verify the
identity algebraically.

Answer:

280 calories and 12 grams of dietary fiber

Step-by-step explanation:

because 210(2/3) = 140

= 140 ÷ 1/2 = 280

we do the same steps with grams

9(2/3) = 6

= 6 ÷ 1/2 = 12

The equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2

The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.

Here,

The midpoint of the line segment joining (-2, -9) and (-6, 7) can be found using the midpoint formula:

Midpoint = ( (x₁+x₁)/2 , (y₁+y₁)/2 )

Midpoint = ( (-2-6)/2 , (-9+7)/2 )

Midpoint = (-4,-1)

Next, we need to find the slope of the line joining the two points (-2, -9) and (-6, 7). We can do this using the slope formula:

Slope = (y₂ - y₁) / (x₂ - x₁)

Slope = (7 - (-9)) / (-6 - (-2))

Slope = 4

The slope of the line perpendicular to the line segment is the negative reciprocal of the slope of the line joining the two points. So the slope of the perpendicular line is -1/4.

Using the point-slope form of a line, the equation of the perpendicular bisector can be written as:

y - y₁ = m(x - x₁), where (x₁, y₁) is the midpoint and m is the slope of the line.

Plugging in the values we found, we get:

y - (-1) = (-1/4)(x - (-4))

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

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

y = (-1/4)x - 2

Therefore, the equation of the perpendicular bisector of the line segment joining (-2, -9) and (-6, 7) is y = (-1/4)x - 2.

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Answer:

Step-by-step explanation:

(a) (i) The mean of the original data set is denoted as μ and the constant value being added to each data point is denoted as c.

The formula for the new mean is simply μ + c, so the new mean is μ + 6 = 10 + 6 = 16.

(a) (ii) The standard deviation of the original data set is denoted as σ. Adding a constant value to each data point does not change the spread of the data set, so the new standard deviation is still σ = 3.

(b) (i) The mean of the original data set is denoted as μ and the constant value being multiplied to each data point is denoted as k.

The formula for the new mean is μ * k, so the new mean is μ * 6 = 10 * 6 = 60.

(b) (ii) The variance of the original data set is denoted as V. To find the new variance after multiplying each data point by k, we can use the formula: k^2 * V.

So, the new variance is 6^2 * V = 36 * V.

--------

Here is a definition of each variable:

μ: The mean of a set of data is the sum of all the values divided by the number of values. It represents the average value of the data set.

σ: The standard deviation of a set of data is a measure of the spread of the data set about the mean. It is the square root of the variance.

V: The variance of a set of data is the sum of the squares of the deviations of each value from the mean, divided by the number of values. It is a measure of the spread of the data set about the mean, but it is measured in squared units.

c: A constant value added to each data point.

k: A constant value multiplied to each data point.

Step-by-step explanation:

The total distance biked by Yasmin on the first four days can be calculated as follows:

45 + 60 + 68 + 52 = 225 km

To find out how many kilometers she needs to bike on the last day to achieve an average of 58 km per day over the 5 days, we can set up an equation based on the formula for the mean:

(45 + 60 + 68 + 52 + x) / 5 = 58

Where x is the number of kilometers Yasmin needs to bike on the last day. Expanding the equation:

225 + x = 5 * 58

225 + x = 290

Subtracting 225 from both sides:

x = 65

So Yasmin needs to bike 65 kilometers on the last day to achieve an average of 58 kilometers per day over the 5 days

The percentage of middle school students that prefer each season and the percentage of high school students that prefer each season is 57.93% and 42.07% respectively.

The percentage is the ratio of the composition of value to the overall composition of value multiplied by 100.

Here,
Total number of students = 93 + 31 + 36 + 54 = 214

The percentage of students in middle school prefer spring,
= number of students in middle school prefer spring / total student × 100%
= 93/214 × 100%
= 43.45%

Similarly,
The percentage of students in middle school prefer winter,
= number of students in middle school who prefer winter/ total students × 100%
= 31/214 × 100%
= 14.48%

Thus, the percentage of middle school students that prefer each season and the percentage of high school students that prefer each season are 43.45 + 14.48 = 57.93% and 100-57.93% = 42.07%.

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The tables with their equations are

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

Tables and equations

Table (a)

Here, we notice that:

The output is the reciprocal of the input

This is represented as

y = 1/x

Table (b)

Here, we notice that:

The output is the square root of the input

This is represented as

y = √x

Table (c)

Here, we notice that:

The output is the cube of the input

This is represented as

y = x³

Table (d)

Here, we notice that:

The output is the same as the input

This is represented as

y = x

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The solution is, the equation is y=2/3x.

In math, a graph can be defined as a pictorial representation or a diagram that represents data or values in an organized manner. The points on the graph often represent the relationship between two or more things.

