How i can answer this question, NO LINKS, if you answer correctly i will give u brainliest!

Answer:

729

Step-by-step explanation:

9x9x9 = 729 in^3

The system of equation that could have led to the equation 9x = 27 is

7x - 2y = 15

x + y = 6

The correct option is the third option

7x - 2y = 15

x + y = 6

From the question, we are to determine the system that could have led to 9x = 27

1.

9x + 2y = 21

-9x - 2y = 21

Subtracting, we get

9x + 2y = 21

-9x - 2y = 21

-------------------

18x + 4y = 0

2.

10x - y = 15

x + y = - 12

Subtracting, we get

10x - y = 15

x + y = - 12

---------------------

9x -2y = 27

3.

7x - 2y = 15

x + y = 6

Here, multiply the second equation by 2

2 × [x + y = 6]

2x + 2y = 12

Now, add to the first equation

7x - 2y = 15

2x + 2y = 12

------------------

9x = 27

4.

4x + 3y = 24

-5x - 3y = 3

Subtracting, we get

4x + 3y = 24

-5x - 3y = 3

---------------------

9x + 6y = 21

Hence, the system of equation that could have led to the equation 9x = 27 is

7x - 2y = 15

x + y = 6

The correct option is the third option

7x - 2y = 15

x + y = 6

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Answer and Step-by-step explanation:

The y-intercept is (0, 3)

The value 3 is in the y place.

#teamtrees #WAP (Water And Plant)

D.y = 10x + 250

y = 12x + 150 is the correct answer to the question

The amount you will have in 5 years with an initial deposit of $2,500 in an account that pays .51 percent interest compounded quarterly is $2,767.74.

To calculate the interest earned for the next 5 years at a quarterly compounding rate of .51 percent, we use the formula given below;A = P(1 + r/n)^(nt)

where, A is the amount,P is the principal, r is the interest rate in decimal, n is the number of times compounded per year and t is the number of years we will invest in.

Using the formula, we can get the answer. Therefore, the amount you will have in 5 years with an initial deposit of $2,500 in an account that pays .51 percent interest compounded quarterly is $2,767.74.

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Answer:

AB = 9.06

Step-by-step explanation:

Side AB is adjacent to angle B, To calculate it, the  cosine trig ratio is used:

\(cos39^{o} =\frac{AB}{11.66}\)

\(AB=11.66cos39^{o} =9.06\)

Hope this helps

Answer:

The ball is 7 feet above the ground 2 seconds after it is thrown.

Step-by-step explanation:

As per the given statement, we are given a graph of function \(f(x)\) where 'x' is time (in seconds) in the current scenario.

Time is plotted on x axis and height of football is plotted on y axis.

\(f(x)\) is the height of football according to change in time.

Following are the few things that can be observed from the given curve:

1. Initial Height of football is ~4.8 feet i.e. at 0 seconds of time.

2. Football reaches a maximum height of ~7.2 feet at 1.5 seconds.

3. After 1.5 seconds, the height of football starts decreasing.

Here f(2) means, the height of ball at 2 seconds of time.

It is clearly visible from the given graph that height is 7 feet at 2 seconds.

Please refer to the attached answer image. Height at 2 seconds is marked as point P.

Hence, The ball is 7 feet above the ground 2 seconds after it is thrown.

The best linear approximation to the function f(x) = e^x near x = 0 is L(x) = x + 1.

The given function is f(x) = e^x near x = 0.

To find the best linear approximation, L(x), we use the formula:

L(x) = f(a) + f'(a)(x-a),

where a is the point near which we are approximating.

Let a = 0, so that a is near the point x = 0.

f(a) = f(0) = e^0 = 1

f'(x) = d/dx (e^x) = e^x;

so f'(a) = f'(0) = e^0 = 1

Substituting these values into the formula: L(x) = 1 + 1(x-0) = x + 1

Therefore, the best linear approximation to f(x) = e^x near x = 0 is L(x) = x + 1.

For instance, linear approximation is used to approximate the change in a physical quantity due to a small change in another quantity that affects it.

