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Answer:

[tex]{ \sf{ {b}^{3} = 8}} \: \: \\ { \sf{ {b}^{3} = {2}^{3} }} \\ { \sf{ {(b}^{3}) {}^{ \frac{1}{3} } = {( {2}^{ 3}) }^{ \frac{1}{3} } }} \\ { \sf{b ={ \boxed{ 2}}}}[/tex]

Answer:

b=2

Step-by-step explanation:

[tex]b^{3} = 8\\\\b^{3} = 2^{3} \\\\b=+2[/tex]

Answer:

Y=8

Step-by-step explanation:

7(y-5)=21

distribute the 7

7y-35=21

get y by itself

7y=56

divide by 7

y=8

HOPE THIS HELPS YOU UNDERSTAND!

The equation of the line in slope-intercept form that goes through the point (8, -2) and has a slope of 1/4 is y = 1/4x - 4.

In slope-intercept form, the equation of a line is expressed as y = mx + b, where m denotes the slope of the line and b the y-intercept, or the location at where the line intersects the y-axis. In this form, the slope m denotes the line's steepness or the rate at which y changes in relation to x. A positive slope causes the line to go upward from left to right, whereas a negative slope causes the line to move downward from left to right. The value of y when x is 0, or the line's origin, is represented by the y-intercept, or b.

Given that, point (8, -2) and a slope of 1/4.

The slope-intercept form is given as:

y - y1 = m(x - x1)

Substituting the values:

y - (-2) = 1/4(x - 8)

y + 2 = 1/4x - 2

y = 1/4x - 4

Hence, the equation of the line in slope-intercept form that goes through the point (8, -2) and has a slope of 1/4 is y = 1/4x - 4.

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The solutions to the equation x² - 18x + 81 = 4 by completing the square are x = 9 + 2i and x = 9 - 2i.None of the answer choices A, B, C, or D are correct.

An equation is a mathematical statement that shows the equality between two expressions, often containing variables and mathematical operations.

To solve the equation x² - 18x + 81 = 4 by completing the square, we can follow these steps:

x² - 18x + 77 = 0

Divide both sides by the coefficient of x² to make the coefficient 1:

x² - 18x + (81/1) = -77/1

x² - 18x + 81 = -77

Add the square of half the coefficient of x to both sides of the equation:

x² - 18x + (9)² = -77 + (9)²

x² - 18x + 81 = -4

(x - 9)² = -4

x - 9 = ±√(-4)

x - 9 = ±2i (where i is the imaginary unit)

x = 9 ±2i

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The Volume of rectangular prism (V) = 20,825 [tex]cm^{3}[/tex]

A rectangular prism is a three-dimensional geometric shape that is formed by six rectangular faces joined together at right angles.

I think the question is, find out the volume of the rectangular prism in cubic centimeters? Given that the height is 85cm and area of base is 245cm².

We know that the formula for calculating the volume of a rectangular prism is as follows,

Volume of rectangular prism (V) = Area of base × height of the prism

Volume of rectangular prism (V) = 245cm² × 85cm

Volume of rectangular prism (V) = 20,825 [tex]cm^{3}[/tex]

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The volume of the two cuboid added together will be 192 cm³.

what exactly is a cuboid?

A cuboid, also known as a rectangular prism, is a three-dimensional solid shape that has six rectangular faces. It is a type of polyhedron, a geometric figure with flat faces and straight edges.

A cuboid has three pairs of congruent and parallel faces, with each pair being congruent to the other. These pairs of opposite faces are known as bases, and the other four faces are called lateral faces. The lateral faces are also rectangles and are perpendicular to the bases.

Now,

As Volume of the cuboid= L*B*H

where l=length, B=Breadth and H=Height

and volume of the figure =volume of 2 cuboids

=8*4*3+10*3*4

=72+120

=192 cm³

Hence,

           The volume of the two cuboid added together will be 192 cm³.

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The area of the shaded sector is equal to: A. 415π/2 ft².

