Solve the equation 3 sinx+3 = 1 for 0°

The most appropriate choice for rationalization will be given by

What is rationalization?

When a surd is present in the denominator of a fraction, the surd has to be removed form the denominator. The process by which surds in the denominator of a fraction can be eliminated is called rationalization.

Here,

let [tex]\sqrt{x}[/tex] = a

[tex]x = a^2[/tex]

[tex]\frac{2a-9}{a^2 -5a + 6} - \frac{a + 3}{a-2} - \frac{2a+1}{3-a}[/tex]

[tex]\frac{2a-9}{a^2 -2a-3a + 6} - \frac{a + 3}{a-2} - \frac{2a+1}{3-a}[/tex]

[tex]\frac{2a-9}{a(a -2)-3(a -2)} - \frac{a + 3}{a-2} + \frac{2a+1}{a - 3}[/tex]

[tex]\frac{2a-9}{(a-2)(a-3)} - \frac{a + 3}{a-2} + \frac{2a+1}{a-3}[/tex]

[tex]\frac{2a-9 - ((a + 3)(a-3)) + (2a+1)(a-2)}{(a-2)(a-3)}[/tex]

[tex]\frac{2a-9-a^2+9+2a^2-4a+a-2}{(a-2)(a-3)}[/tex]

[tex]\frac{2a-a^2+2a^2-3a-2}{(a-2)(a-3)}[/tex]

[tex]\frac{a^2-a-2}{(a-2)(a-3)}[/tex]

[tex]\frac{a^2-2a+a-2}{(a-2)(a-3)}[/tex]

[tex]\frac{a(a-2)+1(a-2)}{(a-2)(a-3)}[/tex]

[tex]\frac{(a-2)(a+1)}{(a-2)(a-3)}[/tex]

[tex]\frac{\sqrt{x} +1}{\sqrt{x} -3}[/tex]

[tex]\frac{(\sqrt{x} +1)(\sqrt{x}+3) }{(\sqrt{x} -3)(\sqrt{x} +3)}[/tex]

[tex]\frac{x + 3\sqrt{x} + \sqrt{x} +3 }{x -9}[/tex]

[tex]\frac{x + 4\sqrt{x} +3 }{x -9}[/tex]

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The correct statement for the best definition of an angle is,

''two rays that share a common endpoint called the vertex''.

Option B is true.

What is mean by angle?

A figure which is formed by two rays or lines that shares a common endpoint is called an angle.

Given that;

Define an angle with the help of definition.

Now,

Since, We know that;

A figure which is formed by two rays that shares a common endpoint vertex is called an angle.

Thus, the best definition of an angle is,

''two rays that share a common endpoint called the vertex''.

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Answer:

number line with open point at 10 with arrow pointing left

Step-by-step explanation:

Answer:a

Step-by-step explanation:

The equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe is D. y=x+5.5; x is any real number greater than or equal to 0, and y is any real number greater than or equal to 5.5

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe.

The equation will be:

y = 5.5 + x

where y = total wheat

The option that correctly reflects this is D.

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Answer:

The answer is D

Step-by-step explanation:

The time would be 6 AM at the place at 90-degree West longitude.

This is a problem with coordination and time. We can solve this problem by using a few steps.

We should recall that each degree west is equivalent to 4 minutes before.

The given place is at 90-degree West longitude. Therefore, the total time difference is (90 × 4) = 360 minutes.

360 minutes is equal to 360/60 = 6 hours.

We have to deduct the time from GST, (12 - 6) = 6 AM

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7 days would the skier have to go skiing in order to make the season pass less expensive than the daily​ passes.

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. Every mathematical equation begins with L.H.S = R.H.S.

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.

Let s be the cost of skiing per day.

So,  the season pass plus ski rentals equates to daily skiing plus ski rentals

450 + 20s = 64s + 20s

450 = 64s

7.03 ≈ s

Hence, 7 days would the skier have to go skiing in order to make the season pass less expensive than the daily​ passes.

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Answer:

Step-by-step explanation:

1) First find the y-intercept point

You can find it easily by finding the number without the variable. In this case, it is -1. With this draw a point on the y-axis line down to -1.

2) Find the slope.

Next, you can find a point by substituting a number for x. So in this example, I will be subbing x for 1.

y = -3(1) - 1

y= -3 - 1

y= -4

So there will be a point at (1,-4).

3) Graphing.

After you find that you can easily draw a straight line through both points.

Answer: 7/6

Step-by-step explanation:

4/6 + 3/6

4+3+6

=7/6

A thing's extent, size, or the total amount is its quantity.

