Jenny and Hong each opened a savings account today. Jenny opened her account with a starting amount of $160, and she is going to put in $50 per month.
Hong opened his account with no starting amount, and he is going to put in $90 per month.
Let x be the number of months after today.
(a) For each account, write an expression for the amount of money in
the account after x months.
Amount of money in Jenny's account (in dollars) =
Amount of money in Hong's account (in dollars) =
(b) Write an equation to show when the two accounts have the same
the fol
amount of money?

2(x+4)

hope this helps!!!

The second term of the expression represent the total depreciation value of the laptop. Therefore, the answer is C.

Pamela purchased a new laptop for her schoolwork.  She plans to sell it sometime in the future; however, its value depreciates monthly.

The expression below shows the depreciated sales value of the laptop.

Therefore, the meaning of the second term in the expression can be calculated as follows:

Therefore,

856 = The amount she bought the laptop

The second term 17m is the total depreciation value of the laptop where m = number of months.

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The volume of the solid as shown in the diagram is 540 cm².

Volume is the space occupied by a solid shape.

To calculate the volume of the of the solid, we use the formula below

Formula:

Where:

From the diagram in question,

Given:

Substitute these values into equation 1

Hence, the volume is 540 cm³.

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The value of arc PQ is 110°

The circumference of a circle is the length of the 360 degree arc of that circle. Therefore the sum of the arc on a circumference of a circle is 360°

Therefore ,

8x-10+ 6x + 10x+10 = 360

24x -10+10 = 360

24x = 360

divide both sides by 24

x = 360/24

x = 15

therefore the value of x is 15

Arc PQ = 8x -10

substitute 15 for x

ArcPQ = 8×15-10

= 120-10

= 110°

therefore the value of arc PQ is 110°

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Answer:

yes

Step-by-step explanation:

The red line on the graph may also include other lines that represent related data, such as the total amount of solid waste generated by all people in the United States per year, or the period of time in years being measured.

Red line on the graph represents the average amount of solid waste generated by each person in the United States per year.

The red line on the graph is a useful tool for understanding the impact of solid waste on the environment and society as a whole.

It helps us to identify areas where we can make changes to reduce waste and improve our overall environmental performance and serves as a reminder of the importance of responsible consumption and waste management practices.

Red line on the graph represents the average amount of solid waste generated by each person in the United States per year.

This is a key metric in measuring the environmental impact of waste production in the country.
The average amount of solid waste generated per person is an important figure because it provides a more accurate picture of individual behavior and consumption patterns.

It takes into account factors such as population growth, changes in household size, and shifts in lifestyle and consumption habits.

By tracking this metric over time, policymakers and environmental advocates can gain insight into trends and patterns in waste generation and identify opportunities for reducing waste and promoting sustainability.

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Buy-side order flow is the number of individual buy orders and the total number of shares that wish to buy. ​

This is a crucial metric that is used by traders, investors, and analysts to gauge the demand for a particular security or asset.

The buy-side order flow refers to the number of shares that market participants want to purchase at a given time, and it provides valuable insights into the sentiment of the market. If there are more buy orders than sell orders, then there is a higher demand for the security, which can lead to an increase in the price of the asset. On the other hand, if there are more sell orders than buy orders, then there is a higher supply of the security, which can lead to a decrease in the price of the asset.

Traders and investors use buy-side order flow data to help them make informed decisions about when to buy or sell a security. By analyzing the number of buy orders and the total number of shares that wish to buy, they can identify trends and patterns in the market, and adjust their strategies accordingly. Additionally, buy-side order flow data can be used to help identify potential support and resistance levels for a security, which can be useful in setting stop-loss orders and other risk management measures.

Overall, the buy-side order flow is an important metric that provides valuable insights into the sentiment of the market and helps traders and investors make informed decisions about their investments.

