Find the area of the right triangle.

Step-by-step explanation:

Answer: take a look at the picture as you see a and be is at the bottom line c and a attach and c and be attach that how

Step-by-step explanation:

Answer:

y = 7x

Step-by-step explanation:

I answered a similar question posted by you. The logic is the same so you should be able to figure it out

To graph y = 7x, use a graphing calculator.

If you wish to plot manually, take 2 values of x, find the y value using the equation and draw a straight line through those points

Point 1: When x = 0, y = 7 · 0 = 0. So (0,0) is one point

Point 2: When x = 1, y = 7; y = 7 · 1 = 7 So (7, 1) is the second point.

Draw a straight line through these points and you get your graph

The graph will be as shown.

Answer:

They are 5 and -4

The given equation's zeroes are 5 and -4.

In quadratic equations, it is a polynomial with a degree of 2 or the maximum power of the variable is 2. It has two options because its maximum power is two.

Given the equation y=3(x-5)(x+4). The zeroes will be calculated as:-

y = 3 (x - 5 ) ( x + 4 )

y = 0

Solve the equation for the zeroes as below,

3(x-5)(x+4) = 0

( x - 5 ) = 0

x = 5

x + 4 = 0

x = -4

Therefore, the zeroes are 5 and -4.

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It will take 12 more minutes for the remaining 75% of the movie to download using algebra.

To determine how many minutes are needed for the remaining 75% of the movie to download, we will follow these steps:

1. Observe that the movie has been downloading for 4 minutes and has downloaded 25%. This means that the time taken to download 25% of the movie is 4 minutes.
2. Now, we need to determine the time taken to download the remaining 75% of the movie. Since we know the time taken for 25%, we can use this information to find the time for 75%.
3. We can set up a proportion: (time taken for 25%)/(time taken for 75%) = 25%/75%. This proportion helps us understand the relationship between the time taken for both percentages.
4. Plug in the known value: 4 minutes/(time taken for 75%) = 25%/75%. Now, we need to solve for the unknown variable (time taken for 75%).
5. To solve for the unknown variable, we can cross-multiply. Multiply 4 minutes by 75% and 25% by the time taken for 75%: (4 minutes x 75%) = (25% x time taken for 75%).
6. Calculate 4 minutes x 75%: 4 minutes x 0.75 = 3 minutes. So, 3 minutes = (25% x time taken for 75%).
7. Now, divide both sides of the equation by 25% (or 0.25) to find the time taken for 75%: 3 minutes ÷ 0.25 = 12 minutes.

So, it will take 12 more minutes for the remaining 75% of the movie to download.

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Ted can mow the lawn in 5 minutes by using his power mower. Galen takes 15 minutes to mow the same lawn using a push-type mower.

Let's calculate the amount of work done by Ted in 1 minute.WORK = 1/5Let's calculate the amount of work done by Galen in 1 minute.WORK = 1/15

Let's calculate the amount of work done by both of them working together in 1 minute. WORK = 1/5 + 1/15 Simplify, LCM of 5 and 15 = 15 So, 3/15 + 1/15 = 4/15Hence, working together Ted and Galen can mow the lawn in 15/4 or 3.75 minutes or 3 minutes and 45 seconds.

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The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2. The solution has been obtained by using the concept of probability.

What is probability?

To calculate the chance of an event, use the mathematical notion of probability. It only enables us to estimate the likelihood that an event will take place. On a scale of 0 to 1, where 0 represents impossible and 1 represents a certain event.

We are given that Renata is a 5-year-old girl from a poor family in the united states, who is about to enter kindergarten.

The chances of Renata being ready to complete kindergarten tasks when she enters school are about 1/2 because it is not necessary that she will be able to do all the tasks. She might be able to do and she might not be able to do.

So, there are equal chances of both.

Hence, chances of Renata being ready to complete kindergarten tasks are 1/2.

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To find the roots of the auxiliary equation for the given differential equation x^2y'' - 12y = 0, we need to assume a solution of the form y = e^(rx) and substitute it into equation to obtain characteristic equation.

Assuming a solution of the form y = e^(rx) for the differential equation x^2y'' - 12y = 0, we can substitute it into the equation and simplify to obtain the characteristic equation. Differentiating y twice with respect to x, we have y' = re^(rx) and y'' = r^2e^(rx). Substituting these expressions into the differential equation, we get:

x^2(r^2e^(rx)) - 12e^(rx) = 0.

Factoring out e^(rx), we have:

e^(rx)(x^2r^2 - 12) = 0.