The mixture must contain 10 pounds of affordable tea.

An answer to the question "how much?" is a quantity, which might be an amount, number, or measurement.

Numbers or unconventional units can be used to express quantities.

Quantity in more complex mathematics can also refer to an undetermined amount in an equation.

Affordable tea costs $2.00.

The price for superior tea is $5.

The price of blended tea is $4.25.

Solution:

$4.25 multiplied by 40 pounds of blended tea equals $170.

Let x represent the quantity of affordable tea, and

The superior tea quantity is (40 - x).

4.25 * 40 = 2x + 5(40 - x)

170 = 2x + 200 -5x

-3x = -30

x = 10

Therefore, the mixture should contain 10 pounds of affordable tea.

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Answer:

B

Step-by-step explanation:

It says she thought half which equals to 1/2 or 0.5

Answer:

$1.27

Step-by-step explanation:

Answer:

Step-by-step explanation:

Exponents are powers or indices. An exponential expression consists of two parts, namely the base, denoted as b and the exponent, denoted as n. The general form of an exponential expression is b n.

How to Subtract Exponents?

The operation of subtracting exponents is quite easy if you have a good understanding of exponents. In this article, you will learn the rules and how to apply them when you need to subtract with exponents.

But before we can embark on subtracting with exponents, let us remind ourselves some of the basic terms about exponents.What is an exponent?

Well, an exponent or power denotes the number of times a number is repeatedly multiplied by itself. For example, when we encounter a number written as, 53, it simply implies that 5 is multiplied by itself three times. In other words, 53 = 5 x 5 x 5 = 125The same format of writing exponents applies with variables.  Variables are represented by letters and symbols. For instance, when x is multiplied repeated by itself 3 times, then we write this as; x3. Variables are usually accompanied by coefficients. A coefficient is therefore an integer that is multiplied by variable.

For instance, in 2x3, the coefficient is the number 2 and x is the variable. When a variable has no number before it, the coefficient is always 1. This is also true when a number has no exponent. The coefficient of 1 is normally negligible, and therefore cannot be written with a variable.

Subtraction of exponents really does not involve any a rule. If a number is raised to a power. You simply compute the result and then perform the normal subtraction. If both the exponents and the bases are the same, you can subtract them like any other like terms in algebra. For example, 3y – 2xy = x y.

Subtracting exponents with the same base

Let’s explain this concept with the help of a few examples.

Example 1

23– 22 = 8 – 4 = 4

53 – 52 = 75 – 25 = 50

Subtract x 3 y 3 from 10 x 3 y 3

In this case the coefficients of exponents are 10 and 1

The variables are like terms and hence can be subtracted

Subtract the coefficients = 10 – 1

= 9

Thus, 10x 3y 3– x 3y 3 = 9 (xy)3

You can notice that, the subtraction of exponents with like terms is done by finding the difference of their coefficients.

Subtract 8x2 – 4x2

In this case, the variables 4x2 and 8x2 are like terms and their coefficients are 4 and 8 respectively.

= 8x2 – 4x2

= (8-4) x2.

= 4 x2

Work out (-7x) – (-3x)

Here, -7x and -3x are like terms

= -7x – (-3x)

= -7x + 3x,

= -4x.

15x – 4x – 12y – 3y

Subtract like terms

15x – 4x = 11x

12y – 3y = 9y

Thus, the answer is 11x – 9y.

Subtract (4x + 3y + z) – (2x + 3y – z).

These variables are like terms

(2x + 3y – z) – (4x + 3y + z)

Open the parenthesis;

= 2x + 3y – z – 4x – 3y – z,

Rearrange the like terms, and perform the subtraction

= 2x – 4x + 3y – 3y – z – z

= -2x + 0 – 2z,

= -2x – 2z

Subtracting exponents with different base

Exponents with different bases are computed separated and the results subtracted. On the other hand, variable with unlike bases can not be subtracted at all.  For, example subtraction of a and b can not be performed and the result is just a -b.

To subtract a positive exponents m and negative exponents n, we just connect both the terms by changing the subtraction sign to a positive sign and write the result in the form of m + n.

Therefore, subtraction of a positive and a negative unlike exponents m and -n = m + n.

Example 2

42 – 32 = 16 – 9 =7

Subtract: 11x – 7y -2x – 3x.

= 11x – 2x – 3x – 7y.

= 6x – 7y

Evaluate 3x2 – 7y2

In this case, the two exponents 3x 2 and 7y2 are unlike terms and so it will remain as it is.