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All five rectangles have the same area of 60, and the sum of their dimensions is:

2 + 30 + 4 + 15 + 6 + 10 + 8 + 7.5 + 10

Let the width of rectangle 1 be w1, the width of rectangle 2 be w2, and so on. We know that all five rectangles have the same area, so we can set up an equation:

[tex]w1 * l1 = w2 * l2 = w3 * l3 = w4 * l4 = w5 * l5[/tex]

We can simplify this equation by dividing both sides by w1 * l1, which gives:

[tex]1 = (w2 * l2) / (w1 * l1) = (w3 * l3) / (w1 * l1) = (w4 * l4) / (w1 * l1) = (w5 * l5) / (w1 * l1)[/tex]

Let's define a new variable x = w2 * l2 = w3 * l3 = w4 * l4 = w5 * l5. Then we have:

[tex]w1 * l1 = xw2 * l2 = xw3 * l3 = xw4 * l4 = xw5 * l5 = x[/tex]

Now we need to find the least possible value of w1 + l1 + w2 + l2 + w3 + l3 + w4 + l4 + w5 + l5. Since w1 * l1 = x, we can rewrite this as:

[tex]w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x)[/tex]

To find the minimum value of this expression, we can take its derivative with respect to w1, set it equal to zero, and solve for w1:

[tex]d/dw1 (w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x)) = 1 - 2 * sqrt(x) / w1^1.5 + 2 * sqrt(x) / w1^2.5 = 0[/tex]

Solving for w1, we get:

[tex]w1 = 2 * x^(1/4)[/tex]

Substituting this back into our expression for the sum of the rectangle dimensions, we get:

[tex]w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x) = 2 * x^(1/4) + 2 * x^(3/4) + 8 * (x / 2)^(1/4)[/tex]

To find the minimum value of this expression, we can take its derivative with respect to x, set it equal to zero, and solve for x:

[tex]d/dx (2 * x^(1/4) + 2 * x^(3/4) + 8 * (x / 2)^(1/4)) = 1/2 * x^(-3/4) + 3/2 * x^(1/4) + 2 / (2 * x)^(3/4) = 0[/tex]

Solving for x, we get:

x = 4

Therefore, the least possible value of w1 is:

w1 =[tex]2 * x^(1/4) = 2[/tex]

And the dimensions of the rectangles are:

Rectangle 1: 2 x 30

Rectangle 2: 4 x 15

Rectangle 3: 6 x 10

Rectangle 4: 8 x 7.5

Rectangle 5: 10 x 6

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Step-by-step explanation:

+ 1.25

every new term is the previous term + 1.25.

with starting value -1.75

f(n) = 1.25n - 1.75

The solution is all values of x greater than -9.

The correct graph for the given inequality "Negative 3x - 7 < 20" is:

From negative 10 to positive 10, a number line runs. An open circle shows up at negative 9. From negative 9 to positive 10, the number line is shaded.

To chart the arrangement, we initially confine the variable by adding 7 to the two sides of the imbalance:

Negative 3x - 7 + 7 < 20 + 7

Negative 3x < 27

Next, we divide both sides by -3, remembering to flip the inequality sign since we're dividing by a negative number:

Negative 3x/-3 > 27/-3

x > -9

Therefore, the arrangement is all upsides of x more prominent than - 9. Since these are the values that satisfy the inequality, we graph this by drawing an open circle at -9 on the number line and shading all values to the right of -9.

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Answer: The dividend yield is the annual dividend payment divided by the stock's current market price, expressed as a percentage.

Dividend yield = (Annual dividend payment / Stock's current market price) x 100%

In this case:

Annual dividend payment = $1.98

Stock's current market price = $41.68

Dividend yield = ($1.98 / $41.68) x 100% = 4.75%

Therefore, the dividend yield for AT&T is 4.75%.

Step-by-step explanation:

Therefore, the length of segment ST is 8/3 cm, assuming that triangles PTQ and RTS are similar.

Triangles are used in various applications, such as in the construction of buildings, bridges, and other structures, as well as in navigation and surveying. They are also important in various fields of mathematics, including trigonometry and geometry.

