Amplitude of y= sin 3x

Answer:

d on edge

Step-by-step explanation:

its just the table flipped

Answer:

it's d

Step-by-step explanation:

∠IJG = ∠FGE (they are corresponding angle)

So, ∠FGE = 50°

Answer:

∠FGE is also 50°

Step-by-step explanation:

they are corresponding angles.

Hey there! I'm happy to help!

If you make a deposit, you add money to your bank account, and if you withdraw, you take money out of it.

We have $185.36 and we put in some deposits. Let's do this below.

$185.36+$13.74+$58.27+$69.30=$326.67

Now, we do some withdrawals and take money out.

$326.67-$19.29-$28.19-$52.55=$80.64

Therefore, Cybil has $226.64 in digital money.

Have a wonderful day! :D

The estimated coefficient for Fitness Center in a regression analysis represents the expected change in the dependent variable associated with a unit increase in the independent variable.

It tells us how much having a Fitness Center affects the rent price. To determine how much the rent price for a 1-bedroom apartment would be if the complex has a Fitness Center, Parking Space, and Wireless Internet, we would need to know the specific coefficients for each of these independent variables in the regression analysis, as well as the constant term. We could then plug in the values for each variable and calculate the predicted rent price. It is important to note that the estimated coefficient for Fitness Center does not necessarily imply causation. Other factors could be influencing both the presence of a Fitness Center and the rent price, and a regression analysis only captures the relationship between the variables that are included in the model. Additionally, the size and direction of the coefficient can vary depending on the data and methodology used in the analysis.

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Answer:

Perimeter of the rectangle is 29x + 1 feet

Step-by-step explanation:

Length of the rectangle = 9.5x + 10 feet

Width of the rectangle = 5x - 9.5 feet

perimeter of rectangle = 2 ( length + width )

perimeter = 2 { (9.5x + 10) + (5x-9.5) }

perimeter = 2 ( 9.5x + 5x + 10 - 9.5 )

perimeter = 2 (14.5x + 0.5)

perimeter =29x + 1 feet

Answer:

53,150 ML

Simply add both of the numbers and you have your answer.

Answer:

see explanation

Step-by-step explanation:

The 4 sides of a rhombus are congruent.

(i)

2y + x - 4 = 2x - y ( subtract 2x - y from both sides )

3y - x - 4 = 0 ( add 4 to both sides )

3y - x = 4 → (1)

and

\(\frac{4x-3y+5}{2}\) = 2x - y ( multiply both sides by 2 to clear the fraction )

4x - 3y + 5 = 4x - 2y ( subtract 4x - 2y from both sides )

- y + 5 = 0 ( subtract 5 from both sides )

- y = - 5 ( multiply both sides by - 1 )

y = 5

substitute y = 5 into (1)

3(5) - x = 4

15 - x = 4 ( subtract 15 from both sides )

- x = - 11 ( multiply both sides by - 1 )

x = 11

(ii)

then

2x - y = 2(11) - 5 = 22 - 5 = 17

perimeter = 4 × 17 = 68 cm

Answer:

36

Step-by-step explanation:

Let a² = x

a²-12a+36=0

or, (a-6)²=0

or, a-6=0

or, a = 6

Now a² = x, so x = 6² = 36

The solution of the given equation is (i) x = 3 ,(iii) x=-1/2 .

Quadratic equation's roots The roots of a quadratic equation are the values of the variables that satisfy the equation. In other words, if f() = 0, therefore x = is a root of the quadratic equation f(x). The x-coordinates of the points where the curve y = f(x) intersects the x-axis are the real solutions of an equation f(x) = 0.

So we can find the root of 2\(x^2\)— 5x —3 = 0 by factorising them.

=> 2x² - 5x - 3 = 0

=> 2x² - 6x + x - 3 = 0

=> 2x(x - 3) + (x - 3) = 0

=> (x-3)(2x+1) = 0

so the value of x = 3 , - 1/2

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Complete question :

For 2\(x^2\)— 5x —3 = 0, determine which of the following are solutions?

(i) x = 3 (ii) x= –2

(iii) x=-1/2 (iv) x=-1/3

Answer:

$56.66

Step-by-step explanation:

Because if you take 45+125 you get 170 and if you divide 170 by 3 which is the months you get 56.66.

