Tell whether this set of numbers is a Pythagorean Triple. (15, 20, 25). Yes or no?

Answer:

the answer is a

Step-by-step explanation:

5x7= 35, 5x8= 40    40-35=5  

After 10 hours the temperature is shown on the graph as 30 degrees.

50 degrees - 30 degrees = 20 degrees.

The temperature dropped 20 degrees in 10 hours.

Divide the change by the time:

20 degrees / 10 hours = 2 degrees per hour.

Because the temperature dropped, the change would be negative.

The answer is D. -2 degrees per hour.

Answer:

Academy A, Arithmetic, and difference makes most sense to me.

Academy A's professional tennis player numbers can be described by an arithmetic sequence due to a constant increase of 10 every year. In contrast, Academy B's numbers can be represented by a geometric sequence because the increase each year is proportionate to the current number of students, at a rate of a 10% increase per year.

The number of players who went on to play professionally at Academy A can be represented by an arithmetic sequence because the numbers of players who went on to play professionally in successive years have a common difference of 10. For Academy A, each year the number increased by a consistent amount, 10 more players, hence the use of an arithmetic sequence.

On the other hand, the number of players who went on to play professionally at Academy B can be represented by a geometric sequence because the numbers of players who went on to play professionally in successive years have a common ratio of 10%. For Academy B, the rate of increase is proportional to the current number of students, which makes it a geometric sequence.

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Answer:

Step-by-step explanation:

The formula for the surface area of a sphere is ...

  A = 4πr²

For a radius of 6 meters, that is ...

  A = 4π(6 m)² = 144π m²

___

The formula for the volume of a sphere is ...

  V = (4/3)πr³ = A·(r/3)

For the same sphere, this is ...

  V = (144π m²)(6 m/3) = 288π m³

Answer:

[tex]5.03\frac{rad}{sec}[/tex]

Step-by-step explanation:

To find the angular velocity divide the revolutions by the time

so

[tex]\frac{16}{20}=0.8\frac{rev}{sec}[/tex]

Remember that

[tex]1\ rev=2\pi \ rad[/tex]

Convert rev/sec to rad/sec

[tex]0.8\frac{rev}{sec}=0.8*(2\pi)=1.6 \pi\frac{rad}{sec}[/tex]

assume [tex]\pi=3.1416[/tex]

[tex]1.6(3.1416)=5.03\frac{rad}{sec}[/tex]

Answer:

5.03

Step-by-step explanation:

Answer:

The answers for your two questions are the following

a)11.606 m

b) As the number of swings approaches infinity

Step-by-step explanation:

We are dealing with an exponential equation  series, where the length of  each swing can be represented as

l = [ 15 *(0.95)^(n-1) ]

n is the corresponding number of the swing.

So, for the first swing, n = 1

[ 15 *(0.95)^(1-1) ] = 15 m

a) How far with the pendulum travel on its 6th swing?

We just need to evaluate the previous formula for n = 6

[ 15 *(0.95)^(6-1) ] =

[ 15 *(0.95)^(5) ] =

[ 15 *(0.7737) ] =

[ 15 *(0.7737) ] = 11.606 m

b) How far will the pendulum swing before it essentially stops? Hint: This is an infinite geometric series.

We previously stated that the length of the arc of each swing can be represented as

l(n)  = [ 15 *(0.95)^(n-1) ]       ,      for n>=1

Since the function approaches zero if and only if n approaches infinity, we can say that the pendulum never stops.

Of course, this only happens mathematically, we can always fin a threshold for which the movement cannot be registered anymore.

Please see attached graph for a representation of the function

Answer:

a) It will travel approx 79.47 meters,

b) It will travel 300 meters.

Step-by-step explanation:

Given,

The initial distance travel on first swing = 15 meters,

Also, Each subsequent swing is 95% of the previous swing.

Thus, there is a G.P. that shows this situation,

Having first term, a = 15,

And, the common difference, r = 95 % = 0.95,

a) Also, for the 6th swing,

Number of terms, n = 6,

Hence, the distance covered by the pendulum on its 6th swing,

[tex]S_{n}=\frac{a(1-r^n)}{1-r}[/tex]

[tex]S_{6}=\frac{15(1-0.95^6)}{1-0.95}[/tex]

[tex]=79.4724328125\approx 79.47\text{ meters}[/tex]

b) When [tex]n=\infty[/tex]

The distance will the pendulum swing before it essentially stops is,

[tex]S_{\infty}=\frac{a}{1-r}[/tex]

[tex]=\frac{15}{1-0.95}[/tex]

[tex]=300\text{ meters}[/tex]

Answer:

a. 0.25

Step-by-step explanation:

The given expression is

[tex]\lim_{x \to 2} \frac{x-2}{x^2-4}[/tex]

Factor the denominator using difference of two squares.

