Which set of numbers can represent the side lengths, in inches, of an acute triangle? 4, 5, 7 5, 7, 8 6, 7, 10 7, 9, 12

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Answer:

See explanation.

Step-by-step explanation:

The question is not very clear, but I am assuming that you are asking how to get from 30/8 to 3 6/8

This is a mere simplification problem. We have simplified 30/8 into 3 6/8.

To start, let's check out the multiples of 8 that are less than 30

8, 16, 24. We want the largest multiple, 24. here we have

\(\frac{24}{8} + \frac{6}{8}\)

Simplify 24/8 into 3.

Now you're done!

3 6/8!

The solution to the given question is given below:(a) f(x) = 3x^2+4/x^2+2To differentiate the given function, we will use the quotient rule of differentiation.

which is given by,(f(x)/g(x))'=[f'(x)g(x)-f(x)g'(x)]/[g(x)]2Now, putting the given values into the formula, we get,f(x) = 3x2+4/x2+2Let f(x) = 3x2+4 and g(x) = x2+2Now,f'(x) = d/dx[3x2+4] = 6xg'(x) = d/dx[x2+2] = 2xAfter substituting all the values in the quotient rule, we get,(f(x)/g(x))'=(6x(x2+2)-2x(3x2+4))/(x2+2)2=(-6x^3-8x+12x^3+16x)/[x^4+4x^2+4] = (6x^3+8x)/[x^4+4x^2+4]Hence, f'(x) = (6x^3+8x)/[x^4+4x^2+4].Therefore, the required derivative of the given function is (6x^3+8x)/[x^4+4x^2+4].(b) f(x) = (x2 - 7x)12To differentiate the given function, we will use the chain rule of differentiation which is given by, d/dx[f(g(x))] = f'(g(x)).g'(x)Now, putting the given values into the formula, we get,Let f(x) = x^12 and g(x) = x2-7xThen,f'(x) = 12x^11g'(x) = d/dx[x2-7x] = 2x-7After substituting all the values in the chain rule, we get,d/dx[f(g(x))] = f'(g(x)).g'(x) = 12(x2-7x)11.(2x-7)Therefore, the required derivative of the given function is 12(x2-7x)11.(2x-7).(c) f(x) = x^4√6x+5To differentiate the given function, we will use the product rule of differentiation which is given by, (fg)' = f'g + fg'Now, putting the given values into the formula, we get,Let f(x) = x^4 and g(x) = √6x+5Then,f'(x) = d/dx[x4] = 4x3g'(x) = d/dx[√6x+5] = 3/√6x+5After substituting all the values in the product rule, we get,(fg)' = f'g + fg' = (4x3).(√6x+5) + (x^4).(3/√6x+5)Hence, f'(x) = (4x3).(√6x+5) + (x^4).(3/√6x+5).Therefore, the required derivative of the given function is (4x3).(√6x+5) + (x^4).(3/√6x+5).

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The derivatives of the functions of the differentiation of the given functions has been calculated.

(a) The rule of differentiation applied to

f(x) = 3x²+4/x²+2 is as follows:

f'(x) = [12x(x²+2)-(6x)(4)] / [(x²+2)²]

=> f'(x) = [12x³-24x] / [(x²+2)²]

=> f'(x) = 12x(1-x²)/[(x²+2)²].

(b) The rule of differentiation applied to f(x) = (x² - 7x)^12 is as follows:

f'(x) = 12(x²-7x)^11(2x-7).

We apply the chain rule, which is the following:

[f(g(x))]' = f'(g(x)) * g'(x).(c)

The rule of differentiation applied to f(x) = x⁴√(6x+5) is as follows:

f'(x) = 4x³ * (6x+5)¹∕² + x⁴ * 1/2(6x+5)^-1/2 * 6

=> f'(x) = [24x³(6x+5) + 3x⁴(6)]/[2(6x+5)¹∕²]

=> f'(x) = [3x³(8x²+15)]/[(6x+5)¹∕²].

Thus, the differentiation of the given functions has been calculated.

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Answer:

Step-by-step explanation:

See attached graph

Two pints selected are:

2 packages = $6

5 packages = $6.80

solve the absolute value,

we know x + 6 = 10 or x + 6 = -10

possibility 1

possibility 2

Therefore,

x = 4 or x = -16

When b is 3, the value of the expression \(2b^3 + 5\) is 59.

To evaluate the expression\(2b^3 + 5\) when b is 3, we substitute the value of b into the expression and perform the necessary calculations.

