write a Pythagorean triplet whose smallest member is 6​

It is true that the line segment AB equals 26

The given parameters are:

AB = x +16

BC = 4x + 11

AC = 77

The two-column proof is as follows:

AC = AB + BC                     Line segment formula

77 = x + 16 + 4x + 11            Substitution property of equation

77 = 5x + 27                        Addition property of equation

5x = 50                               Subtraction property of equation  

x = 10                                    Division property of equation

AB = 10 +16                          Substitution property of equation

AB = 26

Hence, the line segment AB has been proved to equal 26

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Given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

Note that: Area of a circle is expressed as;

A = πr²

Where r is radius and π is constant pi ( π = 3.14 )

Given that;

A = πr²

A = 3.14 × ( 35cm )²

A = 3.14 × 1225cm²

A = 3846.5cm²

Therefore, given the diameter of the surface of the clock, the area of the surface of the alarm clock is 3846.5cm².

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Considering the definition of exponential function, the value of the car is 11,287.25 dollars.

An exponential function is one in which the independent variable x appears in the exponent and has a constant a as its base. Its expression is:

f(x)= aˣ

Being a a positive real, a > 0, and different from 1, a ≠ 1.

When 0 < a < 1, then the exponential function is a decreasing function and when a > 1, it is an increasing function.

In this case, the value of that car depreciates based on the function f(t)=12,000×[tex]0.96^{t}[/tex] where t is measured in years after purchase.

After 3/2 years, the value of the car is calculated as:

f(3/2)=12,000×[tex]0.96^{3/2}[/tex]

Solving:

f(3/2)= 11,287.25

Finally, the value of the car is 11,287.25 dollars.

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Answer: Yes it is possible

Example: Yeast is a single-celled fungus.

There are probably other types of fungus that are single-celled. However, some other fungi are multi-celled. You will likely need more information about the organism under the microscrope before you can classify it properly.

Answer:

tiookvgvc. jbjvth kivtcth jjvf h. bkbgv

Answer:

The IQR of the given distribution is

Step-by-step explanation:

The given distribution has the five-number

28, 34, 43, 59, 62

Divide these numbers in two equal parts.

(28, 34), 43,( 59, 62)

Now divide each parenthesis in two equal parts.

(28), (34), 43,( 59), (62)

It means first quartile is the average of 28 and 34. Third quartile is the average of 59 and 62.

The interquartile range (IQR) of this distribution is

Therefore the IQR of the given distribution is 29.5.

(1) The missing term in the sequence, a₁₂  = 0.8.

(2) The missing term in the sequence, a₈ = 102.5.

(3) The missing term in the sequence, a₈ = 111.

(4) The missing term in the sequence, a₁₂ = -19.

(5) The missing term in the sequence, a₁₂ = 94.

(6)  The missing term in the sequence, a₆ = 40.

(7)  The missing term in the sequence, a₃₆ = -52.

(8)  The missing term in the sequence, a₂₁ = -58.

The missing term in the sequence is determined as follows;

Tₙ = a + (n - 1)d

T₄ = a + 3d

18.4 = a + 3d  ---(1)

T₅ = a + 4d

16.2 = a + 4d  ---(2)

subtract (1) from (2)

-2.2 = d

18.4 = a + 3(-2.2)

a = 25

a₁₂  = a + 11d

a₁₂  = 25 + 11(-2.2)

a₁₂  = 0.8

a₂ = a + d

57.5 = a + d -- (1)

a₅ = a + 4d

80 = a + 4d  --- (2)

solve (1) and (2)

d = 7.5

a = 50

a₈ =  a + 7d

a₈ = 50 + 7(7.5)

a₈ = 102.5

a₁₀ = a + 9d

141 = a + 9d --- (1)

a₁₃ = a + 12d

186 = a + 12d --- (2)

