how did get 180 by solving 15 multiply by 12???

The solution is

A) The vertical asymptote of the function f ( x ) is = -3

B) The holes in the graph of f ( x ) = ( 0 , 6 )

C) The horizontal asymptote of the function f ( x ) is = 6

An asymptote is a line that a curve approaches but never touches. A line where the graph of a function converges is known as an asymptote. When graphing functions, asymptotes are typically not required

There are 3 types of asymptotes

Horizontal asymptote (HA) - It is a horizontal line and hence its equation is of the form y = k. Horizontal Asymptote is when the function f(x) is tending to zero

Vertical asymptote (VA) - It is a vertical line and hence its equation is of the form x = k. Vertical asymptotes are defined when the denominator of a rational function tends to zero

Slanting asymptote (Oblique asymptote) - It is a slanting line and hence its equation is of the form y = mx + b

here, we have,

Given data ,

Let the function be f ( x ) = ( 6x² + 6x - 36 ) / ( x² + 3x )

A)

Now , to find the vertical asymptote

To find the vertical asymptote of a rational function, we simplify it first to lowest terms, set its denominator equal to zero, and then solve for x values

So , when x² + 3x = 0

x ( x + 3 ) = 0

So , x + 3 = 0

x = 0 is a hole in the graph

x = -3 is the vertical asymptote

B) The hole in the graph is ( 0 , 6 )

C)

Now , to find the horizontal asymptote

If both the polynomials have the same degree, divide the coefficients of the leading terms

So , 6x² and x² are the polynomials having the same degree

So , the coefficients are 6 and 1

y = (leading coefficient of numerator) / (leading coefficient of denominator)

y = 6 is the horizontal asymptote

Hence ,

A) The vertical asymptote of the function f ( x ) is = -3

B) The holes in the graph of f ( x ) = ( 0 , 6 )

C) The horizontal asymptote of the function f ( x ) is = 6

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Complete question:

Find the following for the rational function

f (x) =6x²+62-36/x²+3

A. Find the vertical asymptote(s) of f.

B. Find the (x, y) coordinates of any holes in the graph of f.

C. Find the horizontal asymptote(s) of f.

this is ez, make sure to give me brainliest
Answer: ∠BAC = x = 15 degrees

Step-by-step explanation:

since AC is diameter, ∠ABC = 90 degrees
let ∠BAC = x
then ∠BCA = 5x
now, x + 5x + 90 = 180
6x = 90
x = 90/6 = 15
so, ∠BAC = x = 15 degrees

The probability that three cards chosen at random from a standard 52-card deck that are not all the same color is 3/4.

Total number of combinations of three cards: There are 52 choose 3 = 22,100 ways to choose three cards from a standard deck of 52 cards.

Number of combinations that are not all the same color: There are two possibilities for the colors of the three cards:

a. Two red cards and one black card: There are 26 choose 2 ways to choose two red cards and 26 choose 1 ways to choose one black card, for a total of (26 choose 2) * (26 choose 1) = 325 * 26 = 8,450 combinations.

b. Two black cards and one red card: There are 26 choose 2 ways to choose two black cards and 26 choose 1 ways to choose one red card, for a total of (26 choose 2) * (26 choose 1) = 325 * 26 = 8,450 combinations.

The total number of combinations that are not all the same color is 8,450 + 8,450 = 16,900.

The probability that three cards chosen at random are not all the same color is:

P(not all the same color) = (number of combinations that are not all the same color) / (total number of combinations of three cards) = 16,900 / 22,100 = 3/4.

Therefore, the probability that three cards chosen at random from a standard 52-card deck are not all the same color is 3/4.

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Based on the information provided, 2 is not a solution of x>5 because a possible solution requires a number greater than 5.

Inequalities include symbols such as >, ≤, ≥, among others that should be interpreted correctly to solve the inequality. In this case, the symbol in the inequality is >, which means greater than. Based on this, the value of x should be greater than 5, for example, 7, 19, 2948, etc.

Therefore, 2 is not a solution to the inequality x>5 because a number greater than 5 rather than less than 5 is required to solve this expression.

Note: This question is incorrect and incomplete; here is the complete question:

Explain why 2 is NOT a solution of x>5

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Price values, p, of new mountain bikes that Maddie can afford is 375 + 215 ≥ p

Inequality is a relationship between two expressions or values that are not equal to each other.

The inequality that can be used to find the possible price values, p, of new mountain bikes that Maddie can afford is:

375 + 215 ≥ p

This inequality represents the total amount of money Maddie has saved and the amount her grandmother will give her being greater than or equal to the cost of the bike. If the left side of the inequality is greater than or equal to the right side, Maddie can afford the bike at that price.

