what is the square root of a perfect square always rational

Answer:

8

Step-by-step explanation:

the perimeter is the sum of the 3 sides of the triangle.

Given perimeter = 26 , then

2a - 3 + 2a + 3a + 1 = 26 , that is

7a - 2 = 26 ( add 2 to both sides )

7a = 28 ( divide both sides by 7 )

a = 4

then

shortest side = 2a - 3 = 2(4) - 3 = 8 - 3 = 5

longest side = 3a + 1 = 3(4) + 1 = 12 + 1 = 13

the difference between the 2 sides is 13 - 5 = 8

the longer side is 8 units bigger than the shortest side

The 2021st term of the sequence is (- n - 2017).

Given,

A sequence is constructed by listing all the possible numbers that contain no digit greater than 3 in ascending order.

We need to find out what is the 2021st term of this sequence.

An arithmetic sequence is a sequence where the difference between the consecutive terms is the same.

Example: 2, 4, 6, 8, 10

4 - 2 = 2

6 - 4 = 2

8 - 6 = 2

The nth term of an arithmetic sequence is given by:

= a + ( n - 1 ) d

Where a = the first term

d = common difference

Let the sequence that contains no digit less than 3 in ascending order be:

3 - n, 3 - (n + 1), 3 - (n+2), 3 - (n+3), 3 - (n+4),......

Where n = any real number from 1.

We see that the common difference is -1.

3 - (n+1) - (3 - n)

= 3 - n - 1 - 3 + n

= -1

3 - (n+2) - [3-(n+1)]

= 3 - n - 2 - 3 + n + 1

= -1

Find the 2021st term.

We have,

a = 3 - n

d = -1

n = 2021

= a + ( n - 1 ) d

= (3 - n) + ( 2021 - 1 ) (-1)

= 3 - n - 2020

= - n - 2017

Thus the 2021st term of the sequence is - n - 2017.

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The relation that is represented in the table is a function. YES.

For every relation that represents a function, the each of the x-value (domain element/input) corresponds to exactly one y-value (range element/output).

In the table given showing a relation, every single x-value (input) has exactly only one possible y-value (output) that it is assigned to. The x-values, 1, -1, 3, and 5, each have a specific y-value they each correspond to.

Thus, based on the definition of a function, the relation that is represented in the table is a function. YES.

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The daily recommended grams of fat  by the nutritional label is 98 grams.

The nutritional label on a food stated that one serving contained 3 grams of fat which is 3.06% of the daily recommended level.

let

the recommended level = x

Therefore, the product of the percentage and the required daily  recommendation level is equals to the 3 grams.

grams of fat = 3.06% × x

3 =  3.06% × x

3 = 3.06 / 100 × x

3 = 3.06x / 100

cross multiply

3 = 3.06x / 100

300 = 3.06x

300 = 3.06x

divide both sides by 3.06

300 / 3.06 = 3.06x / 3.06

x = 98.0392156863

x = 98 grams

Therefore, the daily recommended grams of fat  by the nutritional label is 98 grams.

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Using linear function concepts, it is found that:

i) The equation of BC is given by: [tex]y = -\frac{2}{3}x + \frac{20}{3}[/tex].

ii) The coordinates of C are C(0,10) and the coordinate of D are D(14,6).

The diagram is missing, and is shown in the graph at the end of the answer.

A linear function is modeled by:

y = mx + b

In which:

For this problem, the coordinates are given as follows:

A(2, 14), B(-2,8) and C(x,0).

From the diagram, AB and BC are perpendicular, meaning that the multiplication of their slopes is of -1.

Given two points, the slope is given by change in y divided by change in x. Hence the slope of AB is given as follows:

mAB = (8 - 14)/(-2 - 2) = 3/2.

The slope of BC is given as follows:

mBC = (0 - 8)/(x - (-2))

mBC = -8/(x + 2).

The multiplication of the slopes is of -1, hence:

mAB x mBC = -1

-12/(x + 2) = -1

- x - 2 = -12

x = 10.