Here,

Let's denote the length of segment ST as x, and the corresponding sides in triangle PTQ and RTS as y and z, respectively. We can set up the following proportion:

y / PR = z / RT

Substituting the given values, we get:

y / 12 = z / 14

Now, we can use the fact that triangles PTQ and RTS are similar to set up another proportion involving the length of segment ST:

y / x = z / 16

Substituting the value of y / 12 = z / 14 from the first proportion, we get:

(z / 14) / 12 = z / 16 / x

Simplifying this equation, we get:

z = (14 / 12) * (16 / x) * z

z cancels out on both sides, and we are left with:

x = (16 * RT) / (14 * PR)

Substituting the given values, we get:

x = (16 * 14) / (14 * 12)

= 8/3

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The value of 2m + k is 14.

The continuity of a function at a point is a fundamental concept in calculus. A function f(x) is said to be continuous at a point x = a

In other words, a function is continuous at a point if we can draw its graph without lifting the pencil from the paper at that point. This means that there are no jumps, breaks, or holes in the graph of the function at that point.

Here we have

To determine if f(x) is continuous at x = 2, we need to check if the left-hand limit and the right-hand limit of f(x) as x approaches 2 are equal, and if they are both equal to f(2).

First, let's calculate the left-hand limit of f(x) as x approaches 2:

lim x → 2- f(x) = lim x → 2- (-x² + 2m) = -(2²) + 2m = 2m - 4

Next, let's calculate the right-hand limit of f(x) as x approaches 2:

lim x → 2+ f(x) = lim x → 2+ (5x - k) = 5(2) - k = 10 - k

Now alculate f(2):

f(2) = -2² + 2m = 2m - 4

For f(x) to be continuous at x = 2, the left-hand limit, right-hand limit, and the function value at x = 2 must all be equal. So we have:

2m - 4 = 10 - k = 2m - 4

Simplifying, we get:

10 - k = 2m - 4

k + 2m = 14

Therefore,

The value of 2m + k is 14.

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Answer:

2.50 + 9.50h

Step-by-step explanation:

Sky Launch Trampoline Park charges customers $9.50 per hour they spend jumping. Each customer must also pay $2.50 for grip socks.

Let the number of hours be h.

The equation will be:

= 2.50 + (9.50 × h)

= 2.50 + 9.50h

The slope of the line in the reduced form is 4 / 7.

The slope of a line is the change in the dependent variable with respect to the change in the independent variable.

Therefore,

slope = m = change in y / change in x

slope = m = y₂ - y₁ / x₂ - x₁

P = (2, 3)

Q = (9, 7)

x₁ = 2

x₂ = 9

y₁ = 3

y₂ = 7

Therefore,

slope = 7 - 3 / 9 - 2

slope = 4 / 7

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Answer:

QR=8

Step-by-step explanation:

When two lines are perpendicular, they form two 90-degree angles. So:

m∠QSR = m∠QSP = 90°

We also know that the line segment PS is congruent to the line segment SR.

Lastly, by the reflexive property, QS is congruent to itself.

Thus, ΔPSQ ≅ ΔRSQ by SAS (side-angle-side).

Now that we know these triangles are congruent, we can further state that PQ is congruent to QR by CPCTC (corresponding parts of congruent triangles are congruent).

If PQ is congruent to QR, then their measures are also congruent, and we can get this equation (by using substitution and algebra):

[tex]3n-1=5n-7=\\6=2n=\\n=3[/tex]

Plug in n to the length of QR:

[tex]5n-7=\\5(3)-7=\\15-7=\\8[/tex]

So, QR=8.

This means that the corresponding sides of the two triangles are in proportion, and therefore CD is parallel to AB, as required.

A triangle is a polygon with three sides and three angles. It is one of the basic shapes in geometry and is often used in mathematics, science, engineering, and art. Triangles can be classified into different types based on the length of their sides and the size of their angles. Triangles are used in various applications, such as in the construction of buildings, bridges, and other structures, as well as in navigation and surveying. They are also important in various fields of mathematics, including trigonometry and geometry.

Here,

To use similarity theorems to show that CD is parallel to AB, we need to first establish that triangles AEB and CED are similar. If we can show that these triangles are similar, then we can use the corresponding angles theorem, which states that if two pairs of corresponding angles are congruent, then the lines containing the sides are parallel.