For the equation to hold true, either e^(rx) = 0 (which is not a valid solution) or (x^2r^2 - 12) = 0.

Setting the expression x^2r^2 - 12 equal to zero, we obtain the auxiliary equation:

x^2r^2 - 12 = 0.

To find the roots of this equation, we can factor it or use the quadratic formula. In this case, the equation is already factored, so the roots of the auxiliary equation are given by:

r = ±sqrt(12)/x.

The roots of the auxiliary equation determine the form of the solutions to the differential equation. To obtain the general solution, we consider the two cases: r = sqrt(12)/x and r = -sqrt(12)/x. For the case r = sqrt(12)/x, the solution takes the form y = c1e^(sqrt(12)/x), where c1 is a constant. For the case r = -sqrt(12)/x, the solution takes the form y = c2e^(-sqrt(12)/x), where c2 is a constant. Therefore, the general solution to the given differential equation is y = c1e^(sqrt(12)/x) + c2e^(-sqrt(12)/x), where c1 and c2 are arbitrary constants.

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9514 1404 393

Answer:

Step-by-step explanation:

It is helpful to remember that opposite angles of an inscribed quadrilateral are supplementary. This lets you find the value of m.

  ∠A +∠K = 180°

  8m° +10m° = 180°

  18m = 180

  m = 180/18 = 10

Using this value we can find ...

  ∠H = 5m° = 5·10° = 50°

  ∠A = 8m° = 8·10° = 80°

  ∠W = 180° -∠H = 180° -50° = 130°

Answer:

c right triangle

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

A: Method that is used to find either the legs or the hypotenuse of a right triangle.

B: Diagonal line of a right triangle, also used in the Pythagorean Theorem

C: 3-sided shape with a 90-degree angle

D. Lenth and height of a right triangle, used in the Pythagorean Theorem

Answer:

3

Step-by-step explan4ation:

Always include the steps and/or background required to get to the final answer. Let’s help other people understand and solve future problems on their own.

The new tuition for the fall will be $4,025 per semester. This is exactly what we get by using equation B, since: 1.15 • 3500 = 4025

The correct equation to find the new tuition for the fall is: B. 1.15 • 3500 = x

Here's why: The problem states that there is a 15% increase in tuition, which means that the new tuition will be the current tuition plus 15% of the current tuition. Mathematically, we can represent this as:

new tuition = current tuition + 15% of current tuition

Using x to represent the new tuition, and 3500 to represent the current tuition, we can write this equation as:

x = 3500 + 0.15(3500)

Simplifying the right side, we get:

x = 3500 + 525

x = 4025

Therefore, the new tuition for the fall will be $4,025 per semester. This is exactly what we get by using equation B, since: 1.15 • 3500 = 4025

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Answer:

21/7=3

3 times bigger.

Step-by-step explanation:

Answer:

D. trapezoids

X is the variable that we have assigned the agriculture column of swiss to. Running this code would give us the interquartile range of x.

a. To calculate the sample median of x, we can use the median function in R. So, the code would be:
median(x)
where x is the variable that we have assigned the agriculture column of swiss to. Running this code would give us the sample median of x.
b. To find the .34 quantile of x, we can use the quantile function in R. The code would be:
quantile(x, 0.34)
where x is the variable that we have assigned the agriculture column of swiss to, and 0.34 represents the desired quantile. Running this code would give us the value of the .34 quantile of x.
c. To calculate the interquartile range of x, we can use the IQR function in R. The code would be:
IQR(x)
where x is the variable that we have assigned the agriculture column of swiss to. Running this code would give us the interquartile range of x.

The "fertility", "Switzerland", and "x <- swiss $ agriculture" terms.
a. To calculate the sample median of x (the agriculture column in the Swiss dataset), use the following R command:
median_x <- median(swiss$agriculture)
b. To find the 34th percentile (0.34 quantile) of x using the R quantile function, use the following R command:
quantile_x <- quantile(swiss$agriculture, probs = 0.34)

c. To calculate the interquartile range of x (the agriculture column in the Swiss dataset) using R, use the following R commands:
Q1 <- quantile(swiss$agriculture, probs = 0.25)
Q3 <- quantile(swiss$agriculture, probs = 0.75)
IQR_x <- Q3 - Q1
This will give you the interquartile range (IQR) of the agriculture column in the Swiss dataset.

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a is called the real part of the complex number and bi is called the imaginary part of the complex number. In the complex number 6 - 4i, for example, the real part is 6 and the imaginary part is -4i.

