The area of the right triangle shown is 24 square feet. Which equations can be used to find the lengths of the legs of the triangle? Select three options. 0.5(x)(x + 2) = 24 x(x + 2) = 24 x2 + 2x – 24 = 0 x2 + 2x – 48 = 0 x2 + (x + 2)2 = 100

Answer:

x = 2v-3y

Step-by-step explanation:

x+3y=2v

x = 2v - 3y    [  rearrange and transpose 3y to the other side making it negative]

I hope im right!

Answer:  1/30 fraction of the songs in Devin's music library are rock songs that feature a guitar solo.

To find the fraction of songs in Devin's music library that are rock songs featuring a guitar solo, we can multiply the fractions.

The fraction of rock songs in Devin's music library is 1/3, and the fraction of rock songs featuring a guitar solo is 1/10. Multiplying these fractions, we get (1/3) * (1/10) = 1/30.

Therefore, 1/30 of the songs in Devin's music library are rock songs that feature a guitar solo.

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50 different greek armies, the upper class and the lower class soldiers battalions can be sent.

The Greek army can form different battalions by choosing 4 upper class soldiers and 8 lower class soldiers from a total of 5 upper class soldiers and 10 lower class soldiers. This problem can be solved using a combination formula known as a binomial coefficient.

The number of different battalions that can be sent is:

(5 choose 4) * (10 choose 8) = 5*10 = 50

Different battalions can be formed by choosing 4 upper class soldiers and 8 lower class soldiers from a total of 5 upper class soldiers and 10 lower class soldiers. Therefore, 50 different battalions can be sent.

So, 50 different battalions can be sent.

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Answer:

2/3 pages per minute

Step-by-step explanation:

First we do 6/9. Then simplyfy. This equals 2/3. (I'm sorry if this is incorrect! )

Answer:

2.

Step-by-step explanation:

To find the number of trailing zeroes, given n!, we take n and divide it by increasing powers of 5. For example, the number of trailing zeroes in 50! = 50/5 = 10, 50/25 = 2, 10 + 2 = 12 trailing zeroes.

In this case, 10/5 = 2, and since we cannot get an integer from dividing 10 and 25, we are left with this answer.

I hope this helps!

Answer:

499

Step-by-step explanation:

Answer:

300 ft³

Step-by-step explanation:

The easiest thing to do is to separate it into 3 cuboids.  Then work out the volumes of each cuboid and add them together.

Volume of a cuboid = width x height x depth

The left cuboid has a width of 12 - 5 - 4 = 3 ft

From inspection, it has a height of 4 ft and a depth of 5ft.

So the volume of this is 3 x 4 x 5 = 60 ft³

The middle cuboid has a height of 6 + 2 = 8 ft

From inspection, it has a width of 5ft and a depth of 5ft

So the volume of this is  8 x 5 x 5 = 200 ft³

Finally, the right cuboid has a width of 4ft, a height of 2 ft and a depth of 5ft.  So the volume is 4 x 2 x 5 = 40 ft³

Therefore, the total volume = 60 + 200 + 40 = 300 ft³

The horizontal distance between the base of the ladder and the wall is approximately 8.892 feet.

Here, we have,

To find the horizontal distance between the base of the ladder and the wall, we can use trigonometric functions.

In this case, the ladder forms an angle of 69 degrees with the ground. We can label this angle as θ.

We know the length of the ladder is 26 feet. We can label the horizontal distance as x.

Using trigonometric functions, specifically cosine, we have:

cos(θ) = adjacent/hypotenuse

cos(69) = x/26

To find x, we can rearrange the equation:

x = 26 * cos(69)

Using a calculator, we can calculate:

x ≈ 26 * 0.3420

x ≈ 8.892

Therefore, the horizontal distance between the base of the ladder and the wall is approximately 8.892 feet.

