the length of the longer leg of a right triangle is more than twice the length of the shorter leg. the length of the hypotenuse is more than twice the length of the shorter leg. find the side lengths of the triangle.

Answer:

t/sin T = r/sin R

where T and R are the measures of the opposite angles of t and r, respectively.

First, we need to find the measures of T and R in radians:

T = 48° * pi/180 = pi/4

R = 37° * pi/180 = 37 * pi/180

Next, we can use these values in the formula:

t/sin T = r/sin R

t = r * sin T / sin R

t = 71 * sin(pi/4) / sin(37 * pi/180)

Using a calculator, we can estimate t to the nearest 10th of a centimeter:

t ≈ 107.9 cm

So the length of t is approximately 107.9 cm to the nearest 10th of a centimeter.

Answer:87.7

Step-by-step explanation:

The polygons are similar. The  correct similarity statement is JKML ~ PQRS.

Similar polygons are two polygons with the same shape, but different sizes.  If two polygons are similar, then the ratio of the lengths of any two corresponding sides is called the scale factor.

Therefore, the corresponding sides have the same proportion. The corresponding angles of similar polygons are also the same.

Therefore, let's check if the polygons are similar as follows:

Hence,

2.5 / 1.5 = 8  /4.8

Hence, the polygon are similar as follows:

JKML ~ PQRS

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The contrapositive of the statement "if x is irrational, then so is 1/x" is proven.

Proof by contrapositive: Suppose that x is not irrational, meaning that x can be written as a fraction of two integers, x = a/b, where a and b are integers and b ≠ 0.

If x can be written as a fraction of two integers, then 1/x can be written as a fraction as well: 1/x = b/a.

Since 1/x can be written as a fraction of two integers, it follows that 1/x is rational.

Therefore, if x is not irrational (i.e. it is rational), then 1/x is also rational.

Thus, the contrapositive of the statement "if x is irrational, then so is 1/x" is proven.

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149.190781 decibels are emitted from a jet plane with a sound intensity of 8.3 x 102 watts per square meter.

The given formula is:

D = 10 log ([tex]I[/tex] / [tex]I_{0}[/tex])

The intensity of the sound emitted by the jet plane is (I) :

8.3 x 102 watts per square meter

The lowest level of sound that the average person can hear [tex]I_{0}[/tex] :

[tex]10^{-12}[/tex]

Therefore, the intensity of the sound emitted from the given jet plane:

D = 10 log (8.3 x [tex]10^{2}[/tex] / [tex]10^{-12}[/tex])

  = 10 log (8.3 x [tex]10^{2}[/tex] x [tex]10^{12}[/tex] )

  = 10 log (8.3 x [tex]10^{14}[/tex])

  = 10 (log 8.3 + log [tex]10^{14}[/tex])                    (since log (a x b) = log a + log b)

  = 10 (0.9190781 + 14 log 10)             (log 10 = 1)

  = 10 (0.9190781 + 14)

  = 149.9190781  

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Answer:

The type of number -5.41 is a rational number.

Step-by-step explanation:

What type of number is -5.41?

A rational number is a number that can be expressed as a fraction of two integers. 5.41 can be expressed as -5.41 / 1000.

An integer and whole number is a number that does not have any fraction or decimal. -5.41 is a decimal number, thus it is not an integer and a whole number.

The fourth-order Taylor series expansion is

f(x+h) = f(x) + hf'(x) + (h²/2!)f''(x) + (h³/3!)f'''(x) + (h⁴/4! ) )f⁽⁴⁾(x) + ... where a = pi/4

The taylor polynomial with 4 nonzero terms of The function f(x)=sin(4x)f(x)=sin⁡(4x) has a series. find the first 4 nonzero terms in the series is f(x) = 4x - (4x)³ + (4x)⁵ - (4x)⁷ + ...

                                       3!        5!      7!

The taylor polynomial can be calculate as follows:

f(x) = sin(4x)

f' = 4cos(4x)

f'' = -16 sin(4x)

f''' = -64 cos(4x)

f⁽⁴⁾ = 256 sin(4x)

f⁽⁵⁾ = 1024 cos(4x)

The fourth-order Taylor series expansion is

f(x+h) = f(x) + hf'(x) + (h²/2!)f''(x) + (h³/3!)f'''(x) + (h⁴/4! ) )f⁽⁴⁾(x) + ...

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The angle between the ladder and the ground is 78.78

Ladder is a structure for climbing up or down that consists essentially of two long sidepieces joined at intervals by crosspieces on which one may step.

It is given that the length of the ladder is 36 foot and the distance between the base and the ladder is 7 feet.