Hence, the slope of BC is:

mBC = -8/(x + 2) = -8/12 = -2/3.

Then:

y = -2/3x + b.

When x = 10, y = 0, hence we can find b as follows:

0 = -2/3(10) + b

b = 20/3.

Hence:

The equation of BC is given by: [tex]y = -\frac{2}{3}x + \frac{20}{3}[/tex].

From the diagram, we also have that AB and CD are parallel, meaning that they have the same slope, hence, considering D(x,y), we have that:

mCD = mAB

y/(x - 10) = 3/2

y = 1.5(x - 10)

y = 1.5x - 15.

AD and BC are also parallel, hence:

mAD = mBC

(y - 14)/(x - 2) = -2/3

Since y = 1.5x - 15, we have that:

(1.5x - 15 - 14)/(x - 2) = -2/3

(1.5x - 29)/(x - 2) = -2/3

3(1.5x - 29) = -2(x - 2)

4.5x - 87 = -2x + 4.

6.5x = 91

x = 91/6.5

x = 14.

y = 1.5x - 15 = 1.5(14) - 15 = 21 - 15 = 6.

Hence:

The coordinates of C are C(0,10) and the coordinate of D are D(14,6).

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The unit rate in minutes per meter is 25/2

We are given the time taken to fill an empty aquarium = 15/2 minutes

Also, the depth of aquarium = 3/5 meters

To find the unit rate in minutes per meter, we will simply keep the values in formula. We do not need to change the units, as they are already in required ones, which are minutes and meters.

Unit rate = minutes ÷ meter

Unit rate = 15/2 ÷ 3/5

Rewriting the fraction

Unit rate = 15×5 ÷ 3×2

Performing multiplication in both numerator and denominator

Unit rate = 75 ÷ 6

Performing division of both numerator and denominator by 3

Unit rate = 25/2

So, the unit rate in minutes per meter is 25/2.

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Answer:

[tex]\boxed {y = \dfrac{1}{3}x - \dfrac{7}{3}}[/tex]

Step-by-step explanation:

If we have a line y = mx + b where m is the slope and be is the y-intercept then a line perpendicular to this line will have slope -(1/m)

So the slope of the line perpendicular to y = -3x + 5 will be [tex]-\dfrac{1}{3}[/tex] = + 1/3 = 1/3

So the perpendicular line equation is

y = (1/3)x + b where b is the y intercept of this line

Since it passes through the point x = 4, y = -1 we plug in these values for x and y and solve for b

We get
[tex]-1=\dfrac{1}{3}\cdot \:4+b[/tex]

Switch sides
[tex]\dfrac{1}{3}\cdot \:4+b=-1[/tex]

[tex]\dfrac{4}{3}+b=-1[/tex]

Subtract  [tex]\dfrac{4}{3}[/tex]  from both sides

[tex]b = -1 - \dfrac{4}{3} = -\dfrac{3}{3} -\dfrac{4}{3} = -\dfrac{7}{3}[/tex]

So the equation of the perpendicular line is
[tex]\boxed {y = \dfrac{1}{3}x - \dfrac{7}{3}}[/tex]

Answer: 1

Step-by-step explanation:

In order to find GCF, take the prime factorization of 3 and 13.

3: 1*3 ==> Prime factorization of 3

13: 1*13 ==> Prime factorization of 3

The common factor is 1.

GCF of 13 and 3 is 1

The number of new setups the internet service company perform in the neighborhood is 22 setups.

The correct answer is option B

Number of new setups the internet service company perform = Total amount the internet service company earned ÷ Amount the internet service company charge per new setup

= $770 / $35

= 22 setups

Therefore, the number of new setups the internet service company perform in the neighborhood is 22 setups.

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When p = 0.125 the equation -3p + ( 1/8 ) = ( - 1/4 ) is true.