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the breadth of the rectangle is 3

A rectangle is composed of two sides: length (L) and width (W). The length of a rectangle is the longest side, whereas the width is the shortest side. The width of a rectangle is sometimes referred to as the breadth (b).

Area =9x -6 ,

length=3x-2,

 breath =?​

Therefore, the area of a rectangle formula states that:

Area of rectangle = Length x Width

A = L * W, where A is the area, L is the length, W is the width or breadth.

now put the given value in the formula

9x-6 = (3x-2 )*W

3( 3x -2) / (3x-2) = W

W =3

Hence , the breadth of the rectangle is 3

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This directly proportional relationship between p and q is written as p∝q  where that middle sign is the sign of proportionality. The value of y can be found as shown below.

Let there are two variables p and q

Then, p and q are said to be directly proportional to each other if

 p = kq

where k is some constant number called the constant of proportionality.

This directly proportional relationship between p and q is written as

 p∝ q  where that middle sign is the sign of proportionality.

In a directly proportional relationship, increasing one variable will increase another.

Now let m and n be two variables.

Then m and n are said to be inversely proportional to each other if

\(m = \dfrac{c}{n} \\\\ \text{or} \\\\ n = \dfrac{c}{m}\)

(both are equal)

where c is a constant number called the constant of proportionality.

This inversely proportional relationship is denoted by

\(m \propto \dfrac{1}{n} \\\\ \text{or} \\\\n \propto \dfrac{1}{m}\)

As visible, increasing one variable will decrease the other variable if both are inversely proportional.

1.) The relation can be written as,

y ∝ x

y = kx

27 = k × 3

k = 9

Value of y, when x=4 is,

y = 9 × 4 = 36

2.)  The relation can be written as,

y ∝ x²

y = k x²

160 = k × 4²

160 = k × 16

k = 10

Value of y, when x=6 is,

y = 10 × 36 = 360

3.) The relation can be written as,

y ∝ (1/x)

y = k/x

16 = k × (1/2)

k = 32

Value of y, when x=17 is,

y = 32 × (1/17) = 1.8823

4.)  The relation can be written as,

y ∝ (1/x²)

y = k(1/x²)

64 = k × (1/4²)

64 = k × (1/16)

k = 1024

Value of y, when x=7 is,

y = 1024 × (1/49) = 20.8979

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Answer:

SO... y=3x+0b

Or... y = -3x+0b

Step-by-step explanation:

-4°F is equal to -20°C, or 253°K, which is the temperature above absolute zero. Thus, the temperature at midnight was 759°K, or almost 1400°F.

The physical concept of temperature indicates in numerical form how hot or cold something is.

A thermometer is used to determine temperature.

Thermometers are calibrated using a variety of temperature scales, which historically defined distinct reference points and thermometric substances.

The most popular scales are the Celsius scale, sometimes known as centigrade, with the unit symbol °C, the Fahrenheit scale (°F), and the Kelvin scale (K), with the latter being mostly used for scientific purposes. One of the seven base units in the International System of Units is the kelvin (SI).

The lowest point on the thermodynamic temperature scale is absolute zero, or zero kelvin, or 273.15 °C. It can be very closely approximated experimentally but never actually reached, as stated in the third rule of thermodynamics.

Hence, -4°F is equal to -20°C, or 253°K, which is the temperature above absolute zero. Thus, the temperature at midnight was 759°K, or almost 1400°F.

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Answer:

1,500 G

Step-by-step explanation:

1 Kilogram (Kg) = 1,000 Grams (G)

8-6.5= 1.5

1.5x1,000=1,500

Answer:

24%

Step-by-step explanation:

x-(11/100)x

89/100x

followed by

89/100x-13/100x

76/100x

so the total decrease is calculated as

x-76/100x

(24/100)x

i.e 24% decrease

P(80 < X < 125) = 0.9525 - 0.0918

P(80 < X < 125) = 0.8607

This means that approximately 86.07% of people have IQ scores between 80 and 125.

