Simplify the trigonometric expression (sin^2(x/2)) (1 + cos(x)) using Half-Angle Identities.

4x + y = 42 => y = 42 - 4x

3x - 2y = 26 => 3x - 2×(42 - 4x) = 26 => 3x - 84 + 8x = 26

=> 11x - 84 = 26 => 11x = 110 => x=10

y = 42 - 4x => y = 42 -4×10 => y= 42 - 40 => y= 2

Answer:

[tex]x = 10[/tex] and [tex]y = 2[/tex]

Step-by-step explanation:

That appears to be a parallelogram, so we can make the assumption that one side of the shape is equal to the side opposite to it because they are parallel lines.

With that assumption, we can set-up the equations, namely

[tex]42 = 4x+y[/tex] (eq. 1)

[tex]26 = 3x-2y[/tex] (eq. 2)

We can solve for x and y either through substitution or elimination, and it seems like elimination could be a faster way to do it.

Multiply eq. 1 by 2 and add it to eq. 2

[tex]84 = 8x+2y\\26 = 3x-2y[/tex]

-> [tex]110 = 11x[/tex]

[tex]x = 10[/tex]

And then we can substitute it back to any equation, and the result will be

[tex]y = 2[/tex].

The slope of the given line that passes through (4, 2) and (6, 3) is m = 1/2.

The general equation of a straight line is -

y = mx + c

{m} - slope.

{c} - intercept along the y - axis.

Given are the statements regarding the slope of the line as given.

The line passes through the points -

(4, 2) and (6, 3)

The slope of the line will be -

m = (3 - 2)/(6 - 4)

m = 1/2

Therefore, the slope of the given line that passes through (4, 2) and (6, 3) is m = 1/2.

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Lena is not correct in her statement that she will use more pages if she puts 5 stickers on a page instead of 10 stickers on a page.

Is it true that if you put 8 stickers on a page instead of 4, you will use less pages?

Yes, it is true that if you put 8 stickers on a page instead of 4, you will use less pages. The total number of stickers divided by the number of stickers per page determines the number of pages needed. In general, the more stickers per page, the less pages will be needed to hold the same number of stickers.

If Lena puts 10 stickers on a page, she will need fewer pages than if she puts 5 stickers on a page.

For example, if she has 50 elephant stickers, she would need 5 pages if she put 10 stickers on a page, but she would need 10 pages if she put 5 stickers on a page.

This is because the total number of stickers divided by the number of stickers per page determines the number of pages needed. In general, the fewer stickers per page, the more pages will be needed to hold the same number of stickers.

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Answer: y = -x+7

Step-by-step explanation:

Let's first set up it in slope-intercept form.

y = -x+b

We can find b using point (4,3).

Substitute 4 for x and 3 for y to get:

-3 + b = 4

b = 7

Therefore, the line is y = -x+7

Answer:

5

Step-by-step explanation:

adde it all upa and get the answer

The solution to the expression -11/14 x (-1/17) is 11/238

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

-11/14x(-1/17)

Express properly

So, we have the following representation

-11/14 x (-1/17)

Remove the brackets

This gives

-11/14 x (-1/17) = 11/14 * 1/17

So, we have

-11/14 x (-1/17) = 11/238

Hence, the solution is 11/238

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Answer: 30

Step-by-step explanation:

n= -3

-3^2 = 9

9(-3) = -27

9-(-27)-6 = 30

Answer:

We can start solving the problem by using a system of equations. Let x be the number of pieces of fruit on a small tray, and y be the number of pieces of fruit on a large tray.

From the information given, we know that:

Yesterday: x + 4y = 166 (1)

Today: 4x + 4y = 232 (2)

We have two equations and two unknowns, so we can use substitution to solve for one variable in terms of the other, and then substitute that back into the other equation.

From equation (1) we can solve for x:

x = 166 - 4y

Now we can substitute this into equation (2)

4(166 - 4y) + 4y = 232

Simplifying and solving for y:

-672 + 16y = 232

16y = 904

y = 56.5

This means that each large tray has 56.5 pieces of fruit.

Now we can substitute this value back into the first equation:

x + 4(56.5) = 166

x = 166 - 226

x = -60

This solution doesn't make sense, because the number of pieces of fruit can't be negative. This means that there is no solution to the system of equations, and it is impossible to determine the number of pieces of fruit on each size tray based on the information given.

