If the terminal side of angle θ goes through the point (10√10,310√10) on the unit circle, then what is cos(θ)?

Give an exact answer in the form of a fraction.

The value of the equation is y = 4c + 18 , where c is the cost of each teacup and c = $ 6

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 equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The total cost Rebecca spend on teacups = $ 42

The cost of the large teapot = $ 18

The cost of small teacups be = c

The number of small teacups = 4

So , the equation will be

Total cost Rebecca spend on teacups = cost of the large teapot + ( number of small teacups x cost of small teacups )

Substituting the values in the equation , we get

42 = 18 + 4c

y = 4c + 18   be equation (1) , where y is the total cost

On simplifying the equation , we get

Subtracting 18 on both sides of the equation , we get

4c = 24

Divide by 4 on both sides of the equation , we get

c = $ 6

Therefore , the cost of each teacup is $ 6

Hence , the equation is y = 4c + 18

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Answer:

To simplify the expression (a÷b)³×(b÷c)×(c÷a)³ when a=3, b=a², c=a³, we can substitute the given values and perform the calculations.

Substituting the values of a, b, and c:

a = 3

b = a² = 3² = 9

c = a³ = 3³ = 27

Now let's simplify the expression:

(a÷b)³×(b÷c)×(c÷a)³

(3÷9)³×(9÷27)×(27÷3)³

Simplifying each term:

(3÷9) = 1/3

(9÷27) = 1/3

(27÷3) = 9

Now we can substitute the simplified values back into the expression:

(1/3)³×(1/3)×9

Simplifying further:

(1/27)×(1/3)×9

1/9

Therefore, the simplified expression is 1/9.

Answer:

.marcus is taller by 6.25

Step-by-step explanation:

Answer:

on which subject.

Step-by-step explanation:

Answer:

D.

Step-by-step explanation:

D.Increase in quantity demand..

Step-by-step explanation:

it's step by step explanation

I. The solution to the system of equations using Gaussian elimination is x = 1, y = -1, and z = 2.

II. For the LU-decomposition method, we need to have a square coefficient matrix, which is not the case in the given system. Therefore, we cannot directly apply the LU-decomposition method.

III. For this method to converge, the coefficient matrix must be diagonally dominant, which is not the case in the given system. Therefore, the Gauss-Jacobi method cannot be directly applied either.

IV. It requires the coefficient matrix to be diagonally dominant, which is not satisfied in the given system. Hence, the Gauss-Seidel method cannot be directly used.

I. Gaussian Elimination Method:

To solve the system of linear equations using Gaussian elimination, we perform row operations to reduce the system into upper triangular form. The augmented matrix for the given system is:

| 6 2 -1 | 4 |

| 1 5 1 | 3 |

| 2 1 4 |27 |

We can start by eliminating the coefficients below the first element in the first column. To do this, we multiply the first row by a suitable factor and subtract it from the second and third rows to eliminate the x coefficient below the first row. Then, we proceed to eliminate the x coefficient below the second row, and so on.

After performing the necessary row operations, we obtain the following reduced row-echelon form:

| 6 2 -1 | 4 |

| 0 4 2 | -1 |

| 0 0 3 | 6 |

From this form, we can easily back-substitute to find the values of x, y, and z. We have z = 2, y = -1, and x = 1.

II. LU-Decomposition Method:

LU-decomposition is a method that decomposes a square matrix into a product of two matrices, L and U, where L is lower triangular and U is upper triangular.

III. Gauss-Jacobi Method:

The Gauss-Jacobi method is an iterative numerical method to solve systems of linear equations.

IV. Gauss-Seidel Method:

Similar to the Gauss-Jacobi method, the Gauss-Seidel method is an iterative method for solving linear systems.

Therefore, out of the four methods mentioned, only the Gaussian elimination method can be used to solve the given system of linear equations.