Here we can see that the hypotenuse is 36 foot and the base is 7 feet.

To find the angle between the ladder and the ground we take the cos inverse of 7÷36

Let the angle between the ladder and the ground is ‘x’.

We know, cosx  = base

                           hypotenuse

⇒ cosx 7

            36

⇒x = cos (-1) 7

                 36

⇒ x = 78.78

Therefore, The angle between the ladder and the ground is 78.78

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The point that is [tex]\sqrt{2}[/tex] units away from the point (-1, 5) is (-1 + [tex]\sqrt{2}[/tex], 5 + [tex]\sqrt{2}[/tex]).

The Pythagorean theorem is a fundamental mathematical principle that relates the lengths of the sides of a right triangle. The theorem states that the square of the length of the hypotenuse (the side opposite the right angle) of a right triangle is equal to the sum of the squares of the lengths of the other two sides. The Pythagorean theorem states that a^2 + b^2 = c^2.

This theorem has many practical applications in mathematics and science, including the calculation of distances, heights, and angles in a variety of geometric and engineering problems. It is also widely used in trigonometry, where the relationship between the sides and angles of a right triangle is studied.

The Pythagorean theorem was named after the ancient Greek mathematician Pythagoras, who is credited with its discovery. However, the theorem was known and used by the Babylonians and Indians well before Pythagoras was born. In fact, the theorem is so important that it is sometimes called the "Pythagorean theorem" despite the fact that it predates Pythagoras by several centuries.

This can be found by using the Pythagorean theorem to find the distance between the two points and then adding or subtracting that distance from the x and y coordinates of the original point.

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llllllllylylylltyllylltlylltl ok bye

The function's multiplicative rate of change will be 0.5. Then, C is the right answer.

Suppose we're trying to determine the multiplication.

To determine the multiplicative power of an item, we just need to divide it by the item immediately preceding it.

Suppose one act is modified

Assume that b is the base, x is the exponent function's power, and an is the leading coefficient.

Exponent is provided as

y = a(b)ˣ

Examples :

Y = 0.125 when x = 2

0.125 = ab² ...1

Y = 0.0625 when x = 3

0.0625 = ab³ ...2

Equation 2 divided by equation 1 yields

b = 0.0625 / 0.125

b = 0.5.

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The complete question is: What is the multiplicative rate of change of the given functions?

a. 1/3

b. 2/3

c. 2

d. 9

Answer:

13.5 sheets of paper have a mass of 300g

Step-by-step explanation:

Since there is a direct correlation between mass and number of sheets, we can find the correlation and then use it as a conversion factor.

We are told that 12 sheets have a mass of 90g.

Make this into a conversion factor:  90g/(12 sheets) = 6.7777 g/sheet

Now use this conversion factor to  answer the question of how many sheets are in 360g.

Let x be the number of sheets required for a mass of 360 g.

 Mass is the product of x times the conversion factor (6.7777 g/sheet):

  x*(6.7777 g/sheet) = 90g

  x =  (90g)/(6.7777 g/sheet)

The units of the right reduce to sheets, since grams cancel and sheets comes to the top.

  X = 13.5 SHEETS

Answer:

At 4:58.

Step-by-step explanation:

The time for the 700th hiccup is 5 * 7000

= 3500 seconds.

= 3500/60

= 58.33 minutes,

When a substrate concentration is much greater than km, the rate of catalysis approaches Vmax.

Km is the Michaelis-Menten constant and represents the substrate concentration at which the reaction rate is half of its maximum rate, Vmax. When the substrate concentration is much greater than km, the rate of catalysis is almost equal to Vmax because the enzymes are saturated with substrate and the reaction rate is limited only by the rate of the catalytic reaction itself, not by the availability of substrate.

In other words, when the substrate concentration is high, there are enough substrate molecules to occupy all of the active sites on the enzymes, so the reaction rate is not limited by the availability of substrate. The reaction rate can only be limited by the rate of the catalytic reaction itself, which is maximum at Vmax.

Therefore, when the substrate concentration is much greater than km, the rate of catalysis approaches Vmax.

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The given argument is invalid by giving values for the predicates p and q over the domain = But both P(a) = p(b) = f There doesn’t exist any x, such that p(x) is true

What is Values?

Depending on where it is in the number, each digit has a different value, which is referred to as value. We figure it out by multiplying the digit's place value by its face value. Place value plus face value equals value. For illustration: If we take 45 into account. Here, the fourth digit is in the tens column.