Given that b = 3, we substitute this value into the expression:

\(2(3)^3 + 5\)

First, we evaluate the exponent, which is 3 raised to the power of 3:

2(27) + 5

Next, we perform the multiplication:

54 + 5

Finally, we add the two terms:

59

Therefore, when b is 3, the value of the expression \(2b^3 + 5\) is 59.

In summary, by substituting b = 3 into the expression \(2b^3 + 5\), we find that the value of the expression is 59.

It's important to note that the provided equation has multiple possible solutions for x, but when b is specifically given as 3, the value of x is approximately 3.78.

It's important to note that in this equation, we substituted the value of b and solved for x, resulting in a specific value for x. However, if we wanted to solve for b given a specific value of x, we would follow the same steps but rearrange the equation accordingly.

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When you divide a fraction by a negative number, it doesn't matter what happens to the denominator because the entire result, or quotient, is the reverse of whatever the original fraction was.

In mathematics, a denominator is the lowest number in a fraction that indicates how many equal parts are divided into a whole.

It is a fraction's divisor. In this case, the denominator is 4, thus there are four components overall.

The top number in a fraction is referred to as the numerator, while the bottom number is referred to as the denominator.

4/5, for instance, is a fraction.

What happens to the denominator of a fraction when you divide it by a negative number is unimportant because the entire result, or quotient, is the opposite of whatever the original fraction was.

Therefore, when you divide a fraction by a negative number, it doesn't matter what happens to the denominator because the entire result, or quotient, is the reverse of whatever the original fraction was.

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Step-by-step explanation:

if m=3(n-4)+2(4n-5)=5(n+2)+16

Answer:

Exponential decay

Step-by-step explanation:

The general form of an exponential function is

\(P=P_{0}a^t\), where P0 is the initial value, a is the base, and t is the exponent.

In your example, P0 is 1 and a is 4/5.

A function is experiencing exponential growth when a > 1.

A function is experiencing exponential decay when 0 < a < 1.

4/5 lies between 0 and 1, so the function is experiencing exponential decay.

Answer:

length is 9 and width is 6

Step-by-step explanation:

List the factors of 54 and choose the numbers that only have a difference of 3. In this case it is 6 and 9, then put them in the order they go based on the instructions.

Using the empirical rule, we can estimate that approximately 97.5% of the students have GPAs that are greater than 1.66 at this university.

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

To apply this rule to the given scenario, we first need to calculate how many standard deviations away from the mean a GPA of 1.66 is.

Z = (X - μ) / σ

Where X is the GPA in question, μ is the mean (2.56), and σ is the standard deviation (0.45).

Z = (1.66 - 2.56) / 0.45 = -2

This tells us that a GPA of 1.66 is 2 standard deviations below the mean.

Now, using the empirical rule, we know that approximately 95% of the data falls within two standard deviations of the mean. Since a GPA of 1.66 is 2 standard deviations below the mean, we can conclude that only about 2.5% (half of the remaining 5%) of the students have a GPA lower than 1.66.

Therefore, the percentage of students who have GPAs that are greater than 1.66 would be approximately 97.5%.

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Answer:

Domain: (-3, 7)

General Formulas and Concepts:

Algebra I

Step-by-step explanation:

According to the graph, the line's x-value span from -3 to 7. Since both are open dot, they are excluded from the domain:

(-3, 7) or -3 < x < 7

The total distance travelled by the speedboat in 1 d.p is 137.5m

A velocity-time graph shows the changing velocity of the sprinter or of any other moving person or object.

The rate of change of displacement with time is velocity.

In a velocity-time graph, the area of the shape of the graph is the total distance travelled.

The shape of this graph is Triangle.

Therefore the area of a triangle is expressed as;

A = 1/2bh

where b is the base and h is the height.

base = 11 and height = 25

A = 1/2 × 11 × 25

A = 275/2

A = 137.5m

Therefore the distance covered by the speedboat is 137.5m

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The lowest point on the graph occurs at point (3π/2,  -1)

One of the three fundamental functions in trigonometry, along with cosine and tan functions, is the sine function.

The ratio of the opposite side of a right triangle to its hypotenuse is known as the sine x or sine theta.

The sine function graph is sinusoidal in nature. This is a sim=ne wave that have smooth periodic oscillation

The attached graph shows sine function graph plotted with the interval [0, 2pi]

The lowest point is observed to occur at  (3π/2,  -1)

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Answer:

62

Step-by-step explanation:

28/4=7
s=7
7*7=49
49+13=62

The value is:

62

Work/explanation:

First, let's solve the little equation 4s = 28.