[tex]\lim_{x \to 2} \frac{x-2}{(x-2)(x+2)}[/tex]

Cancel out common factors;

[tex]\lim_{x \to 2} \frac{1}{(x+2)}[/tex]

We plug in 2 to get

[tex]\lim_{x \to 2} \frac{1}{(x+2)}=\frac{1}{2+2}[/tex]

[tex]\lim_{x \to 2} \frac{1}{(x+2)}=\frac{1}{4}=0.25[/tex]

Answer:

The correct answer option is A. 0.25.

Step-by-step explanation:

We are given the following expression and we are to find its limit:

[tex] lim_\left \{ {{ x = 2 } [/tex] [tex] \frac { x - 2 } { x ^ 2 - 4 } [/tex].

First of all, we will simplify the expression by factorizing the term in the denominator:

[tex] \frac { x - 2 } { x ^ 2 - 4 } = \frac { x - 2 } { ( x - 2 ) ( x + 2 ) }[/tex]

Cancelling the common terms to get:

[tex]\frac{1}{x+2}[/tex]

Substituting the given value for x to get:

[tex]\frac{1}{2+2}[/tex] = 0.25

To find a coterminal angle to 800 degrees within the 0 to 360-degree range, divide 800 by 360 and find the remainder, which is 80 degrees. Hence, 80 degrees is the angle that's coterminal with 800 degrees.

To find an angle that is coterminal with 800 degrees, which means an angle that shares the same terminal side as the 800-degree angle but is between 0 degrees and 360 degrees, we use the concept of coterminal angles. Since a complete circle has 360 degrees, we can subtract or add multiples of 360 degrees to any angle to find a coterminal angle.

Here’s how we find it for 800 degrees:

Therefore, 80 degrees is the angle between 0 degrees and 360 degrees that is coterminal with an angle measuring 800 degrees.

Answer:

The total number of digits required in numbering the pages of a book that has 53 pages would be: 97.

Step-by-step explanation:

This answer would be 97 due to the first nine digits being singular.

The next 44 digits are double, so therefore, you multiply 44 by 2, and you end up with 88.

After that, you take 88 and add the 9, which, is 97 digits in total that you would need to number a 53 page book.

Fine the average rate of change by the difference in N over the difference in T:

3000 - 500 / 4-0 = 2500 / 4 = 625

This means for every 1 T, N = 625.

Now multiply 625 by 8:

625 x 8 = 5000

When T = 8 N = 5,000

The decay rate can be found by dividing -ln(2) by the half life.

Decay rate = -ln(2) / 5715 = -0.00012

The answer is 2x−5

see the image

Answer:

The daughter is 36 years old and the son is 12 years old.

Answer:

The expression would be 43x + 128

Step-by-step explanation:

43 dollars is multiplied by however many feet is used.  Then, the exception(the gate) is added to the charge that is 43x

Answer:

9.48

Step-by-step explanation:

The perimeter of a rectangle is the distance around the the shape. It can be found by adding each side of the shape to find a total. In contrast, the area of a shape is the amount inside a shape. It is found using multiplication or A = l*w. Since the width is w and the length is twice its width or 2w, use these expressions in the area formula to find their amount. Then add them together to find the perimeter.

[tex]A = l*w5 = w(2w)\\5 = 2w^2\\2.5 = w^2\\1.58 = w[/tex]

The width of the rectangle is w = 1.58. The length is 2w = 2 (1.58) = 3.16.

Add these amounts by P = l + l + w + w to find the perimeter.

P = 3.16 + 3.16 + 1.58 + 1.58 = 9.48

Answer:

c)

Step-by-step explanation:

if you look at option c it would be correct because 0.75 (3/4) is bigger than 0.7. Then 11/12 is a bigger proportion then 0.75. there for your answer is correct.

The correct order of the numbers given when converted to decimals for easy comparison is 0.7, 3/4 and 11/12, which corresponds to option b: 0.7 < 3/4 < 11/12.

This is a question about comparing and ordering fractions and decimals. To answer this, we first need to convert all the numbers into the same format. We can convert the fractions 11/12 and 3/4 into decimals for easier comparison.

First, to convert 11/12 to a decimal, you'll do the division to find approximately 0.9167. Secondly, 3/4 can be converted to a decimal by performing 3 divided by 4, which equals 0.75. Now, we can easily compare these decimals to 0.7.