Given,

fx( p(x) – a(x))

f.(p(x))

fx (a(x))

Let p(a)=T

P(b) = F

And a(a) = T

A(b) = T

So, p(a)=a(a)

=T

P(a) – a(b)

= T

And p(b)=T

So, f.(p(x)-a(x))

Fx(p(x))are T

But we have a (a) + A(b) =T

So, there doesn’t exist any x, such that (x) is true

Hence fX (a(x)) Doesn’t follow from the given statement.

This argument is include

b) fx(p(x) v a(x))

fx (a(x))

fx p(x)

Let P(a) = F

P(b) = F

And a(a) = F

A(b) = T

So, p(b) v a(b) = T

A(a) = F

= ft((x))

But both P(a) = p(b)

= f There doesn’t exist any x, such that p(x) is true

Hence fx p(x)) Dose’t follow from the given statements.

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Subtract 1 from each value in the confusion matrix to change it from 1 to 10 to 0 to 9.

To change a confusion matrix from 1 to 10 to 0 to 9, you need to subtract 1 from each value in the matrix. For example, if your original confusion matrix looks like this:

1     2      3

4    5     6

7    8     9

10   11   12

To convert it to a 0 to 9 range, you need to subtract 1 from each value:

0 1 2

3 4 5

6 7 8

9 10 11

This can be easily done using a loop or by using the -1 operator on the entire matrix. The specific method would depend on the programming language and data structure used to represent the matrix.

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Answer:

Below

Step-by-step explanation:

Since you are working with a number line with decimals. You'll have to convert all of these to decimals.

✓14 and ✓15 would be calculator problems with the following solutions:

✓14 = 3.74

✓15 = 3.87

24/7 is pretty much 24 divided by 7

24/7 = 3.43

Now that you have the 3 in decimal form

✓14 can go between 3.7 and 3.8

✓15 can go between 3.8 and 3.9

24/7 can go between 3.4 and 3.5

The partial derivative of the equation with respect to x at the point (3,-2) is 5.07 thousand dollars per square mile.

The value of the land located at the point (x,y) is calculated by the equation V(x,y) = (150+5x)e^(-0.04x-0.04y). Here, x is measured in miles east of city center and y is measured in miles north of city center. To calculate the value of the land at the point (3,-2), we substitute in the equation x = 3 and y = -2. This gives us V(3,-2) = (150+5*3)e^(-0.04*3-0.04*(-2)) = 181.95. Therefore, the value of the land located at the point (3,-2) is 181.95 thousand dollars per square mile. To calculate the partial derivative of this equation with respect to x, we take the derivative of the equation with respect to x while keeping y constant. This gives us Vx(3,-2) = 5e^(-0.04*3-0.04*(-2)) = 5.07. Therefore, the partial derivative of the equation with respect to x at the point (3,-2) is 5.07 thousand dollars per square mile.

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The two people who have same birthday is 1.

Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are going to happen, using it. Probability can range from 0 to 1, where 0 means the event to be an impossible one and 1 indicates a certain event.

The probability formula is defined as the possibility of an event to happen is equal to the ratio of the number of favorable outcomes and the total number of outcomes.

Assuming no leap year

P (two people in a room and they are sharing a birthday) = 1-(364/365)

P (3 people in a room and at least two of them are sharing birthday) = 1-[tex](\frac{364}{365}[/tex]×[tex]\frac{363}{365} )[/tex]

P (4 people in a room and at least two of them are sharing birthday) = 1-[tex](\frac{364}{365}[/tex] ×[tex]\frac{363}{365}[/tex] ×[tex]\frac{362}{365} )[/tex]

and so on, let n people in a room.

P (n people in a room and at least two of them are sharing birthday = 1-[tex]\frac{365!}{365^n(365-n)!}[/tex] )

we find out the nearly after n = 60 this becomes equals to 1.

Therefore, the two people who have same birthday is 1.

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Answer:

24 = 31.4n + (–8.4)

Step-by-step explanation:

The nine and seven hundredths can be written as 9.07. The solution has been obtained by using decimals.

What are decimals?

Decimals are a form of number in algebra that have a full integer and a fractional portion separated by a decimal point. The decimal point is the dot that separates the whole number from the fractional element of the number.

We are required to write the decimal number of the given words by considering the integral part and the decimal part

So, here the integral part is nine i.e. 9 and the decimal part is seven hundredths i.e. 7/100 = 0.07

Now, after adding both the parts, we get

9 + 0.07 = 9.07

Hence, the nine and seven hundredths can be written as 9.07.

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The missing side of Right triangle will be 9.8.

