A polynomial function with real coefficients and roots 1, 3i is f(x) = x^3 - x^2 + 9x - 9.
What is the polynomial functionIf a polynomial function has real coefficients, then complex roots must come in conjugate pairs. That is, if 3i is a root, then -3i must also be a root. Therefore, the polynomial with roots 1, 3i, and -3i is:
(x - 1)(x - 3i)(x + 3i)
Multiplying this out using the difference of squares, we get:
(x - 1)(x^2 - (3i)^2)
Simplifying the expression using (3i)^2 = -9, we get:
(x - 1)(x^2 + 9)
Expanding the expression using FOIL, we get:
x^3 + 9x - x^2 - 9
Simplifying this expression, we get:
f(x) = x^3 - x^2 + 9x - 9
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Which statement describes how to solve
Square both sides once and then solve the resulting linear equation.
Square both sides once and then solve the resulting quadratic equation.
Square both sides twice and then solve the resulting linear equation.
Square both sides twice and then solve the resulting quadratic equation.
The statement "Square both sides twice and then solve the resulting linear equation." describes the correct process to solve √(3x+4)=√3x+4
How to solve √(3x+4)=√3x+4?Given equation:
[tex]\sqrt{3x} + 4= \sqrt[]3{x} + 4[/tex]
Square both sides :
[tex]3x+4=3x + 16+8\sqrt{3x}[/tex]
= [tex]8\sqrt{3x} =-12[/tex]
Square both sides again
[tex]64[/tex] × [tex]3x[/tex][tex]=144[/tex]
= x=3\4
What are linear equations?Linear equations are mathematical expressions that describe a straight line on a coordinate plane. They are used to model relationships between variables that have a constant rate of change or a constant slope.
Linear equations are fundamental and essential in many areas of mathematics, science, and engineering, and are used extensively in algebra, geometry, calculus, statistics, and physics.
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Complete question:
Which statement describes how to solve √(3x+4)=√3x+4?
Help!!!!!!!
Convert this rational number to its decimal form and round to the nearest thousandth. 2/7
Answer: 2/7 as a decimal rounded to the nearest thousandth is 0.286.
Hugo averages 72 words per minute on a typing test with a standard deviation of 7 words per minute. Suppose Hugo's words per minute on a typing test are normally distributed. Let X= the number of words per minute on a typing test. Then, X∼N(72,7). Suppose Hugo types 80 words per minute in a typing test on Wednesday. The z-score when x=80 is ________. This z-score tells you that x=80 is ________ standard deviations to the ________ (right/left) of the mean, ________. Correctly fill in the blanks in the statement above. Select the correct answer below:
Answer:
i don't know
Step-by-step explanation:
good luck bro
(alright I'm just here for the points so yeah bye)
Given mn, find the value of x.
45°
Answer:
X= 135°
Step-by-step explanation:
Let y be equal to x
45° + y = 180°
Y = 180 - 45
Y = 135°
Therefore y = X
The number of meters a student swam this week are listed.
600, 750, 800, 850, 900, 1100
What is the appropriate measure of variability for the data shown, and what is its value?
The mean is the best measure of variability and equals about 833.
The median is the best measure of variability and equals 825.
The range is the best measure of variability and equals 500.
The IQR is the best measure of variability and equals 150.
Answer: The range is the best measure of variability for the given data set and its value is 500.
The range is the difference between the maximum and minimum values in a data set, and in this case, the maximum value is 1100 and the minimum value is 600, so the range is 1100-600=500. The range gives us an idea of how spread out the data is, but it can be affected by outliers. In this case, it seems like a reasonable measure of variability since there are no extreme values that would greatly affect the range.
Step-by-step explanation:
From the data of the number of meters swam by students , range is the best measure of variability and equals 500
What are domain and range?The domain of a function is the set of values that we are allowed to plug into our function. This set is the x values in a function such as f(x). The range of a function is the set of values that the function assumes. This set is the values that the function shoots out after we plug an x value in.
The range is the set of outputs of a relation or function. In other words, it's the set of possible y values. Recall that ordered pairs are of the form (x,y) so the y coordinate is listed after the x. The output is listed after the input.
