Math help please! What are the possible solutions to this system?

The correct answer is Part A: The dimensions of the new deck are 9 feet for the base and 5.4 feet for the height.Part B: The area of the original deck is 67.5 square feet, and the area of the new deck is 24.3 square feet.Part C: The ratio of the areas (new deck to original deck) is 0.36, which is different from the scale factor of 3:5.

Part A: To find the dimensions of the new deck, we need to scale the base and height of the original deck by a factor of 3:5.

The scale factor from the original deck to the new deck is 3:5.

The scaled base of the new deck can be found by multiplying the original base by the scale factor:

Scaled base = Original base * Scale factor = 15 feet * (3/5) = 9 feet

The scaled height of the new deck can be found by multiplying the original height by the scale factor:

Scaled height = Original height * Scale factor = 9 feet * (3/5) = 5.4 feet

Therefore, the dimensions of the new deck are 9 feet for the base and 5.4 feet for the height.

Part B: To find the area of the original deck and the new deck, we'll use the formula for the area of a triangle:

Area = (base * height) / 2

For the original deck:

Area of original deck = (15 feet * 9 feet) / 2 = 67.5 square feet

For the new deck:

Area of new deck = (9 feet * 5.4 feet) / 2 = 24.3 square feet

Part C: To compare the ratio of the areas to the scale factor, we'll divide the area of the new deck by the area of the original deck:

Ratio of areas = Area of new deck / Area of original deckRatio of areas = 24.3 square feet / 67.5 square feet = 0.36

The ratio of the areas is 0.36.

Comparing this ratio to the scale factor (3:5), we can see that they are not equal. The scale factor represents the ratio of the corresponding sides, not the ratio of the areas.

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Answer:

I believe it is (-6, 6)

Step-by-step explanation:

Hope this helps!

p.s. could I get brainliest if possible (I only need one more for the next category or whatever)

Answer:

Pythagorean Theorem

Step-by-step explanation:

Because they give you the hypotenuse and the adjacent angle.

Answer:

Pythagorean Theorem

Step-by-step explanation:

Because they give you the hypotenuse and the adjacent angle.

The ratio of adults to children that came into the restaurant is 5:2. This means that for every 5 adults, there were 2 children who came into the restaurant.

To find the ratio of adults to children that came into the restaurant, we need to divide the number of adults by the number of children.

According to the given information, 12 children and 30 adults came into the restaurant over an hour.

Ratio = Number of Adults / Number of Children

Ratio = 30 adults / 12 children

To simplify the ratio, we can divide both the numerator and denominator by their greatest common divisor (GCD).

In this case, the GCD of 30 and 12 is 6.

Ratio = (30 / 6) adults / (12 / 6) children

Ratio = 5 adults / 2 children

So, the ratio of adults to children that came into the restaurant is 5:2.

This means that for every 5 adults, there were 2 children who came into the restaurant.

In conclusion, the ratio of adults to children that came into the restaurant is 5:2.

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Answer: 1/3

Step-by-step explanation:

The slope of a perpendicular line is the opposite reciprocal.

For example, if slope of line A is a/b, then slope of line B which is perpendicular will be -b/a.

Substitute 1 and 3 for a and b. Apply the formula and get 1/3.

Hello there, I hope you are having a splendid day. :)

Perpendicular lines have slopes that are opposite reciprocals.

This means you take a number, flop it over, and make it negative.

The opposite reciprocal of -3 is

\(\frac{1}{3}\)

This is our answer. Hope it helps. Ask me if you have any queries. :)

~An emotional teen who helps others with joy

\(MagicalNature\)

Good luck. :)

The properties of the rational exponents are given and a rational equation is of the form b = aˣ

When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.

The different Laws of exponents are:

mᵃ×mᵇ = mᵃ⁺ᵇ

mᵃ / mᵇ = mᵃ⁻ᵇ

( mᵃ )ᵇ = mᵃᵇ

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

m⁻ᵃ = ( 1 / mᵃ )

Given data ,

Let the rational exponent equation be A

Now , the properties of the exponent equations are

mᵃ×mᵇ = mᵃ⁺ᵇ

The powers of the exponents are added together

mᵃ / mᵇ = mᵃ⁻ᵇ

The powers of the exponents are subtracted together

( mᵃ )ᵇ = mᵃᵇ

The powers of the exponents are multiplied together

mᵃ / nᵃ = ( m / n )ᵃ

m⁰ = 1

Any number raised to the power of 0 is 1

m⁻ᵃ = ( 1 / mᵃ )

Hence , the exponents are solved

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Using the perpendicularity concept, the perpendicular line is given at the end of the answer.