From this, we can see that 0.7 is less than 0.75 (3/4) and both 0.7 and 0.75 are less than 0.9167 (11/12). So the correct order of the numbers from least to greatest would be 0.7 < 3/4 < 11/12.

So the correct option is b. 0.7 < 3/4 < 11/12.

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Answer:

-9 C

Step-by-step explanation:

Subtract 4 from -5 will equal -9

Answer:

The answer is 28ft.

Step-by-step explanation:

A radius will always be exactly half of the diameter: meaning, the diameter is double the length of the radius.

Answer:

18.

Step-by-step explanation:

Mean of the values = (70+95+35+90+85) / 5

=  75.

Mean absolute deviation  :-

70 - 75 = |-5|  = 5  (absolute value is taken

95 - 75 = 20

35-75 = 40

90-75 = 15

85-75 = 10

Mean Absolute Deviation = (5 + 20 + 40 + 15 + 10) /  5

= 18.

Answer: 18

Step-by-step explanation: it was correct on ttm

Answer:

Answer: 56*pi

Step-by-step explanation:

The easiest way is to find the area of the circle and subtract the area of the sector.

Area of the circle

d = 16 cm              given

d = 2*r                   definition

16 = 2*r                  divide by 2

16/2 = 2r/2

r = 8

Area of the circle = pi * r^2

Area of the circle = pi * 8^2

Area of the circle = 64 pi

Area of the sector

Area of sector = (theta/360) * pi * r^2

Area of sector = 45/360 * pi * 64

Area of sector = 1/8 * pi * 64

Area of sector = 8 * pi

Area of the shaded area

Area of the shaded area = 64 * pi - 8*pi = 56*pi

Note: There is a shorter way, but one can never be confident of getting an angle greater than 180 correct.

360 - 45 = 315

Area of the sector = 315/360 * pi * r2

Area of the sector = 7/8 * pi * 64

Area of the sector = 7 * pi * 8

Area of the sector = 56*pi

Answer:Michelle paid $56.15 for her shoes

Step-by-step explanation:

Since Michelle paid $3.89 more for her shoes compared to Conrad, who paid $52.26. This means you have to add $3.89 to $52.26.

$3.89+$52.25= $56.15

Final answer:

Michelle paid $56.15 for her shoes, which is $3.89 more than the $52.26 that Conrad paid for his.

Explanation:

The question involves a simple arithmetic calculation to determine how much Michelle paid for her shoes. To find the answer, we will add $3.89, which is the additional amount Michelle paid, to $52.26, which is the amount Conrad paid for his shoes.

Step-by-step calculation:

Therefore, Michelle paid $56.15 for her shoes.

Answer:

Option D. [tex]42.4\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of the cone (juice treats) is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=3/2=1.5\ in[/tex] ----> the radius is half the diameter

[tex]h=3\ in[/tex]

assume

[tex]\pi=3.14[/tex]

substitute

[tex]V=\frac{1}{3}(3.14)(1.5)^{2}(3)=7.065\ in^{3}[/tex]

Multiply the volume of one juice treats by 6

[tex](6)7.065=42.39=42.4\ in^{3}[/tex]

Answer:

the answer is 16Ft^2

Step-by-step explanation:

Square A's area is 9 so take its square root =3

then do the same for Square c =5

then use pythagram theory which is

3^2 + 5^2 = 4^2 = 16

Answer:

area = 16 ft²

Step-by-step explanation:

The area of the green square = 9 ft²

area of the yellow square = 25 ft²

Area of the red square can be computed as follows:

area of a square = L²

Since one side of each triangle forms a part of the triangle knowing the length of sides of the green and yellow triangle can be use to get the sides of the red square and invariably the area.

Green square

L² = 9

square both sides

√L² = √9

L = 3 ft

Yellow square

L² = 25

square both sides

√L² = √25

L = 5 ft

use Pythagoras theorem to get the third side of the triangle which is the b

c² = a² + b²

b² = c²  - a²

a = 3 ft

c = 5 ft

b² =  5² - 3²

b² = 25 - 9

b² = 16

square both sides

√b² = √16

b = 4

Red square

area = L²

area = 4²

area = 16 ft²

Answer:

Step-by-step explanation:

Is a ≤ b < c are the side lengths of a right triangle, then

[tex]a^2+b^2=c^2[/tex]

A. 6cm, 8cm, 10cm.

Substitute:

[tex]6^2+8^2=10^2\\36+64=100\\100=100\to TRUE[/tex]

B. 12cm, 35cm, 37cm.

Substitute:

[tex]12^2+35^2=37^2\\144+1225=1369\\1369=1369\to TRUE[/tex]

C. 4cm, 6cm, 10cm.

It's not the side lengths of a triangle, because 4 + 6 = 10.