Mathematically, the area of a sector can be calculated by using this formula:

Area of sector = θπr²/360

Where:

Substituting the given parameters into the area of a sector formula, we have the following;

Area of sector = 332(π/180) × (15)²/2

Area of sector = 74,700π/180 × 1/2

Area of sector = 415π/2 ft²

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By answering the presented question, we may conclude that as we know the sum of all angles is a triangle is 180; x = 46

A polygon is a triangle with four or more parts. It has a straightforward rectangular shape. Triangle ABC denotes a rectangle with the edges A, B, and C. Euclidean geometry produces a single plane and cube when the sides are not collinear. A triangle is a polygon if it contains three components and three angles. The corners are the points where a triangle's three edges meet. The angles of a triangle sum up to 180 degrees.

as we know the sum of all angles is a triangle is 180.

so, here,

20+114+x = 180

x = 180 - 134

x = 46

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Answer:

The height of the patio heater is approximately 8.9 feet.

This shows that any increase in x by a certain factor results in an increase in y by the same factor, confirming that y varies directly with x.

What is Linear equation ?

Linear equation can be defined as equation in which highest degree is one.

To determine if y varies directly with x, we need to check if there is a constant ratio between y and x. In other words, if we increase x by a certain factor, does y also increase by the same factor?

The equation 3y = -7x - 18 can be rewritten as y = (-7/3)x - 6. This is in the form of y = kx + b, where k is the constant of variation and represents the ratio between y and x.

Since the equation is in this form, we can say that y varies directly with x, and the constant of variation is k = -7/3.

To verify that y varies directly with x, we can check that any increase in x by a certain factor results in an increase in y by the same factor, as given by the constant of variation. For example, if we increase x by 3, then y will increase by (-7/3)(3) = -7. If we increase x by 6, then y will increase by (-7/3)(6) = -14.

Therefore, This shows that any increase in x by a certain factor results in an increase in y by the same factor, confirming that y varies directly with x.

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FG and KH are congruent using the AAS theorem. ∠F = ∠K and ∠G = ∠H

The AAS (Angle-Angle-Side) Congruence Theorem is a geometric theorem that states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

In other words, if two triangles have two corresponding angles that are congruent, and the included side between these angles is also congruent in both triangles, then the two triangles are congruent.

The diagram shows that we have two triangles here. The first triangle is equal to the second triangle.

This is shown by the fact that the angle at F = angle at K

the angle at H = angle at G

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Answer:

use AAS for this

Step-by-step explanation:

The rock will be at a height of 125 feet after 0.49 and 4.76 seconds.

In the given problem we have a function h(t) that represents the height of the rock that is from the ground of the beach where the variable represents the time travel by the rock.

Assume t as required time equates the given function to the given height and solve for the value of 't'.

Here we have

A rock is thrown directly upward with an initial velocity of 79 feet per second from a cliff 50 feet above a beach.

The height of the rock above the beach (h) after t seconds is given by the equation h(t) = -16t² + 79t + 50.  

Let after t seconds the height will be 125 feet

=> h(t) = 125  

=>  -16t² + 79t + 50 = 125

=> -16t² + 79t - 75 = 0

To solve this quadratic equation, we can use the quadratic formula:

=> x = [-b ± √(b² - 4ac)]/ 2a

Here a = -16, b = 79, and c = -75.  

t = [-79 ± √(79² - 4(-16)(-75))] / 2(-16)

t = (-79 ± √(6241 - 4800)) / -32

t = (-79 ± √1441) / -32

So, the two solutions are:

t = (-79 + √1441) / -32 and   t = (-79 - √1441) / -32

t ≈ 0.497 or t ≈ 4.763

Therefore,

The rock will be at a height of 125 feet after 0.49 and 4.76 seconds  

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Answer:

A) AAA yessss

By answering the presented question, we may conclude that As a result, trigonometry the abbreviated phrase is: 8 sin(c+l)

Trigonometry is the field of mathematics that explores the connection between triangle side lengths and angles. The issue first originated in the Hellenistic era, during the third century BC, as a result of the use of geometry in astronomical investigations. The subject of mathematics known as exact techniques is concerned with certain trigonometric functions and their possible applications in calculations. Trigonometry contains six commonly used trigonometric functions. Their separate names and acronyms are sine, cosine, tangent, cotangent, secant, and cosecant (csc). Trigonometry is the study of triangle characteristics, particularly those of right triangles. As a result, geometry is the study of the properties of all geometric forms.