We used the fact that y goes to 1 as x goes to infinity to determine the value of the constant C in the equation we got from part B. This allowed us to find the equation for the curve.

C) To find the equation for the curve given the condition that as x goes to infinity, y goes to 1, we need to use the solution obtained in part B and determine the constant C. Here's how to do it:

As x approaches infinity, we have:
1 = sqrt((x^4 + 8x^2 + 16) / (2x)) + C

Since x is going to infinity, we can consider x^4 to be dominant over the other terms in the numerator, so:
1 ≈ sqrt((x^4) / (2x)) + C

Simplifying the above expression, we get:
1 ≈ sqrt(x^3 / 2) + C

As x goes to infinity, the term sqrt(x^3 / 2) also goes to infinity. For the equation to hold true, C must be equal to negative infinity. However, since C is a constant and not a variable, we cannot consider it to be equal to negative infinity.

Thus, there seems to be a mistake in the solution obtained in part B, as it does not satisfy the given condition in part C. Please double-check the solution and steps taken in part B to ensure the correctness of the answer.

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positive correlation :relationship between the number of hours a student studies and their grade point average (GPA).

negative correlation :relationship between the number of hours a student spends watching television and their grade point average (GPA).

Correlation is a statistical term that describes the relationship between two variables. When two variables are positively correlated, it means that as one variable increases, the other variable also increases. When two variables are negatively correlated, it means that as one variable increases, the other variable decreases.

An example of a positive correlation is the relationship between the number of hours a student studies and their grade point average (GPA). As the number of hours a student studies increases, their GPA also tends to increase. This is a positive correlation because both variables are increasing together.

An example of a negative correlation is the relationship between the number of hours a student spends watching television and their grade point average (GPA). As the number of hours a student spends watching television increases, their GPA tends to decrease. This is a negative correlation because one variable is increasing while the other is decreasing.

It's important to note that correlation does not imply causation. Just because two variables are correlated it does not mean that one variable causes the other. It could be that some other variable is causing both variables to change, or that the relationship is not causal at all.

In summary, correlation is a statistical term that describes the relationship between two variables. Positive correlation means that as one variable increases, the other variable also increases.

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The following ordered pairs are the solutions to 5x+2y=-1 :

(1,-3) and (-3,7)

Given we have the ordered pairs and the equation.

To find out whether the ordered pair is a solution or not, we just need to replace the x and y values from the ordered pair (x,y) and check if both the sides equate.

a. (1,-3)

5x+2y=-1

5(1)+2(-3) = -1

consider L.H.S

5-6

= -1

Therefore, L.H.S = R.H.S

hence the ordered pair (1,-3) is a solution to 5x+2y=-1.

b. (2,8)

5x+2y=-1

5(2)+2(8) = -1

consider L.H.S

10+16

= 16

Therefore, L.H.S ≠ R.H.S

hence the ordered pair (2,8) is not a solution to 5x+2y=-1.

c. (-4,-6)

5x+2y=-1

5(-4)+2(-6) = -1

consider L.H.S

-20-12

= -32

Therefore, L.H.S ≠ R.H.S

hence the ordered pair (-4,-6) is not a solution to 5x+2y=-1.

d. (-3,7)

5x+2y=-1

5(-3)+2(7) = -1

consider L.H.S

-15+14

= -1

Therefore, L.H.S = R.H.S

hence the ordered pair (2,8) is a solution to 5x+2y=-1.

Therefore the ordered pairs which are solutions to 5x+2y=-1 are:

(1,-3) and (-3,7)

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So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

The image of the reflection over the x-axis is (-7, 3)

Remember that for a general point (x, y), a reflection over the x-axis just changes the sign of the y-value.

Then the transformation is:

(x, y) --> (x, -y)

If here the point is (-7, -3)

This transformation will give us:

(-7, -3) ---> (-7, -(-3)) = (-7, 3)

That is the image of the reflection.

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The statements that are true about the function are: The vertex of the function is at (1,-25), and the graph is negative on the entire interval -4 < x < 6.