Subtract (1) from (2)

d = 15

a = 6

a₈ = a + 7d

a₈ = 6 + 7(15)

a₈ = 111

a₂₂ = a + 21d

-49 = a + 21d ---- (1)

a₂₅ = a + 24d

-58 = a + 24d --- (2)

subtract (1) from (2)

d = -3

a = 14

a₁₂ = a + 11d

a₁₂ = 14 + 11(-3)

a₁₂ = -19

a₄ = a + 3d

-2 = a + 3d --- (1)

a₈ = a + 7d

46 = a + 7d ---- (2)

Subtract (1) from (2)

d = 12

a = -38

a₁₂ = a + 11d

a₁₂ = -38 + 11(12)

a₁₂ = 94

a₉ = a + 8d

64 = a + 8d --- (1)

a₁₂ = a + 11d

88 = a + 11d --- (2)

Subtract (1) from (2)

d = 8

a = 0

a₆ = a + 5d

a₆ = 0 + 5(8)

a₆ = 40

a₂₀ = a + 19d

-4 = a + 19d ---- (1)

a₂₃ = a + 22d

-13 = a + 22d --- (2)

Subtract (1) from (2)

d = -3

a = 53

a₃₆ = a + 35d

a₃₆ = 53 + 35(-3)

a₃₆ = -52

a₂₈ = a + 27d

5 = a + 27d ---- (1)

a₃₃ = a + 32d

50 = a + 32d --- (2)

Subtract (1) from (2)

d = 9

a = -238

a₂₁ = a + 20d

a₂₁ = -238 + 20(9)

a₂₁ = -58

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Answer:

-50

Step-by-step explanation:

1 - 2 + 3 - 4 + 5 - 6 + 7 - 8...99 - 100

just means,

1 - 2 = -1

3 - 4 = -1

5 - 6 = - 1

7 - 8 = - 1

99 - 100 = -1

basically, -1 + -1 + -1 + -1 + ....+ -1 or -1 - 1 - 1 - 1 - ... - 1

[tex](-1)^{n}[/tex]

Treating Grandi's series as a divergent geometric series we may use the same algebraic methods that evaluate convergent geometric series to obtain a third value:

S = 1 − 1 − 1 + ..., so

1 − S = 1 − (1 − 1 − 1 ...) = 1 − 1 − 1 ... = S

1 - S = S

1 = 2*S

resulting in S = 1/2. The same conclusion results from calculating −S, subtracting the result from S, and solving 2S = 1

1/2 of the last term is 100 x 1/2 = 50

This because you are using 2 numbers per -1

example: 1 - 2 = -1 or 3 - 4 = -1 resulting in 50 of the -1 being subtracted

[tex]\text{Nth term of an arithmetic series} = a +(n-1)d \\\\\text{Nth term of an geometric series}= ar^{n-1}\\\\\text{where,}\\\\\text{a = first term.}\\\\\text{d = common difference.}\\\\\text{r = common ratio.}[/tex]

Answer:

√121 = 11

Explanation:

11 × 11 = 121

Answer:

11

Step-by-step explanation:

The square root of 121 is 11.

= 11*11 = √(121)

= 121 = 11

done

Answer:

67m²

Step-by-step explanation:

12m + 6m + 4m + 36 m 8m = 67m²

Answer:

51 pounds, 48 pounds, 44 pounds and 40 pounds in that chronological order.

Answer:

D) 9

Step-by-step explanation:

x = ½ × 13 = 6.5

y = ½ × 5 = 2.5

6.5 + 2.5 = 9

So the length of PC is 9

HOPE THIS HELPS AND HAVE A NICE DAY <3

Two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.

Multiplication is one of the four basic arithmetic operations, alongside addition, subtraction, and division. Multiplication essentially means the repeated addition.

The two given numbers are -84 and 17.

We need to write two numbers that multiply to the value on top (-84) and add to the value on the bottom (17).

If we multiply 21 and -4, we get the product as -84.

That is, 21×(-4)=-84

If we add 21 and -4, we get the sum as -17.

That is, 21+(-4)=21-4=17

Therefore, two numbers multiply the value on top (-84) and add to the value on the bottom (17) is 21 and -4.