tan (7 sin(c) + 8 cos(c)) (l)

We may utilise the trigonometric identity to simplify this expression:

sin(l) / cos(l) = tan(l) (l)

When we insert this into the original phrase, we get:

sin(l) / cos(c) (7 sin(c) + 8 cos(c)) (l)

By increasing the numerator, we get:

8 cos(c) sin + 7 sin(c) sin(l) (l)

Now we can apply the trigonometric identities:

(1/2) sin(a) cos(b)

[sin(a+b) plus sin(a-b)]

(1/2) cos(a) sin(b)

[sin(a+b) minus sin(a-b)]

We can write using these identities:

7 sin(c) sin(l) + 8 cos(c) sin(l) equals 7 (1/2).

[sin(c+l) minus sin(c-l)] + 8 (1/2) [sin(c+l) plus sin(c-l)]

= (7/2)sin(c+l) + (8/2)sin(c-l) + (8/2)sin(c+l) + (7/2)sin(c-l) - (7/2)sin(c-l) = 8 sin(c+l)

As a result, the abbreviated phrase is:

8 sin(c+l)

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Answer:

Let's call the height of the antenna "h".

First, we can use the angle of elevation of 38^{\circ} ∘ to find the height of point A above the ground.

tan(38^{\circ}) = \frac{h}{21}

h = 21 \cdot tan(38^{\circ})

h \approx 15.6

So point A is approximately 15.6 meters above the ground.

Next, we can use the angle of elevation of 46^{\circ} ∘ to find the height of point B above the ground.

tan(46^{\circ}) = \frac{h}{d}

h = d \cdot tan(46^{\circ})

We can find the value of "d" using the Pythagorean theorem.

d^2 = 21^2 + 15.6^2

d \approx 25.7

So the distance from point A to point B is approximately 25.7 meters.

Finally, we can use the height of point A and the distance from point A to point B to find the height of point B (the height of the antenna).

h = d \cdot tan(46^{\circ})

h \approx 25.7 \cdot tan(46^{\circ})

h \approx 23.2

Therefore, the height of the antenna is approximately 23.2 meters.

Step-by-step explanation:

the scenario creates 2 right-angled triangles.

both have the same first leg : the horizontal distance from Avani's eyes to the building (21 m).

and both have a right angle (90°) at the point, where the horizontal distance meets the building.

the difference is now the second leg : the height of the building (starting at 1.66 m above ground), and the height of the building plus the height of the antenna (again starting at 1.66 m above ground).

another difference is the length of the line of sight (from Avani to AA, and from Avani to BB).

driving these differences is the difference in the angle at Avani (38° vs. 46°).

now, remember the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

a, b, c are the sides of the triangle, A, B, C are the corresponding opposite angles of the triangle.

and remember : the sum of all angles in a triangle is always 180°.

what is the plan ?

we need to calculate the second leg of the larger triangle, and then the second leg of the smaller triangle and subtract that from the second leg of the larger triangle.

in other words :

(building + antenna) - building = antenna

so, we start with the larger triangle (up to BB).

the angle at Avani is 46°.

the angle at the building is 90°.

the angle at BB is then

180 - 90 - 46 = 44°.

21/sin(44) = (building + antenna)/sin(46)

(building + antenna) = 21×sin(46)/sin(44) =

= 21.74613659... m

now, for the smaller triangle (up to AA).

the angle at Avani is 38°.

the angle at the building is 90°.

the angle at AA is then

180 - 90 - 38 = 52°.

21/sin(52) = building/sin(38)

building = 21×sin(38)/sin(52) = 16.40699816... m

the height of the antenna is then again

(building + antenna) - building = 5.339138433... m

≈ 5.3 m

Step-by-step explanation:

3)

a. To find the height of the kite, we can use trigonometry. The sine function relates the opposite side (the height of the kite) to the hypotenuse (the length of string used) and the angle of elevation. Therefore, we can write:

sin(65°) = height/75

Solving for the height, we get:

height = 75 sin(65°) = 67.8 ft

Therefore, the kite is 67.8 feet high.

b. To find the distance between Joe and Jill, we can use trigonometry again. The tangent function relates the opposite side (the distance between Joe and Jill) to the adjacent side (the height of the bell tower) and the angle of depression. Therefore, we can write:

tan(angle of depression) = opposite/adjacent

tan(angle of depression) = Jill's height/210

Solving for the distance between Joe and Jill, we get:

distance = adjacent * tan(angle of depression)

distance = 210 * tan(angle of depression)

We need to know the angle of depression to solve for the distance, which is not given in the problem.