The given equation is:

-3p + ( 1/8 ) = ( - 1/4 )

On the left-hand side of the equation, the denominator of the two terms is not the same.

So, the LCM of 1 and 8 is 8.

Therefore,

- 3p × ( 8 / 8 ) + ( 1 / 8 ) × ( 1 / 1 ) = ( - 1 /4 )

- 24p / 8 + 1 / 8 = - 1 / 4

( - 24p + 1 ) / 8 = - 1 / 4

Now multiplying each side of the equation by 8.

We get,

[ ( - 24p + 1 ) / 8 ] × 8 = ( - 1 / 4 ) × 8

- 24p + 1 = - 8 / 4

- 24p + 1 = - 2

Subtracting 1 from each side of the equation,

- 24p + 1 - 1 = - 2 - 1

-24p = - 3

Now, divide each side of the equation by 24.

- 24p / 24 = - 3 / 24

- p = ( - 1 / 8 )

Multiplying by - 1 on each side of the equation,

( - p ) × ( - 1 ) = ( - 1 / 8 ) × ( - 1 )

p = 1 / 8

p = 0.125

The value of p = 0.125 will make the equation true.

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The average number of viewers over the two weeks is  4. 85  x 10^5. Option D

Average is simply a number taken as the representative of a list of numbers.

It is determined by taking the sum of the numbers divided by the number of listed numbers.

Given the number of viewers as;

5.6 x 105 viewers  and 4.1 x 105 viewers

Average = 5. 6 x 10^5 + 4.1 x 10^5 / 2

Average = 9. 7  x 10^5 / 2

Average = 4. 85  x 10^5

The average number of viewers over the two weeks is  4. 85  x 10^5

Thus, the average number of viewers over the two weeks is  4. 85  x 10^5. Option D

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The value of x is 6° and value of z is 67°

We know that when two lines intersect then the vertically opposite angles are equal.

So according to the given figure

      (11x + 47)° = (6x + 77)°

Solving the above equation for x we get

        11x° + 47° = 6x° + 77°

         5x° = 30°

          x = 6°

Thus the value of x is 6°

Also note that the linear pair of angles make 180°. That is sum of the two angle is 180°. As we can see from the figure ∠z  and (6x + 77)° make linear pair of angles, therefore there sum will be equal to 180°.

Thus,   ∠z  + (6x + 77)° = 180°

             ∠z + (6*6 + 77)° = 180°

            ∠z + 113° = 180°

             ∠z = 67°

Hence the value of z is 67°

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Answer:

1870

Step-by-step explanation:

Answer:

c) 1,870

Step-by-step explanation:

374 multiplied 5 times, or 374 in a group of 5, equals 1,870.

Have a good day <333

The numbers are 20 and 36.

As per the information in question, let the smaller number x. So, according to question, large number will be (x + 16).

Now, writing the equation that will form -

x + x + 16 = 56

Performing addition of variables on Left Hand Side

2x + 16 = 56

Shifting the number from Left Hand Side to Right Hand Side

2x = 56 - 16

Performing subtraction on Right Hand Side

2x = 40

Shifting 2 to denominator on Right Hand Side

x = 40÷2

Performing division to find the value of x

x = 20

So, smaller number is 20.

Larger number = x + 16

Larger number = 20 + 16

Larger number = 36

Hence, the numbers are 20 and 36.

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Answer:

Step-by-step explanation:

I hope this answer help you

Answer:

h = 16.0 cm

Step-by-step explanation:

Note: I am assuming that the surface area of 258 is the total surface area which includes the Lateral Area (L) and Base Area(B)

Total Surface Area of a right cone

= Lateral Area(L) + Base Area(B)

All numbers in intermediate calculations are rounded to tenth of centimeter i.e. 1 decimal point

Base Area is the area of the circle with radius 4 = [tex]\displaystyle \pi \cdot16 = 50.3[/tex] cm²
Total Area = 258 cm²