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Answer: The discount is $13.75, which is found by multiplying the original price by the discount percentage, 0.25.

Step-by-step explanation:

The solution is, the value of lengths are x & 4.

Area of a rectangle (A) is the product of its length (l) and width (w).

A= l. w

here, we have,

from the given figure we get,

area = 5x+20

where, two rectangles are with areas 5x & 20

now, from the diagram we have,

the area as product = 5 ( x+ 4)

so, we get,

1st rectangle , length = 5,

area = 5x

so, width = x ,

again. 2nd rectangle, length = 5

area = 20

so. width = 4

Hence, The solution is, the value of lengths are x & 4.

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In linear equation,  30 is the depth of the two dives by first rounding to the nearest ten.

What in mathematics is a linear equation?

An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation.

                          Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.

= 75-43 feet,

= 32 feet.

Round 32 to the nearest ten, and you get 30 feet.

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The complete question is -

A scuba diver plans to go on two dives in one day. In the first, she will descend to 75 feet, and in the second she plans to descend to 43 feet. Estimate the difference between the depth of the two dives by first rounding to the nearest ten.

A) 30 feet

B) 40 feet

C) 120 feet

D) 32 feet

The required slope of the linear function shown on the graph passing through (-5, -1) to (5, 1) is given as positive 1/5. Option A is correct.

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,
A coordinate plane with a straight line. The line starts at (-5, -1) and continues up and to the right passing through (0, 0) and (5, 1).

The slope of a linear function is given as,
M = (y₂ - y₁) /  (x₂ - x₁)

m = 1 + 1 / 5 + 5
m = 2 / 1 0
m = 1 / 5

Thus, the required slope of the linear function shown on the graph passing through (-5, -1) to (5, 1) is given as positive 1/5. Option A is correct.

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Answer:

the answer is a

Step-by-step explanation:

Answer: A general solution of a differential equation is a solution that contains all possible solutions of the equation, including all arbitrary constants. It provides a general form of the solution that can be customized to fit the specific conditions of the problem.

For example, the general solution of a second-order linear homogeneous differential equation of the form

y'' + p(x)y' + q(x)y = 0

is a combination of two linearly independent functions, often represented by y = c1y1(x) + c2y2(x), where c1 and c2 are arbitrary constants and y1(x) and y2(x) are two linearly independent solutions of the differential equation.

The general solution represents the most general form of the solution that takes into account all possible solutions, including all arbitrary constants. To find a specific solution, one must apply initial or boundary conditions to determine the values of the arbitrary constants.

Step-by-step explanation:

By definition of trigonometric functions, the exact value of sine trigonometric function of angle S is equal to 2 / 9.

In this problem we find the case of a right triangle, of which two of its three sides are known, the hypotenuse (r) and the leg opposite to angle S (y). The exact value of sine trigonometric function is defined below:

sin S = y / r

sin S = QR / QS

sin S = 2 / 9

The sine trigonometric function of angle S is equal to 2 / 9.

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Answer:

2:1

Step-by-step explanation:

We know

To get from F to G, we have to go from -2 to 2, for which the length is 4.

To get from F' to G', we have to go from -2 to 0, for which the length is 2.

What is the ratio of the sides from the big to the small rectangle?

The ratio is 4:2 = 2:1

Answer: 0

Step-by-step explanation:

-7,-6,-5,-4,-3,-2,-1,0

7 times

The equation that represents the transformation is y = (1/4)f(x-3) + 7

From the question, we have the following parameters that can be used in our computation:

This equation applies the following transformations to the graph of y = f(x):

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The team plans to use 30% of all donations and car wash proceeds for new equipment, so they will have $430 * 0.30 = $129 to spend on new equipment.

We can start by finding the total amount of money raised from the car wash and donations on Saturday and Sunday.  If the team charged $5 per car wash, then the total amount of money raised from car washing on Saturday is 25 * 5 = $125. The total amount raised from donations and car washing on Saturday is $125 + 95 = $220. Similarly, the total amount of money raised from car washing on Sunday is 19 * 5 = $95. The total amount raised from donations and car washing on Sunday is $95 + 115 = $210. The total amount of money raised over the weekend is $220 + $210 = $430. The team plans to use 30% of all donations and car wash proceeds for new equipment, so they will have $430 * 0.30 = $129 to spend on new equipment.  Next, we can find the total amount raised from donations over the weekend. On Saturday, the team raised $25 + 95 = $120 from donations. On Sunday, the team raised $19 + 115 = $134 from donations. So, the total amount raised from donations is $120 + $134 = $254. Finally, we can find the total amount the team raised over the weekend by adding the amount raised from car washes and the amount raised from donations: $220 + $254 = $474.