Given data ,
Let the data set be represented as A
Now , the value of A is
A = { 600, 750, 800, 850, 900, 1100 }
The appropriate measure of variability for the given data is the range. The range is the difference between the largest and smallest values in the data set.
And , range = 1100 - 600
R = 500
Hence , the range of the data set is R = 500
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what is -7 in binary and also what is -5 in binary
Answer:
-7 in binary is -0b111.
-5 in binary is -0b101.
Step-by-step explanation:
Answer:
-111
-101
Step-by-step explanation:
Binary uses powers of 2.
2^0 = 1
2^1 = 2
2^2 = 4
2^3 = 8
2^4 = 16
7 = 4 + 2 + 1
7 = 1 × 2^2 + 1 × 2^1 + 1 × 2^0
7 in binary is 111
-7 in binary is -111
5 = 4 + 1
5 = 1 × 2^2 + 0 × 2^1 + 1 × 2^0
5 in binary is 101
-5 in binary is -101
Ivanna runs 10 miles in 96 minutes. How many minutes does she take per mile?
Answer:
Ivanna takes 9.6 minutes per mile.
To find out, you can divide the total time by the total distance:
time per mile = total time ÷ total distance
time per mile = 96 minutes ÷ 10 miles
time per mile = 9.6 minutes/mile
Step-by-step explanation:
the sum of the base and the height of a triangle is 22cm find the dimension for which the area is a maximum height and base
Answer: Let's call the base of the triangle "b" and the height of the triangle "h". We are given that the sum of the base and the height is 22 cm, so we can write:
b + h = 22
We want to find the dimensions for which the area of the triangle is a maximum. The formula for the area of a triangle is:
A = (1/2)bh
We can use the equation b + h = 22 to solve for h in terms of b:
h = 22 - b
We can substitute this expression for h into the formula for the area:
A = (1/2)b(22 - b)
Simplifying this expression, we get:
A = 11b - (1/2)b^2
To find the value of "b" that maximizes the area, we can take the derivative of this expression with respect to "b" and set it equal to zero:
dA/db = 11 - b = 0
Solving for "b", we get:
b = 11
Substituting this value of "b" back into the equation b + h = 22, we get:
h = 22 - b = 22 - 11 = 11
Therefore, the dimensions for which the area of the triangle is a maximum are:
base = 11 cm
height = 11 cm
And the maximum area is:
A = (1/2)bh = (1/2)(11 cm)(11 cm) = 60.5 square cm
Step-by-step explanation:
pls help im very stuck
Answer:
Step-by-step explanation:
zachary climed 9.5 m
erin climed 8.8m
to 2 dp
zachary-9.51
erin-8.76
Consider the table, showing the official mean weight and estimated standard deviation for five U.S. coins. Suppose a
vending machine is designed to reject all coins with weights more than 2 standard deviations above or below the
mean.
Click the icon to view the table.
For each coin, find the range of weights that are acceptable to the vending machine. Complete the table below.
Range of weight (grams)
Coin
Cent
Nickel
Dime
Quarter
Half dollar
n example
(Round to three decimal pla
...
Get more help.
Data table
Coin
Cent
Nickel
Dime
Quarter
Half dollar
h
Weight (grams) Estimated standard deviation
(grams)
2.500
5.000
2.268
5.670
11.340
0.04
0.09
0.03
0.08
0.13
Answer:
no sé talvez sería
bueno no sé jajaja
Find the value of X using Trigonometry. Round your answer to the nearest tenth.
Answer:
x ≈ 10.4
Step-by-step explanation:
using the tangent ratio in the right triangle
tan41° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{9}{x}[/tex] ( multiply both sides by x )
x × tan41° = 9 ( divide both sides by tan41° )
x = [tex]\frac{9}{tan41}[/tex] ≈ 10.4 ( to the nearest tenth )
Answer:
x=10.34
Step-by-step explanation:
tanФ=opposite ÷ adjacent
tan41°=9/x
0.87=9/x
x=9/0.87
=10.34
Which is equivalent to 3√2
? Select all that apply
Responses
tan 45°
tan 45°
cos 45°
cos 45°
sin 45°
sin 45°
sin 30°
sin 30°
sin 60°
sin 60°
cos 30°
cos 30°
tan 30°
Answer:
Sin 60°
Sin 60°
Cos 30°
Cos 30°
I will mark you brainiest!