A diagram representing a system of connections or interrelations among two or more things by a number of distinctive dots, lines, bars, etc.

here, we have,

so the line is in slope intercept form

y=mx+b, m=slope and b=y intercept

we know the slope so just solve for b

y=2/3x+b

subsitute

3 for x and 2 for y

2=2/3(3)+b

2=2+b

subtract 2 from both sdies

0=b

so the equaiton is

y=2/3x+0 or just simply

y=2/3x

here is the graph

just input values for x and get y values exg

x=3 y=2

x=6 y=4

x=0 y=0

x=-3 y=-2

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The given expression is proved.

Trigonometry is a branch of mathematics that studies relationships between side lengths and angles of triangles.

here, we have.

tan∅/(1+ sec∅)

=(sin∅/cos∅)/(1+ sec∅)                  [tan∅=(sin∅/cos∅)]

=(sin∅/cos∅)/(1+1/cos∅)

=sin∅/1+cos∅

multiplying both numerator & denominator by 1-cos∅, we get,

=sin∅(1-cos∅)/ sin^2∅

=(1-cos∅)/sin∅

=cosec∅ - cot∅

Hence, The given expression is proved.

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Only Equation I is a linear equation. A linear equation is defined as an equation where the highest power of the variable is 1, and the relationship between the variables is a straight line.

What is Straight line?

A straight line is a type of geometric shape that is defined as a line with no curvature, extending infinitely in both directions. In other words, it is a one-dimensional object that extends indefinitely without bending or curving. Straight lines are often represented mathematically as y = mx + b, where m is the slope (or gradient) of the line and b is the y-intercept.The slope determines the steepness of the line, and the y-intercept determines where the line crosses the y-axis. Straight lines play a crucial role in mathematics, especially in geometry and linear algebra.

Only Equation I is a linear equation.

A linear equation is defined as an equation where the highest power of the variable is 1, and the relationship between the variables is a straight line. In Equation I, P is equal to 4 times s, so the highest power of the variable (s) is 1, making this a linear equation.

In Equation II, the right-hand side of the equation contains a single constant ($3), not a variable, and therefore it is not a linear equation.

Equation III is not a linear equation because it is just a constant equal to 2 and does not contain a variable.

So the answer is: 1. Equation I, only.

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The volume of the cylinder is 72π cubic centimeters.

Volume is a measure of the amount of space occupied by an object or a substance. It is typically measured in cubic units such as cubic meters, cubic centimeters, cubic feet, or cubic inches.

For solid objects, volume refers to the amount of space the object occupies in three-dimensional space.

The formula for the volume of a cylinder is:

V = Bh

where B is the area of the base of the cylinder, and h is the height of the cylinder.

In this problem, the cylinder has a diameter of 6 centimeters, which means the radius is 3 centimeters. The area of the base of the cylinder is therefore:

B = πr²

B = π(3 cm)²

B = 9π cm²

The height of the cylinder is given as 8 centimeters. Therefore, we can use the formula for the volume of a cylinder to find the volume V:

V = Bh

V = (9π cm²)(8 cm)

V = 72π cubic centimeters

Therefore, The volume of the cylinder is 72π cubic centimeters.

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The points are scattered in the scatterplot and thus, a line would not be appropriate because the points follow a nonlinear pattern.

Hence, option b is the correct answer.

Numerous different kinds of associations between two variables can be found using a scatterplot.

When there is no pattern visible in the points on a scatterplot, a relationship has no correlation.

When the points on a scatterplot exhibit a pattern rather than a straight line, a relationship is non-linear.

When the points on a scatterplot exhibit a largely straight line pattern, a relationship is linear. We shall look at this relationship in detail.

From the given graph we observe that the points do not follow a linear pattern.

The points are scattered and thus, a line would not be appropriate because the points follow a nonlinear pattern.

Hence, option b is the correct answer.

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The correct question is:

Answer:1 5/12 or written the other way 17/12

Step-by-step explanation:

A graph of the triangle after a 90 degrees counterclockwise rotation about the origin is shown in the image attached below.

In Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices for D, the coordinates of the vertices of the image point D' are as follows:

(x, y)                               →            (-y, x)

Ordered pair A  = (-3, 4) → Ordered pair A' = (-4, -3)

Ordered pair B  = (-5, -1) → Ordered pair B' = (1, -5).

Ordered pair C  = (-1, 2) → Ordered pair C' = (-2, -1).

In this exercise, we would use an online graphing calculator to plot the vertices of triangle A'B'C' as shown in the graph attached below.

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Answer:

Step-by-step explanation:

The boundary line of the shaded region in the graph, which is represented by the equation -5x + 2y = -2, can be used to write the inequality that represents the shaded region. To do this, we first need to determine which side of the boundary line the shaded region is on.