1. The vertex of the function is at (1,-25): To determine the vertex of the function, we need to find the x-coordinate by using the formula x = -b/2a, where a and b are the coefficients of the quadratic function in the form of \(ax^2\) + bx + c. In this case, the function is f(x) = (x + 4)(x - 6), so a = 1 and b = -2. Plugging these values into the formula, we get x = -(-2)/(2*1) = 1. To find the y-coordinate, we substitute the x-coordinate into the function: f(1) = (1 + 4)(1 - 6) = (-3)(-5) = 15. Therefore, the vertex of the function is (1,-25).

2. The graph is negative on the entire interval -4 < x < 6: To determine the sign of the graph, we can look at the factors of the quadratic function. Since both factors, (x + 4) and (x - 6), are multiplied together, the product will be negative if and only if one of the factors is negative and the other is positive. In the given interval, -4 < x < 6, both factors are negative because x is less than -4.

Therefore, the graph is negative on the entire interval -4 < x < 6.

The other statements are not true because the vertex of the function is at (1,-25) and not (1,-24), and the graph is negative on the entire interval -4 < x < 6 and not just on one interval where x < -4.

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Answer:

the shoes cost $134.43 with tax

Given:

She is required to read a total = \(10\dfrac{5}{6}\) hours a week.

Monday she read \(1\dfrac{1}{3}\) hours.

Tuesday she read \(\dfrac{3}{4}\) of an hour.

Thursday she read 3 hours.

To find:

The total hours does she still need to read in order to get full credit.

Solution:

Total time = \(10\dfrac{5}{6}\) hours a week.

Total time she already read \(=1\dfrac{1}{3}+\dfrac{3}{4}+3\) hours

                                              \(=\dfrac{1\times 3+1}{3}+\dfrac{3}{4}+3\) hours

                                              \(=\dfrac{4}{3}+\dfrac{3}{4}+3\) hours

                                              \(=\dfrac{16+9+36}{12}\) hours

                                              \(=\dfrac{61}{12}\) hours

Now,

Remaining time = Total time - Total time she already read

                         \(=10\dfrac{5}{6}-\dfrac{61}{12}\)

                         \(=\dfrac{65}{6}-\dfrac{61}{12}\)

                         \(=\dfrac{130-61}{12}\)

                         \(=\dfrac{69}{12}\)

                         \(=\dfrac{23}{4}\)

                         \(=5\dfrac{3}{4}\)

Therefore, the required time is  \(5\dfrac{3}{4}\) hours.

The slope of the line in the reduced form is 4 / 7.

The slope of a line is the change in the dependent variable with respect to the change in the independent variable.

Therefore,

slope = m = change in y / change in x

slope = m = y₂ - y₁ / x₂ - x₁

P = (2, 3)

Q = (9, 7)

x₁ = 2

x₂ = 9

y₁ = 3

y₂ = 7

Therefore,

slope = 7 - 3 / 9 - 2

slope = 4 / 7

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Answer:

14

Step-by-step explanation:

5+(3*3)

5+9

14

the number is 40.

In mathematics, the system of linear equations is the set of two or more linear equations involving the same variables. Here, linear equations can be defined as the equations of the first order, i.e., the highest power of the variable is 1. Linear equations can have one variable, two variables, or three variables. Thus, we can write linear equations with n number of variables. In this article, you will get the definition of the system of linear equations, different methods of solving these systems of linear equations and solved examples.

If the tens digit of the number is X and the ones digit is Y then the number is equal to 10*X + Y

If you reverse the digits then the number is equal to 10*Y + X

If reversing the digits decreases the number by 36 then

10*Y + X = 10*X + Y - 36

The sum of the digits is 4 so X + Y = 4  ==>  X = 4 - Y

Substitute this value of X into the 1st equation

10*Y + (4 - Y) = 10*(4 - Y) + Y - 36

9*Y + 4 = 40 - 9*Y - 36

18*Y = 0

Y = 0

So X = 4 - 0 = 4 and the number is 40

Check:  40 - 04 = 36

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The number of people are 72.

Highest Common Factor is the full name for HCF in mathematics.

According to the laws of mathematics, the highest positive integer that divides two or more positive integers without leaving a residual is known as the greatest common divisor, or gcd.

Least Common Multiple is the full name for LCM in mathematics.

LCM (a,b) in mathematics stands for the least common multiple, or LCM, of two numbers, such as a and b. The smallest or least positive integer that is divisible by both a and b is known as the LCM.

We need to know the size of the pieces in order to calculate how many people can be fed equal-sized pieces of cake from a 16 by 18-inch cake.