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Answer:

\(\textsf{19.} \quad \dfrac{(x+4)^2}{12}+\dfrac{(y-1)^2}{8}=1\)

\(\textsf{20.} \quad \textsf{Center}: \;\;(-4, 1)\)

\(\textsf{21.} \quad \textsf{Major axis}:\;\;4\sqrt{3}\)

\(\textsf{22.} \quad \textsf{Minor axis}:\;\;4\sqrt{2}\)

\(\textsf{23.} \quad \textsf{Sum of the focal radii}:\;\;4 \sqrt{3}\)

\(\textsf{24.} \quad \textsf{Foci}:\;\;(-6, 1)\;\; \textsf{and}\;\;(-2,1)\)

\(\begin{aligned}\textsf{25.} \quad &\textsf{Vertices}:\;\;(-4-2\sqrt{3}, 1) \;\; \textsf{and}\;\; (-4+2\sqrt{3}, 1)\\ &\textsf{Co-vertices}:\;\;(-4, 1-2\sqrt{2}) \;\; \textsf{and}\;\; (-4, 1+2\sqrt{2})\end{aligned}\)

\(\textsf{26.} \quad \textsf{Eccentricity}\;\;\dfrac{\sqrt{3}}{3}\)

27.  See attachment.

Step-by-step explanation:

\(\boxed{\begin{minipage}{5 cm}\underline{General equation of an ellipse}\\\\$\dfrac{(x-h)^2}{a^2}+\dfrac{(y-k)^2}{b^2}=1$\\\end{minipage}}\)

Given equation:

\(2(x+4)^2+3(y-1)^2=24\)

To write the equation of the ellipse in standard form, divide both sides by 24 so that the right side of the equation is equal to one:

\(\implies \dfrac{2(x+4)^2}{24}+\dfrac{3(y-1)^2}{24}=\dfrac{24}{24}\)

\(\implies \dfrac{(x+4)^2}{12}+\dfrac{(y-1)^2}{8}=1\)

Therefore:

The center of the ellipse is (h, k).

Therefore, the coordinates of the center are (-4, 1).

As a > b, the ellipse is horizontal, so 2a is the major axis and 2b is the minor axis.  Therefore:

The focal radius is the distance from a point on the ellipse to a focus.

The sum of the focal radii is equal to the length of the major axis.

Therefore, the sum of the focal radii is 4√3.

As a > b, the coordinates of the foci are (h±c, k).

As c² = a² - b², first find the value of c:

\(\implies c^2=12-8\)

\(\implies c=\sqrt{4}=2\)

Therefore, the coordinates of the foci are:

As a > b, the coordinates of the vertices are (h±a, k):

and the coordinates of the co-vertices are (h, k±b):

The eccentricity of the ellipse is:

\(\implies e=\dfrac{c}{a}=\dfrac{2}{2\sqrt{3}}=\dfrac{\sqrt{3}}{3}\)

Answer:

Yes. 34.79 is a rational number because it can be written as a fraction.

Step-by-step explanation:

Hoped this helped.

15552|2

7776|2

3888|2

1944|2

972|2

486|2

243|3

81|3

27|3

9|3

3|3

1

\(15552=2^6\cdot 3^5=(2^3\cdot3^2)^2\cdot 3\)

\((3+1)\cdot(2+1)=4\cdot 3=12\)

It's 12

Plugging in the values, we see that object 1 has more potential energy (the ball to the left)

Answer:

(B.) f(x) = |x|

Step-by-step explanation:

Just took the test%

a. the sum of the first 200 natural numbers is 20,100. b. when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).

(a) To find the sum of the first 200 natural numbers, we can use the formula for the sum of an arithmetic series.

The sum of the first n natural numbers is given by the formula: Sn = (n/2)(a + l), where Sn represents the sum, n is the number of terms, a is the first term, and l is the last term.

In this case, we want to find the sum of the first 200 natural numbers, so n = 200, a = 1 (the first natural number), and l = 200 (the last natural number).

Substituting these values into the formula, we have:

Sn = (200/2)(1 + 200)

  = 100(201)

  = 20,100

Therefore, the sum of the first 200 natural numbers is 20,100.

(b) The ball rebounds three-fourths of the distance it drops, so each time it hits the pavement, it travels a total distance of 1 + (3/4) = 1.75 times the distance it dropped.

For the 6th rebound, we need to find the distance the ball traveled when it hits the pavement.

Let's represent the initial drop distance as h (30 ft).