If the shaded region is on the same side of the line as the open half-plane that contains the y-axis, then the inequality is given by:

-5x + 2y > -2

If the shaded region is on the same side of the line as the closed half-plane that does not contain the y-axis, then the inequality is given by:

-5x + 2y ≥ -2

So, the inequality that represents the shaded region depends on the specific context and requirements of the problem, as well as the interpretation of the graph.

Answer:

the final answer is 7x + 5xy.

Step-by-step explanation:

3x + 4x = 7x

3xy + 2xy = 5xy

So, the final answer is 7x + 5xy.

Answer:

5xy+7x

Step-by-step explanation:

You see which ones have the same exact variables (x or xy)

Then you add the ones with the same variables together.

3x+4x=7x

3xy+2xy = 5xy

5xy+7x

(Depending on your teacher, they may not have to be in this order)

The provided statement indicates that Jim and Terrence each possess eight model automobiles, whereas Terrence owns six, making an 8:6 ratio. Jim is the owner of the 48 model card, then.

If b is really not equal to 0, then an arrangement of the numbers a and b expressed as a/b is a ratio. An equation known as a percent establishes two ratios with the identical value. You might, for instance, write the ration as described in the following: 1: 3 in the case of 1 male and 3 girls.

You are aware that Jim and Terrence own an 8:6 ratio in terms of the total number of model automobiles they own.

Accordingly, you can answer the task as follows: Let's say Jim owns x model automobiles.

8/6 = x/36

x = 36*8/6

x = 288/6

x = 48

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Types of Goals in line with Anelisa's story:

Goal setting helps individuals focus their efforts, prioritize their time and resources, and measure their progress towards achieving their goals. In the context of career choice, goal setting can help individuals:

Challenges Anelisa experienced:

Anelisa's personal values, such as determination, resilience, and a strong work ethic, likely played a significant role in her success. These values likely gave her the motivation and drive to pursue her goals, despite the challenges she faced. Additionally, her values may have helped her stay focused on her goals, maintain her sense of purpose, and make decisions that aligned with her vision for her life.

Relationships can impact the achievement of goals in both positive and negative ways. On the positive side, supportive relationships can provide individuals with emotional support, encouragement, and practical resources that can help them achieve their goals. On the negative side, relationships can also be a source of conflict and distraction, especially if they are not aligned with the individual's goals or values.

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Answer:

Step-by-step explanation:

lack of financial stability Nd resoouces

The required, each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.

A fraction is a mathematical concept that can be used to express a portion of a whole or a number that can be written as the ratio of two integers.

here,
To divide the 2 cakes equally among 7 people, we can use division. We can think of the total amount of cake as 2 whole cakes or 2/1 cakes. To find out how much cake each person can have, we can divide the total amount of cake by the number of people:

2/1 cakes ÷ 7 people = 2/1 × 1/7 = 2/7 cakes per person

So each person can have 2/7 of a cake. This fraction cannot be simplified any further, so the answer is 2/7.

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By calculating , The value of x we get is  5 as a final resultant.

What is trapezoid ?

A trapezoid is a quadrilateral with two parallel sides, called the "bases," and two non-parallel sides, called the "legs." The parallel sides can have different lengths, and the trapezoid can be either right-angled or oblique. In other words, a trapezoid is a geometric shape that has two parallel sides, two non-parallel sides and four angles.

Since a Trapezoid has 360 Degrees total and since the sides are equal we can say that

180=110+17x-15

70=17x-15

85=17x

x=5

Therefore, By calculating , The value of x we get is 5 as a final resultant.

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On solving the provided question we can say that the net change will be 17 and average rate of change = 17/1 = 17.

The subject οf mathematics includes quantities and their variatiοns, equations and related structures, shapes and their locations, and places where they can be fοund.

The term "functiοn" refers to the relationship between a set of inputs, each of which has an associated output. A cοnnection between inputs and outputs in which each input leads to a single, distinct result is known as a functiοn.

Each function is given a dοmain and a codomain, or scope. Usually, f is used to denote functiοns (x). input is an x. There are fοur main types of functions accessible. based οn the following factors: οn functions, one-to-one functions, many-tο-one functions, inside functiοns, and on functions.

The functiοn will be

h(4)=2(4²)-4

=32-4

=28

h(5)=2(5²)-5

=50-5

=45

Net change is 45-28 = 17

average rate of change = 17/1 = 17

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The start point the graph of a function of this form is (h, k)

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

f(x) = a√(x - h) + k

The domain is given as

x ≥ h

This means that the initial x value is h

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

f(h) = a√(h - h) + k

Evaluate

f(h) = k

Hence, teh initial point is (h, k)

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The expression equivalent to 5x +10y -15 by taking the common factor is 5(x + 2y - 3).