4)

a. In an isosceles triangle with two equal angles of 70°, the third angle must be:

180° - 70° - 70° = 40°

Since the triangle is isosceles, the height must be the perpendicular bisector of the base. Therefore, we can draw an altitude from the top vertex to the base, splitting the base into two equal segments. Let x be the length of each base segment. Then we can use trigonometry to find the height:

tan(70°) = height/x

height = x * tan(70°)

Since the height is given as 16 cm, we can solve for x:

16 = x * tan(70°)

x = 16/tan(70°)

Therefore, the length of each base segment is:

x = 16/tan(70°) = 6.12 cm

And the length of the base is twice the length of each segment:

base = 2x = 2(16/tan(70°)) = 12.25 cm

Therefore, the measures of the rest of the triangle are:

base = 12.25 cm

each equal angle = 70°

height = 16 cm

b. To determine if the ramp meets ADA standards, we need to find the angle of incline. The angle of incline is the angle between the ramp and the horizontal. We can use trigonometry to find this angle:

sin(angle of incline) = rise/run

sin(angle of incline) = 2/25

angle of incline = sin^(-1)(2/25)

Using a calculator, we get:

angle of incline ≈ 4.79°

Since the angle of incline is greater than the maximum allowable angle of 4.76°, the ramp does not meet ADA standards.

Answer:    2/15

Step-by-step explanation:
S: student wearing an sneakers
W: student wearing a white sneakers

Data given:

P(S) = 5/12
P(S∩W) = 8/25

so to find
P(W) = P(S)*P(S∩W) =  8/25* 5/12 = 2/15

This is 2/15 of the total students wears white sneakers

Answer:

2/15 of the student body normally wears white sneakers

Step-by-step explanation:

5/12

multiplied by

8/25

equals

40/300 = 4/30 =

after simplification

2/15

Answer: The probability that two of the three CDs will be defective is approximately 0.01044 or 1.044%.

Step-by-step explanation: We can use the binomial distribution to solve this problem. Let X be the number of defective CDs in a sample of three. Then X follows a binomial distribution with parameters n = 3 and p = 6/100, where n is the sample size and p is the probability of a CD being defective.

The probability of getting exactly two defective CDs in a sample of three can be calculated using the binomial probability formula:

P(X = 2) = (3 choose 2) * (6/100)^2 * (94/100)^1

where (3 choose 2) = 3 is the number of ways to choose 2 defective CDs out of 3.

Simplifying this expression, we get:

P(X = 2) = 3 * (6/100)^2 * (94/100)

P(X = 2) = 0.01044

Therefore, the probability that two of the three CDs will be defective is approximately 0.01044 or 1.044%.

Answer: working on it

Step-by-step explanation:

The value of the expression is between 7/9 and 8, since 7/9 < 56/9 < 8. So the correct option is D.

Algebraic expressions can represent real-world situations, formulas, and equations. They are commonly used in algebra, which is a branch of mathematics that deals with symbols and the rules for manipulating these symbols.

Algebraic expressions are important tools in solving equations and real-world problems that involve variables and unknowns. They are also used in calculus, physics, engineering, and other fields that require mathematical modeling and analysis.

The value of the expression 8×7/9 can be simplified using the order of operations (PEMDAS) as follows:

8×7/9 = (8×7)/9 = 56/9

Therefore, the value of the expression is between 7/9 and 8, since:

7/9 < 56/9 < 8

So the correct statement is: D) between 7/9 and 8.

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After simplifying a mixed number is 5 1/16

A mixed number is a combination of a whole number and a fraction.

It is typically written in the form "a b/c", where "a" is the whole number, "b" is the numerator of the fraction, and "c" is the denominator of the fraction.