To answer this question, we need to calculate the standardized score (also known as z-score) for both 80 and 125:

z-score for 80: (80-100)/15 = -1.33

z-score for 125: (125-100)/15 = 1.67

Once we have the z-scores, we can use a standard normal distribution table or calculator to find the proportion of scores between them. Alternatively, we can use the following formula:

P(80 < X < 125) = P(Z < 1.67) - P(Z < -1.33)

Using a standard normal distribution table or calculator, we can find that P(Z < 1.67) is approximately 0.9525 and P(Z < -1.33) is approximately 0.0918.

Therefore:

P(80 < X < 125) = 0.9525 - 0.0918

P(80 < X < 125) = 0.8607

This means that approximately 86.07% of people have IQ scores between 80 and 125.

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Answer:

DC like the DC superheroes

Step-by-step explanation:

Question 1a

To calculate the book value at the end of the first year using straight-line depreciation, we need to determine the annual depreciation expense first. The straight-line method assumes that the asset depreciates by an equal amount each year over its useful life. Therefore, we can use the following formula to calculate the annual depreciation:

Annual Depreciation = (Cost - Salvage Value) / Useful Life

Substituting the given values, we get:

Annual Depreciation = ($200,000 - $20,000) / 10 years = $18,000 per year

This means that the tractor will depreciate by $18,000 each year for the next 10 years.

To determine the book value at the end of the first year, we need to subtract the depreciation expense for the year from the original cost of the tractor. Since one year has passed, the depreciation expense for the first year will be:

Depreciation Expense for Year 1 = $18,000

Therefore, the book value of the tractor at the end of the first year will be:

Book Value = Cost - Depreciation Expense for Year 1

= $200,000 - $18,000

= $182,000

So the book value of the tractor at the end of the first year, December 31, 2022, using straight-line depreciation is $182,000. so the answer is D

Question 1(b)

To determine the farmer's noncurrent liabilities, we need to use the information provided to calculate the total liabilities and then subtract the current liabilities from it. Here's the step-by-step solution:

Calculate the total current liabilities using the current ratio:

Current Ratio = Current Assets / Current Liabilities

2 = $80,000 / Current Liabilities

Current Liabilities = $80,000 / 2

Current Liabilities = $40,000

Calculate the total liabilities using the debt/equity ratio:

Debt/Equity Ratio = Total Liabilities / Owner Equity

1.0 = Total Liabilities / $100,000

Total Liabilities = $100,000 * 1.0

Total Liabilities = $100,000

Subtract the current liabilities from the total liabilities to get the noncurrent liabilities:

Noncurrent Liabilities = Total Liabilities - Current Liabilities

Noncurrent Liabilities = $100,000 - $40,000

Noncurrent Liabilities = $60,000

Therefore, the farmer's noncurrent liabilities are $60,000. so the answer is B.

To verify if each given function is a solution of the differential equation, we need to substitute the function into the differential equation and check if the equation holds true.

For the differential equation y" - 4y = 0:

a) Substitute y(t) = e^(2t):

y" = (e^(2t))'' = 4e^(2t)

4y = 4e^(2t)

The equation y" - 4y = 0 holds true.

b) Substitute y(t) = cosh(t):

y" = (cosh(t))'' = cosh(t)

4y = 4cosh(t)

The equation y" - 4y = 0 holds true.

For the differential equation y" + 2y - 3y = 0:

a) Substitute y(t) = e^(-3t):

y" = (-3e^(-3t))

2y = 2e^(-3t)

The equation y" + 2y - 3y = 0 holds true.

b) Substitute y(t) = e^(t):

y" = e^(t)

2y = 2e^(t)

The equation y" + 2y - 3y = 0 holds true.