Two lines are perpendicular, they intersect at and angle of 90º. Hence, for this problem, to construct a line through P that is perpendicular to the line, we just need to draw a line crossing P at an angle of 90º.

Thus, the perpendicular line is plotted at the end of the answer, with a line inserted crossing P at an angle of 90º.

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The relation represented by the matrix [1 1 1 1 0 1 1 1 1] is reflexive and symmetric.

Reflexive: A relation is reflexive if every element is related to itself. In the given matrix, all the diagonal elements are 1, indicating that each element is related to itself.

Symmetric: A relation is symmetric if whenever (a, b) is in the relation, then (b, a) is also in the relation. In the given matrix, all the off-diagonal elements are 1, indicating that if a is related to b, then b is related to a.

The relation is not antisymmetric as there are pairs of elements (e.g., (1,5)) for which both (a, b) and (b, a) are in the relation and a ≠ b.

Since the matrix represents a binary relation, the concept of transitivity cannot be determined from the given information.

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Answer:

Step-by-step explanation:

Given the height at which an ogject dropped modelled by the function f(x)=-16x^2+144

The height of the body on the ground occurs at when f(x) = 0

0 =-16x^2+144

16x^2 = 144

x^2 = 144/16

x^2 = 9

x = 3

The ball reached the ground after 3 secs

The domain of a function is the input function that will make the function exist. Based on the function given, the function can exist on all given input value of x. Hence the domain of the function will be;

Domain =(-\infty, infty)

The domain of the function is required.

The domain of the function is the set of real numbers

\(x\in(-\infty,\infty)\)

The function is

\(f(x)=-16x^2+144\)

The y intercept of the function is

\(y=-16\times 0+144\\\Rightarrow y=144\)

\((0,144)\)

The y intercept is the maximum height here.

The x intercepts are the points where the object is on the ground.

They are

\(0=-16x^2+144\\\Rightarrow 16x^2=144\\\Rightarrow x=\pm\sqrt{\dfrac{144}{16}}\\\Rightarrow x=\pm3\)

\((3,0),(-3,0)\)

The domain of the function is the set of real numbers

\(x\in(-\infty,\infty)\)

The graph of the figure is attached.

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Answer:

18 pages

Step-by-step explanation:

that means you can read 2 pages in 10 minutes.

an hour and a half is 90 minutes.

90 is 9 times more than 10.

so we do 2 * 9 = 18 pages

The expression sin(e^37) does not have a well-defined limit as x approaches 0 from the left side since the argument e^37 is not an angle and is a constant.

To find the limit of the function sin(e^37) as x approaches 0 from the left side, we need to evaluate the limit and analyze the behavior of the function near 0.

The expression sin(e^37) represents the sine of a very large number, approximately equal to 5.32048241 × 10^16. The sine function oscillates between -1 and 1 as the input increases, but it does so in a periodic manner.

As x approaches 0 from the left side (x < 0), the function sin(e^37x) will oscillate rapidly between -1 and 1. However, since the argument of the sine function (e^37) is an extremely large constant, the oscillations will occur at a much higher frequency.

To calculate the limit, we can directly evaluate the function at x = 0 from the left side.

sin(e^37 * 0) = sin(0) = 0.

Therefore, the limit of sin(e^37) as x approaches 0 from the left side is equal to 0.

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The probability is approximately 0.7745 for the Gaussian random variable and approximately 0.4323 for the Laplace random variable.

Let's first find the probability P(-1 < Y < 2) when Y is a Gaussian random variable with mean 1 and variance 0.5.

We can standardize the random variable Y as follows:

Z = (Y - μ) / σ

where μ is the mean and σ is the standard deviation.

In this case, we have:

μ = 1 and σ²

= 0.5, so σ

= sqrt(0.5)

= 0.7071.