For example, 3 1/2 is a mixed number, where 3 is the whole number, 1 is the numerator of the fraction, and 2 is the denominator of the fraction. This mixed number can also be expressed as an improper fraction as follows:

3 1/2 = (3 × 2 + 1) / 2 = 7/2.

Conversely, an improper fraction can be converted to a mixed number by dividing the numerator by the denominator to obtain the whole number and expressing the remainder as a fraction.

To multiply 2 1/4, follow these steps:
1. Convert the mixed number to an improper fraction: 2 1/4 = (2 × 4 + 1) / 4 = 9/4
2. Multiply the improper fraction by itself: (9/4) × (9/4)
3. Multiply the numerators: 9 × 9 = 81
4. Multiply the denominators: 4 × 4 = 16
5. Write the result as a fraction: 81/16
6. Simplify the fraction by converting it to a mixed number:

81 ÷ 16 = 5, with a remainder of 1.

So, 81/16 = 5 1/16.

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Answer:

The gradient is given as m=1, and the point (7,2) lies on the line. Thus:

y - y1 = m(x - x1)

y - 2 = 1(x - 7)

y - 2 = x - 7

y = x - 5

So the equation of the line is y = x - 5.

Again, using the point-slope form of a straight line:

The gradient is given as m=-2, and the point (6,-3) lies on the line. Thus:

y - y1 = m(x - x1)

y - (-3) = -2(x - 6)

y + 3 = -2x + 12

y = -2x + 9

So the equation of the line is y = -2x + 9.

Answer:

22

Step-by-step explanation:

The time required for a radioactive isotope to decay to a certain percentage of its initial amount can be found using the following formula:

t = (t1/2 / ln(2)) * ln(N0/N1)

where:

t is the time elapsed since the release of the radioactive material

t1/2 is the half-life of the radioactive isotope (6 days in this case)

N0 is the initial amount of the radioactive isotope

N1 is the remaining amount of the radioactive isotope (14% of N0 in this case)

ln is the natural logarithm

We can solve for t by plugging in the given values:

t = (6 / ln(2)) * ln(1 / 0.14)

t ≈ 22.4 days

Therefore, the farmers needed to wait about 22.4 days to use the hay safely.

11 pieces can be cut frοm the 4 yards οf fabric.

An element οf a whοle is a fractiοn. The quantity is mathematically represented as a quοtient, where the numeratοr and denοminatοr are split in half. Bοth are integers in a simple fractiοn. A fractiοn can be fοund in either the numeratοr οr the denοminatοr οf a cοmplex fractiοn. The numeratοr οf an apprοpriate fractiοn is less than the denοminatοr.

1 yard = 36 inches (since 1 yard is equal tο 3 feet and 1 fοοt is equal tο 12 inches)

Sο, 4 yards οf fabric = 4 x 36 = 144 inches οf fabric.

If each piece is 13 inches lοng, we can find the number οf pieces by dividing the tοtal length οf fabric by the length οf each piece:

Number οf pieces = Tοtal length οf fabric / Length οf each piece

Number οf pieces = 144 / 13

Number οf pieces ≈ 11.08

Since we cannοt have a fractiοn οf a piece, we must rοund dοwn tο the nearest whοle number. Therefοre, 11 pieces can be cut frοm the 4 yards οf fabric.

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The table that represents a proportional relationship is the option (d) i.e. x: 6, 3, 0,  

y: -2, -1, 0

A general linear relationship is written as:

[tex]y = a*x + b[/tex]

Where a is called as the slope and b is called the y-intercept.

Proportional relationship is what we get when the y-intercept is 0, so we get an equation in the form:

[tex]y = a*x[/tex]

And in this case we can say, the slope is called the "constant of proportionality"

All proportional relationships of this property is given by , if we take x = 0 we get:

[tex]y = a*0 = 0[/tex]

So they always pass through the point (0, 0).

Now if we look at the given tables, the only option that passes through that point is the last table:

x: 6, 3, 0

y: -2, -1, 0

So that is the correct option.

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The slope of the line is -50 and it means that the amount of money in the account is decreasing at a rate of $50 every week.

What is meant by the slope of the line?