Answer:

...what's the question??

The number of pheasants in 2012 was 1832. The number of pheasants in 2016 was 422. The minimum viable density is 100 pheasants per hectare.

So, we need to find out the year in which the population will fall below 100 pheasants per hectare.

First, we need to find out the rate of decline per year which can be calculated as follows: Rate of decline per year = (1832 - 422) / (2016 - 2012)= 1410 / 4= 352.5 per yearNow, let the number of pheasants per hectare be y after t years from 2012.

Then, y = 1832 - 352.5t (as we know the rate of decline per year)We need to find the year in which the population will fall below 100 pheasants per hectare. So, we need to solve the equation:1832 - 352.5t = 100⇒ 352.5t = 1732⇒ t = 1732 / 352.5⇒ t = 4.91 Therefore, the population will fall below the minimum viable density of 100 pheasants per hectare after 4.91 years from 2012, which is around 2017 or 2018.

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The probability that a randomly selected adult from this group has an IQ greater than 124.9 is 0.0706.

Given the information, assume that adults have IQ scores that are normally distributed with a mean of 96 and a standard deviation of 19.5.

To find the probability that a randomly selected adult has an IQ greater than 124.9.

We need to calculate the Z score.

\(Z = (X - \mu) / \sigma\)

Where X is the IQ score, μ is the mean, and σ is the standard deviation.

Now, we can plug in the given values,

Z = (124.9 - 96) / 19.5

= 1.475

We can use a standard normal distribution table to find the probability that a randomly selected adult has an IQ greater than 124.9.

From the table, we can see that the area to the right of Z = 1.475 is 0.0706.

Hence, the probability that a randomly selected adult from this group has an IQ greater than 124.9 is 0.0706 (Round to four decimal places as needed).

Conclusion: The probability that a randomly selected adult from this group has an IQ greater than 124.9 is 0.0706.

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The area under the curve to the right of z = 1.47 gives the required probability.

Let X be the IQ scores for adults with mean μ = 96 and standard deviation σ = 19.5.

Therefore, X ~ N(96, 19.5^2).

We need to find P(X > 124.9).

Standardizing X using the formula: z = (X - μ)/σ

where z ~ N(0, 1).

z = (124.9 - 96)/19.5 = 1.47

Using a standard normal distribution table, the probability of z > 1.47 is 0.0708.

Therefore, the probability that a randomly selected adult from this group has an IQ greater than 124.9 is approximately 0.0708.

Answer: 0.0708 (rounded to four decimal places).

Note: The graph would be a standard normal distribution curve with mean 0 and standard deviation 1.

The area under the curve to the right of z = 1.47 gives the required probability.

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The minimal approximation error A-A 2achievable by a rank-1 approximation A to A is

||A - A1||₂=0 where A is 2×2 matrix.

We have given a matrix A as seen in above figure or A = [ 5 15 ; 6 18 ; -1 -3 ; -4 -12 ; 2 6]

note here that C₂= 3C₁

where Cᵢ --> iᵗʰ column

v = [ 5 ; 6 ; -1 ; -4 ; 2]

||v||² = 82 => ||v|| = √82

and A At v = 820 v

and A At = [ 82 246 ; 246 738]

AAt [1;3] = 820[1;3]

=> v1 = 1/√10(1,3)^t

Then the best rank of 1 approx

= √820 /√80√10 [ 5 ; 6 ; -1 ; -4 ; 2] [ 1 3]

= A

Since , the rank of matrix A is one so, the minimal approx. value is ||A - A1||2 = 0

Hence, the minimal Approx. ||A - A1||2 = 0 .

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Complete question:

Consider the matrix A: A = [5 15] 6 18 -1 -3 -4 -12 [26] What is the minimal approximation error A-A 2 achievable by a rank-1 approximation A to A? Hint: Can you determine this without explicitly calculating the SVD?

The value of the principal is \($10,000\).

The equation:

A = P(1 + 0.043t)

A represents the amount of money earned on a savings account with 4.3% annual simple interest, P represents the principal (initial amount of money), and t represents the time in years.

We are also given that the account balance is \($15160\) after 12 years.

To substitute these values into the equation and solve for the principal:

A = \($15160\)

t = 12

0.043 = 4.3%

\($15160\) = P(1 + 0.043(12))

\($15160\) = P(1 + 0.516)

\($15160\) = P(1.516)

P = \($10000\)

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Answer:

D.