Substituting these values, we get:

Z = (Y - 1) / 0.7071

Now, we can find the probability P(-1 < Y < 2) in terms of Z as follows:

P(-1 < Y < 2) = P((-1 - 1) / 0.7071 < (Y - 1) / 0.7071 < (2 - 1) / 0.7071)

P(-2.8284 < Z < 1.4142)

Using a standard normal table or calculator, we can find that this probability is approximately 0.7745.

Now, let's find the probability P(-1 < Y < 2) when Y is a Laplace random variable with pdf \(0.5e^-|y|\).

We can integrate the pdf between -1 and 2 as follows:

P(-1 < Y < 2) = \(∫₋₁² 0.5e^-|y| dy\)

Since the pdf is even, we can simplify this as:

P(-1 < Y < 2) = \(2∫₀² 0.5e^-y dy\)

P(-1 < Y < 2) =\(e^-1 - e^-2\)

Using a calculator, we can find that this probability is approximately 0.4323.

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Number of degrees of freedom should we​ use for sample size of 15 at 95% confidence interval is 14.

Given:

Suppose we are making a​ 95% confidence interval for the population mean from a sample of size 15.

Degrees of freedom:

Degrees of freedom indicate the number of independent pieces of information used to calculate a statistic; in other words - they are the number of values that are able to be changed in a data set.

we know that,

Degrees of freedom df = n - 1.

where n = sample size

df = sample size - 1

= n - 1

= 15 - 1

= 14

Therefore number of degrees of freedom should we​ use for sample size of 15 at 95% confidence interval is 14.

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Answer:

D

Step-by-step explanation:

9 is the constant of proportionality

Have a great day

Answer:

..........uh ok but u do know that u need to answer questions and get points to talk to users....right..?

Answer:    3097083766196255

Step-by-step explanation:

Answer:

360°

Step-by-step explanation:

According to the properties of parallel lines, the following deductions can be made:

<a and <c are exterior angles of same side, therefore they are supplementary.

Thus,

m<a + m<c = 180°

<b and <d, are alternate interior angles, therefore, they are supplementary.

Thus, m<b + m<d = 180°.

The total numbers of degrees of a, b, c, d will all sum up to give 360°.

The work done by the force F in moving the object along the curve from t = 1 to t = e is eʸ(eᵉ - e) + ln(x)ln(e) + 3e² - 3 joules. Note that the values of x and y are not given, so we cannot compute the exact numerical value of the work done.

To find the work done by the force F, we need to integrate the dot product of the force and the differential displacement dr = r'(t)dt along the curve from t = 1 to t = e:

W = ∫ F · dr from 1 to e

First, we need to compute r'(t) = eᵗᶦ + (1/t)j + 2tk. Then, we can write:

F · dr = (eʸᶦ + ln(x)j + 3zk) · (eᵗᶦ + (1/t)j + 2tk)dt

= eʸ eᵗᵈᵗ + ln(x)(1/t)dt + 6t dt

Integrating each term over the interval [1, e], we get:

W = ∫ F · dr from 1 to e

= ∫1e (eʸ eᵗ + ln(x)(1/t) + 6t) dt

= eʸ(eᵉ - e) + ln(x)(ln(e) - ln(1)) + 3e² - 3

Therefore, the work done by the force F in moving the object along the curve from t = 1 to t = e is eʸ(eᵉ - e) + ln(x)ln(e) + 3e² - 3 joules. Note that the values of x and y are not given, so we cannot compute the exact numerical value of the work done.

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Answer:

4X + 5

Step-by-step explanation:

We start with the unknown number, X.

Doubling the number :

⇒ 2 × X

⇒ 2X

Adding 5 to double the number :

⇒ 2(2X) + 5

⇒ 4X + 5

To find the probability of having 7 or fewer successes in 11 trials with a probability of success of 0.2, we can use the binomial probability formula. The probability, Pr(X <= 7), is calculated as 0.982.

Explanation:

Given a binomial random variable with a probability of success of 0.2 and 11 independent trials, we want to find the probability of having 7 or fewer successes. To calculate this, we sum up the probabilities of having 0, 1, 2, 3, 4, 5, 6, and 7 successes.

Using the binomial probability formula, the probability of having exactly x successes in n trials with a probability of success p is given by:

P(X = x) = (n choose x) * p^x * (1 - p)^(n - x)

For this problem, p = 0.2, n = 11, and we need to calculate Pr(X <= 7), which is the sum of probabilities for x ranging from 0 to 7.