What is taking out common factors?

The takeout of the common factor is the procedure, ab + ac = a(b + c). Think about how the expression 5x + 10 gets factored. The common factor 5, which was previously in front of the brackets, has been removed.

Figuring out what to multiply to create an expression. It is comparable to "splitting" an expression into numerous smaller expressions.

Given, the expression is 5x + 10y -15

So, 5x +10y -15 = 5x + 5*2y - 5*3

                         = 5(x + 2y - 3)

Hence, the required answer is 5(x + 2y - 3).

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Answer:

A = w*6

Step-by-step explanation:

W = A/6

Multiply both sides by 6 using the multiplication property of equality.

A = W*6

or

A = W x 6

Hope this helps!

The solution set for the given equation is (0, 227), (1, 91) and (2, -45.45)

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 75x + 0.55y = 125.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Substitute x=0, 1, 2, 3, 4, 5,....

When x=0

75(0)+0.55y=125

0.55y=125

y=125/0.55

y=227

When x=1

75(1)+0.55y=125

0.55y=50

y=50/0.55

y=91

When x=2

75(2)+0.55y=125

0.55y=-25

y=-25/0.55

y=-45.45

Therefore, the solution set for the given equation is (0, 227), (1, 91) and (2, -45.45)

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Answer:

  B.  24.28 square feet

Step-by-step explanation:

You want the area of a figure composed of a rectangle, triangle, and semicircle.

The formulas for the areas of the parts of the figure are ...

  A = LW . . . . rectangle of length L and width W

  A = 1/2bh . . . . triangle with base b and height h

  A = π/2r² . . . . . . semicircle of radius r

The area of the rectangle is ...

  A = (4 ft)(3 ft) = 12 ft²

The area of the triangle is ...

  A = 1/2(4 ft)(3 ft) = 6 ft²

The semicircle has a radius that is half the diameter. The diameter is shown as 4 ft so the radius is 2 ft. The area of the semicircle is ...

  A = π/2(2 ft)² = 4(3.14)/2 ft² = 6.28 ft²

The area of the composite figure is the sum of the areas of its parts:

  Area = 12 ft² +6 ft² +6.28 ft² = 24.28 ft²

The area of the composite figure is about 24.28 ft².

The speed of Petra will be 0.55 mile/minute.

What exactly is speed?

The definition of speed is:

The pace at which an object's location changes in any direction.

Speed is defined as the ratio of distance travelled to time spent travelling. Because it has just one direction and no magnitude, speed is a scalar number.

Formula for Speed

The speed formula is shown below:

s=d/t

Where,

s is the speed in metres per second, d is the distance travelled in metres, and t is the duration in seconds.

Now,

As given petra jogs 60 miles in 110 minutes

then in one minute she will jog =60/110 mile

=0.5454 mile/min

Hence,

           The speed of Petra will be 0.55 mile/minute.

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Answer:

You will pay 81.25

Step-by-step explanation:

If the cost is 35% off, you will need to pay 100% - 35% = 65%

125 * 65 %

125 *.65

81.25

You will pay 81.25

The solution of the expression 3h(n) + 2g(n) will be 2n³ -8n +16.

Expression in maths is defined as the relation of numbers variables and functions by using mathematical signs like addition, subtraction, multiplication, and division.

Given that the two values are h(n) =4n+2 and g(n)= n³ +5 - 2n. The value of the expression 3h(n) + 2g(n) will be calculated as:-

E = 3h(n) + 2g(n)

E = 3 ( 4n+2 ) + 2 (n³ +5 - 2n)

E = 12n + 6 + 2n³ + 10 -4n

E = 2n³ + 8n + 6

Therefore, the answer to the equation 3h(n) + 2g(n) is 2n3 -8n +16.

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The true argument is option B) The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false

The argument presented lacks logical reasoning and does not provide enough information to support the conclusion. The premise that "Bob is 13 feet tall" is a factual statement, but it is not sufficient to conclude that "Bob is taller than most other people." Without further information about the height distribution of people.

It is impossible to make such a conclusion based solely on Bob's height. Additionally, the argument does not provide any logical reasoning to connect the premise to the conclusion, so it is not a valid deductive argument.

Therefore, the correct option is (B)

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The given question is incomplete, the complete question is :

Bob is 13 feet tall So, Bob is taller than most other people Suppose there are no implicit premises: this is the whole argument. Which of the following is true about this argument?

A The premise entails the conclusion because, if the premise is true, the conclusion has to be true

B The premise does not entail the conclusion because, if the premise is true, the conclusion could still be false (setting aside facts not supplied by the premise)

C The premise entails the conclusion because, setting aside facts not supplied by the premise, there is no way the premise could be true and the conclusion false.

D The premise does not entail the conclusion because it has no suppositional strength