Angles in trigonometry are those determined by the ratios of the trigonometric functions. In trigonometry, the relationship between a triangle's angles and sides is studied. The angle value is between 0 and 360 degrees. Angles 0°, 30°, 45°, 60°, 90°, 180°, 270°, and 360° are significant in trigonometry.

A subfield of mathematics called trigonometry is concerned with the study of triangles. It is sometimes known by the colloquial term "trig." In trigonometry, mathematicians look at how triangles' sides and angles relate to one another.

We have,

Hypotenuse = 18 cm

Perpendicular = x cm

One of the angle = 33°

Using the Trigonometric angles,

[tex]$${Sin 33^{\circ}=\frac{\text { Perpendicular }}{\text { Hypotenuse }}$[/tex]

substitute the values in the above equation, we get

So, [tex]$${Sin} 33^0=\frac{x}{18}$[/tex]

simplifying the equation, we get

[tex]$$x=18 Sin 33^0$[/tex]

x = 9.8

The missing side is 9.8.

Therefore, the missing side of Right triangle will be 9.8.

The complete question is:

Find the missing side. Round to the nearest tenth.

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Answer:

Why not and what??

Step-by-step explanation:

wait why is that and also that not even a question

Sums of terms with the pattern k.[tex]x^{n}[/tex]—where k is any positive integer and n is an arbitrary number—are known as polynomials. A polynomial is something like 3x+2x-5.

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Answer:

he can buy total snack with $20

four hot dogs and four peanuts

four hot dogs = $12

four peanuts= $6

6 + 12 = 20

Step-by-step explanation:

Answer:

Either 63.5 + 76.5 + 2x = 180 or some variation of it.

Step-by-step explanation:

The sum of all the angles in a triangle equals 180 so any answer would have to add up the three angles given and set them equal to 180.

If none of the answers on your end match anything I've wrote, try to write the answer choices in the comments or add a picture so I can further help you.

If Mirka is 5 years old, her parents start to give her pocket money of 50p per week , then the amount of pocket money does Mirka get in the first year is £26 .

the amount that Mirka gets per week is = 50p ;

Age of Mirka is = 5 years ;

When Mirka is 5 years old, she starts to receive 50p per week in pocket money. On her birthday, her parents increase her pocket money by 50p.

that means ;

So, for the first year, the pocket money will be 50p per week for 52 weeks (1 year),

Pocket money in the first year = 50p × 52 weeks = £26 .

Therefore , Mirka will get £26 in the first year of her birthday .

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[tex]3(4-x)=18[/tex]

Distribute everything outside of parentheses:

[tex](3)(4)+(3)(-x)=18[/tex]

[tex]-3x+12=18[/tex]

Subtract 12 from both sides:

[tex]-3x+12-12=18-12[/tex]

[tex]-3x=6[/tex]

Divide both sides by -3:

[tex]\dfrac{-3x}{-3} =\dfrac{6}{-3}[/tex]

[tex]\fbox{x = -2}[/tex]

Answer:

[tex] \sf \: x = - 2[/tex]

Step-by-step explanation:

Given equation,

→ 3(4 - x) = 18

Now the value of x will be,

→ 3(4 - x) = 18

→ 12 - 3x = 18

→ -3x = 18 - 12

→ -3x = 6

→ x = 6 ÷ (-3)

→ [ x = -2 ]

Hence, the value of x is -2.

Answer: 630 rabbits

Step-by-step explanation: it shows that the population of rabbits grows by 70 each 4 years so we will have to add 70 to 560 which is 630 rabbits.

The population of rabbits in the year 2014 will be growing exponentially.

So, we can write a function

P = A · [tex]\alpha ^{x}[/tex]

where,

A is the original rabbits

[tex]\alpha[/tex] is the ratio of the increase

[tex]x[/tex] is the time (the unit is year)

In 2004, the population of the rabbits was 490

∴ P = 490 · [tex]\alpha ^{x}[/tex]

In 2008, the population increases to 560

∴ 560 = 490 · [tex]\alpha ^{2008-2004}[/tex]

   560 = 490 · [tex]\alpha ^{4}[/tex]

  [tex]\alpha ^{4\\[/tex] = [tex]\frac{560}{490}[/tex] = [tex]\frac{8}{7}[/tex]

  [tex]\alpha[/tex]   = [tex]\sqrt{\frac{2\sqrt{14} }{7} }[/tex]

In 2014, x = 2014- 2004 = 10

P = 490 · [tex]\sqrt{\frac{2\sqrt{14}}{7} } ^{10}[/tex]

  ≅ 684

Hence, the population of rabbits in the year 2014 will be approximately 684.

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