Calculating the individual probabilities and summing them up, we find that Pr(X <= 7) is approximately 0.982 when rounded to three decimal places.

Therefore, the probability of having 7 or fewer successes in 11 trials with a probability of success of 0.2 is 0.982.

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Answer:

0.01

Step-by-step explanation:

i hope this help only that u need to do next time is to divide 966 with a number that is close to the sum

Answer:

C. 54%

Step-by-step explanation:

Answer:

C. 54%

Step-by-step explanation:

The volume of the square pyramid-shaped roof with a height of 5 feet and a side length of 6 feet is 60 cubic feet.

A square pyramid has a square base and four triangular sides that come together to form a single point. To calculate the volume of a square pyramid, you can use the formula: 1/3 x Base x Height, where the base is the area of the square base and the height is the height of the pyramid.

In the given scenario, the rooftops of the village are shaped like square pyramids. The height of the roof is 5 feet and the length of the sides is 6 feet. Let us calculate the volume of the roof using the formula mentioned above:

The base of the square pyramid = side * side= 6 * 6= 36 sq. ft, Height of the square pyramid = 5 ft. Volume of the square pyramid= 1/3 * Base * Height= 1/3 * 36 sq. ft * 5 ft= 60 cubic feet. Therefore, the volume of the roof is 60 cubic feet.

Summary: A square pyramid has a square base and four triangular sides that come together to form a single point. The formula to calculate the volume of a square pyramid is 1/3 x Base x Height. The rooftops of the village are shaped as square pyramids with a height of 5 feet and the length of the sides is 6 feet. To calculate the volume of the roof, we can use the formula and find the volume of the roof. The volume of the roof is 60 cubic feet.

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Answer:

1 1/2

Step-by-step explanation:

1/2 times 1/3:

1/3 = 1/2

2/3 = 1

3/3 (1) = 1 1/2

When Tracey pours all the water from the smaller 5-inch cube container into the larger 7-inch cube container, the water will be approximately 7 inches deep in the larger container.

To find out how deep the water will be in the larger container, we need to consider the volume of water transferred from the smaller container. Since both containers are cube-shaped, the volume of each container is equal to the length of one side cubed.

The volume of the smaller container is 5 inches * 5 inches * 5 inches = 125 cubic inches.

When Tracey pours all the water from the smaller container into the larger container, the water completely fills the larger container. The volume of the larger container is 7 inches * 7 inches * 7 inches = 343 cubic inches.

Since the water fills the larger container completely, the depth of the water in the larger container will be equal to the height of the larger container. Since all sides of the larger container have the same length, the height of the larger container is 7 inches.

Therefore, the water will be approximately 7 inches deep in the larger container.

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Answer: 15 - 6i

Step-by-step explanation:

3(5-2i)

3×5+3×(−2i)

Do the multiplications.

15−6i

Ranking the speeds from the fastest unit rate to the slowest unit rate is as follows:

The unit rate describes the ratio comparing two quantities or values.

The unit rate is computed as the quotient between the numerator and the denominator

⁷/₄ miles in ²/₅ hour = 4.375 miles per hour (⁷/₄ ÷ ²/₅ )

⁴/₅ miles in ¹/₄ hour = 3.2 miles per hour (⁴/₅ ÷ ¹/₄)

¹/₄ miles in ¹/₁₀ hour = 2.5 miles per hour (¹/₄ ÷ ¹/₁₀)

¹/₂ miles in ¹/₃ hour = 1.5 miles per hour (¹/₂ ÷ ¹/₃).

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The probability Amelie spins either an odd number or a red number is:

P = 4/5

We want to find the probability of spinning a red or odd number, this is equal to the quotient between the number of odd numbers + the number of red numbers and the total number of numbers in the spinner.

Then there are 5 + 3 = 8 numbers that are either red or odd, and a total of 10 numbers, this means that the probability of spinning an odd number or a red number is:

P = 8/10 = 4/5

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Answer:

Step-by-step explanation:

Calculation

Divide your interest rate by the number of payments you'll make that year. ...

Multiply that number by your remaining loan balance to find out how much you'll pay in interest that month. ...

Subtract that interest from your fixed monthly payment to see how much in principal you will pay in the first month.