The total distance traveled after the 6th rebound is given by the sum of a geometric series:

Distance = h + h(3/4) + h(3/4)^2 + h(3/4)^3 + ... + h(3/4)^5 + h(3/4)^6

Using the formula for the sum of a geometric series, we can simplify this expression:

Distance = h * (1 - (3/4)^7) / (1 - 3/4)

Simplifying further:

Distance = h * (1 - (3/4)^7) / (1/4)

        = 4h * (1 - (3/4)^7)

        = 4 * 30 * (1 - (3/4)^7)

Calculating the value:

Distance ≈ 4 * 30 * (1 - 0.1335)

        ≈ 4 * 30 * 0.8665

        ≈ 104 ft

Therefore, when the ball hits the pavement for the 6th time, it will have traveled approximately 104 feet in total (up and down).

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Answer:

(-5, -3)

Step-by-step explanation:

Divide by 2

The function that can be used to get the height of the helicopter above the ground is: H=280m−1,500

A function is a statement, rule, or law in mathematics that establishes the link between an independent variable and a dependent variable (the dependent variable).

How to solve for the function

The value 280 is the constant rate that the helicopter is said to be descending.

The altitude from which it is coming down is given as 1500 feet

The function would be written as H=280m−1,500

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The required, 4.5 × 10⁵ as an ordinary number is 450,000.

An ordinary number is a number that is expressed in the usual way, using digits 0-9 without any exponent notation or other mathematical symbols.

4.5 × 10⁵ means 4.5 multiplied by 10 raised to the power of 5. To write this as an ordinary number, we simply need to perform this multiplication:

4.5 × 10⁵ = 4.5 × 100,000 = 450,000

Therefore, 4.5 × 10⁵ as an ordinary number is 450,000.

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The horizontal asymptote of the function is y = 0.
The function g(x) has two vertical asymptotes, one at\(x = (-r + \sqrt (r^2 + 24))/6\) and the other at \(x = (-r - \sqrt(r^2 + 24))/6\), and a horizontal asymptote at y = 0.

The asymptotes of a function, we need to determine when the function is undefined.

Vertical asymptotes occur when the denominator of a fraction is equal to zero, while horizontal asymptotes occur when the value of the function approaches a constant as x approaches infinity or negative infinity.
Starting with the given function \(g(x) = (22 + 5x + 4)/(3x^2 + r - 2)\), we can find the vertical asymptotes by setting the denominator equal to zero and solving for x:
\(3x^2 + r - 2 = 0\)
This is a quadratic equation, and we can solve for x using the quadratic formula:
\(x = (-r \± \sqrt (r^2 + 24))/6\)
Since we don't know the value of r, we cannot determine the exact values of the vertical asymptotes.

We can say that there are two vertical asymptotes, one at \(x = (-r + \sqrt (r^2 + 24))/6\)and the other at\(x = (-r - \sqrt (r^2 + 24))/6\).
To find the horizontal asymptotes, we need to look at the behavior of the function as x approaches infinity and negative infinity.

We can do this by dividing both the numerator and denominator by the highest power of x:
\(g(x) = (22/x^2 + 5/x + 4/x^2) / (3 - 2/x^2 + r/x^2)\)
As x approaches infinity, the terms with the highest power of x dominate the fraction, so we can simplify the expression to:
\(g(x) \approx 22/3x^2\)
As x approaches negative infinity, the terms with the highest power of x are still dominant, so we get the same result:
\(g(x) \approx 22/3x^2\)

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Answer: see below...

Step-by-step explanation:

a) no: 50% of 4,000 is 2,000. 50% of 2,000 is a 1,000. So the car is not “free”, you will have to pay a $1,000.

b) $1,000

In quadrilateral EFGH, sides FG and EH are congruent because they each have a length of 7.07. Sides EF and GH are not congruent. The area of quadrilateral EFGH is closest to 41 square units.

For the width, we would determine the distance between the vertices F (-1, 4) and G(4, -1)

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance FG = √[(4 - (-1))² + (-1 - 4)²]

Distance FG = √[5² + (-5)²]

Distance FG = √50

Distance FG = 7.07 units.

Distance EH = √[(1 - (-4))² + (-4 - 1)²]

Distance EH = √[5² + (-5)²]

Distance EH = √50

Distance FG = 7.07 units.