Since the team plans to use 30% of all donations and car wash proceeds for new equipment, they will have 0.30 * $474 = $142.20 to spend on new equipment.

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1. Complete the identities

a = -4

b = 34

c = 1

d = 3

2. Complete the identities

3x - 24 = 3(x - 8)

0 + x = x

5(x + 5) = 5x + 25

(a + b) + c = c + (a + b)

(x - a)(x - b) = x² - (a + b)x + ab

Before solving the above equation, we need to know the algebraic formula. The algebraic formula is

a(x + b) = ax + ab

1.

- 6(x - 4) + 2(x + 5) = ax + b

⇒ -6x + 24 + 2x + 10 = ax + b

   -6x + 2x + 24 + 10 = ax + b

   -4x + 34 = ax + b

So we get the values ​​a and b.

-4x = ax ⇔ a = -4

b = 34

− 3(x + c) − 4(x + d) = - 7x - 15

-3x - 3c - 4x - 4d = -7x - 15

-3x - 4x - 3c - 4d = -7x - 15

-7x - (3c + 4d) = -7x - 15

-7x + 7x - (3c + 4d) = - 15

- (3c + 4d) = - 15

3c + 4d =  15

Let c = 1

3c + 4d =  15

3(1) + 4d = 15

3 + 4d = 15

4d = 15 - 3

4d = 12

d = 3

2.

3x - 24

= 3 × x - 3 × 8

= 3(x - 8)

.... + x = x

-x + x = 0

5(x + 5) = 5 × x + 5 × 5

            = 5x + 25

(a + b) + c = c + (a + b)

Let (x + a)(x + b)

(x + a)(x + b) = x² + ax + bx + ab

                    = x² + (a + b)x + ab (not eligible)

Let (x + a)(x - b)

(x + a)(x - b) = x² + ax - bx - ab

                    = x² + (a - b)x - ab (not eligible)

Let (x - a)(x + b)

(x - a)(x + b) = x² - ax + bx - ab

                    = x² - (a - b)x - ab (not eligible)

Let (x - a)(x - b)

(x - a)(x - b) = x² - ax - bx + ab

                    = x² - (a + b)x + ab (eligible)

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The height is 2,236.66 feet.

An estimate of the line that depicts the actual, but unidentified, linear relationship between the two variables is called a regression line. When the value of the explanatory variable is known, the regression line's equation is used to predict (or estimate) the value of the response variable.

Given:

The model obtained using a regression solver with Coefficient

ŷ = 219.28876X + 109.56303

height = y

x = time

Using the model obtained;

The height, to the nearest foot, at a time, x = 9.7seconds.

ŷ = 219.28876X + 109.56303

ŷ = 219.28876(9.7) + 109.56303

ŷ = 2,236.66

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Answer:

Step-by-step explanation:

V = (1/2bh)l

= (1/2(5x2))4

= (5)(4)

= 20cm^3

[tex]A=\frac{b*h}{2} \\\\a^2+b^2=c^2\\\\2^2+5^2=c^2\\4+25=c^2\\\sqrt{29}=c\\ \\A=\frac{\sqrt{29}*4 }{2}\\ A=\frac{\sqrt{29}*\sqrt{16}}{2}\\ A=\frac{\sqrt{464}}{2}\\[/tex]

nvm this is wrong lol, too many "solve for the missing side" problems bouncing around in my head

[tex]A=\frac{(5*2)(4)}{2} \\A=\frac{5*2*4}{2}\\A=5*4\\A=20[/tex]

this is right

The standard form of the quadratic function with the given vertex is f(x) = 9x² + 6x + 10.

Quadratic functions are polynomial functions where the highest degree of the variable is 2..

The general form of a quadratic function is f(x) = ax² + b x + c.

We know that, graph of a quadratic function is parabola.

General equation of a parabola is a(x - h)² + k.

Here (h, k) is the vertex.

Given vertex = (-1/3, -1)

Substituting,

a(x - h)² + k = a(x + 1/3)² - 1

Also we have a point (x, y) = ((0, -10/9)

a(0 + 1/3)² - 1 = -10/9

a/9 - 1 = -10/9

a/9 = -1/9

a = -1

General form is -1(x + 1/3)² - 1 = -1(x² + 2/3 x + 1/9) - 1

                                                = -x² - 2/3 x -10/9

                                                = 9x² + 6x + 10

Hence the standard form of the function is f(x) = 9x² + 6x + 10

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the probability that he found his dog. alive is 15%.