Let's compare the two triangles AEB and CED:

Angle AEB is congruent to angle CED (both are vertical angles).

Angle EAB is congruent to angle ECD (both are alternate interior angles formed by a transversal cutting parallel lines AB and CD).

Angle BAE is congruent to angle DCE (both are alternate interior angles formed by a transversal cutting parallel lines AB and CD).

Therefore, we have established that triangles AEB and CED are similar by the angle-angle-angle similarity theorem.

Now that we have shown that the triangles are similar, we can use the corresponding sides theorem, which states that the corresponding sides of similar triangles are in proportion, to find out if CD is parallel to AB.

The corresponding sides of AEB and CED are:

AE/CE = AB/CD

Substituting the given values, we have:

AC + CE / CE = AB / BD

4 + 12 / 12 = AB / (14/3)

16/12 = AB / (14/3)

AB = (16/12) x (14/3)

= 56/9

Now we can use the corresponding sides theorem to find the length of CD:

AE/CE = AB/CD

Substituting the values we have found, we get:

4/12 = (56/9)/CD

CD = (56/9) x (12/4)

= 14

Since we have found that AB = 56/9 and CD = 14, we can see that:

AB/CD = (56/9)/14

= 4/3

This means that the corresponding sides of the two triangles are in proportion, and therefore CD is parallel to AB, as required.

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The number of possible letter combinations in the words presented is as follows:

CANNON: 2520

BANANA: 120

TOMORROW: 2520

REFERENCE: 20160

It is used to determine how many distinct arrangements can be made from a given set of elements.

1) CANNON: CANNON is made up of seven letters, two of which are identical 'N's. So, the following formula can be used to get the total number of permutations for CANNON:

Total number of permutations = 7! / 2!

= (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!

= 2520

2) BANANA: BANANA is made up of six letters, three of which are the letter 'A' and are similar. The total amount of BANANA combinations can be calculated using the formula below:

Total number of permutations = 6! / 3!

= (6 x 5 x 4 x 3 x 2 x 1) / 3!

= 120

3) TOMORROW: The word TOMORROW is made up of seven letters, two of which are identical 'O's. Thus, the sum of TOMORROW's permutations can be determined as follows:

Total number of permutations = 7! / 2!

= (7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!

= 2520

4) REFERENCE: Eight letters make up REFERENCE, two of which are identical 'E's. So, the following formula can be used to determine the total number of permutations for REFERENCE:

Total number of permutations = 8! / 2!

= (8 x 7 x 6 x 5 x 4 x 3 x 2 x 1) / 2!

= 20160

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Answer:

x = -5/9

Step-by-step explanation:

-2(8x - 5) + 2x = 4(x + 5)

-16x + 10 + 2x = 4x + 20

-16x + 2x + 10 = 4x + 20

-14x + 10 = 4x + 20

+14x        = +14x       (Add 14 to both sides)

10 = 18x + 20

-20 =       -20      (Subtract 20 from both sides)

-10  = 18x

18   =  18          (Divide by 18)

-10/18 = x

Simplified:

-5/9 = x

Answer:

Step-by-step explanation: Distribute -2 to the parenthasis, and 4 to the other parenthasis. two double negatives make a positive. Combine like terms. get the x and regular numbers on different sides of the equal sign, and divide to find the x=

-16x +10 +2x=4x+20

-14x+10=4x+20

-14x            -20

-10x= -10

/-10    /-10

x=1

The lower and upper control limits that the manufacturer should use in the resulting control chart are LCL = 0.023,UCL = 0.043

To calculate the lower and upper control limits for the control chart, we need to use the following formula:
Lower control limit (LCL) = average proportion of defects - 3 x square root of [(average proportion of defects x (1 - average proportion of defects)) / sample size]
Upper control limit (UCL) = average proportion of defects + 3 x square root of [(average proportion of defects x (1 - average proportion of defects)) / sample size]
Using the given information, we can plug in the values to get:
LCL = 0.01 - 3 x square root of [(0.01 x 0.99) / 30] = -0.023
UCL = 0.01 + 3 x square root of [(0.01 x 0.99) / 30] = 0.043
However, since control limits cannot be negative, the lower control limit should be set to zero.