Here 3x and 7y both are unlike terms so it will remain as it is.

Therefore, the answer is 3x2 – 7y2

Evaluate 15x – 12y – 11x

= 15x5 – 11x5 – 12y5

= 4x5 – 12y5

The original price of the laptop is $479.40.

Given:

Discount on the laptop = 25%

HST paid on the laptop = 13%

Total price of the laptop = $677.15

Let the original price of the laptop be $x.

Price of the laptop after 25% off = x + 25% of x

                                                      = $ (125x/100)

Total Price of the laptop after paying 13% HST

= (125x/100) + 13% of (125x/100)

= (125x/100) + (65x/400)

= $ (565x/400)  

Now, it is given that the total price paid is $677.15 at the cash register.

565x/400 = 677.15

x = (677.15 × 400)/565

x = $479.40      

Therefore, the original price of the laptop is $479.40.

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The collection of all points in the plane with the form (x, f(x)) that make up a function f's graph. Alternatively, we may say that the graph of f is the graph of the equation y.

A function is a type of rule that produces one output for a single input. Source of the image: Alex Federspiel. This is illustrated by the equation y=x2. Any input for x results in a single output for y. Considering that x is the input value, we would state that y is a function of x.

Up until function composition, that is essentially all there is to "operations on functions." Don't be alarmed by the topic's notation; it simply means what it says: add, subtract, multiply, or divide; then, when necessary, simplify and evaluate.

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Step 1- Write out the Present Value of Annuity formula:

Where

Step 2- Write out the given values and substitute them into the formula:

Substituting the values into the formula, we have:

Therefore,

Dividing both sides by 72.0260, we have:

Hence, the monthly payment is $327.78.

The total amount T paid is given by:

Hence, the interest I is given by:

Therefore, the monthly payment is $327.78 and the interest paid is $7858.08

log (m + n) = log m+ log n and proved it m =n/n-1​

Given;

If log (m + n) = log m+ log n

To show that the m =n/n-1​

Now, According to the question:

We know that,

Log (m + n) = log m + log n

Log (m + n ) = log (mn).                 [log a + log b = log ab ]

Cancelling the log on both sides.

then,

m + n = mn

=> n = mn - m

=> n = m (n - 1)

=> m = n / n - 1

Hence Proved

log (m + n) = log m+ log n and proved it m =n/n-1​

What is Logarithm?

A logarithm is the power to which a number must be raised in order to get some other number (see Section 3 of this Math Review for more about exponents). For example, the base ten logarithm of 100 is 2, because ten raised to the power of two is 100: log 100 = 2.

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Answer:

Step-by-step explanation:

Given pairs of points that define three lines, you want to know their slopes, and whether line pairs are parallel or perpendicular.

The lines are defined by point pairs ...

The slope of a line is given from a pair of points by the formula ...

  m = (y2 -y1)/(x2 -x1)

Lines with the same slope are parallel.

Lines with opposite reciprocal slope are perpendicular.

Line 1 slope = (8 -4)/(-3 -0) = 4/-3 = -4/3

Line 2 slope = (4 -(-2))/(4 -(-4)) = 6/8 = 3/4

Line 3 slope = (4 -1)/(8 -4) = 3/4

The slopes of the lines are ...

Lines 1 and 2 have slopes that are opposite reciprocals (-4/3 and 3/4), so are perpendicular.

Lines 1 and 3 have slopes that are opposite reciprocals (-4/3 and 3/4), so are perpendicular.

Lines 2 and 3 have identical slopes (3/4 and 3/4), so are parallel.

Given that the 45° line is appropriately positioned in the graph, we may conclude that the aggregate expenditure line does not accurately depict the economy's equilibrium. [See attached Image]

The economy reaches equilibrium when the 45° line intersects the Aggregate Expenditure line. It is worth noting that this occurs at a real domestic output of 280, rather than 340, as indicated by the dashed lines in the graph.

It is to be noted that Aggregate spending is a measure of national income in economics. The present value of all finished products and services in the economy is described as aggregate spending. Thus, aggregate spending is the total of all expenditures made in the economy by the factors over a certain time period.

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Answer:

y + 2 = 3/4 (x - 1)

Step-by-step explanation:

You would pick one of the points in this case I picked (1, -2), for point-slope form your equation is y - y1 = m(x-x1).

Finding the slope (m) is easy you just do rise (up/down) OVER run (left/right).