What is probability?

The chance of an event can be calculated using the probability formula by simply dividing the favourable number of possibilities by the total number of outcomes. The likelihood of an event occurring can be anything between 0 and 1, as the favourable number of outcomes can never exceed the total number of outcomes. Probability theory is a branch of mathematics that focuses on calculating the likelihood that an event will occur. Probability measures how likely something is to happen.

if he searched in a for two days and b for two days

P(A) = 0.4

P(B) = 0.6

P(Dn D-1 F-1)= n n+2

P(FnA, Sn, F-1) = 0.25

P(FB, S, F-1) = 0.15

Hence the probability that he found his dog. alive is 15%.

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The next number in the Fibonacci sequence after 34 (found by adding 21 and 34) is 55.

The Fibonacci sequence is a series of numbers where each number is the sum of the two numbers preceding it. The sequence starts with 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, ... and continues infinitely. The number 34 is found by adding the two numbers before it (13 and 21), and the next number in the sequence is 55, which is the sum of 34 and 21. This pattern continues, with each subsequent number being the sum of the two numbers before it.

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The solution of the given expression for multiplication is 3 / 2.

Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.

Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.

Given that the expression of the multiplication is 1¹/₂ x 9 / 10.

The numbers will be multiplied as below:-

E =  1²/₃ x 9 / 10.

E = ( 5 / 3 ) x ( 9 / 10 )

E = 3 / 2

Therefore, the solution will be 3 / 2.

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The number Joe is thinking of is -36.

To find the number Joe is thinking of, use algebraic expression and equation.

Let x be the number Joe is thinking of

According to the problem, "Eleven more than one third of the number is -1". We can translate this into an algebraic expression such as:

x/3 + 11 = -1

To find the value of x, we'll isolate it on one side of the equation:

x/3 = -12

Next, we'll multiply both sides of the equation by 3 to cancel out the fraction:

x = -36

Therefore, the number Joe is thinking of is -36.

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Answer:

Step-by-step explanation:

To find the function rule for the relationship between x and f(x), we can perform a linear regression analysis on the given data points. This can be done using a spreadsheet software or a statistical software. One way to do this is to use the equation of a straight line, which is y = mx + b, where y is the output (f(x)), x is the input, m is the slope, and b is the y-intercept.

The slope m can be calculated as:

m = (Δy / Δx) = (f(x2) - f(x1)) / (x2 - x1) = (9 - 6) / (3 - 0) = 3

The y-intercept b can be calculated as:

b = f(x) - mx = 6 - 3x

So the function rule is:

f(x) = 3x + 6

To graph the function, we can plot the given data points and then draw a straight line that passes through those points. The graph of the function should look like this:

[!graph of f(x) = 3x + 6]

The function rule for the relationship between x and f(x) can be found using a similar process. Using the given data points, we can calculate the slope and y-intercept:

m = (Δy / Δx) = (f(x2) - f(x1)) / (x2 - x1) = (-2 - (-3)) / (1 - 0) = 1

b = f(x) - mx = -3 - x

So the function rule is:

f(x) = x - 3

The graph of the function should look like this:

[!graph of f(x) = x - 3]

For the third example, we can find the function rule using a similar process:

m = (Δy / Δx) = (f(x2) - f(x1)) / (x2 - x1) = (6 - 4) / (2 - 1) = 2

b = f(x) - mx = 4 - 2x

So the function rule is:

f(x) = 2x + 4

The graph of the function should look like this:

[!graph of f(x) = 2x + 4]

The graph shows the  inequality x² ≤ 16

An inequality is a relationship that makes a non-equal comparison between two numbers or other mathematical expressions e.g. 2x > 4.

Inequalities are often used to describe conditions or constraints in real-world problems.

You will notice that the values represented in the graph ranges from -4 to 4. Thus, solving x² ≤ 16 will produce these values. That is:

x² ≤ 16

x ≤ ±√16

x ≤ ±4

x ≤ -4 or x ≤ 4

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Yes, there is a statistically significant association between the variables when a p-value of 0.0000005 is obtained after running a chi-square test.

The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming that the null hypothesis is true.

In most cases, if the p-value is less than 0.05 (5%), it is considered statistically significant. This means that there is less than a 5% chance that the results observed in the chi-square test are due to random chance, and that there is likely a real association between the variables being tested.

In the case of a p-value of 0.0000005, this is much less than 0.05 and therefore, it can be concluded that there is a statistically significant association between the variables.

This means that the observed differences between the actual values and expected values are not due to chance, but rather, there is a strong relationship between the two variables being tested.

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