Which of these sets of side lengths are Pythagorean triples? Check all that apply.
A. 10, 24, 26
B. 14, 48, 49
C. 9, 12, 16
D. 9, 40, 41
E. 15, 20, 25

Height of the ladder on the wall in decreasing at the rate of ≈ 6m/s

Finding a function's derivative, or rate of change, is the process of differentiation in mathematics. The practical approach of differentiation can be performed utilizing only algebraic operations, three fundamental derivatives, four principles of operation, and an understanding of how to manipulate functions, in contrast to the theory's abstract character.

let ym be the height of wall at  which ladder touches

Also let the foot of ladder be xm away from the wall

then by the pythagoras theorem we have ,

[tex]x^{2} +y^{2} =[/tex] 64 [ length of ladder = 8 m ]

⇒ y = [tex]\sqrt{64 - x^{2} }[/tex]

then , the rate of change of height (y) with respect to time (t) is given by

[tex]\frac{dy}{dt}=\frac{-x}{\sqrt{64 - x^{2} }} . \frac{dx}{dt}[/tex]

it is given that [tex]\frac{dx}{dt}[/tex] = 5 m/s

∴ [tex]\frac{dy}{dt}=[/tex] [tex]\frac{-5x}{\sqrt{64 - x^{2} }}[/tex]

now when x = 6m , we have :

[tex]\frac{dy}{dt} = \frac{-5 * 6}{\sqrt{64 - 6^{2} }}[/tex]

  = -30 / 5 .3

  = -5.660377358490566

therefore height of the ladder on the wall in decreasing at the rate of ≈ 6m/s

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On simplifying the given expression 4/x-2/x^2+1-2/x+1 we get solution as (2x^2 + 2x - 2)/x^2.

What is the meaning of simplifying a n equation?

To simplify a phrase, create an equivalent expression without any terms that are identical. The expression will then be rewritten using the fewest terms feasible.

We have given:

[tex]\frac{4}{x} - \frac{2}{x^2} +1 - \frac{2}{x} + 1[/tex]

Adding the numbers:

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

Making a common denominator:

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

Combining the values with common denominator:

[tex]\frac{2x^2 + 2x - 2}{x^2}[/tex]

This the the simplified result of the given expression.

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The average rate of change of f is less than the average rate of change of g.

What is average rate ?

This expression represents the average rate of change of the function f over the range a≤x≤b is less than or equal to x, and is less than or equal to b:

f(b)−f(a) / b - a

It is the average amount by which the function changed per unit throughout that time period.

Here, in Average rate of change in function g over [-3, 0]

=> a = -3, b = 0

=> f(a) = 5 , f(b) = 14

Average rate of change = (14 - 5) / (0 - (-3))

                                        = 3

​

Now, in Average rate of change in function f over [-3, 0]

=> a = -3, b = 0

=> f(a) = -3, f(b) = 0

Average rate of change = (0 - (-3)) / (0 - (-3))

                                        = 1

Therefore, The average rate of change of f is less than the average rate of change of g.

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Answer:

7.2 × 10^-6

Step-by-step explanation:

7.2 are the two last digits of the notation

and the reason its to the power of -6 is because there are 6 digits until you reach 7

Answer:

27

Step-by-step explanation:

length+base+heigth+breath

=6cm+10cm+4cm+7cm

=27cm

but I am not very sure so when it is correct the give me thanks or rate the answer so I will know it is correct

Answer:

Perimeter (to the nearest tenth) = 24.3

Step-by-step explanation:

59.25 euros is the the total cost of the cans of weedkiller needed to cover the lawn

A trapezium is a convex quadrilateral with exactly one pair of opposite sides parallel to each other

The figure that is formed is the following with the respective measurements, now to calculate the area we need the height, for Pythagoras we have:

17 ²= h ² + 8 ²

h ² = 289 - 64

h ² = 225

h = 15

now the figure area is as follows:

A = h × (b + a) / 2

b long side 20 m and short side 12 cm, replacing:

A = 15 × (12 + 20) / 2

A = 240 m²

We are told that each can of weed killer can cover up to 100m ^ 2

Thus:

240/100 = 2.4, so you would need 3 cans of weedkiller

each can costs 19.75, which means that the total cost is:

19.75 × 3 = 59.25 euros

Hence 59.25 euros is the the total cost of the cans of weedkiller needed to cover the lawn.