Without looking at it, we will check equality

[tex]4^2+6^2=10^2\\16+36=100\\52=100\to FALSE[/tex]

D. 10cm, 24cm, 26cm.

Substitute:

[tex]10^2+24^2=26^2\\100+576=676\\676=676\to TRUE[/tex]

The measurement that could not represent the side length of a right triangle is  4 cm, 6 cm, 10 cm.

A right triangle is a triangle that consists of three sides. The longest side is the hypotenuse. The other sides are the base and the length. The sum of angles in a triangle is 180 degrees.

According to this theorem, the square of the hypotenuse should be equal to the sum of the square of the other two sides.

The Pythagoras theorem: a² + b² = c²

where:

a = length

b = base

c = hypotenuse

6² + 8² = 10²

36 + 64 = 100

Option B = 12² + 35

= √144 + 1225

= √1369

= 37

Option C = 4² + 6²

16 + 36

= √52

= 7.2

Option D: 10² + 24² = 26²

100 + 576

= √676

= 26

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chur answer is gonna be 63787 km

The answer is C because it’s length x width x height

Answer:

C) V = (10)(5)(2)

Step-by-step explanation:

V = (10)(5)(2) To find the volume of a right rectangular prisms, multiply the length times the width times the height. -- V = lwh.

[tex] \cos t (\sec t - \cos t) = \sin^2 t [/tex]

[tex] \cos t (\dfrac{1}{\cos t} - \cos t) = \sin^2 t [/tex]

[tex] \dfrac{\cos t}{\cos t} - \cos^2 t = \sin^2 t [/tex]

[tex] 1 - \cos^2 t = \sin^2 t [/tex]

Use the identity: [tex] \sin^2 t + \cos^2 t = 1 [/tex] and solve for [tex] \sin^2 t [/tex]. You get: [tex] \sin^2 t = 1 - \cos^2 t [/tex]

Do the substitution on the left side to get:

[tex] \sin^2 t = \sin ^2 t [/tex]

[tex] \cos \: t ( \sec \: t - \cos \: t) = \sin^{2}t \\ \\ 1. \: 1 - \frac{ \cos \: t }{ \sec \: t } = \sin^{2} t \\ 2. \: 1 - \cos \: t \cos \: t = \sin^{2} t \\ 3. \: 1 - \cos^{2} t = \sin^{2} t \\ 4. \: 1 - \cos^{2} t - \sin^{2} t = 0 \\ 5. \: 1 - 1 = 0 \\ 6. \: 0 = 0 \\ 7. \: infinitely \: many \: solutions[/tex]

Final answer:

The explicit formula for the salary increases represented as a geometric sequence is a_n= 38,000(1.035)^(n-1), and the recursive formula is a_1= $38,000 and a_n= a_(n-1) × 1.035 for n > 1, reflecting an annual raise of 3.5%.

Explanation:

The starting salary at a company is $38,000 per year with an annual raise of 3.5%. To represent the salary increases as a geometric sequence, we need both explicit and recursive formulas.

The explicit formula for a geometric sequence is an= a1 × r(n-1), where a1 is the first term, r is the common ratio, and n is the term number. In this case, a1= $38,000 and r = 1.035 (since the salary increase is 3.5%, or 0.035 in decimal form, plus the original amount, hence 1 + 0.035). Therefore, the explicit formula is an= 38,000(1.035)(n-1).

The recursive formula defines each term based on the previous term. It can be written as a1= $38,000, an= a(n-1) × 1.035, for n > 1. This means that starting from the second year (when n > 1), the salary is obtained by multiplying the previous year's salary by 1.035.

The answer is: True.

A counterexample is a way that we can prove that something is not true about a mathematical expression or equation, it could be considered as an exception to a rule, so to check if the answer is true or false, we must prove that a counterexample of the given expression is 0°, so:

The given expression is:

[tex]sinytany=cosy[/tex]

Then,

[tex]sin(0)*\frac{sin(0)}{cos(0)}=cos(0)\\\\0*\frac{0}{1}=1\\\\0*0=1\\0=1[/tex]

We can see that the equation is not fulfilled, so 0° is a counterexample of [tex]sinytany=cosy[/tex] and the answer is true.

Have a nice day!

Answer:

x = -1

Step-by-step explanation:

-2 to 2 is 4 units, so -3x + 1 = 4.

We subtract 1 from both sides to get -3x = 3.

Then we divide each side by -3 to get x = -1.