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Answer:

30 and 0 is an easy answer

Step-by-step explanation:

30 times 0 equals 0

0 is 30 less than 30

Answer:

Step-by-step explanation:

6. Which of the following equations represents the data in the table?

Х

-4

0

4

8

y

5

2

-1

-4

O A. y = x + 2

O B. y = -x + 2

oc. y = x + 8

OD. y = -

3 + 8

M

help plzzzzzzzzzzzzzzzzzzzzz

Answer:

4.2.1)  R140 000

4.2.2)  R144 758.28

4.2.3)  Option 2

Step-by-step explanation:

To calculate the return on Ayanda's investment using Option 1, we can use the simple interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Simple Interest Formula}\\\\$ I =Prt$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000 \cdot 0.12 \cdot 6\)

\(I=24000 \cdot 6\)

\(I=144000\)

Therefore, the return on Ayanda's investment using Option 1 is R144000.

\(\hrulefill\)

To calculate the return on Ayanda's investment using Option 2, we can use the compound interest formula.

\(\boxed{\begin{minipage}{7 cm}\underline{Annual Compound Interest Formula}\\\\$ I=P\left(1+r\right)^{t}-P$\\\\where:\\\\ \phantom{ww}$\bullet$ $I =$ interest accrued \\ \phantom{ww}$\bullet$ $P =$ principal amount \\ \phantom{ww}$\bullet$ $r =$ interest rate (in decimal form) \\ \phantom{ww}$\bullet$ $t =$ time (in years) \\ \end{minipage}}\)

Given values:

Substitute the given values into the formula and solve for I:

\(I=200000(1+0.095)^6-200000\)

\(I=200000(1.095)^6-200000\)

\(I=200000(1.72379142...)-200000\)

\(I=344758.28426...-200000\)

\(I=144758.28426...\)

\(I=144758.28\)

Therefore, the return on Ayanda's investment using Option 2 is R144758.28.

\(\hrulefill\)

Comparing the returns from both options, we find that Option 1 offers a return of R144000, while Option 2 offers a return of R144758.28. As R144758.28 > R144000, then Option 2 will render the most money for Ayanda's investment.

Answer:

(-5n)-2=26-2n

Step-by-step explanation:

i think -9 1/3

well, let's say that number is "a", so it's opposite will just be "-a".

what's that number times -5?

-5*a => -5a

let's reduce that by 2

-5a -2

what would it be twice the opposite of it?

2(-a)

what is it 26 less than that?

2(-a) - 26.

\(-5a-2=2(-a)-26\implies -5a-2=-2a-26\implies -2=3a-26 \\\\\\ 24=3a\implies \cfrac{24}{3}=a\implies \boxed{8=a}\)

Answer:

45%

Step-by-step explanation:

9/20

Answer:

the slope is 3

Answer:

Step-by-step explanation:

<E = <T                                Given

M is the midpoint of TE      Given

TM = ME                               Definition of a  midpoint

<TMI = <RME                        Property of Vertically Opposite Angles

ΔTMI = ΔRME                       ASA = ASA

MI = ME                                 Corresponding parts of Congruent triangles                                    are Congruent

answer:                              reasoning:

<E = <T                                given

M is the midpoint of TE      given

TM = ME                               definition of a  midpoint

<TMI = <RME                        property of Vertically Opposite Angles

ΔTMI = ΔRME                       ASA = ASA

MI = ME                                 corresponding parts of congruent triangles                                    are Congruent

hope this helps!

The statement which is true about the given system of equations as required is; The system of equations represents parallel lines.

As evident in the task content; The two equations given are;

y = 3x + 9 and y = 3x - 4

By comparison with the slope-intercept form equation of a line; y = mx + c;

The slope of both equations are equal while the y-intercepts are different.

Ultimately, the system of equations represents a pair of parallel lines.

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The type of scale commonly used on maps is a graphic scale, which uses a line or bar to represent distances accurately.

The type of scale used on a map is known as a map scale. It is a graphical representation that shows the relationship between distances on the map and their corresponding measurements in the real world. A map scale allows us to understand the size and proportion of features depicted on the map.

