Which of the following is equivalent to cos(α+β)/cosβ for all values of α and β for which cos(α+β)/cosβ is defined?
Choices
cosαcotβ+sinα
cosαcotβ-sinα
cosαcosβ-sinα
cosα−sinαtanβ
cosα+sinαtanβ

Answer:

Step-by-step explanation:

The center of a hyperbola is located at the point where the two foci (focii) are located. In this case, the center of the hyperbola is located at point (3,-2), which is option D.

The  quotient of the fraction is -3/4 * p²/q²

We should know that when a number is divided by another number, the result is the quotient of the number

We have to find the quotient of the following division, -3/4 * p²/q²

This implies that (15p⁻⁴q⁻⁶)/(-20p⁻¹²q⁻³)

Now, (15p⁻⁴q⁻⁶)/(-20p⁻¹²q⁻³) will give

3/4p[(⁻⁴(⁻¹²)]q²(⁻⁶-(⁻³)]

We know that  all the terms in the expression are in product form, so we can treat them separately}

Hence  we know the property of exponent as aˣ/aᵇ=a(ᵇ⁻ˣ]

Hence this implies that -3/4 * p⁶/q²

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Sarah can blow 7 minutes to blow 21 balloons

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: Sarah can blow 3 balloons in 1 minute

Then unit rate of sarah is 3 balloons per minute

Thus the time she would take to blow 21 balloons is 21/3=7 minutes

Hence, Sarah can blow 7 minutes to blow 21 balloons

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Answer:

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

The line passes through the origin, therefore one point on the line is sufficient to determine the equation:

The point on the line is (1, - 3), so the line is:

Answer:

[tex]y=-3x[/tex]

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

From inspection of the given graph, two points on the line are:

Substitute the two points into the slope formula to calculate the slope of the line:

[tex]\implies m=\dfrac{-6-(-3)}{2-1}=\dfrac{-3}{1}=-3[/tex]

[tex]\boxed{\begin{minipage}{5.8 cm}\underline{Point-slope form of a linear equation}\\\\$y-y_1=m(x-x_1)$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $(x_1,y_1)$ is a point on the line.\\\end{minipage}}[/tex]

Substitute the found slope and one of the points on the line into the point-slope formula:

[tex]\implies y-(-3)=-3(x-1)[/tex]

[tex]\implies y+3=-3x+3[/tex]

[tex]\implies y=-3x[/tex]

By setting y = 0 and factoring, we can determine the roots of other polynomial functions. Because there is only one value of x for which x - 3 = 0 and no values of x for which x2 + 3x + 9 = 0.

A mathematical expression made up of coefficients and uncertainty that only makes use of additions, subtractions, multiplications, and positive integer powers of variables is known as a polynomial. The formula x2 4x + 7 denotes a single indeterminate x polynomial. An expression in mathematics known as a polynomial is made up of variables (also known as indeterminates) and coefficients that may be added, subtracted, multiplied, and raised to negative integer powers of non-variables. An algebraic statement with variables and coefficients is called a polynomial. An expression can only contain the operations addition, subtraction, multiplication, and non-negative integer exponents. Polynomials are the name for these expressions.

By setting y = 0 and factoring, we can determine the roots of other polynomial functions. Because there is only one value of x for which x - 3 = 0 and no values of x for which x2 + 3x + 9 = 0, the equation y = x3 -27 = (x - 3)(x2 +3x2 + 9) has only one root (x = 3). (the discriminant is negative).

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Answer: To calculate the percent decrease of water in the tank, we can use the following formula:

Percent decrease = (Initial value - Final value) / Initial value x 100%

In this case, the initial value of water in the tank is 5 inches and the final value is 3 inches. So, the percent decrease is:

(5 - 3) / 5 x 100% = 2 / 5 x 100% = 40%

So, the percent decrease of water in the tank is 40%.

Step-by-step explanation:

Therefore , the solution of the given problem of expressions comes out to be n= 19.

Addition, subtraction, division, and the term multiply are examples of numerical computations that are possible. The words are arranged as follows: An equation, a calculator, and an integer or variable A mathematical expression is mainly composed of constants, numbers, and processes (such as additions, subtraction, multiplying, or dividing, etc.). Contradictory claims or expressions and variable are possible.

Here,

Given : a^15.a^4

to find a^n

thus,

=>a^15.a^4 = a^n

=> a^(15+4) = a^n

=> a^19 = a^n

So, on comparing above expression

We get ,

n= 19

thus , n=19 is the solution for this problem

Therefore , the solution of the given problem of expressions comes out to be n= 19.

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Answer:

x<3

Step-by-step explanation:

3x+5<14

Your first step is to simplify the inequality.

To do this, always look to see if you can subtract any numbers from both sides to isolate a variable.

You can subtract 5 from both sides to isolate the 3x on one side.

After that, you will get 3x<9

Next, you must divide both sides by 3 to try and get x by itself, completing the inequality.

9/3 = 3

Your are left with: x<3

Done!

Answer:

x < 3

Step-by-step explanation:

3x + 5 < 14  subtract 5 from both sides

3x + 5 - 5 < 14 - 5

3x < 9  Divide both sides by 3

[tex]\frac{3x}{3}[/tex] < [tex]\frac{9}{3}[/tex]

x < 3

The algebraic formula to represent Giselle's profit is $b*1 - $18.72, or $b - $18.72, where $18.72 is spent on supplies.

A statement that contains at least two numbers or variables, along with at least one mathematical operation, is referred to as a mathematical expression. Any one of the following mathematical operations could be used: addition, subtraction, multiplication, or division. The following are an expression's fundamental parts: : (Number/Variable, Math Operator, Number/Variable). A statement that includes at least two numbers or variables, at least one mathematical operation, and the word "expression" is referred to as a mathematical expression. Let's review expressive writing. The alternative number, which is known as x, is 6 more than half of the given number. This sentence is denoted by the phrase x/2 + 6 in mathematics.

given

number of bracelets = b

profit = $b*1 - $18.72

The algebraic formula to represent Giselle's profit is $b*1 - $18.72, or $b - $18.72, where $18.72 is spent on supplies.

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Answer:

Step-by-step explanation:

To find the height of an obtuse angle in a triangle, you can use the following steps:

It is important to note that the hypotenuse of the right triangle (the base) must be the side opposite to the obtuse angle, and the other two sides should be the legs of the triangle. Also, the altitude can fall inside or outside of the triangle, it does not affect the calculation of the height.

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Answer: D

Step-by-step explanation:

The correct group is 3rd. (Option C)

The groups of numbers that are ordered correctly from least to greatest are :

-13,−16,12,1

-110,0.2,310,14

-112,−0.75,−0.25,112

The first group has -13, -16, 12 and 1. -13 and -16 are the smallest numbers and 1 is the largest, so it is ordered incorrectly from least to greatest.

The second group has -110,0.2,310,14 and -110 is the smallest number and 310 is the largest, so it is ordered incorrectly from least to greatest.

The third group has -112, -0.75, -0.25 and 112. -112 is the smallest number and 112 is the largest, so it is ordered correctly from least to greatest.

The last group has -8,-34,-3,14 and -34 is the smallest number and 14 is the largest, so it is not ordered incorrectly from least to greatest.

Therefore, the correct group is 3rd. (Option C)

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Answer:

20 ducks

Step-by-step explanation:

4+5=9

4/9:x/45

9*5=45

4*5=20ducks

The vertices of the polygon in the graph have co-ordinates as J(6,3) K(2,3) L(2,-3) M(6,-3)

In geometry, a polygon is a plane figure that is described by a finite number of straight line segments connected to form a closed polygonal chain.

Given here: A polygon JKLM

From the graph we can observe the co-ordinates as J(6,3) K(2,3) L(2,-3) M(6,-3)

Hence, the vertices of the polygon in the graph have co-ordinates as J(6,3) K(2,3) L(2,-3) M(6,-3)

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Rachel has 0.41 quarters that can be obtained using the equation Q + D + N = T.

We can start by using the following equation to find the number of quarters Rachel has: Q + D + N = T

Where Q is the number of quarters, D is the number of dimes, N is the number of nickels, and T is the total amount of money in dollars. We know that T is $4.65, and we know that Rachel has twice as many nickels as quarters, and three more quarters than dimes.

Let's assume that Rachel has x number of quarters

So we can write the above equation as:

x + (x+3) + 2x = 4.65

4x+3 = 4.65

4x = 1.65

x = 0.4125

Rachel has 0.4125 quarters, Which is not possible as it is a decimal. So we need to round it off to the nearest whole number.

Rachel has 0.4125 quarters which is equivalent to o.41 quarters.

Therefore, Rachel has 0.41 quarters that can be obtained using the equation Q + D + N = T.

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The length and width of the rectangle with 88 feet perimeter are 33 feet and 11 feet respectively

An equation is used to show the relationship between numbers and variables.

The perimeter of a shape is the sum of the distance along its sides. For a rectangle:

Perimeter = 2(length + width)

Let L represent the length and W represent the width of a rectangle with a perimeter of 88 feet

If the length of the rectangle is 3 times its width, hence:

L = 3W

Perimeter = 2(L + W)

88 = 2(L + W)

But L = 3W:

88 = 2(3W + W)

44 = 3W + W

4W = 44

W = 11 feet

L = 3W = 3(11) = 33 feet

The length and width are 33 feet and 11 feet respectively

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The four methods to solve quadratic equations are factorising, quadratic formula, graphing and completing the square.

Factorising is nothing but the method of equating the given equation to zero.

Quadratic formula method is by placing the coefficients of the given quadratic equation into the formula and obtaining the solutions.

Completing the square method is when a quadratic equation has a square term. We would once more have a linear equation if we could place two square terms on either side of the quality sign.

We can find the solution of a quadratic equation using a graph. Rearrange the equation so that one side corresponds to the graphed function. Plot this function and write y = the other side of the equation. To obtain the answers, draw vertical lines from the intersection spots down to the x-axis.