Divide each side by 4:

\(\bf{4s=28}\)

\(\bf{s=7}\)

Now, plug in 7 into 7s + 13:

\(\bf{7(7)+13}\)

\(\bf{49+13}\)

\(\bf{62}\)

Answer:d≈5.2cm

Step-by-step explanation:

d=3a=3·3≈5.19615cm

Answer:  16

Step-by-step explanation:

multiply 6 by the answers below  until you get 1/3 of 384.

The expression 5y da d is evaluated over the set of points (x, y) that satisfy the conditions 0 ≤ 2x π ≤ y and y ≤ sin(x).

To evaluate the expression 5y da d, we need to consider the set of points (x, y) that meet the given conditions. The first condition, 0 ≤ 2x π ≤ y, ensures that y is greater than or equal to 2x π, meaning the y-values should be at least as large as the double of x multiplied by π. The second condition, y ≤ sin(x), restricts y to be less than or equal to the sine of x.

In essence, we are evaluating the expression 5y over the region defined by these conditions. This involves integrating the function 5y with respect to the area element da d over the set of valid points (x, y).

To compute the result, we would need to perform the integration over the specified region. The specific mathematical calculations depend on the shape and boundaries of the region, and may involve techniques such as double integration or evaluating the definite integral.

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Answer:

A. 10x + 30 = 110; 8 hours

Step-by-step explanation:

We get A as our answer because we know that there is an hourly fee of 10 so we can write that as 10x. Next we know we have an inital fee of 30. So in our equation we would just write it as 30. Finally we know what the total was. 110. So that would go into our equation as 110. So our final equation would be 10x + 30 = 110. Then when you solve it you get 8 for our missing number. In this cause 8 = x.

Answer:

40

Step-by-step explanation:

First, find the length of the rectangle. We know the width is 4, and the ratio of the width to length is 2:5, making the width ratio four, it is 4:10. Therefore, the length of the rectangle is 10. Since the pentagon is regular, and one side of the pentagon is 4, multiply 4 by 4 =16. Then we can find the perimeter of the figure: 16+ 10 + 10 + 4 = 40.

The solution to the word problem 4 less than a number n is -15 is n = -11

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

4 less than a number n is represented as:

n - 4

Hence, 4 less than a number n is -15 is given by:

n - 4 = -15

adding 4 to both sides:

n - 4 + 4 = -15 + 4

n = -11

The value of n is -11

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Given:

Jan and Julie started their ride at 09:30 and finished at 15:15.

Stopped for a drink = 20 minutes

Lunch = 45 minute

Rest = 10 minutes

To find:

Time they are riding on their bikes (excluding stops).

Solution:

Jan and Julie started their ride at 09:30 and finished at 15:15.

So, total time of ride including stops is 5 hours 45 minutes or we can say 345 minutes calculated as

\(30+60+60+60+60+60+15=345\text{ minutes}\)

We need subtract Drink, lunch and rest time from the total time to get the Time they are riding on their bikes (excluding stops) is

\(345-20-45-10=270 \text{ minutes}\)

Therefore, the total time they are riding on their bikes (excluding stops) is 270 minutes.

please see the photo down below it shows the work and answer

H. 12 ft

Given c=15, and a=9, you can use Pythagorean’s theorem a^2+b^2=c^2 to find b, the height

9^2+b=15^2

81+b^2=225

b^2=144

b=12

Height = 12

Answer:

3600

Step-by-step explanation:

First, solve the innermost brackets first.

=> 55/11 [120 /2{4 + (10 + 5 - 7)}]

=> 55/11 [120 /2{4 + (8)}]

=> 55/11 [120 /2{4+8}]

=> 55/11 [120 /2{12}]

=> 55/11[ 60 x 12]

=> 55/11 [720]

=> 5 [720]

=> 3600

Answer:

336ft

Step-by-step explanation:

So, here is what we know:
There is 1 square

There are 8 triangles(each side has 2 triangles)

The base of the square = 12 ft, which is also the base of two triangles combined.

This means the base of each triangle is 6 ft.

The height of the triangle is 8ft

The hypotenus, which is 10ft, is not important to this question.

The formula for finding the area of a square is b^2(the square's base = b)

The formula for finding thh area of a triangle is 1/2 *b * h(the triangle's base = b)

So b^2 = 12^2 = 144

1/2bh = 1/2*6*8 = 24

Remember we have 8 triangles, so we multiply the area of one triangle by 8:

8*24 = 192

Now we add the traingles' area and the square's area:

144 ft+192 ft = 336 ft^2
So F is our answer!

Hope this helps!