So in this case your slope (m) is 3/4.

then you just plug everything in but because two negatives equal a positive you equasion should look like this y + 2 = 3/4(x - 1)

Answer:27/5

Step-by-step explanation: divid 8 1/2 by 1 9/16 and get 5.4 then you put that in fraction form and if I’m correct you get 27/5

The box contains 40 bolts, each weighing 280 g. The package weighs 405 g when there are 65 bolts inside. The bolt's mass is thus 5g, while the box's mass is 80g.

In many practical applications in daily life, linear equations are a crucial tool in science.

They let scientists, among other things, make predictions, compute rates, and characterize connections between two variables in the physical world. In order to see trends, linear equations are often graphed.

A condition on a variable is an equation when it ensures that two expressions in the variable have the same value.

The variable’s value for which the equation holds true is referred to as the equation’s solution.

Bolts are kept in a box for an assembly line. The package weighs 280 g when there are 40 bolts inside.

Let ‘x’ be the mass of each bolt and ‘y’ be the mass of the box, then we have:

40x + y = 280(1)

65x + y = 405(2)

If we subtract these 2 equations that are for (2) – (1) we get:

25x = 125

X = 5

Using (1) we get

Y = 280-40x

Y = 280-40*5

Y = 80.

Hence the mass of the bolt is 5g and the mass of the box is 80g.

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a) The small tire would  make 38  rotations

   The large tire would make 127  rotations

b) A bicycle with two large wheels would allow traveling faster with each rotation of the pedal .

The problem we are dealing with relates to rotations and circumference where rotation refers to the distance from the center to any point on the shape that remains the same and whereas the circumference is the perimeter of a circle. In one revolution a wheel covers a distance which is rise to its perimeter.Since we are provided that the diameter of the large wheel is 60 inches, so the radius will be 30 inches ( radius = diameter/2) and the radius of the small wheel is 9 inches.

The circumference of a circle  is 2πr

for a large wheel  the circumference is 2 x 3.14 X 30 = 188.4 inches

for a small  wheel, the circumference is  56.52

Since, we know 1 inch is equal to 0.0833333, as the traveling distance = 600 feet = 7200 inches.

Number of rotation = distance / circumference

For large wheel = 7200 /188.4 =38.21 = spprox 38

For small wheel = 7200/56.52 =127.38 = approx 127

Since we bicycle with bigger wheels is preferable as they can go faster than the ones with little wheels since their circumference is more as they cover more area in fewer rotations.

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If the point (x, y) rotated 180 degrees about the origin, then its image is (-x, -y)

Since point H is (1, 0), then

H' = (-1, 0)

Since point I is (4, 0), then

I' = (-4, 0)

Since point J is (2, 1), then

J' = (-2, -1)

Since point K is (-1, 1), then

K' = (1, -1)

The coordinates of the image after rotated 180 degrees about the origin are

H' (-1, 0), I' (-4, 0), J' (-2, -1), K' (1, -1)

300

1) Converting 5 hours

1 hour----------60 minutes

5 -------------- x

x = 300, since 5 times 60 is equal to 300 minutes.

So A, 300 minutes.

The value of n is 1650 after oil is transferred from Tank A and Tank B to Tank C.

It is given that initially,

Oil in tank A = n

Oil in tank B = n + 150

Oil in tank C = 0

Amount of oil transferred to tank C by tank A = 500 liters

Let us say 'x' amount of oil was transferred to tank C from tank B.

The amount of oil left in tank A after transferring 500 liters to tank C = n-500

Amount of oil left in tank B after transferring 'x' litres to tank C

= n + 150 - x

Amount of oil in tank C now = 500 + x

Since it is given that all three tanks contain the same amount of oil now. i.e. the new amount of oil in tank A = new amount of oil in tank B

n - 500 = n + 150 - x

x = 650

The new amount of oil in tank B = new amount of oil in tank C

n + 150 - x = 500 + x

n = 350 + 2x

Since x = 500

n = 350 + 2*650

n = 1650

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Answer: She got the sign of the slope wrong

Step-by-step explanation:

She did  -4y         -2 - 15x

                -4      =       -4

and turned that into ,

 -2         -     -15x  

 -4    (minus)  -4

which is wrong, because she did the negative twice. Therefore, she mixed up the sign of the slope.

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Answer: 4(6-y)

Step-by-step explanation: Since you are multiplying 4 by the difference of 6 and y, you put 6 and y in parenthesis with the 4 on the outside. Then 6-y goes inside the parenthesis.

Also the second one would be (6+9)n=20

Step-by-step explanation:

x is the number of students than can still join.

x <= 27 - 18

so,

x <= 9

max. 9 more students can join.