So Lateral Area = 258 - 50.3 = 207.7 cm²

Lateral Area is given by the formula
[tex]\displaystyle L = \pi r s \textrm{ where s is the slant height }[/tex]

So we get

[tex]\displaystyle \rm pi \cdot 4 \cdot s = 207.7\\\\\textrm {This gives } s = \dfrac{207.7}{4\pi} = 16.5\\\\[/tex] cm

Slant height is given by the formula:
[tex]s = \sqrt{r^2 + h^2} \textrm{ where r is the radius and h the height}[/tex]
Plugging in values we get
[tex]16.5 = \sqrt{4^2 + h^2} = \sqrt{16 + h^2}[/tex]

Square both sides
[tex]16.5^2 = 16 + h^2[/tex]

==> [tex]h^2 = 16.5^2 - 16 = 256.25\\\\h = \sqrt{256.25} = 16.003 = 16.0[/tex]  rounded to 1 decimal place

So final answers is h = 16 cm

The retail price of the CD rack is $45.

From the information, the storage rack it's sold to stores at a wholesale price of $18 and the store has a 150% markup.

The retail price will be:

= $18 + (150% ×$18)

= $18 + $27

= $45

Therefore, the retail price of the CD rack is $45.

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If earth is approximately 5×[tex]10^{9}[/tex] years old, the the approximate age of earth is option C 4,953,000,000 years

Given,

The age of Earth =  5×[tex]10^{9}[/tex] years old

We know,

5×[tex]10^{9}[/tex]= 5000000000 years old

From the given option the closest number to 5×[tex]10^{9}[/tex] is 4,953,000,000 years old

Hence, if earth is approximately 5×[tex]10^{9}[/tex] years old, the the approximate age of earth is option C 4,953,000,000 years

Complete question is:

Earth is approximately 5x109 years old. For which of these ages could this be an approximation? Select all that apply.

A. 4.37 x 100 years

B. 4.679999999 x 10º years

C. 4,953,000,000 years

D. 4,625,800,000 years

E. 50,000,000,000 years​

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Answer:21/2

Step-by-step explanation:

Answer:

-7/6

Step-by-step explanation:

If the temperature changes by -7/18 degrees, that shows us that it will continue to decrease, so we can assume the answer will be negative, which means we can get rid of the answers 21/6 and 7/6. If you add and multiply -7 by 3, you'll get -21, which would be -21/18. Then you would simply the answer, giving you -7/6.

Hope this helps!!! :)

By using algebra properties and given that the linear equation 4 · x + 2 · y = 20, the value of (8 · x + 4 · y) / 5 is equal to 8.

Herein we find a linear equation equal to a given number and we are asked to find a number associated with a modified form of the formula, this can be done by using algebra properties. The complete procedure is shown below:

4 · x + 2 · y = 20                               Given

2 · (4 · x + 2 · y) = 20 · 2                  Compatibility with multiplication

8 · x + 4 · y = 40                               Associative and distributive properties

(1 / 5) · (8 · x + 4 · y) = (1 / 5) · 40      Compatibility with multiplication

(8 · x + 4 · y) / 5 = 8                          Multiplication of fractions / Result

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The hours travelled on the highway is 1.3 hours.

The first step is to determine the distance Sam travelled on the city road. The formula that would be used is the average speed formula. The average speed is the ratio of total distance travelled and the total time travelled.

Average speed = distance /time

average speed x time = distance

Distance = 35 x 1.5 = 52.50 miles

The second step is to determine the distance travelled on the highway.

Distance travelled on the high way = 140 - 52.50 = 87.50 miles

Now, determine the total hours travelled:

Hours travelled = distance / average speed

87.50 / 65 = 1.3 hours

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Answer: Sam traveled 1.3 hours.

Step-by-step explanation:

Answer: π=v/(hr^2)

Step-by-step explanation:

v=pi r^2 h solve for pi

v=πhr^2 solve for π

v/h=πhr^2/h

v/h=πr^2

1/r^2 * v/h = πr^2 * 1/r^2

v*1/(h*r^2) = πr^2/r^2

π=v/(hr^2)

Step-by-step explanation:

the ratio is 4:8:5 for Richard, Allan and Fliss.

the sequence is important.

the money pool between them has 4+8+5 = 17 equal units.