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The manufacturer should use control limits of 0 for the lower limit and 0.136 for the upper limit in their control chart for monitoring the proportion of unacceptable phones in their quality assurance program.

Determine the lower and upper control limits for the manufacturer's control chart, we first need to calculate the standard deviation of the proportion of unacceptable phones based on the given information.
To do this, we can use the formula:
[tex]Standard deviation = \sqrt(p\times(1-p)/n)[/tex]
p is the proportion of unacceptable phones (0.01), and n is the sample size (30 phones per day for 7 days = 210 total phones).
Plugging in these values, we get:
[tex]Standard deviation = \sqrt(0.01\times(1-0.01)/210) = 0.042[/tex]
Next, we can use this standard deviation to calculate the control limits. The lower control limit (LCL) is given by:
[tex][tex]LCL = p - 3\times\sqrt(p\times(1-p)/n)[/tex][/tex]
and the upper control limit (UCL) is given by:
[tex]UCL = p + 3\times\sqrt(p\times(1-p)/n)[/tex]
Plugging in our values, we get:
[tex]LCL = 0.01 - 3\times0.042 = -0.075[/tex]
[tex]UCL = 0.01 + 3\times0.042 = 0.095[/tex]
Values don't make sense - the proportion of unacceptable phones cannot be negative, and the UCL is above 1, which is also impossible.
To correct for this, we can use the formula:
[tex]LCL = max(0, p - 3\times\sqrt(p\times(1-p)/n))[/tex]
[tex]UCL = min(1, p + 3\times\sqrt(p\times(1-p)/n))[/tex]
This ensures that the control limits are within the range of possible values for the proportion of unacceptable phones.
Plugging in our values with this formula, we get:
[tex]LCL = max(0, 0.01 - 3\times0.042) = 0[/tex]
[tex]UCL = min(1, 0.01 + 3\times0.042) = 0.136[/tex]

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Answer:

distribute x as 3:

3²+10(3)+24

=63

An equation of a line that is parallel to the line y=-5x-8 and passes through the point (7, -2) is y = -5x + 33.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

Since the line is parallel to y=-5x-8, the slope is equal to -5.

At data point (7, -2) and a slope of -5, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - (-2) = -5(x - 7)  

y + 2 = -5x + 35

y = -5x + 35 - 2

y = -5x + 33

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The equation of the line that is parallel to y = -5x - 8 and passes through the point (7,-2) is y = -5x + 33, in slope intercept form.

To find an equation that is parallel to the line y = -5x - 8, we know that it must have the same slope. So the slope of the new line is -5.

Now we use the point-slope form of a linear equation to find the equation of the line passing through (7,-2) with slope -5:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is the given point.

Substituting the values we get:

y - (-2) = -5(x - 7)

Simplifying and solving for y, we get:

y + 2 = -5x + 35

y = -5x + 33

Therefore, the equation of the line that is parallel to y = -5x - 8 and passes through the point (7,-2) is y = -5x + 33, in slope intercept form.

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The total distinguishable ways can the donors be in line is 362,736.

The total number of distinguishable ways:

9! = 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 362,880

To subtract the number of in-distinguishable arrangements:

(4! x 3!) + (3! x 2!) = 144

There are 362,736 distinguishable ways in which four donors with type O blood, three donors with type A blood, and two donors with type B blood can be in line.

This is calculated by first determining the total number of distinguishable arrangements, which is 9!.

Then,

The number of indistinguishable arrangements is subtracted from the total.

Which is done by multiplying the number of arrangements for each blood type separately and then adding them together.

The result is then subtracted from the total, leaving the number of distinguishable ways.