Step-by-step explanation:

Answer:[tex]\frac{15}{8}[/tex] or [tex]2 \frac{7}{8}[/tex]

Step-by-step explanation:

Adding,

[tex]\frac{1}{2}+\frac{3}{4}+\frac{5}{8} =\frac{4+6+5}{8} =\frac{15}{8}[/tex][tex]=2\frac{7}{8}[/tex]

Answer: Because the slope doesn't tell you any actual points on the line. It only tells you whether the line tilts up or down, and how steeply.

Step-by-step explanation:

D

ok is the force that I have to go in and out for the June exam and the Zumba

Answer: A. To find out how much concentrated cleaner the worker used, we can set up the equation: x + 15 = 5x/2, where x is the amount of concentrated cleaner used in quarts. Solving for x, we find that the worker used 15 quarts of concentrated cleaner.

B. Since we know that the worker used 15 more quarts of water than concentrated cleaner, we can find out how much water she used by adding 15 quarts to the amount of concentrated cleaner used. In this case, the worker used 15 quarts + 15 quarts = 30 quarts of water.

C. To find out how much solution the worker made, we add the amount of concentrated cleaner used and the amount of water used. In this case, the worker made 15 quarts + 30 quarts = 45 quarts of solution.

Step-by-step explanation:

The correct option is B.

The Equation that represents the line that has a slope of 1/3 and an x-intercept of 5 is y-0 = 1/3(x-5)

The slope of a line is the measure of the steepness of a line and its direction. It can be used to predict whether the lines are parallel, perpendicular, or none.

The slope of any line can be calculated using any two distinct points lying on the line.

y -y1 = m(x-x1)

where y1 = 0

x1 = x-intercept = 5

y-0 = 1/3(x-5)

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The price of each bag of popcorn and the price of each drink is $7.5 and $4 respectively.

Let the drinks be represented as d.

Let the popcorn be represented as p.

From the information, Xochitl went into a movie theater and bought 6 bags of popcorn and 4 drinks, costing a total of $65. Thus will be:

6p + 4d = 65

Alonso went into the same movie theater and bought 9 bags of popcorn and 8 drinks, costing a total of $107.50. This will be:

9p + 8d = 107.50

Equating the equation

6p + 4d = 65 ..... i

9p + 8d = 107.50 ..... ii

Multiply equation i by 8

Multiply equation ii by 4

48p + 32d = 520

36p + 32d = 430

12p = 90

Divide

p = 90/12

= 7.5

6p + 4d = 65 .

6(7.5) + 4d = 65

4d = 65 - 45

4d = 20

d = 20/4 = 5

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The system of inequalities which can be used to determine the number of dogs, d, and the number of cats, c, Nadia can house in the facility on any given day is:

A. 3.45c + 4.60d ≤ 200.

    c + d ≤ 50.

In order to write a system of linear inequalities to describe this situation, we would assign variables to the number of dogs and number of cats respectively, and then translate the word problem into algebraic equation as follows:

Since the daily cost for her facility to house a cat is $3.45 and $4.60 for a dog, with a budget of $200, a linear inequality which represents this situation is given by;

3.45c + 4.60d ≤ 200.

Additionally, the facility has a total of 50 pens;

c + d ≤ 50.

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The properties of exponents used to simplify the expression are:

(a^m)^n = a^(m*n)

(a^m)^n = (a^n)^m

(a*b)^n = a^n * b^n

(a/b)^n = a^n / b^n

Using these properties, we can simplify the expression as follows:

(y3/2 x -1/2)^4

= (y^3/2 * x^-1/2)^4

= y^3/2 4 * x^-1/2 4

= y^(3/24) * x^(-1/24)

= y^6 * x^-2

So the simplified expression is: y^6 * x^-2

The probability that the hospital has 7 fatalities this week is approximately 0.0199

The probability that the hospital has 7 fatalities in a week, given an average of 7 fatalities per week, can be calculated using the Poisson distribution. The Poisson distribution is a discrete probability distribution that models the number of events (in this case, fatalities) that occur in a fixed interval of time (in this case, a week) with a certain average rate (in this case, 7 fatalities per week). The probability of k events happening in a given interval of time is given by the following formula:

P(k;λ) = (e^(-λ))*(λ^k)/k!

Where λ is the average number of events per interval of time and k is the number of events we are interested in.