For the differential equation 12y" + 5ty' + 4y = 0, t > 0:

a) Substitute y(t) = t^2:

y" = 2

y' = 0

5ty' = 0

12y" + 5ty' + 4y = 12(2) + 0 + 4(t^2) = 24 + 4t^2

The equation 12y" + 5ty' + 4y = 0 holds true.

b) Substitute y(t) = t^2:

y" = 2

y' = 0

5ty' = 0

12y" + 5ty' + 4y = 12(2) + 0 + 4(t^2) = 24 + 4t^2

The equation 12y" + 5ty' + 4y = 0 holds true.

For the differential equation y" + y = sec(t):

a) Substitute y(t) = sec(t):

y" = sec(t)tan(t)

y = sec(t)

The equation y" + y = sec(t) holds true.

b) Substitute y(t) = sec(t):

y" = sec(t)tan(t)

y = sec(t)

The equation y" + y = sec(t) holds true.

Therefore, each given function is a solution to its respective differential equation.

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4. We start with the base case of \(5^0 = 1\) and recursively generate the next element in the set by multiplying the previous element by \(5\).

5. if a divides \(b\) and \(b\) divides \(a\), either a equals \(b\) or \(a\) equals negative \(b\).

4. The recursive definition of the set of positive integer powers of 5 can be expressed as follows:

Base case: \(5^0 = 1\) is in the set.

Recursive step: If n is in the set, then \(5^(n+1)\) is also in the set.

Using this definition, we start with the base case of \(5^0 = 1\)and recursively generate the next element in the set by multiplying the previous element by \(5\).

5. To prove that if a divides \(b\) and \(b\)divides \(a\), then a equals \(b\) or \(a\) equals negative \(b\), we can use the definition of divisibility.

Assume that \(a\) divides \(b\), denoted as \(a | b\) , and \(b\) divides \(a\), denoted as \(b | a.\)

By definition, if a divides b, there exists an integer k such that b = ak.

Similarly, if \(b\) divides \(a\), there exists an integer m such that \(a = bm.\)

Substituting the expression for\(b\) in terms of \(a\), we have \(bm = ak.\)

Dividing both sides by b (since b is nonzero), we get m = a/b.

Since \(m\) is an integer, \(a/b\) must be an integer, which means \(a\) is divisible by \(b\).

If \(a/b\)  is an integer, it implies that \(b/a\)is also an integer, which means \(b\) is divisible by \(a\).

Therefore, if \(a\) divides \(b\) and \(b\) divides \(a\), it follows that \(a/b\) and \(b/a\) are both integers.

If \(a/b = m\) and \(b/a = k\), then we have \(a = bm\) and\(b = ak.\)

\(If m = k = 1, then $a = b.\)

\(If m = k = -1, then a = -b.\)

Therefore, if \(a\) divides \(b\) and \(b\) divides \(a\), either \(a\) equals \(b\) or \(a\) equals negative \(b\).

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8 percentage of the buttons were large. The solution has been obtained using arithmetic operations.

What are arithmetic operations?

There are four fundamental operations that all real numbers in mathematics must comprehend:

1. Adding the numbers together to get their total (with a "+").

2. Using the "-" sign to subtract two numbers yields the difference between the values.

3. Multiplication('×') is used to create the numbers' product.

4. The division('÷') procedure, which determines the numbers' quotient.

We are given that Victoria bought a bag of mixed buttons and she got 12 large buttons and 138 small buttons.

So, the total number of buttons = 138 + 12 = 150

Out of 150, she got 12 large buttons.

So, percentage of large buttons = 12*100/150 = 8%

Hence, 8 percentage of the buttons were large.

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Answer:

=4x2+12x+9

hope it helps you!

Step-by-step explanation:

Answer:

4x2−12x+9

Step-by-step explanation:

expand using the foil method

Simplify and combine like terms

and you get the answer

Answer:

= 27

Step-by-step explanation:

36×3/4

36 × 3

--

4

9 × 3

= 27

Answer:Y< 5x2 - 5 because it will be squared making it an exponential function

Step-by-step explanation:

56 employees chose purple as their favorite color choice for sales tags.