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The customer can purchase 1.19788 pounds of cheese (approximately 1.2 pounds).

We are given with the cost of ham is $2.49 per pound and

Cost of swiss cheese is $3.79 per pound.

So, the cost of 2 pounds of ham will be given as-

= 2× $2.49

= $4.98

Since, the customer has a total of  $9.50 to spend on 2 pounds of ham and some cheese,

∴ Let the number of pounds of cheese she can purchase be x.

Then the equation will be this:

2.49*2 + 3.79*x = 9.50

4.98 + 3.79x = 9.50

Subtracting 4.98 from each side we get-

4.98 -4.98 + 3.79x = 9.50-4.98

3.79x = 4.54

x  [tex]=\frac{4.54}{3.79}[/tex]

x = 1.19788 pounds of cheese (approximately 1.2 pounds).

Hence, the customer can purchase 1.19788 pounds of cheese (approximately 1.2 pounds).

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Answer:9 days

Step-by-step explanation:A lot of division is required, but because 8.75 probably isn't an answer, I rounded up to 9.

Answer: there is no picture again. just take a good guess

Step-by-step explanation:

The value of y when x = -7 according to the function defined y = w(x) is; 9.

It follows from the task content that the value of y when x = -7 is to be determined according to the given expression; y = w(x).

Since it follows from the task content that;

y = w(x)

Therefore, it follows that when; x = -7; we have;

y = w(-7).

However, recall from the function instances given that; w(-7) = 9;

Therefore, y = w(-7) = 9.

Ultimately, the value of y when x = -7 as required in the task content is; 9.

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Applying logarithm properties, the solution of the highlighted question is given as follows:

x = 4.

The logarithmic equation is given as follows:

[tex]\log_{a}(x + 2) = \frac{1}{3}\log_{a}{8} + \log_{a}{3}[/tex]

First, we apply the power rule, meaning that the multiplying coefficient of the logarithm can be the power of the given term, hence:

[tex]\frac{1}{3}\log_{a}{8} = \log_{a}{8^{\frac{1}{3}}} = \log_{a}{\sqrt[3]{8}} = \log_{a}{2}[/tex]

Then the equivalent expression is:

[tex]\log_{a}(x + 2) = \log_{a}{2} + \log_{a}{3}[/tex]

Now we apply the product rule, as the sum of two logarithms of same base can be written as a single logarithm, keeping the base and multiplying the terms.

Hence the equivalent expression is:

[tex]\log_{a}(x + 2) = \log_{a}{(2 \times 3)}[/tex]

[tex]\log_{a}(x + 2) = \log_{a}{6}[/tex]

The logarithm function is one-to-one, meaning that if they have the same input, they will have the same output, hence we can solve for x as follows:

x + 2 = 6

x = 6 - 2

x = 4.

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The correct option or equation that applies to the given situation is 7*6 = (4*6) + (3*6).

According to the question,

We have the following information:

Akela drew smaller arrays to find the product of a larger array.

Now, we have two figures where one has 6*3 boxes (6 horizontal boxes and 3 horizontal boxes) and in the second figure we have 6*4 boxes (6 horizontal boxes and 4 vertical boxes).

Now, to find the correct option, we will look for these two in options:

So, the option that has both of them is  7*6 = (4*6) + (3*6).

Now, we can verify whether the sides of the equation given are correct or not.

We have:

7*6 = 42

On right hand side, we have:

(4*6) + (3*6)

24+18

42

Hence, the correct option is 4th one.