Answer:

Area = 336 ft²

Step-by-step explanation:

1. Find the area of the square:

It's given that one side of the square is equal to 12 ft. In a square, all sides are equal, so to find the area of the square you do base x height.

12 ft x 12 ft = 144 ft²

2. Find the area of one of the triangles:

Since we already know that all sides of the square are equal to 12 ft, we know that the base of all four triangles are equal to 12 ft.

It is also given that the height of the triangle (the dotted line) is 8 ft while the hypotenuse of the triangle is 10 ft.  

So, to find the area of the whole triangle you need to do 1/2 base x height.

\(\frac{1}{2} * 12 * 8 = \frac{96}{2} = 48\) ft²

3. Multiply the area of one of the triangles with 4:

There are four triangles, so you want to take the area we got for one of the triangles and multiply that by four to get the total area of all the triangles.

48 x 4 = 192 ft²

4. Add the total area of all four triangles and the square together:

Now, for the final step, add the total area of all four triangles together along with the area of the square from Step 1 to get the final total surface area in square feet.

192 ft² + 144 ft² = 336 ft²

Final Answer: 336 ft²

Using the slope concept, it is found that the shelf should have a measure of 0 degrees relative to the floor.

In this problem, the shelf and the floor are parallel, hence they have the same slope, meaning that the difference of their angles is of 0 degrees, thus, the shelf should have a measure of 0 degrees relative to the floor.

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D. The energy used is the same for both segments, the power while running is greater.

Walking and running both require energy, but the distance covered and the time taken are different. In this case, the person covers the same distance of 1 km in both segments.

Therefore, the energy used is the same for both. However, since running involves covering the same distance in less time, the power while running is greater. Power is the rate at which energy is used, and since running takes less time, the power output is higher.

D. The energy used is the same for both segments, the power while running is greater.

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Answer:

b my

Step-by-step explanation:

valentines

bbg

In the kitchen triangle,  the largest angle will be at counter

A triangle is a three-sided polygon that consists of three edges and three vertices.

Given that kitchens have a working triangle between the sink (S), the counter (C), and the oven (O).

The distance between the sink in the oven is 8 feet.

The distance between the sink and the counter is 6 feet,

The distance between the oven and the counter at 7 feet.

we need to find in the kitchen triangle, where is the largest angle

SO=8

SC=6

OC=7

Hence, in the kitchen triangle,  the largest angle will be at counter

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In order to solve this problem, we'll use the Combinations Formula. This is because the order in which the coins are flipped is unimportant; all that matters is the total number of heads and tails. We'll begin by counting the number of ways to get exactly 4 tails and exactly 8 tails, then the number of ways to get 5 tails and 6 tails, and finally the number of ways to get 7 tails. We will then add all of these numbers together to get the final answer.

When you toss a coin, there are only two possibilities: heads or tails.

Let's call the number of times you get tails "t." We want to find the number of ways to toss the coin 11 times so that

4 <= t <= 8.

Here's how we can do it:

First, we'll find the number of ways to get exactly 4 tails. We know that we're flipping the coin 11 times, so there are 11 choose 4 ways to choose which 4 of those tosses will be tails. The other 7 tosses will be heads. Using the Combinations Formula, this gives us:

11 choose 4 = 330

Next, we'll find the number of ways to get exactly 8 tails. This is similar to the previous step, except that we're choosing 8 of the 11 tosses to be tails. The other 3 tosses will be heads. Using the Combinations Formula, this gives us:

11 choose 8 = 330

Again, using the Combinations Formula, we can find the number of ways to get exactly 5 tails and 6 tails:

11 choose 5 = 462

11 choose 6 = 462

Finally, we need to find the number of ways to get exactly 7 tails. This is a little trickier, but we can do it by splitting the problem into two cases: when the first toss is a tail and when the first toss is a head.

Case 1: The first toss is a tail. Then we need to get 6 tails in the remaining 10 tosses. There are 10 choose 6 ways to choose which 6 of the remaining 10 tosses will be tails. Using the Combinations Formula, this gives us:

10 choose 6 = 210

Case 2: The first toss is a head. Then we need to get 7 tails in the remaining 10 tosses. There are 10 choose 7 ways to choose which 7 of the remaining 10 tosses will be tails.

Using the Combinations Formula, this gives us:

10 choose 7 = 120

Adding up all of these numbers, we get:

330 + 330 + 462 + 462 + 210 + 120 = 1914

So there are 1914 ways to toss a coin 11 times so that the number of tails is between 4 and 8 inclusive.

Thus, the required answer is 1914.

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