There are three main types of map scales: verbal scales, graphic scales, and representative fraction scales.

Verbal Scale: A verbal scale uses words to describe the relationship between distances on the map and real-world measurements. For example, a verbal scale might state "1 inch represents 1 mile" or "1 centimeter represents 10 kilometers." Verbal scales are commonly used on small-scale maps, where the level of detail is not as important.

Graphic Scale: A graphic scale, also known as a bar scale or linear scale, uses a line or a bar marked with specific distances. This line is divided into equal segments that represent units of measurement. By comparing the length of the line on the map to the corresponding distance in the real world, you can determine distances accurately. Graphic scales are often found on the margin or the legend of a map and are commonly used on medium- to large-scale maps.

Representative Fraction (RF) Scale: A representative fraction scale expresses the relationship between map distances and real-world distances using a ratio. For example, a representative fraction of 1:100,000 means that one unit of measurement on the map represents 100,000 of the same units in the real world. This type of scale is useful because it allows for precise calculations and conversions between map distances and real-world distances. Representative fraction scales are commonly used on topographic maps and engineering plans.

It's important to note that a map may include multiple scales to accommodate different levels of detail. For instance, a large-scale map of a city may have a more detailed scale than a small-scale map of an entire country.

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Explanation:

A = set of odd numbers = {1,3,5}

B = set of factors of 12 = {1,2,3,4,6}

A U B = union of set A and set B

A U B = {1,3,5} union {1,2,3,4,6}

A U B = {1,3,5,       1,2,3,4,6}

A U B = {1,2,3,4,5,6}

The set union operation combines two sets into one bigger set. Duplicates are tossed out.

There are 6 elements in the set A U B = {1,2,3,4,5,6} out of 6 faces of the number cube.

Therefore, the probability event  A U B happens is 6/6 = 1 = 100%; i.e. it is guaranteed to happen. Each face of the number cube is either odd, a factor of 12, or both.

Side notes:

For constant A to be -4 (option 1) the system of equations have exactly one real solution.

NOTE: We are working with the problem statement: Y=-3 Y=Ax2+4x-4 In the system of equations above, a is constant. For which of the following values of a does the system of equations have exactly one real solution?

We have given, y=-3

y= Ax^2+4x-4

Therefore, -3= Ax^2+4x-4

or, Ax^2+4x-1=0

For second order equation of ax^2+bx+c=0 have a solution for

x= [-b± (√b^2-4ac)]/2a]   [Ax2 + Bx + C = 0 is the Sridharacharya equation, where a, b, and c are real values and a 0. The Sridharacharya formula, which is stated as x = (-b (b2 - 4ac)) / 2a, provides the answer to the Sridharacharya equation.]

For single solution b^2-4ac=0

here, Ax^2+4x-1=0

4^2 - 4a(-1)=0

16+4a=0

a= -(16)/4

a= -4

option A is correct .

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This is only true equation when A is equal to -2. Therefore, the correct answer is B) -2.

B) -2

The given system of equations can be written as:

Y = A*x^2 + 4*x - 4

We can solve this equation by using the Quadratic Formula. The Quadratic Formula states that the solutions to the equation are given by:

x = [-b +/- sqrt(b^2-4ac)]/2a

where a, b, and c are the coefficients of the equation. In this case, a = A, b = 4, and c = -4.

Substituting these values into the equation, we get:

x = [-4 +/- sqrt(4^2-4*A*(-4))]/2A

Simplifying this, we get:

x = [-4 +/- sqrt(16 + 16A)]/2A

For the system of equations to have two real solutions, the value of the square root must be greater than or equal to zero. This means that 16 + 16A must be greater than or equal to zero.

This is only true when A is equal to -2. Therefore, the correct answer is B) -2.

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Answer:

The commission rate is 15%

Step-by-step explanation:

commission = commission rate x sales

where the commission rate is expressed as a decimal.