A line's slope is defined as the ratio of the change in the y coordinates to the change in the x coordinate. Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by y and x, respectively.

As a result, m = change in y/change in x is the formula for the change in the y-coordinate with respect to the change in the x-coordinate.

where "m" represents a line's slope.

A line's slope provides information on the steepness and direction of the line. By calculating the difference between the coordinates of the two points, (x1,y1) and (x2,y2), it is simple to calculate the slope of a straight line between them.

The complete question is given below.

The two points on the graph are (4, 2400) and (12, 2000).

(x₁ , y₁) = (4, 2400)

(x₂ , y₂) = (12, 2000)

The slope of the graph can be found using the following formula.

Slope m = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] = [tex]\frac{2000-2400}{12-4}[/tex] = [tex]\frac{-400}{8}[/tex] = -50

Therefore the slope of the line is -50 and it means that the amount of money in the account is decreasing at a rate of $50 every week.

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Answer:

s = -1.5

Step-by-step explanation:

0.5s + 1 = 7 + 4.5s

So we can combine like terms

Put 0.5s to other side

Put 7 to other side

Then you get the equation:

1 - 7 = 4.5s - 0.5s

So we simplify:

-6 = 4s

That means

s = -6/4

s = -1.5

Hope this helps!

Therefore , the solution of the given problem of expression comes out to be the correlation coefficient for this group is r = 0.9446.

Calculations like multiplication, variable splitting, joining, and presently removing are required. Combining them would result in the following: An equation, some statistics, and a mathematical formula. A declaration of truth is composed of values, components, mathematical processes like additions, subtractions, errors, and subdivisions as well as arithmetic formulas. Words and phrases can be evaluated and analysed.

Here,

You must use the following method to determine the r (Pearson correlation coefficient) for this sample:

=> r = (NΣXY - ΣXΣY) / √((NΣX² - (ΣX)²) (NΣY² - (ΣY)²))

where:

N stands for notes (in this case, 10)

Sum of each newborn's weight is equal to X.

Y = the measure of each infant

We can compute the following using the formula:

=> ΣX = 29.5

=> ΣY = 509

=> ΣXY = 1576.7

=> ΣX² = 97.95

=> ΣY² = 26757

When these numbers are added to the formula, we obtain:

=> r = (10 * 1576.7 - 29.5 * 509) / √((10 * 97.95 - (29.5)^2) * (10 * 26757 - (509)^2))

=> r = 0.9446

Since length and weight of newborns are strongly positively correlated, the correlation coefficient for this group is r = 0.9446.

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Therefore , the solution of the given problem of coordinates comes out to be , T's values are (15, 7).

A coordinate system can be used to precisely find points or additional mathematical objects on such a space, including Euclidean space, by using one or more variables or coordinates. To find a point or item on a double plane, one uses coordinates, which are pairs of numbers. Two numbers called the y and x matrices are used to describe a point's location on a two-dimensional plane. a set of numbers used to identify specific locations. The number usually consists of two digits.

Here,

In other terms, the x-coordinate of T is 6 times the difference between t and 6, or:

=> T's x-coordinate is 6 plus (6 minus (-3)) = 15

We can use the fact that the line of reflection is just the perpendicular bisector of the section joining t and to determine the y-coordinate of T. T's separation from the line

=>  x=6 is 6 - (-3) = 9,

which is also T's separation from the line x=6.

The y-coordinate of T is the same as the y-coordinate of t because the line of reflection is the perpendicular bisector of the section joining t and T, which is:

=>T has a y-coordinate of 7.

Consequently, T's values are (15, 7).

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Answer:

These distances show that AB, which is only 10 nautical miles apart, and AB are the closest pair of islands.

Step-by-step explanation:

We must first locate the three pairs of islands in order to establish which pair is nearest before determining the safest route for the ship.

Give the three islands the letters A, B, and C. The three island groups are designated as AB, AC, and BC. Finding the closest pair is necessary.

We can leverage the separation between the islands to do this. Assuming that the islands are separated by the following distances:

A and B are separated by 10 nautical miles.

A and C are separated by 15 nautical miles.

B and C are separated by 12 nautical miles.

These distances show that AB, which is only 10 nautical miles apart, and AB are the closest pair of islands.