What is the area of a rhombus whose sides are all 15 units and whose height is 6 units?
A) 90 units2
B) 88 units2
C) 76 units2
D) 63 units2
The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and online. Audience estimates, costs, and maximum media usage limitations are as shown:
Constraint Television Radio Online
Audience per advertisement 140,000 18,000 30,000
Cost per advertisement $1,500 $200 $550
Maximum media usage 15 19 12
To ensure a balanced use of advertising media, radio advertisements must not exceed 45% of the total number of advertisements authorized. In addition, television should account for at least 15% of the total number of advertisements authorized.
(a) If the promotional budget is limited to $24,100, how many commercial messages should be run on each medium to maximize total audience contact? If your answer is zero enter “0”.
Advertisement Alternatives No of commercial
messages
Television
Radio
Online
What is the allocation of the budget among the three media?
Advertisement Alternatives Budget Allocation
Television $
Radio $
Online $
What is the total audience reached?
(b) By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number.
Increase in audience coverage of approximately
The commercial message that need to be run on every medium to maximize the audience is x = 15, y = 7 and z = 12.
Linear programming: What is it?A mathematical method called linear programming is used to maximise a linear objective function under the restrictions of linear equality and inequality. Finding choice variable values that maximise or decrease the objective function while meeting the limitations is required.
Let us suppose the number of advertisement run on television = x.
Let us suppose the number of advertisement run on radio = y.
Let us suppose the number of advertisement run on online = z.
Then,
140,000x + 18,000y + 30,000z
The constraints on the ads run on are as follws:
1,500x + 200y + 550z <= 24,100 (budget constraint)
x <= 15 (television usage limit)
y <= 19 (radio usage limit)
z <= 12 (online usage limit)
y <= 0.45(x+y+z) (radio usage limit as a percentage of total usage)
x >= 0.15(x+y+z)
Using the linear programming model we have:
x = 15, y = 7 and z = 12.
Substitute the value of x, y, and z:
140,000(15) + 18,000(7) + 30,000(12) = 2,910,000
Hence, the commercial message that need to be run on every medium to maximize the audience is x = 15, y = 7 and z = 12.
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Slope models the direction and steepness of a line, while the y intercept defines the starting point. Explain what following equation of a line represents y=-2/3x+6
The equation y = (-2/3)x + 6 represents a line that is decreasing from left to right and intersects the y-axis at the point (0, 6).
What is the Slope?The slope refers to the measure of the steepness of a line or a curve. It is defined as the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line or the curve.
The equation of a line can be written as with the help of slope intercept form is given by:
y = mx + b
Where "b" is the y-intercept and "m" is the line's slope of the line.
In the equation y = (-2/3)x + 6, we can see that the slope 'm' is -2/3, which means that for every unit increase in x, the y-value decreases by 2/3 of a unit. This tells us that the line represented by this equation is decreasing (i.e., sloping downwards) from left to right.
The y-intercept 'b' is 6, which means that the line intersects the y-axis at the point (0, 6). This is the starting point of the line, where the value of y is 6 when x is 0.
Therefore, the equation y = (-2/3)x + 6 represents a line that is decreasing from left to right and intersects the y-axis at the point (0, 6).
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The sum of the sides of a regular polygon is 96ft, find the measure of it side.
Answer:
two are supplementary. the measure of one of these angles is 12 degrees less than one-third the measure of the other.what is the measure of each angle
Let's call the measures of the two angles x and y, where x is the larger angle. We know that the two angles are supplementary, which means they add up to 180 degrees:
x + y = 180
We also know that one of the angles (let's say y) is 12 degrees less than one-third the measure of the other angle (x):
y = (1/3)x - 12
Now we can substitute the second equation into the first equation to solve for x:
x + (1/3)x - 12 = 180
Multiplying both sides by 3 to get rid of the fraction, we have:
3x + x - 36 = 540
Combining like terms, we get:
4x - 36 = 540
Adding 36 to both sides, we get:
4x = 576
Dividing both sides by 4, we get:
x = 144
Now we can use the first equation to solve for y:
144 + y = 180
Subtracting 144 from both sides, we get:
y = 36
Therefore, the measures of the two angles are 144 degrees and 36 degrees.