In this case, we are looking for the probability that there are 7 fatalities this week, given that the average number of fatalities per week is 7. So we can plug in the values into the equation:

P(7;7) = (e^(-7))(7^7)/7! =0.149

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Según el álgebra de números reales, la potencia del producto es el producto de las potencias.

De acuerdo con la pregunta, tenemos el caso del producto de dos números reales a, b elevados a un potencia n, cuya descripción matemática se presenta a continuación:

(a · b)ⁿ

De acuerdo con el álgebra de números reales, este caso tiene la siguiente equivalencia:

(a · b)ⁿ = aⁿ · bⁿ

De modo, pues, que la potencia de un producto de dos números reales es igual al producto de las potencias de los números reales.

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Answer:

y = 3x -8

Step-by-step explanation:

8 times less means something will have to be (-8)

3 times the value of x is equal to (3x)

by looking at the answers we can deduct that our answer in fact is y = 3x -8

The mean of the numbers, given the stem and leaf plot of the number of classrooms in each school in the city, is 84 classrooms

To find the mean of the schools, you first need to add up the number of classrooms in each school and then divided this sum by the number of schools that Evelyn used in the social studies project.

When using a stem and leaf plot in this instance, the stem is the tens figure and the leaf is the ones figure.

This means that a stem of 7 and lead of 7 means 77 classes.

The sum of the number of classrooms is therefore :

= 77 + 77 + 81 + 81 + 82 + 82 + 83 + 84 + 84 + 85 + 85 + 87 + 90 + 90 + 92

= 1, 260 classrooms

The mean is therefore :

= 1, 260 / 15 schools

= 84 classrooms

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Pretest-posttest experimental designs are common is true for the t-test for dependent means rather than t-tests in general.

The correct answer is option B.

The use of pretest-posttest designs extends the posttest alone design with nonequivalent groups, one of the most fundamental methods for assessing the effectiveness of an intervention. One group in this two-group design undergoes therapy, and the final results are produced for the other group.

In conclusion, quasi-experimental design has long been a popular research methodology. An intervention that has been delivered to a group of study participants may be easily evaluated using pre-test and post-test designs, a sort of quasi-experimental research. A pretest is an assessment tool used by study participants before they get any form of therapy. Participants in a study are given a posttest, which is an evaluation tool, following their participation in the study.

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Cos 120 is in the second quadrant and therefore is a negative signed value

A plane is divided into four sections, or quadrants, by an x-axis and a y-axis in a rectangular coordinate system. The letter O stands for the origin, which is the place where the two axes converge.

In the first quadrant, there are angles between 0 and 90.

In the second quadrant, there are angles between 90 and 180.

In the third quadrant, there are angles between 180 and 270.

In the fourth quadrant, there are angles between 270 and 360.

Cos is only positive in the first quadrant and in the 4th quadrant and always negative in the second and third quadrant

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The evaluation of the functions in the question are as follows;

1. a) [tex]y = \dfrac{1}{x^2+5} -3[/tex]is not a quadratic function

b) The function is a quadratic function

c) The function is a quadratic function

d) The function is a quadratic function

2. Please find attached the graph of the function, y = -2·(x + 3)² + 4, created (for clarity) with MS Excel

a) The axis of symmetry is; x = -3

b) The maximum value is; (-3, 4)

c) The x-intercepts are; √2 - 3, and -√2 + 3

d) y-intercept is (0, -14)

e) The domain is the set of all real numbers

The range is (-∞, 4]

A function is a rule that maps an input value unto an output, such that each input has exactly one output.

A quadratic function is a function of the form; y = a·x² + b·x + c

a) The function [tex]y = \dfrac{1}{x^2+5} -3[/tex], when simplified, we get;

[tex]y = \dfrac{1 - 3\cdot x^2 - 15}{x^2+5}[/tex], which is a rational polynomial.