The total number of distinguishable ways is:

362,880 - 144 = 362,736

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Answer:

the angle of depression is approx 22 degrees

Step-by-step explanation:

Model drawn below to visualize

I represented the angle of depression as x

Since two side lengths are given, we can use tangent to find the angle of depression

tan x= 3/7.5

We then use inverse tangent to find the angle measure:

m<x=[tex]tan^{-1}[/tex](3/7.5)

m<x is approx 21.8 or 22 when rounded to the nearest degree

(when using tan, inverse tan, sin, cos, inv... use deg on calculator when finding angle of depression, solving triangles, etc.)

An equation uses two operations is equal to C = n × p + T.

Relationship between variables is C represents total cost where as 'n × p' is cost of meal per person and T is additional cost.

Total cost of a meal at a restaurant is a function of the number of people and the price per dish.

Represent the variables as follows,

Let us use the variable 'C' to represent the total cost of the meal.

Let us use the variable 'n' to represent the number of people at the table.

Let us use the variable 'p' to represent the price per dish.

An equation that uses two operations, use multiplication and addition.

C = n × p + T

'n × p' represents the cost of the meal per person,

'T' represents any additional costs, such as taxes or tips.

By adding these two values together, total cost of the meal.

Relationship between the variables is as follows,

Total cost of the meal C is directly proportional to both the number of people n and the price per dish p.

Increase either n or p, total cost of the meal will increase proportionally.

For example,

Double number of people at the table n,

Total cost of meal C will also double,

Assuming price per dish p remains constant.

Similarly,

Double the price per dish p,

Total cost of the meal C will also double,

Assuming number of people at the table n remains constant.

Constant term T represents any additional costs.

That are independent of n and p, such as taxes or tips.

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Answer:

1.a

2.c

3.d

4.b

Step-by-step explanation:

Therefore , the solution of the given problem of equation comes out to be 10x - y = 51 is the point-slope form of the equation of the line passing through the points (6, -9) and (7, 1).

Variable words are frequently used in complex algorithms to show consistency between two arguments that are opposed to one another. Academic expressions called equations are used to show the equality of various academic figures. Take into account the details in the z + 7 proposals.

Here,

The equation for the line passing between the points (6, -9) and (7, 1) must be found in the point-slope form.

Using the equation m = (y2 - y1) / (x2 - x1), find the slope (m) of the line, where (x1, y1) and (x2, y2) are the coordinates of the two points.

=> (x1, y1) = (6, -9)

=> (x2, y2) = (7, 1)

=> m = (1 - (-9)) / (7 - 6)

=> m = 10 / 1 m = 10

Consequently, the line's slope is 10.

=> y - y1 = m(x - x1)

=> m = 10 (x1, y1) = (6, -9)

=> y - (-9) = 10(x - 6)

=> y + 9 = 10x - 60

=> 10x - y = 51

Therefore, 10x - y = 51 is the point-slope form of the equation of the line passing through the points (6, -9) and (7, 1).

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The position of point S after dilating will be half of the original. The dilated point S' has been shown below.

What is dilation?

Using a modification known as dilation, an object can be resized. Through dilatation, the objects can be resized or enlarged. This transformation results in a shape that is a perfect replica of the original image. The form's dimensions do vary, though. An expansion or contraction of the original form is required for a dilatation. This shift is referred to as a scale factor.

We are given a graph showing position of point S.

Now, on dilating the point by a scale factor of [tex]\frac{1}{2}[/tex], we get that the point will be located at half of the original.

The point has been located and attached in the image below.

Hence, the required solution has been obtained.

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The length of the side b for the right triangle ABC is equal to 5.276, and the measures of angle A and B are 64 and 26 to the nearest degree using the sine rule.

The sine rule is a relationship between the size of an angle in a triangle and the opposing side.

The side length b is derived using the Pythagoras rule as follows:

b = √(12.2² - 11²)

b = 5.276

Using the sine rule;

12.2/sin90 = 11/sinA

A = sin⁻¹(11 × sin90)/12.2 {cross multiplication}

A = 64.4

12.2/sin90 = 5.3/sinB

B = sin⁻¹(5.276 × sin90)/12.2 {cross multiplication}

B = 25.6

Therefore, the length of the side b for the right triangle ABC is equal to 5.276, and the measures of angle A and B are 64 and 26 to the nearest degree using the sine rule.

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