The sum of the sides of a regular polygon is 96ft, find the measure of it side.
Let's say that the regular polygon has n sides, and each side has length s. The formula for the sum of the sides of a regular polygon is:
sum of sides = n * s
We know that the sum of the sides is 96ft, so we can write:
96 = n * s
We want to find the length of each side, so we need to isolate s on one side of the equation. We can do this by dividing both sides by n:
s = 96/n
Now we can substitute this expression for s into the formula for the perimeter of a regular polygon:
Perimeter = n * s
Perimeter = n * (96/n)
Simplifying this expression, we get:
Perimeter = 96
We know that the perimeter of a regular polygon is the sum of the lengths of all its sides, so we can divide the perimeter by the number of sides to find the length of each side:
s = Perimeter / n = 96 / n
Therefore, the length of each side of the regular polygon is 96/n feet. We cannot determine the value of n from the given information in the problem.
I NEED HELP ON THIS EQUATION PLEASE. Simplify the radical expression so that you can be written as k h^r s^t
[tex]\cfrac{\sqrt[5]{1024h^{-8}s^5}}{\sqrt[5]{h^{-5}s^9}}\implies \sqrt[5]{\cfrac{1024h^{-8}s^5}{h^{-5}s^9}}\implies \left( \cfrac{2^{10}h^{-8}s^5}{h^{-5}s^9} \right)^{\frac{1}{5}}\implies \left( \cfrac{2^{10}}{h^{-5}h^8s^{-5}s^9} \right)^{\frac{1}{5}}[/tex]
[tex]\left( \cfrac{2^{10}}{h^{8-5}s^{9-5}} \right)^{\frac{1}{5}}\implies \left( \cfrac{2^{10}}{h^3 s^4} \right)^{\frac{1}{5}}\implies \cfrac{2^{10\cdot \frac{1}{5}}}{h^{3\cdot \frac{1}{5}}s^{4\cdot \frac{1}{5}}} \\\\\\ \cfrac{2^2}{h^{\frac{3}{5}}s^{\frac{4}{5}}}\implies {\Large \begin{array}{llll} \stackrel{k ~ ~~ ~ r ~~~ t }{4h^{-\frac{3}{5}}s^{-\frac{4}{5}}} \end{array}}[/tex]
Find the value of a that makes the ordered pair a solution of the equation. Y=3x+7; (-3, a)
When a is equal to -2, the ordered pair is an equational solution.
What Exactly Is a Linear Equation's Solution?The places where the lines representing the intersection of two linear equations intersect are referred to as the solution of a linear equation. In other words, the set of all feasible values for the variables that satisfy the specified linear equation is the solution set of the system of linear equations.
Given:y=3x+7
Ordered pair (-3,a)
introducing x=-3 as a value in the equation
y=3(-3)+7
y=-9+7
y=-2
Hence,value of a is -2 that makes the ordered pair a solution of the equation.
y=3x+7 represents the equation of a straight line. So, it can satisfy infinite ordered pair.
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7,707 ÷ 24
what is also the R
Answer:321.125 and i think the R that you are trying to say stands for remainder
Step-by-step explanation:
A firm’s profit increased from 2020 to 2021 by 20%, but it decreased by 17% from
2021 to 2022. Which of the years 2020 and 2022 had the higher profit
Answer:
Step-by-step explanation:
Let the profit in 2020 be P.
The profit in 2021 would then be 1.20P (20% increase).
The profit in 2022 would be 0.83(1.20P) = 0.996P (17% decrease from 2021).
We can see that the profit in 2020 was P, while the profit in 2022 was less than P (0.996P).
Therefore, the higher profit was in 2020.
The solution is, the higher profit was in 2020.