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The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the length of the field and y represent the width of the field, hence:

Deion has 62 m of fencing:

2(x + y) = 62

x + y = 31

y = 31 - x     (1)

The area of the land is 228 square meters. hence:

xy = 228

x(31 - x) = 228

x² - 31x + 228 = 0  

x = 12 or x = 19

when x = 12; y = 31 - 12 = 19

when x = 19; y = 31 - 19 = 12

The dimensions of the the plot of land is a length of 19 meters and width of 12 meters.

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The length of the intervals of the given frequency table is

500 ft.

The given list shows the lengths in feet of the 25 longest bridges in the United States.

we have to determine the median and mode of the bridge data.

The median is the middle number of the data set arranged in ascending order.

1010, 1053, 1200, 1207, 1380, 1470, 1495, 1596, 1600, 1600, 1600, 1632, 1750, 1800, 1850, 2000, 2150, 2150, 2300, 2310, 2800, 3500, 3800, 4200, 4260.

The median is 1750.

Mode is the number that appears most often in the data set.

1010, 1053, 1200, 1207, 1380, 1470, 1495, 1596, 1600, 1600, 1600, 1632, 1750, 1800, 1850, 2000, 2150, 2150, 2300, 2310, 2800, 3500, 3800, 4200, 4260

The mode is 1600.

Therefore the correct option is Median: 1750, Mode: 1600

So the length of the intervals of the given frequency table is

500 ft.

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Answer:

y = 9

Step-by-step explanation:

given that y varies inversely as x then the equation relating them is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

to find k use the condition y = 12 when x = 6

12 = [tex]\frac{k}{6}[/tex] ← multiply both sides by 6 to clear the fraction

72 = k

y = [tex]\frac{72}{x}[/tex] ← equation of variation

when x = 8 , then

y = [tex]\frac{72}{8}[/tex] = 9

Step-by-step explanation:

Scale factor red to blue meaning 42 to 7

42÷7=6

Scale factor is 6

Perimeter of the blue quadrilateral = ?

If perimeter of red = 204

Then we use this following proportion

[tex]204 \div 42 = x \div 7[/tex]

[tex] \frac{204}{42} = \frac{x}{7} [/tex]

Then we cross multiply

42x=7×204

42x=1428

x=34

Area of the blue quadrilateral = ?

If area of the red quadrilateral = 2880

Then we use the following proportion

[tex]2880 \div 42 = x \div 7[/tex]

[tex] \frac{2880}{42} = \frac{x}{7} [/tex]

Then we cross multiply

42x=2880×7

42x=20160

x=480

Answer:

Hi,

Step-by-step explanation:

sin(a-b)=sin(a) cos(b)+ cos(a) sin(b)

a=45° and b=30°

[tex]sin(45^o-30^o)=sin(45^o)*cos(30^o)+cos(45^o)*sin(30^o)\\\\=\dfrac{\sqrt{2}}{2}* \dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{2}}{2}*\dfrac{1}{2}\\\\\\\boxed{sin(15^o)=\dfrac{\sqrt{2}}{4}*(1+\sqrt{3} )}\\[/tex]

Family background refers to the culture and tradition of the family into which a person is born.

Family background refers to the culture and tradition of the family into which a person is born. it is worthy of note that most of this family traditions are unspoken yet are firmly entrenched in the psyche of individual as he/she grows.

My family is strictly conservative having  had a Southern Baptist orientation. My dad believes deeply in  religion and a moralist and perfectionist.

As a  result of this, I find myself always grappling with the unfortunate disorder in the world; always trying to bring order to my world as much as I can.