The circle graph is a visual representation of the data, where each sector's angle is proportional to the percentage of the total number of employees who chose that color. This graph is an effective way to communicate complex data quickly and easily.

From the circle graph, we can see that the sector for purple covers 20% of the total circle, which represents the percentage of employees who chose purple as their favorite color choice for sales tags. To find the actual number of employees who chose purple, we need to calculate 20% of the total number of employees surveyed.

20% of 280 is equal to (20/100) x 280 = 56.

Therefore, 56 employees chose purple as their favorite color choice for sales tags.

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The value of the rate of growth in Japan is - 0.55.

From the question above, :Birth rate = 7.7 per thousand

Death rate = 9.8 per thousand

Net migration = 0.55 per thousand

The rate of growth can be calculated using the following formula:

r = (birth rate - death rate) + net migration

Where,r = rate of growth

birth rate = number of live births per thousand in a population in a given year

death rate = number of deaths per thousand in a population in a given year

net migration = the difference between the number of people moving into a country (immigrants) and the number of people leaving a country (emigrants) per thousand in a given year

Putting the values in the formula we get,r = (7.7 - 9.8) + 0.55r = - 1.1 + 0.55r = - 0.55.

Therefore, the rate of growth in Japan is - 0.55.

Your question is incomplete but most probably your full question was:

thenet migration is confusing me. i thought of using the formula:[ (births + immigration) - (deaths + emmigration)] / total

population • 100 but im not sure how to do it with net migration.

Japan's birth rate is 7.7 per thousand and its death rate is 9.8 per thousand with a net migration of 0.55 ner thousand. Calculate r for Japan

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Answer:

Perimeter of rectangle is larger by 6 cm

Step-by-step explanation:

area of rectangle = 48 * 27 = 1296

√1296 =  36

length of square = 36 cm

Perimeter of square = 36 + 36 + 36 + 36 = 144

Perimeter of rectangle = 48 + 48 + 27 +27 = 150

Perimeter of rectangle is larger by 6 cm

The probability of getting a subject who is not diabetic, given that the test result is negative, is approximately 0.1786.

To find the probability of getting a subject who is not diabetic, given that the test result is negative, we can use the data provided in the table. From the table, we can see that out of the total subjects tested, 5 are not diabetic and have a negative test result. The total number of subjects with a negative test result is 28.

To calculate the probability, we divide the number of subjects who are not diabetic and have a negative test result (5) by the total number of subjects with a negative test result (28).

Probability = Number of subjects who are not diabetic and have a negative test result / Total number of subjects with a negative test result

Probability = 5 / 28

Simplifying this fraction, we get:

Probability ≈ 0.1786

Therefore, the probability of getting a subject who is not diabetic, given that the test result is negative, is approximately 0.1786.

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The population grows at a rate proportional to its size approximately 15 minutes.

Since the bacteria population grows at a rate proportional to its size, we can use the exponential growth formula: P(t) = P(0)  e^(kt), where P(t) is the population at time t, P(0) is the initial population, k is the growth rate constant, and e is the base of the natural logarithm.

Given that the initial count is 400, we have P(0) = 400. After 1 hour (60 minutes), the population is 1600, so P(60) = 1600.

To find the growth rate constant (k), we can substitute the values into the exponential growth formula:

1600 = 400 e^(k * 60)

Dividing both sides by 400:

4 = e^(k * 60)

Taking the natural logarithm of both sides:

ln(4) = k * 60

Solving for k:

k = ln(4) / 60

To determine the doubling time, we need to find the value of t when the population reaches twice its initial count (800):

800 = 400  e^[(ln(4) / 60)  t]

Dividing both sides by 400:

2 = e^[(ln(4) / 60)  t]

Taking the natural logarithm of both sides:

ln(2) = (ln(4) / 60)  t

Solving for t:

t = (60 / ln(4))  ln(2)

Calculating this value, we find that the population of bacteria doubles in approximately 15 minutes.

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