What is percentage?A percentage is a number or ratio that can be expressed as a fraction of 100. A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used. A percentage is a dimensionless number; it has no unit of measurement.
here, we have,
Let the profit in 2020 be P.
The profit in 2021 would then be 1.20P (20% increase).
The profit in 2022 would be 0.83(1.20P) = 0.996P (17% decrease from 2021).
We can see that the profit in 2020 was P, while the profit in 2022 was less than P (0.996P).
Therefore, the higher profit was in 2020.
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Select the correct answer. Given: p || q, and r || s. Linear pair theorem that is angle 1 is supplementary to angle 2 moves down to angle 2 equals angle 6. As for parallel lines cut by a transversal, corresponding angles are congruent. This moves down to blank box with question mark. Prove: ∠1 and ∠14 are supplementary angles. Two vertical parallel lines p and q runs through two horizontal parallel lines r and s to form 16 angles numbered from 1 to 16. What is the next step in the proof? Choose the most logical approach. A. Statement: ∠6 ≅ ∠14 Reason: For parallel lines cut by a transversal, corresponding angles are congruent. B. Statement: ∠6 ≅ ∠7 Reason: Vertical Angles Theorem C. Statement: ∠6 and ∠5 are supplementary. Reason: Linear Pair Theorem D. Statement: m∠6 + m∠8 = 180° Reason: angle addition
Pleaseeeeeeeeeeeee help!
The symbolic quantified statement is given as:
For all real integers x and y, if x³ = y³, then x = y.
Using quantifiers, this can be written as:
∀x,y∈ℝ, (x³ = y³) → (x = y)
What is the explanation for the above?
The symbolic quantified statement represents the original sentence using logical symbols and quantifiers.
The universal quantifier (∀) is used to denote "for all," while the implication arrow (→) represents "if... then." The statement asserts that if the cubes of any two real integers x and y are equal, then x and y are equal as well.
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Find the linear function with the following properties.
f(−3)=−12
f(−7)=4
Answer:
To find the linear function with the given properties, we need to determine the slope and y-intercept of the function.
We can use the slope-intercept form of a linear function, which is:
y = mx + b
where m is the slope and b is the y-intercept.
First, we can find the slope using the two given points:
slope = (y2 - y1) / (x2 - x1)
slope = (4 - (-12)) / (-7 - (-3))
slope = 16 / (-4)
slope = -4
Now that we have the slope, we can use one of the given points to find the y-intercept. Let's use the point (-3, -12):
y = mx + b
-12 = (-4)(-3) + b
-12 = 12 + b
b = -24
Therefore, the linear function that satisfies the given properties is:
f(x) = -4x - 24
Directions: Answer problem #2
The trigonometry equations when evaluated are ∅ = 82π/125 and ∅ = 28π/23
How to evaluate the trigonometry equationEquation 1
Given that
cos ∅ = -8/17, π/2 < ∅ < π
Take the arc cos of both sides of the equation
So, we have the following
∅ = 82π/125
Equation 2
The trigonometry equation from the question is given as
tan ∅ = 2/5
The domain of the function is given as
π < ∅ < 3π/2
This means that the definition of the function is
tan ∅ = 2/5, π < ∅ < 3π/2
Take the arc tan of both sides of the equation
So, we have the following
∅ = tan⁻¹(2/5), π < ∅ < 3π/2
Express fraction as decimal
This gives
∅ = tan⁻¹(0.4), π < ∅ < 3π/2
Evaluate the arc tan
∅ = 28π/25
Hence, the measure of the angle is approximately 28π/23
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The graph of y= h (x) is shown. Draw the graph of y = - h (x) - 4
Answer:
See graph
Step-by-step explanation:
The transformation is as follows
The transformation of h(x) to -h(x) - 4 is a combination of two transformations
1. A reflection around the x -axis. Every point(x, y) in h(x) becomes (x', y') where x' = x and y' = -y so (x, y) → (x, -y)
2. A translation of each reflected point 4 units down; x value does not change but y values are shifted down so the new y is y'-4 = -y -4
The result of both transformations is:
every coordinate (x, y) in h(x) will be transformed to (x, -y -4)
Seeing as the graph consists of two straight lines meeting at the origin, all we need to do is take any 3 points in h(x), find the transformed coordinates and connect them with straight ilnes
h(x0 -h(X) - 4
(-2, 4) ⇒ (-2, -4-4) = (-2, -8)
(0, 0 ) ⇒ (0, -0 - 4) = (0, -4)
(4, 2) ⇒ (4, -2 -4) = (4, -6)
take these three points and plot
I have tried x-1*2 and it didn't work. Please help
Answer:
(x - 1 ) × 3or3x - 3Step-by-step explanation:
I think a number
x
tke away 1x - 1
multiply the result by 3 (to do t his you have to put the brackets at x - 1)(x - 1 ) × 3
solve(x - 1 ) × 3 =
3x - 3
Let C be a unit circle centred at the origin, evaluate the complex integral of zdz/((z-a)^2) when; a<1 and a>1
The complex integral of [tex]\frac{zdz}{(z-a)^2}[/tex] over the unit circle C is [tex]\frac{-4\pi i}{a}[/tex] if a < 1, and 0 if a > 1.