Richard has 4 units of these 17, Allan has 8 units, and Fliss has the remaining 5 units.

we don't know the value of such a unit yet.

this we get from the second hint :

Allan gets £9 more than Fliss.

remember, Allan has 8 units, Fliss 5.

so, Allan has 3 units more than Fliss.

that means these 3 units are worth £9.

and that means each unit is worth 9/3 = £3.

Richard has 4 units, that means he has

4×3 = £12

Answer:

Slope = - 3

Step-by-step explanation:

The function of the line:

y = - 3x + 7

=> Slope = - 3

Answer:

your question is did you mean why 2n is 2n 2 serve that this queston with not involved

Side length of Rhombus ABCD is  8+2√2 unit

EFGH is a rectangle :

We know that ,

E, F , G , H are midpoints of AB, BC, CD , DA respectively

Since ABCD is a rhombus

AB = BC = CD = DA

AB ll CD  and BC ll DA

since,  E, F , G , H are midpoints of AB, BC, CD , DA respectively

from the figure below we can say that ,

1) AB ll CD ll FH and AB= CD = FH

2) BC ll DA ll GE and BC = DA = GE

Using mid point theorem we can say that ,

GH = EF = 1/2 AC and FG= EH = 1/2 BD

Since for the figure EFGH opposite sides are equal and and parallel , and the diagonals are equal in length we can say that EFGH is a rectangle.

Perimeter of a rectangle = 2(a+b) = 2( GH + EH ) = 2 (EF + GF) = 2 ( 1/2 AC + 1/2 BD )

= 2 x 1/2 ( AC + BD ) = 16

⇒ AC + BD = 16  (1)

now area of a rectangle is given by

A = ab = GH x EH = EF x GF = 1/2 AC x 1/2 BD = 1/4 (AC x BD) = 14

⇒AC x BD = 14 x 4 = 56

from equation (1)

AC ( 16 - AC) = 56

= 16 AC - AC ^2 = 56

⇒ AC^2 - 16 AC + 56 = 0

AC = 8 +/- 2√2

BD = ( 16 - AC) = 8 +/- 2 √2  = side length of rhombus ABCD

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The probability of getting a number 6 as the first card and a queen as the second card is 4/663.

Probability is mathematically defined as the ratio of the number of outcomes of a particular event or occurrence to the total number of outcomes.

For a standard deck, there are 52 total outcomes since there are 52 cards. A standard deck is divided into four suits - hearts, clubs, spades, and diamonds - with 13 cards each. Each suit has nine numbered cards from 2 to 10, three face cards (king, queen, and jack), and an ace.

The probability of having a numbered 6 card is 4/52. The probability is the same for getting a queen. Although, the probability of getting 6 as the first card and the queen as the second is different. This kind of probability requires the multiplication rule.

First card probability = 4/52

Second card probability = 4/51

The total number of outcomes for the second card is reduced since the first card is not replaced.

Probability (6 then queen) = (4/52)(4/51)

Probability (6 then queen) = 4/663

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The area of the third square is 24 units square.

The squares forms a right angle triangle.

The side length of a square are equal.

Therefore, the side length of each square contribute to the three sides of the right triangle formed. The unknown length of the right triangle is the hypotenuse side of the triangle. That unknown length is the side length of the square.

area of a square = l²

where

area of the first square = l²

√8 = l

l = 2√2 units

area of the second square = l²

√16 = l

l = 4 units

The length of the squares are the legs and hypotenuse of the right triangle formed.

using Pythagoras theorem,

Therefore,

(2√2)² + 4² = c²

16 + 8 = c²

c = √24

c = 2√6 units

area of the third square = (2√6)² = 24 unit²

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