In this case, the salesperson earned a commission of $345 for selling $2,300 in merchandise. Therefore, we have:

345 = commission rate x 2300

To solve for the commission rate, we can divide both sides by 2300:

commission rate = 345/2300

Simplifying this expression, we get:

commission rate = 0.15

So, the commission rate is 15%

Answer: (6,-6)

Step-by-step explanation:

To find the coordinates of point B, we can use the midpoint formula:

Midpoint formula: The midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is given by:

M = ((x1+x2)/2, (y1+y2)/2)

Here, we know that the midpoint M is (4, -2), and one endpoint A is (2, 2). Let B be the other endpoint, so we can use the midpoint formula to find B:

4 = (2+x2)/2 --> 8 = 2+x2 --> x2 = 6

-2 = (2+y2)/2 --> -4 = 2+y2 --> y2 = -6

Therefore, point B has coordinates (6, -6).

As for the second question, without a graph or information about the equation of line t and point P, it is not possible to determine which points lie on the line passing through P and perpendicular to t.

Answer:

$0.30 x b

$10.20

Step-by-step explanation:

The equation is

$0.30 x b

Since we know JoAnn uses 34 beads, we can replace b with 34

$0.30 x 34 = $10.20

Answer:

they started trip at 10:00 am

Step-by-step explanation:

Let's call the starting time "S".

The arrival time is 11:37AM,

difference in time after break to park arrived : 11:37 am - 10:48 am = 49 minutes

remaining time : 97-49= 48 minutes

starting time= 10:48 am -48 minutes = 10:00 am

Answer:

Step-by-step explanation:

Let's assume Kendra can rent the vacuum for $30 for "x" number of days.

The cost per day for renting the vacuum is $12, which means Kendra will spend $12x for renting the vacuum for "x" days.

In addition to the daily charge, Kendra also has to pay a flat rate of $7.95 for renting the vacuum.

So, the total cost Kendra will incur for renting the vacuum for "x" days will be:

Total cost = $7.95 + $12x

We need to find the maximum number of days "x" for which the total cost is less than or equal to $30.

So, we can set up the following inequality:

$7.95 + $12x ≤ $30

Subtracting $7.95 from both sides:

$12x ≤ $30 - $7.95

$12x ≤ $22.05

Dividing both sides by $12:

x ≤ 1.84

Since Kendra can only rent the vacuum for a whole number of days, the maximum number of days she can rent the vacuum without exceeding her spending limit is 1 day. Therefore, Kendra can rent the vacuum for 1 day without exceeding her spending limit of $30.

Answer: the fraction is 4over 12

Step-by-step explanation:

first you multiply the top and bottom number then u divide the number by the bottom.

Answer:

1/2

Step-by-step explanation:

If you were to multiply 1/2 by -50 you would get -25, which is greater than -50.

The same goes for 1/5, if you were to multiply 1/5 by -50, you would get -10.

Another example is 1/10 times -50, that would be -5.

Answer:

\(-4\)

Step-by-step explanation:

So we have the two functions:

\(h(x)=4x+5\text{ and } g(x)=3x+5\)

And we want to find:

\((h+g)(-2)\)

This is the same as:

\(h(-2)+g(-2)\)

Let's substitute them for their functions:

\(=(4(-2)+5)+(3(-2)+5)\)

Multiply:

\(=(-8+5)+(-6+5)\)

Add:

\(=-3-1\)

Subtract:

\(=-4\)

And we're done!

Answer:

I think you can answer it with a chart, I guess, of course I'm not sure‍♀️

The scholarship money used by Hector  to purchase books is $990

Hector earned $2640 through an academic scholarship.

Hector used three-eighths of his  earned academic scholarship of $2640 to buy books

This is a problem of fractions

In simple words, Fractions means the parts of a whole. The whole can be an object or a group of objects. For example, when we cut a piece of cake from the whole of it, then the portion is the fraction of the cake.

The fraction is also termed as a portion or section of any quantity.

Money used for buying books = 3/8 of $2640

= 3/8 × 2640

= 7920/8

= 990

Hence, the scholarship money used by Hector  to purchase books is $990

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