to follow the PEMDAS order.

Parentheses

Exponents

Multiplication

Division

Addition

Subtraction

We have to do 5x62 first, which is 310. Next, we multiply 6 and 33, which gets us 198. Then, we add 310 to 198, which is 508. Finally, we subtract 68 from 508 to get 440.

Hope this helps!

Have a wonderful day! :D

Answer:

slope = 1

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 )

y = x - 31 ← is in slope- intercept form

with slope m = 1

Answer:

Ratio= 45/135 = 1/3 = 1:3

Step-by-step explanation:

Look at the attachment

The values compared to the greatest :

-2 1/4,-1 1/4,-1 3/4, 1/4

Comparing and ordering fractions is an essential part of developing a sense of numbers. This is also an essential skill to have when facing practical questions, such as:

"Would you like to have {\displaystyle {\frac{3}{4}}}{\frac{3}{4 }} d 'a pizza does not, or {\displaystyle {\frac{6}{7}}}{\frac{6}{7}} of a pizza?" There are several ways to compare and order fractions. If you have a calculator, the fastest way is to convert fractions to decimals. If you don't have a calculator, you can make comparisons easily by finding a common denominator or simply using your reasoning skills and what you already know about fractions.

In this way, the given fractions are compared from largest to smallest

-2 1/4,-1 1/4,-1 3/4, 1/4

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Answer: -1.9696969696969696969696

Step-by-step explanation:

Answer:

Exact form: -65/33

Decimal form: -1.96

Mixed number: - 1 32/33

Step-by-step explanation:

The required solution is,

1. Gardner can put a maximum of 4 flowers in each row

2. At 150 minutes both the student will meet each other

In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,

Here,

1. For the planting of trees in even rows,

The greatest number of plants he can have in each row to keep the rose bushes and tulips in their own rows,

Taking HCF of number of plants 24 and 28

HCF of 24 and 28 is 4

Thus, Gardner can put a maximum of 4 flowers in each row.

2.

Time taken by the first student to complete one lap is 25 minutes,

So,

1 lap = 25 minute

1 minute = 1 / 25 lap

For the second student,

1 lap = 30 minute

1 minute = 1/30 lap

At time x minute both will meet each other,

x/25 -x/30 = 1

5x/750 = 1

x = 750/5

x = 150 minute

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Answer:

4

Step-by-step explanation:

A set of 25 blocks are arranged into 5×5 square, different combination of 3 blocks such that no two are in same column or row is 3600.

As given,

Set of 25 blocks arranged into 5×5 square.

Arrange 3 blocks

Delete column and row belong to filled block

Possibility for

First block =25 ways

Second block=16 ways

Third block =9 ways

Total ways =25×16×9

                 =3600

Therefore, set of 25 blocks are arranged into 5×5 square, different combination of 3 blocks such that no two are in same column or row is 3600.

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The possible coordinates of point G on this number line are either -10 or 14.

A number line can be defined as a type of graph with a graduated straight line which contains both positive and negative numerical values that are placed at equal intervals along its length.

Given the following data:

E = 2.

EG = 12.

On this number line, the coordinate of EG is given by this mathematical expression:

EG = |E - G|

Substituting the given parameters into the expression, we have;

12 = |2 - G|

2 - G = ±12

G = 2 ± 12

Simplifying and evaluating the above expression, we have:

G = 2 + 12

G = 14.

OR

G = 2 - 12

G = -10

Therefore, the possible coordinates of point G on this number line are either -10 or 14.

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Complete Question:

On a number line, suppose point E has a coordinate of 2, and EG= 12. what are the possible coordinates of point G?

The lateral area of the regular octogonal prism is 528 square inches.  

Regular octogonal prisms has two regular octogonal base sides and eight rectangular lateral sides. In this problem we must look for the sum of the areas of the eight rectangular lateral sides, where each area is equal to the product of base side (l) and height (h), both in inches. Then,

A = l · h

A = (6 in) · (11 in)

A = 66 in²

A' = 8 · A

A' = 8 · (66 in²)

A' = 528 in²

The lateral area of the regular octogonal prism is 528 square inches.

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Answer:

Do you have a picture or anything to show the problem? I am having a hard time understanding what you have wrote.

Step-by-step explanation:

Answer:

my result is 0 = -7 It has no solutions though since it is a contradiction