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Answer:

discount = $8.25   Total=$46.75

Step-by-step explanation:

[tex]\frac{x}{55}[/tex] = [tex]\frac{15}{100}[/tex]                                        55.00-8.25= $46.75    

[tex]\frac{100x}{100}[/tex] = [tex]\frac{825}{100}[/tex]                                          total= $46.75

x=8.25

discount = 8.25

Answer: The discount is $8.25, the total price you pay is $46.75

Step-by-step explanation:

To find the discount, you multiply the decimal of the percent, which is .15 by the total. So 55*.15=8.25. That is how much of a discount you get.

To find the total amount you pay after the discount you simply subtract the discount from the total, so 55-8.25=46.75

Answer:

26.208 miles

Step-by-step explanation:

42.195 / 1.61 = 26.208 miles

Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.

The alternative hypothesis states that political beliefs and marijuana use depend on one another within the population, contrary to the null hypothesis that asserts these two variables are independent.

H₀ : Pij = Pi · Pj ; i = 1, 2, 3 ; j = 1, 2, 3

Ha : at least one Pij ≠ Pi · Pj

We want to test whether there is a relationship between political views and marijuana usage levels. The results of a random sample of size n = 1353 are derived from the following formula;

e = (Row total) x (Column total) /Total sample size

We are told to use the 0.01 level of significance to test the null hypothesis. Thus, α = 0.01. The table has r = 3 rows and c = 3 columns. An r × c table has degrees of freedom df = (r - 1) x (c - 1). So, a 3×3 table has degrees of freedom df = (3 - 1) x (3 - 1) = 4. From formula the df = 4 and α = 0.01, χ²₀.₀₁ = 13.277. Reject the null hypothesis if X² ≥ 13.277 where

x² =Σ(a - e)²/e

Substituting the observed and expected frequencies summarized in the table above into the formula for x², we get

X² = 68.732

Rejection Region → X² ≥ 13.277

Test statistic → X² = 68.732

Since X² (68.732) > X²₀.₀₁ (13.277), we reject the null hypothesis and conclude that There is evidence that political views and level of marijuana usage are related.

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Answer:

39.

Step-by-step explanation:

50779 divided by 590 is 86, with a remainder of 39.

-119

1) Let's evaluate that polynomial when y=4, note that to evaluate is to find out the corresponding value when we plug into that another one:

2) Hence, the answer is -119

[tex](\frac{3}{8} )^{-2}[/tex]

[tex](\frac{8}{3})^{2}[/tex]

[tex](\frac{8}{3} )\times(\frac{8}{3} )[/tex]

[tex]\frac{8\times8}{3\times3}[/tex]

[tex]\frac{64}{9}[/tex] or [tex]7.1111111[/tex]

The solution for x + 3 is greater than or equal to 2x - 6 is x ≤ 9.

Given,

x + 3 is greater than or equal to 2x - 6

That is,

x + 3 ≥ 2x - 6

Solve for x in this solution.

So,

x + 3 ≥ 2x - 6

Here,

6 + 3 ≥ 2x - x

Then,

9 ≥ x

That is,

The solution for x + 3 is greater than or equal to 2x - 6 is x ≤ 9.

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If the knowledge that an event "a" has occurred implies that another event "b" cannot occur, then the events "a" and "b" are said to be disjoint events.

As per the question statement, the knowledge that an event "a" has occurred implies that another event "b" cannot occur.

We are required to determine the characteristic name for the above mentioned events.

And here, if event "a" occurs, even "b" does not, implying the fact that, events "a" and "b" cannot occur simultaneously. Hence, as per the above definition of disjoint events,  the events "a" and "b" are be disjoint.

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The ratio of x:y  is 4:3.

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categories ratios. Part to whole ratio is one, while part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings.