Assume that each piece is a square with sides measuring "x" in length. Each piece's area would be x², and the cake's overall area would be 16 x 18 inches, or 288 square inches.

We must divide the entire area of the cake by the area of each piece to determine the maximum number of pieces that can be cut from the cake:

288 / x² = (16*18) / x² = 288 / x²

Choosing a "x" value that evenly splits into 16 and 18 is necessary if we want every piece to be the exact same size. Since 2 is the greatest possible value, we can divide the cake into 8 rows of 9 squares, yielding a total of 72 pieces.

As a result, a cake measuring 16 inches by 18 inches can be divided into 72 equal-sized pieces, each measuring 2 inches by 2 inches.

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We can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

A two-dimensional figure, form, or planar lamina's area is a measurement of how much space it takes up in the plane.

To find out how many people can be served equal-sized pieces of cake from a cake that is 16 inches by 18 inches, we need to first determine the size of each piece of cake.

The total area of the cake is:

16 inches x 18 inches = 288 square inches

To divide the cake into equal-sized pieces, we need to determine the size of each piece. Let's assume we want each piece to be a square. To find the size of each square, we need to find the square root of the total area of the cake:

√(288 square inches) ≈ 16.97 inches

Since we want the pieces to be exactly the same size, we'll round down to the nearest inch, which gives us:

Each piece of cake will be approximately 16 inches by 16 inches.

To find out how many people can be served equal-sized pieces of cake, we need to divide the total area of the cake by the area of each piece:

288 square inches ÷ (16 inches x 16 inches) = 18

Therefore, we can serve 18 people equal-sized pieces of cake from a cake that is 16 inches by 18 inches, assuming each piece is a square and we want the pieces to be exactly the same size.

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Answer:

12 cars per day

Step-by-step explanation:

Answer:

The answer is n + 3

Use analytic methods,

(a) The local extrema,

1) If f'(x) > 0 for all x on (a , c) and f'(x)<0 for all x on (c , b), then f(c) is a local maximum value.

2) If f'(x) < 0 for all x on (a , c) and f'(x)>0 for all x on (c , b), then f(c) is a local maximum value.

(b) The intervals on which the function is increasing

Write properties of function :

Increasing interval : ( - ∞ , 0 )

(c) The intervals on which the function is decreasing

Write properties of function :

Decreasing interval : ( 0 , ∞ )

Given that,

Use analytic methods (a) the local extrema, (b) the intervals on which the function is increasing, and (c) the intervals, then the function is,

A function's growing (or decreasing) periods match the periods when its derivative is positive (or negative). As a result, we can easily determine the intervals where a function increases or decreases by taking its derivative and analyzing it to determine if it is positive or negative.

Let f be continuous on an open interval (a , b) that contains a critical x-value.

1) If f'(x) > 0 for all x on (a , c) and f'(x)<0 for all x on (c , b), then f(c) is a local maximum value.

2) If f'(x) < 0 for all x on (a , c) and f'(x)>0 for all x on (c , b), then f(c) is a local maximum value.

(b) The intervals on which the function is increasing

Write properties of function :

Increasing interval : ( - ∞ , 0 )

(c) The intervals on which the function is decreasing

Write properties of function :

Decreasing interval : ( 0 , ∞ )

Therefore,

Use analytic methods,

(a) The local extrema,

1) If f'(x) > 0 for all x on (a , c) and f'(x)<0 for all x on (c , b), then f(c) is a local maximum value.

2) If f'(x) < 0 for all x on (a , c) and f'(x)>0 for all x on (c , b), then f(c) is a local maximum value.

(b) The intervals on which the function is increasing

Write properties of function :

Increasing interval : ( - ∞ , 0 )

(c) The intervals on which the function is decreasing

Write properties of function :

Decreasing interval : ( 0 , ∞ )

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2x²+3x+7=x

2x²+3x-x+7=0

2x²+2x+7=0

Answer:

x = 7

Step-by-step explanation:

Angle S and angle V are supplementary angles which means their sum is equal to 180°.

We can write the following equation to find the value of x based on the above mentioned information:

8x - 21 + 145 = 180

8x + 124 = 180

8x = 56

x = 7

Answer:3/4

Step-by-step explanation:

3÷1=3

8÷2=4