Evaluating the complex integralFrom the question, we are to evaluate the given complex integral when a <1 and a > 1
We can evaluate the complex integral of [tex]\frac{zdz}{(z-a)^2}[/tex] over the unit circle C using the residue theorem. Since the function has a pole of order 2 at z = a, we need to compute the residue of the function at that point.
If a < 1, then the point a is inside the unit circle C. To compute the residue at z = a, we can expand the function in a Laurent series centered at z = a:
[tex]\frac{zdz}{(z-a)^2}= (\frac{1}{(z-a)})^2 d(z-a)[/tex]
= (1/(z-a))^2 dz - (2/(z-a))^1 da + ...
[tex](\frac{1}{(z-a)})^2dz -(\frac{2}{(z-a)})^1 da + ...[/tex] (Laurent series expansion)
The residue of the function at z = a is given by the coefficient of the [tex](z-a)^{-1}[/tex] term in this expansion, which is:
[tex]Res[z=z0] \frac{z dz}{(z-a)^2} = \frac{-2}{(a - 0)^1} = \frac{-2}{a}[/tex]
Therefore, by the residue theorem, the value of the integral is given by:
[tex]\oint \frac{c zdz}{(z-a)^2} = 2\pi i \times \frac{-2}{a} = \frac{-4\pi i}{a}[/tex]
If a > 1, then the point a is outside the unit circle C. Since the function is holomorphic on and inside the unit circle, it has no singularities inside C and the integral is zero:
[tex]\oint \frac{c zdz}{(z-a)^2} = 0[/tex]
Hence, the complex integral is [tex]\frac{-4\pi i}{a}[/tex] when a < 1, and 0 if a > 1.
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How do l do this I don’t know
Answer:
£6.8
Step-by-step explanation:
to make 1 litre of drink juice and lemonade are in the ratio
= 1: 4
juice costs £6 per litre
lemonade costs 50p per litre
to make 1 litre lemonade will cost 4 * 50p = 200p
1£ = 250p
thus, 200p = £.8
thus, cost to make 1 litre of the fruit drink is £6.8
25. Months A large ship is sailing between three small islands. To do so, the ship must sail between two pairs of islands, avoiding sailing between a third pair. The safest route is to avoid the closest pair of islands. Which is the safest route for the ship?
26. Three cell phone towers form APQR.
The measure of ZQ is 10° less than the measure of LP. The measure of Ris 5° greater than the measure of ZO. Which two towers are closest together?
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.
6. When was Harriet Tubman born?
Answer: 1945
Step-by-step explanation:
Answer:
Harriet Tubman was born in 1820.
Step-by-step explanation:
Showing how brave and resourceful she was in running such a dangerous operation. A black woman operating in slave territory could be highly noticeable. It is a testament to her courage, brains, and fortitude that she was successful. Also, kudos to the many white persons who manned the stations along the Underground Railroad who coordinated with her.
Her impact on America—demonstrating an individual with struggle can accomplish much and correct wrongful structures in our land.