For the length, we would determine the distance between the vertices E (-4, 1) and F (-1, 4)

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance EF = √[(-1 - (-4))² + (4 - 1)²]

Distance EF = √[3² + (3)²]

Distance EF = √9

Distance EF = 3 units.

Distance HG = √[(4 - 1)² + (1 - (-4))²]

Distance HG = √[3² + (5)²]

Distance HG = √34 units.

Mathematically, the area of a rectangle can be calculated by using this formula:

Area of rectangle = length × width

Area of rectangle = √34 × 7.07

Area of rectangle = 41.22 square units.

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Answer:

1/3n - 3<6

n < 27

Step-by-step explanation:

1/3n - 3<6

Add 3 to each side

1/3n -3+3<6+3

1/3 n <9

Multiply by 3

1/3n *3 < 9*3

n < 27

Careful consideration and statistical analysis should be undertaken to determine the appropriate variables to include in a regression model.

By including another variable in a regression analysis, several outcomes are possible. Let's consider the statements you provided one by one:

1. Decrease the regression R^2 if that variable is important:

  - If the added variable is important and has a meaningful relationship with the dependent variable, it can increase the explanatory power of the regression model, thereby increasing the R^2.

However, if the added variable is not relevant or has a weak relationship with the dependent variable, it can decrease the R^2.

2. Decrease the variance of the estimator of the coefficients of interest:

  - Including additional variables in a regression model can sometimes help to reduce the variance of the coefficient estimators for the variables of interest.

This is because including more relevant variables can help to explain some of the variance in the dependent variable, leaving less unexplained variance for the coefficients of interest.

3. Eliminate the possibility of omitted variable bias from excluding that variable:

  - Omitted variable bias can occur when an important variable is not included in the regression model.

Including all relevant variables in the model can help reduce the risk of omitted variable bias, as it allows for a more comprehensive analysis of the relationship between the dependent variable and the independent variables.

4. Look at the t-statistic of the coefficient of that variable and include the variable only if the coefficient is statistically significant at the 1% level:

  - The t-statistic measures the statistical significance of a coefficient. Inclusion of a variable in a regression model is often based on its statistical significance.

If the coefficient of the variable is statistically significant at the desired significance level (e.g., 1%), it suggests that the variable has a meaningful impact on the dependent variable and can be included in the model.

It is important to note that the effect of including an additional variable in a regression model depends on various factors such as the relationship between the variables, sample size, multicollinearity, and the specific research context.

Therefore, careful consideration and statistical analysis should be undertaken to determine the appropriate variables to include in a regression model.

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The probability density function of Y is f_Y(y) = 1, for y ∈ (0, 1).

Given that X has an exponential distribution with λ=1.

Let X be a random variable with an exponential distribution characterized by parameter λ=1. This implies that the probability density function of X is given by:

f_X(x) = λ * e^(-λx) = e^(-x), for x ≥ 0.

Now, we are asked to find the probability density function of Y, where Y = e^(-X). To do this, we'll use the transformation technique. First, we find the inverse transformation X = g(Y) by solving for X:

X = -ln(Y)

Next, we compute the derivative of g(Y) with respect to Y:

dg(Y)/dY = -1/Y

Now, we can use the transformation technique formula to find the pdf of Y:

f_Y(y) = f_X(g(y)) * |dg(y)/dy| = e^(-(-ln(y))) * |-1/y|

Simplifying this expression, we get:

f_Y(y) = y * (1/y) = 1, for y in the range (0, 1).

So, the probability density function of Y is f_Y(y) = 1, for y ∈ (0, 1).

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Answer:20

Step-by-step explanation:

y=1/2x+10

1/2x=y-10

x=2y-20

y=2x-20

In this problem, we want to determine which variables will give us the constant term of the trinomial.

We are given the binomials

When mutliplying these binomials, we can use the distributive property, or we can use the FOIL method.

Using distribution, we get:

Distributing the x and p for each term, we have

Recall that a constant term is any number that does not have a variable "attached" to it. For example, these are constants:

However, this is an abstract example. So for our purposes, the only true variable will be x, while p and q represent some unknown real numbers.

Since x is our variable, we see only the last term has no x attached to it.

Therefore, the constant term of the trinomial is the product of -p and q.

Answer: 13

Step-by-step explanation: