Refer to the equation a-6 equals b if a equals 45 what is the value of b?
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The equivalent trigonometric identity to cot²θ + 1 is cot²θsec²θ

Trigonometric identities are equations which contain the trigonometric ratios.

Since we have the trigonometric identity cot²θ + 1,we need to find its equivalent expression.

So, we proceed as follows

Since cot²θ + 1 = 1/tan²θ + 1     (since cot²θ = 1/tan²θ)

Now taking the L.C.M, we have that

1/tan²θ + 1 = (1 + tan²θ)/tan²θ

We know that the trigonometric identity 1 + tan²θ = sec²θ

So, substituting this into the equation, we have that

(1 + tan²θ)/tan²θ =  sec²θ/tan²θ

Since cot²θ = 1/tan²θ, substituting the values of the variables into the equation, we have that

sec²θ/tan²θ = cot²θsec²θ

So, cot²θ + 1 = cot²θsec²θ

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A linear system has infinite solutions if it consists of exactly the same equations.

The 3  possible solutions of a linear system are:

- Unique or one solution

- Infinite solutions

- No solution

- If the linear equations are exactly (or can be transformed to exactly) the same equations, the solution is infinite.

Example:

3x + 2y = -4  ..... (equation 1)

6x = -4y - 8   ..... (equation 2)

Add 4y to both sides of equation 2:

6x + 4y = -8

Divide both sides by 3:

3x + 2y = -4

Hence, equation 2 is exactly the same as equation 1. If we plot their graphs, they will share the same graph. Any solution of equation 1 is also solution of equation 2. Therefore, this linear system has infinite solutions.

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The way that the new volume compares to the original volume of the block is that the new volume is half of the original volume.

The volume of a rectangular block is gotten from the formula;

Volume = length * width * height

Now, we are given;

Width = 4 cm

Length = 4 cm

Height = 8 cm

Thus;

Volume of block = 4 * 4 * 8

= 128 cm³

Now, if you are cutting the block into 2 exactly equal halves, then you can say that;

New length = 4/2 = 2cm

Thus;

Volume of cut block = 2 * 4 * 8

= 64 cm²

This is concluded to be half of the original block.

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The standard form of the function is f(x) = -x² +4x, The vertex form isf(x) = -(x-2)² + 4

What is a function?

A function from a set X to a set Y assigns exactly one element of Y to each element of X. The set X is known as the function's domain, and the set Y is known as the function's codomain.

Given table is

x           f(x)

-1            -5

0             0

1               3

2              4

3               3

4                0

Find the difference to find the degree of the given function

f(x)                 -5           0           3            4         3          0

1st difference        5           3           1            -1          -3

2nd difference              -2          -2        -2          -2

The degree of the function is 2.

The general form of a second-degree function is

f(x) = ax²+bx+c

Putting x = 0 and f(0) =0 in f(x) = ax²+bx+c:

f(0) = a×0²+b×0+c

0 = c

Now putting x = 1 and f(1) =3 in f(x) = ax²+bx+c:

f(1) = a×1²+b×1+0    [since c=0]

3 = a + b ....(i)

Now putting x = 2 and f(2) =4 in f(x) = ax²+bx+c:

f(2) = a×2²+b×2+0    [since c=0]

4 = 4a + 2b ....(ii)

Solve equations (i) and (ii) by using the elimination method:

Multiply equation (i) by 2 and subtract it from (ii)

4a + 2b  = 4

2a  + 2b  = 6

(-)   (-)         (-)

__________

2a = -2

a = -1

Putting a = -1 in equation (i):

-1 + b = 3

b = 3+1

b = 4

The function is f(x) = -x² +4x

Rewrite the given function in vertex form:

f(x) = -(x² - 4x +4-4)

f(x) = -(x-2)² + 4

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Step-by-step explanation:

the center of the circle is (−3,5) and radius is 16 =

Short term memory is a response variable as it is dependent. Hence Option C is the answer.

A dependent variable is the response variable. It is reliant on the independent variable, which serves as the explanatory variable.

Explanations for the findings revealed by the response variables are provided by the explanatory or independent variables. Explanatory response is qualitative since it is classified based on a category.

The response variable is what the researcher often measures in research studies. The response variable in the example presented above is short-term memory, which is influenced by exercise.

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The null hypothesis exists that the standard deviation σ exists equivalent to 0.62. The alternative hypothesis exists that it does not equivalent 0.62.

Statistical hypothesis testing employs null and alternate hypotheses. While the alternative hypothesis states your research's prediction of an effect or relationship, the null hypothesis of a test always predicts no effect or no association between variables.

A proposed claim or defense in the hypothesis test is referred to as an alternative hypothesis in statistics. In most cases, it supports the research premise and shows that there is a statistical relationship between the variables. It is one of the two statements in statistical hypothesis testing that are mutually exclusive.

H₀: σ = 0.62

H₁: σ ≠ 0.62

The null hypothesis exists that the standard deviation σ exists equivalent to 0.62.

The alternative hypothesis exists that it does not equivalent 0.62.

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The amount of money saved by Andre in 40 weeks is $1280.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis of the given problem.

Given is Andre saves up the same amount of money each week.

We can write the equation, equating the total amount of money saved and the number of weeks as follows. Assume the equation to be -

y = mx + c

Then -

m = (288 - 224)/(9 - 7)

m = 64/2

m = 32

Now -

y = 32x + c

For the point (7, 224), we can write -

224 = 32 x 7 + c

c = 0

For {x} = 48, we can write the amount of money saved as -

y = 32 x 40

y = 1280

Therefore, the amount of money saved by Andre in 40 weeks is $1280.

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The total amount each member of the Nantucket recreation center have to pay after the discount is given by the equation A = $ 840

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount for each person after discount be represented as A

Now , the equation will be

The total number of people in the group = 36

The standard fare for each person = $ 1200

So , the total cost of the fare = total number of people x standard fare for each person

Substituting the values in the equation , we get

The total cost of the fare = 1200 x 36

The total cost of the fare = $ 43,200

Now , the discount percentage = 30 %

So , the amount after discount = total cost of the fare - total cost of the fare x discount percentage

Substituting the values in the equation , we get

The amount after discount = 43,200 - ( 30/100 ) x 43,200

The amount after discount = 43200 - 12960

The amount after discount = $ 30,240

Now ,

Total amount for each person after discount A =amount after discount / 36

Total amount for each person after discount A = 30,240 / 36

On simplifying the equation , we get

Total amount for each person after discount A = $ 840

Therefore , the value of A is $ 840

Hence , the amount is $ 840

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Answer:

2, cause it shows a different function or pattern

An equation representing this situation where Tommy earned $225 washing cars per appointment charge of $30 and tips of $45 while paying $10 for water per appointment is D. (30 - 10)y + 45 = 225.

An equation is a mathematical statement that states that two or more mathematical expressions are equivalent or equal.

Equations depict the equality of mathematical expressions using the equation symbol (=).

The total amount earned = $225

Variable charge per appointment = $30

Tips earned = $45

Variable cost per appointment for water = $10

Contribution margin per unit = $20 ($30 - $10)

Let each appointment = y

Total earnings: 225 = (30 - 10y) + 45

Thus, the equation that represents the situation of Tommy's net earnings from washing cars is Option D.

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Answer: 1/2

Step-by-step explanation:

The question is asking you to find how many centimeters in the scale drawing equal 1 foot on the actual building. The answer will be 1/2 because 1 centimeter is equal to 2 feet in reality. But since we want to know the answer of how many centimeters is in 1 foot, we will divide that in half, to get an answer of 1/2 centimeter, or A.

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when the area of the trapezoid is 70 units, and its first and second bases are at 4.6 units,

The size of a region on a flat or curved surface is expressed mathematically as area. The area of a form is defined as the "space encompassed inside the perimeter or the border." The area of various shapes is calculated using mathematical methods.

given

The trapezoid's surface area is 70 units.

first base is worth 20 units, while second base is worth 10 units.

how long CE

[tex]1/2(b1 + b2)*h is the area of a trapezoid.\\70= 1/2 (20 + 10 )*h\\70 = 1/2(30)*h\\4.6 units of h[/tex]

when the area of the trapezoid is 70 units, and its first and second bases are at 4.6 units,

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Answer:

I'm sure its 5=n-12 :))))

Answer:

Step-by-step explanation: its 90

Answer:

y=90°

since,70°+(X+X)+(180°-110°)=180°

or,70°+2X+180°-110°=180°

or,2X-40°=0

or,2X=40°

:.X=20°

Also,

X+y+70°=180°

or,y+90°=180°

:.y=90°

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On solving the provided question, we can say that - the value of the function is f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]; f(x) = x= it doesn't factor

The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.

f(x) = [tex](x+3)^2 - 5[/tex]

f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]

f(x) = x= it doesn't factor



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Answer:

Step-by-step explanation:

(0,-7) is the correct one. How I got this answer is cheese.

Answer:  15cm2

Step-by-step explanation:

5cm+4cm+6cm=15cm2

The inverse of a quadratic graph is a square root function. To graph the inverse, we reverse the domain and range.

The curve-shaped graph of a quadratic function is known as a parabola. The vertex of a parabola is one of its focal points.

On the graph, it is either the highest or lowest point.

We can imagine it as the parabola's endpoint.

A square root function is the inverse of a quadratic function.

We switch the domain and range in order to graph the inverse.

The graph has the same structure but has been rotated to have the original function's domain and range switched.

Therefore, the inverse of a quadratic function is a square root function. To graph the inverse, we reverse the domain and range.

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The pair of linear equations KX − 4y = 3 and 6x − 12y = 9 have an infinite number of solutions when K = 0.

This can be shown by solving the two equations for K. Solving the first equation for K yields K = (4y/X) + 3. Substituting this into the second equation yields: 0 = (4y/X) + 3 - (12y/6x). Simplifying this yields 0 = (2y/X) - (9/6x). This equation simplifies to 0 = (2y - 9x)/X. Since the denominator of the right side of the equation is not equal to 0, the only way to get 0 = 0 is if the numerator is equal to 0 as well. This happens when 2y - 9x = 0. Since y and x are variables, the only way that this equation can be true for all values of x and y is if the coefficient of both of them is equal to 0. Thus, K = 0 is the only value for which this pair of linear equations has an infinite number of solutions.

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Answer:

If you're asking how many books there are its 86.

Step-by-step explanation:

If each book is 1/2 thick that means there are 2 books per inch.

Because there are 43 inches you're going to multiply by 2.

43(2)= 86.

Hope that helped, have a good day!

Therefore, the answer to the time dilemma is 7 am on Friday, which is the right choice.

In mathematics, time is described as a continuously and continuous series of events that take place in chronologically from the past through to the present and into the future. The duration of events, the gaps between them, or even the sequence of occurrences can all be quantified, measured, or compared using time.

Here,

If it is 10 a.m. on Friday in Miami, Florida's Eastern time zone, it is 7 a.m. on Friday in Los Angeles,

California's (120 o W) pacific time region

since Miami, Florida's Eastern time zone is three hours early of Los Angeles.

Thus,

the correct response is 7 am on Friday.

Therefore, the answer to the time dilemma is 7 am on Friday, which is the right choice.

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The side length of the triangle are

A triangle with given ratio of sides as 3 : 5 : 6 and a perimeter of 154 feet is calculated from the formula of perimeter which is

= a + b + c

where

a, b, and c are the dimensions of the side length of the triangle:

Using the values given in the problem we have

let the ratio be a multiple of x such that

154 = 3x + 5x + 6x

154 = 14x

x = 11

a = 3 * 11 = 33 feet

b = 5 * 11 = 55 feet

c = 6 * 11= 66 feet

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The residual of the given situation is 0.8

The residual for each observation is the difference between predicted values of y (dependent variable) and observed values of y.

Given that, The grade can be modelled by the equation y = 0.66x + 33.3, where y is the student's grade as a percentage and x is the number of days that the student attended class. We are asked to find residual if student who was in attendance for 75 days and has a grade of 82%,

Finding the actual value,

y = 0.66 × 75 + 33.3

y = 82.8

The predicted value = 82

Residual = actual y value − predicted y value

Therefore,

Residual = 82.8-82 = 0.8

Therefore, y = 0.8

Hence, the residual of the given situation is 0.8

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Answer:

-3x + 549

Step-by-step explanation:

The order of operations is PEMDAS(parenthesis, exponents, multiplication, division, addition, subtraction)

So, according to PEMDAS, the first thing that we would do is solve the parenthesis. Since we can't solve the parenthesis because they aren't like terms, we're going to use distributive property to solve it instead.

-3(x+8) = -3(x) + -3(8) = -3x -24

Now we have: -3x - 24 ^ 2 -3

Our next step is to solve the exponent

24 ^ 2 or 24 x 24 = 576

Now we have: -3x - 24 + 576 -3

Our next step would be to add and subtract the like terms

-24 + 576 = 552 and 552 - 3 = 549

Now we have: -3x + 549

This would be the simplest form of the equation because -3x and 549 are not like terms

Answer:

O hrs and 30 minutes is the answer

Step-by-step explanation:

want proof?

Answer:

  about 0.04878 hours ≈ 2 minutes 56 seconds

Step-by-step explanation:

You want the time until a whale-watching boat and a whale meet if the boat is traveling south at 83 km/h and the whale is traveling north at 40 km/h when they start 6 km apart.

The speed at which the gap between the boat and the whale is closed is the sum of their respective speeds:

  closing speed = 83 km/h + 40 km/h = 123 km/h

The time it takes to close the 6 km gap is ...

  time = distance/speed

  time = (6 km)/(123 km/h) ≈ 0.04878 h

Converted to minutes and seconds, that is about ...

  0.04878 h ≈ 2 minutes 55.6 seconds

It will be about 2 minutes 56 seconds before the boat and whale meet.

__

Additional comment

NOAA recommends a distance of at least 100 yards be maintained between a boat and a whale. In some areas, the recommended distance is 400 yards when approaching head-on. The recommended boat speed is 15 knots or less, about 28 km/h.

The surface area that can be painted with one complete rotation of the roller is 226.19 inches².

Surface area is defined as the total amount of area that covers the surface or outside of a three-dimensional figure.

A paint roller is in the shape of a cylinder. To determine the surface area that can be painted with one complete rotation of the roller, solve for the surface area of a cylinder without the circular bases.

SA = 2πrh

where SA = surface area

r = radius of the base = 3 inches

h = height of the cylinder = width = 12 inches

Plug in the values and solve for the surface area.

SA = 2πrh

SA = 2π(3 inches)(12 inches)

SA = 226.19 inches²

Hence, the surface area that can be painted with one complete rotation of the roller is 226.19 inches².

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The simplest form is 15z+ 15x²

In algebra, a triangle-shaped grouping of integers known as Pascal's triangle provides the coefficients for the expansion of any binomial formula, such as (x + y)n. Although it is much older, it bears the name of the French mathematician Blaise Pascal from the 17th century.

Because it has so many patterns that can be used to greatly simplify complex calculations, Pascal's triangle is significant.

Given,

(5z+5 x²)3

15z+15x² by simplifying,

3(5z+5 x²)

apply the distributive formula :a (b + c) =ab + ac

3(5z+5 x²) = 5x+3 * 5x²

By simplifying 3 5z+3 , 5x², 15z+15x²

we get

15z+ 15x²

Therefore the simplest form is 15z+ 15x² .

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The measure of angle B where angle B is an acute angle by using the Law Of Sines is 61° .

What is an Acute Angle ?

The Acute Angle can be defined as an angles that measure less than 90° , the acute angle is smaller than Right Angle and also smaller than the Linear Angle ( measuring 180° ).

From the figure ,

we can see that the measure of the sides are given as a = 9 , b = 8 and

the measure of angle A is 79° .

By Applying the Law Of Sines ;

we get ,

[tex]\frac{SinA}{a} =\frac{SinB}{b}[/tex]

Substituting the values in the above equation ,

we get ;

[tex]\frac{Sin79\textdegree}{9} =\frac{SinB}{8}[/tex]

Simplifying further ,

we get ;

[tex]SinB = \frac{Sin79\textdegree}{9} \times 8[/tex]

substituting the value of Sin79° as 0.9816 ;

we get ;

[tex]SinB = \frac{0.9816}{9} \times 8[/tex]

[tex]SinB=0.8725[/tex]

So , B ≈ 61° .

Therefore , the measure of angle B is 61° .

The given question is incomplete , the complete question is

Find the measure of Angle B in the given figure .

Note that the angle B is acute . Round to the nearest degree .

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