Step-by-step explanation:

The image of the trapezoid after a dilation with a scale factor of 12 will have new coordinates K'(-72, 24), L' = (24, 24), M'(48, -48), N'(-96, -48).

A trapezoid is a four-sided polygon that has two parallel sides and two non-parallel sides, which are called the bases and legs respectively. The height of a trapezoid is the shortest distance between the two bases. To find the area of a trapezoid, you can use the formula A = \(\frac{ (b1 + b2)h}{2}\) , where b1 and b2 are the lengths of the two bases and h is the height.

To find the image of the trapezoid after a dilation with a scale factor of 12, we need to multiply the coordinates of each vertex by 12.

The coordinates of the vertices are:

K(-6, 2)

L(2, 2)

M(4, -4)

N(-8, -4)

Multiplying each coordinate by 12, we get:

K': (12 × -6, 12 × 2) = (-72, 24)

L': (12 × 2, 12 × 2) = (24, 24)

M': (12 × 4, 12 × -4) = (48, -48)

N': (12 × -8, 12 × -4) = (-96, -48)

Plotting this we get the following graphs.

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Answer:

(x + 6)(x + 7)

Step-by-step explanation:

To factor the trinomial x^2 + 13x + 42, we need to find two numbers that multiply to 42 and add up to 13.

One way to do this is to list all the pairs of factors of 42 and see which pair adds up to 13:

1, 42 -> 1 + 42 = 43

2, 21 -> 2 + 21 = 23

3, 14 -> 3 + 14 = 17

6, 7 -> 6 + 7 = 13

So the pair of factors that we want is 6 and 7. We can use these numbers to rewrite the middle term of the trinomial:

x^2 + 13x + 42 = x^2 + 6x + 7x + 42

Next, we can group the first two terms and the last two terms:

x^2 + 6x + 7x + 42 = (x^2 + 6x) + (7x + 42)

Now, we can factor out the greatest common factor from each group:

x(x + 6) + 7(x + 6)

Notice that we have a common factor of (x + 6) in both terms. We can factor this out:

(x + 6)(x + 7)

The correct answer is option a. $7,594.46.

To calculate the amount you would reduce the amount you owe in the first year, we can use the formula for the equal installment of a loan. The formula is:

Installment = Principal / Number of Installments + (Principal - Total Repaid) * Interest Rate

In this case, the principal is $45,000, the number of installments is 5, and the interest rate is 8.5%.

Let's calculate the amount you would reduce the amount you owe in the first year:

Installment = $45,000 / 5 + ($45,000 - $0) * 0.085Installment = $9,000 + $3,825

Installment = $12,825

Therefore, you would reduce the amount you owe by $12,825 in the first year.The correct answer is option a. $7,594.46.

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Answer:

1) Yes

2) No

3) Yes

4) Yes

Step-by-step explanation:

Remember the rule: the sum of the two shortest sides must be bigger than the longest side. From there, the answers should be obvious. Just add up the smallest sides for each triplet of lengths and see if that is bigger than the largest side.

7 + 14 > 18, therefore this can be a triangle

3 + 8 < 17, therefore this can't be a triangle

3.2 + 9.0 > 11.5, therefore this can be a triangle

6 + 7 > 8, therefore this can be a triangle

A scatterplot is a graph that displays the relationship between two variables. In this case, the x-axis represents the weight of the furniture, and the y-axis represents the cost.

To analyze the scatterplot, we look for any patterns or trends. If the points on the graph form a straight line, it indicates a strong relationship between the variables. If the points are scattered randomly, it suggests a weak or no relationship.
In Ian's scatterplot, we can observe a positive relationship between weight and cost. As the weight increases, so does the cost of the furniture. The points are roughly aligned in an upward trend, suggesting a positive correlation.
However, it's important to note that scatterplots only show associations and not causation. To determine the strength and significance of the relationship, statistical analysis such as correlation coefficients can be used. But from the given scatterplot, it is clear that heavier furniture tends to be more expensive.
In conclusion, Ian's scatterplot suggests a positive relationship between the weight and cost of furniture, indicating that heavier furniture tends to have a higher price.

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Answer:

= 12x + -15/2

Step-by-step explanation:

4x + 1/4 + 8x + -31/4

(4x+8x) + (1/4 + -31/4)

=12x+ -15/2

Answer:

12x - 15/2

Step-by-step explanation:

(4x + 1/4) + (8x - 31/4)

4x + 1/4 + 8x - 31/4

4x + 8x

12x + 1/4 - 31/4

1/4 - 31/4

12x -15/2