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Answer:

Step-by-step explanation:

true

Answer: True.

Step-by-step explanation: The new United States needed a way to borrow money for its government, its industrial development, and its commercial activity.

All the angles from the polygon path made by the students are;

∠1 = 96°

∠2 = 90°

∠3 = 162°

∠4 = 132°

∠5 = 60°

The images of the polygon are missing and so i have attached them. From the attached image, we can see we have;

Triangle (3-sided polygon)

Square (4-sided polygon)

Pentagon (5-sided polygon)

Hexagon (6 sided polygon)

Now, we know that formula for external angle of a polygon with n sides is 360/n.

Thus, for the 6-sided polygon, the ∠5 = 360/6

∠5 = 60°

Since ∠4 is shared by the pentagon and hexagon, then;

∠4 = (360/5) + 60

∠4 = 72° + 60°

∠4 = 132°

Since ∠3 is shared by the square and pentagon, then;

∠3 = 90 + 72

∠3 = 162°

∠2 = 90° because external angles of a square = 360/4 = 90°

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The value of x in the angle  is -6

                  m ∠B = (x +53)°

                 m ∠C = (x +53)°

         2 (x + 53) + 86 = 180

          2x + 106 + 86 = 180

                 2 x + 192 = 180

                            2x = 180- 192

                            2x = -12

                             x = -6

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Answer:

Rectangular

Step-by-step explanation:

I would be rectangular if you listened in class you would know.

The circumference of the Ferris is 408.2 ft.

We know that the circumference can be described as the distance round the circle. We have to note that the radius of the feriis would be very important as we try to obtain the circumference of the ferris.

We can see that the radius of the Ferris as is clear from the question that we have here is 65 ft. When the circumference can be gotten from the use of;

C = 2πr

Where r = radius and C = circumference

Thus;

C = 2 * 3.14 * 65

C = 408.2 ft

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Answer:

The mean is lower than the median which is lower than the mode.

Step-by-step explanation:

The determinants for solving the linear system is given as follows:

The system of equations for this problem is defined as follows:

The matrix A is composed by the coefficients of x and y, hence:

A = [5 3]

  = [-8 -3]

The determinant of a 2 x 2 matrix is the multiplication of the principal diagonal subtracted by the multiplication of the secondary diagonal, hence:

|A| = 5 x (-3) - 3 x (-8)

|A| = -15 + 24

|A| = 9.

For the matrix Ax, the coefficients of x are replaced by the results of the equalities, hence:

Ax = [17 3]

    = [9 - 3]

|Ax| = 17 x (-3) - 3 x 9

|Ax| = -51 - 27

|Ax| = -78.

For the matrix Ay, the coefficients of y are replaced by the results of the equalities, hence:

Ax = [5 17]

    = [-8 -9]

|Ay| = 5 x (-9) + 17 x 8

|Ay| = 91.

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Answer: Matthew will use 12.25 Gallons of Paint. (I'm not sure if I have the correct amount of cm so if you think/know it's a different amount, use the step by step explanation to figure it out. Good luck :D)

Step-by-step explanation: 28x2.5 = 70. 70 Feet to Square Feet = 4900 square feet. 4900 divided by 400 = 12.25.

Answer:

Step-by-step explanation:

2

The t critical value for a two-sided confidence interval in each of the following situations:

a. Confidence level = 95%, df = 10, t critical value = 1.812

b. Confidence level = 95%, df = 15, t critical value = 1.753

c. Confidence level = 99%, df = 15, t critical value = 2.602

d. Confidence level = 99%, n = 5, t critical value = 3.365

e. Confidence level = 98%, df = 24, t critical value = 2.306

f. Confidence level = 99%, n = 38, t critical value = 2.821

The t-critical value is a value that is used to determine the margin of error in a two-sided t-test with a given level of confidence and degrees of freedom. The t-critical value can be looked up in a t-table, or calculated using a t-distribution calculator.

It is important to note that for a small sample size (n<30) t-distribution is used instead of the normal distribution, in that case, the degrees of freedom is n-1 and the t-critical value is different than the one calculated with degrees of freedom.

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The transformation g(x) = -2(x + 5) is described as follows

Transformation is a term used in mathematics to refer to the movements made by objects.

Translation refers to a type of transformation that involve a linear movement.

The following movements are involved in translation

he left and right movements are on the horizontal direction controlled by the x coordinate. (x + 5) = horizontal shift left 5 units

While the up and down movements are on the vertical direction controlled by the y coordinate. k(x + 5) vertical shift up 5 units

multiplying the equation by a number greater than one leads to vertical stretch since it is a negative number this will be a reflection over the y axis

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The value of the number in the statement is 8

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

A mathematical statement represented as

Five times the difference of twice a number and three is twenty-five

Represent the number with x

So, we have

Five times the difference of twice x and three is twenty-five

When represented as an equation, we have

5(x - 3) = 25

Divide both sides by 5

This gives

x - 3 = 5

Add 3 to both sides

x = 8

Hence, the number is 8

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