For instance, a class has a 12:15 boy-to-girl ratio, but the part-to-whole ratio refers to the relationship between a particular group and the entire. For instance, five out of every ten people enjoy reading. As a result, the ratio of the portion to the total is 5: 10, meaning that 5 out of every 10 persons enjoy reading.

Given:

15% of x=20% of y

So,

15 / 100 × x = 20 / 100 × y

3 / 20x = 1/5y

x / y = 1/5 x 20/3

x / y = 4/3

Hence, the ratio of x:y  is 4:3.

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The equation of the graph of g is represented by y  - 6 =  (x-2)²

The very first step in balancing a variable equation is to correctly identify the specific values of the variables that lead to equality.

The graph of the function is f is y = x²

Now we can see that the graph of g is translated to 2 units to the right and 6 units up.

We know from the properties of translation that when the graph moves 2 units to the right we get the equation as y = (x-2)²

Again when the graph moves 6 units up wards the graph changes by

y  - 6 =  (x-2)²

Therefore the equation of g is  y  - 6 =  (x-2)²

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Answer:

x < 6

Step-by-step explanation:

x/3 + x/4 < 7   | * 12

4x + 3x < 84

7x < 84   | : 7

x < 12

1 - x/6 > 0

1 > x/6   | * 6

6 > x

x < 6

x < 6 and x < 12 gives x < 6

Answer: m11= 180-90= 90 (linear pair)

m12= 180-90= 90 (linear pair)

m13= 90 linear pair

By solving the equation we can conclude that Andre (36,000 steps) walks more than Priya (35,400 steps).

So, the distance that Andre traveled.

He demonstrated his ability to take 6000 steps in 50 minutes.

The pace at which Andre can walk is:

The 5 hours in minutes conversion: 5  × 60 minutes = 300 minutes

Then,

The distance traveled by Andre is:

Where x represents the number of minutes and y is the number of steps.

The formula to convert 5 hours to minutes is:

Replace x with its value in the equation:

35400 steps are taken by Priya.

Therefore, by solving the equation we can conclude that Andre (36,000 steps) walks more than Priya (35,400 steps).

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The correct question is given below:

Andre and Priya are tracking the number of steps they walk. Andre records that he can walk 6000 steps in 50 minutes. Priya writes the equation y=118x, where y is the number of steps and x is the number of minutes she walks, to describe her step rate. This week, Andre and Priya each walked for a total of 5 hours. Who walks more steps?

The new function that can be formed after f(x) transforms horizontally 4 units to the right and then vertically 7 units upwards is
H(x) = h(x) = x² + 11x + 37.

How to shift an equation horizontally?
For a function, f; a brand new function d(x) = f(x - h), where h is a constant, is a horizontal shift of the function f; for positive 'h' the graph shifts right and for negative 'h' the graph shifts left.
How to shift an equation vertically?
For a function, f; a brand new function d(x) = f(x) + k, where k is a constant, is a vertical shift of the function f; for positive 'h' the graph shifts up and for negative 'h' the graph shifts down.

Given, the equation is f(x) = x² + 3x + 2
The new equation formed will be = h(x)
Also, the function horizontally shifts 4 units to the right.
Therefore, h(x) = f(x + 4) = (x + 4)² + 3(x + 4) + 2 = x² + 11x + 30
Again, the function formed in h(x) vertically shifts up by 7 units.
Thus, new equation for h(x) is = h(x) + 7 = x² + 11x + 37
Therefore, the required equation for H(x) = h(x) = x² + 11x + 37

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The algebraic expression should often take one of the following forms: addition, subtraction, multiplication, or division. Bring the variable to the left and the remaining values to the right to determine the value of x. To determine the outcome, simplify the values.

         4x+2x+5x+50= 180

        = 6x+5x+50 =180

        combine 6x and 5x

        =  11x

         11x+50= 180

        subtract 50 both sides

        11x = 180- 5

        =  130

        11x=130

        x= 130/11

          11.81

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