Therefore, the function is not a quadratic function.

b) x² = y - 1

y = x² + 1

The above function is in the form; y = a·x² + b·x + c, where;

a = 1, b = 0, c = 1

c) y = 3·x - 7 + 4·x²

The above function is in the form y = a·x² + b·x + c, where;

a = 4, b = 3, and c = -7

d) The function y = 6·x - 3·√x can be expressed as; √x = z

Therefore; z² = x

Therefore; y = 6·x - 3·√x = 6·z² - 3·z

y = 6·z² - 3·z

The above function is a quadratic function, therefore, the function;

y = 6·x - 3·√3 is a quadratic function

2. The function y = -2·(x + 3)² + 4 is in the vertex form of the equation of a quadratic equation; y = a·(x - h)² + k

Where;

a = The leading coefficient

(h, k) = The coordinates of the vertex

Comparing the values, we get;

The vertex, (h, k) = (-3, 4)

a = -2

When x = 0, we get; y = -2·(0 + 3)² + 4 = -2 × 9 + 4 = -14

With a vertex of (-3, 4), we get;

When x = -6, y = -14

The graph can be obtained by drawing a parabola with vertex at (-3, 4), and passing through the points (0, -14), and (-6, -14)

Please find attached the graph of the function y = -2·(x + 3)² + 4, created with the points (0, -14), (-6, -14), and vertex point (-3, 4), created with MS Excel

a) The axis of symmetry is the line about which the graph is symmetrical

The axis of symmetry is the line x = -3

b) The maximum value is the vertex of the graph, which is the point (-3, 4)

c) The x-intercept are the point the graph intersects the x-axis, which are obtained by plugging in y = 0, as follows;

y = 0 = -2·(x + 3)² + 4

(x + 3)² = -4/(-2) = 2

x + 3 = ±√(2)

x = ±√(2) - 3

The x-intercepts are; x = √2 - 3, and -√2 - 3

d) The y-intercepts are the point the graph intersects the y-axis, which is the point where x = 0

Therefore, the y-intercept is the point (0, -14)

e) The domain is the set of possible input values or x-values

The domain of the function, as presented in the graph is the set of all real numbers

The domain is; (-∞, ∞)

The range is the set of the possible y-values

The graph of the function indicates that the maximum y-value is the point y = 4

Therefore, the range of the function is; -∞ < y ≤ 4, which is (-∞, 4]

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The area of the trapezoid is calculated as: D. 90 square units.

To find the area of the trapezoid that is shown in the image above, we can decompose the trapezoid into three shapes which are one rectangle and two identical triangles.

Area of triangle = 0.5 * base * height

Area of rectangle = length * width.

Given the following:

x = 8 units

y = 2 units

h = 9 units

Area of the 2 triangles = 2(0.5 * y * h) = 2(0.5 * 2 * 9) = 18 units²

Area of rectangle = x * h = 8 * 9 = 72 units²

Area of trapezoid = 18 + 72 = 90 units²

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In matrix C    value of c34 + c51 = 3 + 9 = 12

A matrix is a rectangular or square arrangement of numerical terms where the terms are arranged into rows and columns. Depending on the size of rows and columns, matrix are various types such as square, rectangular, upper triangular, lower triangular and so on.

What is the value of c34+ c51?

we are given a 5 × 5 matrix square matrix that means number of rows and number of columns is both 5.

the matrix is denoted by C.

C = 2  9  5  7  5

      4  2  4  4  3

      3  8  2  3   8

      2  3  4  8   2

      9  7  7   3  1

we know the formula for identify the elements of a matrix is given by

a₁₁  a₁₂  a₁₃  a₁₄  a₁₅

a₂₁  a₂₂ a₃   a₂₄   a₂₅

a₃₁  a₃₂  a₃₃  a₃₄  a₃₅

a₄₁  a₄₂₂  a₄₃  a₄₄  a₄₅

a₅₁  a₅₂    a₅₃  a₅₄  a₅₅

The above is a 5 x 5 square matrix in where the elements are identified by a.

If we compare the two matrices, we can determine that c34 is 3 and c51 is 9.

Therefore, c34 + c51 = 3+9 =12

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Answer:

0 votes

Step-by-step explanation:

On solving the provided question, we can say that the value of the equation here is f(2) = -29 and f(3) = -41

A mathematical equation is a formula that joins two statements and uses the equal symbol (=) to indicate equality. A mathematical statement that establishes the equality of two mathematical expressions is known as an equation in algebra. For instance, in the equation 3x + 5 = 14, the equal sign places the variables 3x + 5 and 14 apart. The relationship between the two sentences on either side of a letter is described by a mathematical formula. Often, there is only one variable, which also serves as the symbol. for instance, 2x – 4 = 2.

the equation here is

f(x)=-x-31 +4

f(2) = -29

f(x) = -x-41+3

f(3) = -41

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