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Answer:

none of the above

Step-by-step explanation:

4x + 7 = x + 2

4x - x + 7 = x - x + 2

3x + 7 = 2

3x + 7 - 7 = 2 - 7

3x = -5

3x / 3 = -5 / 3

x = -5 / 3 = -1.667

5x - 8 = x + 4

5x - x - 8 = x - x + 4

4x - 8 + 8 = 4 + 8

4x = 12

4x / 4 = 12 / 4

x = 3

3x + 2 = 5x + 2

3x - 5x + 2 = 5x - 5x + 2

-2x + 2 = 2

-2x + 2 - 2 = 2 - 2

-2x = 0

x = 0

Integers, As a whole number that can be written without a remainder,

x = 3

x = 0

(Mixed) Fraction

x = -5 / 3 = -1.667

If the definitions of type I and type II regions is the same as in the link provided, then as a type I region the integration domain is the set

[tex]R_{\rm I} = \left\{(x,y) \mid 0 \le x \le 3 \text{ and } \sqrt{x+1} \le y \le 2\right\}[/tex]

and as a type II region,

[tex]R_{\rm II} = \left\{(x,y) \mid 0 \le x \le y^2-1 \text{ and } 1 \le y \le 2\right\}[/tex]

where we solve y = √(x + 1) for x to get x as a function of y.

A. The area of the type I region is

[tex]\displaystyle \iint_{R_{\rm I}} dA = \int_0^3 \int_{\sqrt{x+1}}^2 dy \, dx = \int_0^3 (2 - \sqrt{x+1}) \, dx = \boxed{\frac43}[/tex]

B. The area of the type II region is of course also

[tex]\displaystyle \iint_{R_{\rm II}} dA = \int_1^2 \int_0^{y^2-1} dx \, dy = \int_1^2 (y^2-1) \, dy = \boxed{\frac43}[/tex]

I've attached a plot of the type II region to give an idea of how it was determined. The black arrows indicate the domain of x as it varies from the line x = 0 (y-axis) to the curve y = √(x + 1).

The total area with land based on the information given is 3x² + 60x.

Let the width = x

Let the length = (1.5 × x) = 1.5x

Area = 1.5x × x = 1.5x²

The area along with land:

Width = x + 20

Length = 3 × x = 3x

The total area with land:

= Length × Width

= 3x(x + 20)

= 3x² + 60x.

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Answer:

175 ft^2

Step-by-step explanation:

split the pentagon into 5 triangles with base length 10ft and height 7ft. each triangle then has an area of 10 * 7 * 1/2 = 35 ft^2

then the pentagon has an area 35*5 = 175 ft^2

Answer:

[tex]31.8\%[/tex]

Step-by-step explanation:

The area of the circle is [tex]A=\pi r^2=\pi(4)^2=16\pi[/tex]

The area of the triangle is [tex]A=\frac{bh}{2}=\frac{8*4}{2}=\frac{32}{2}=16[/tex]

Hence, the probability of a randomly selected point within the circle falls in the red shaded area is [tex]\frac{16}{16\pi}=\frac{1}{\pi}\approx0.318\approx31.8\%[/tex]

Answer:

  4 square units

Step-by-step explanation:

The vertices of the figure are on grid points, so it is appropriate to use Pick's theorem to find the area.

__

Pick's theorem tells you the area is ...

  A = i +b/2 -1

where i is the number of grid points interior to the figure (0), and b is the number of grid points on the boundary (10).

Using the counted values in the formula, we find the area to be ...

  A = 0 +10/2 -1 = 4

The area of the polygon is 4 square units.

_____

Additional comment

There are several other ways to find the area. Here are a couple:

decompose the figure

A horizontal line 1 unit up from the bottom will divide the figure into a trapezoid and a triangle. The trapezoid has bases 4 and 1, and height 1, so its area is ...

  A = 1/2(b1 +b2)h = 1/2(4 +1)(1) = 5/2

The triangle has base 1 and height 3, so its area is ...

  A = 1/2bh = 1/2(1)(3) = 3/2

Then the total area is 5/2 +3/2 = 8/2 = 4 square units.

subtract empty space

The figure occupies a 4×4 square with triangles removed from the left side and the top. Each of those triangles has a base of 4 and a height of 3. The remaining (shaded) area is ...

  A = s² -1/2bh -1/2bh

  A = 4² -1/2(4)(3) -1/2(4)(3) = 16 -12 = 4 square units