how can the idea of a sinusoidal function be used to help us model real-world things, or to help us solve real-world problems?

By setting up equations and solving for the variables, we found that Greg weighs 180 pounds and Justin weighs 165 pounds.

Let's start by assigning variables to represent Justin and Greg's weights. Let J represent Justin's weight and G represent Greg's weight.

We are given that Justin weighs 15 pounds less than Greg, which can be written as:

J = G - 15

We are also given that half of Greg's weight is 75 pounds less than Justin's weight. We can write this as an equation:

(1/2)G = J - 75

We can simplify this equation by substituting the first equation (J = G - 15) for J:

(1/2)G = (G - 15) - 75

Now we can solve for G, which represents Greg's weight:

(1/2)G = G - 90

Subtracting G from both sides gives:

(1/2)G - G = -90

Multiplying both sides by 2 gives:

G - 2G = -180

Simplifying gives:

-G = -180

Dividing both sides by -1 gives:

G = 180

So we have found that Greg weighs 180 pounds. We can use the first equation (J = G - 15) to find Justin's weight:

J = 180 - 15

J = 165

Therefore, Justin weighs 165 pounds.

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Answer:

  x < 7

Step-by-step explanation:

You want the solution set for the inequality -8x +40 > -16.

Divide both sides by -8, and we have ...

  x -5 < 2

  x < 7 . . . . . . add 5

The solution set for this inequality is {x | x < 7}.

__

Additional comment

There are many ways to describe a solution set. We have used some different ways. You will want to use a method of describing the set that is appropriate to your answer checker.

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Answer:

When flipping a coin, there are two possible outcomes: heads or tails. The probability of getting heads on any one flip is 1/2, and the probability of getting tails is also 1/2.

To find the probability that all three coins will land on the same side (either all heads or all tails), we can use the multiplication rule of probability, which states that the probability of two independent events occurring together is the product of their individual probabilities.

So, for each coin flip, there are two possible outcomes, and the probability of getting either outcome is 1/2. To find the probability that all three coins will land on the same side, we need to find the probability of getting either all heads or all tails.

The probability of getting all heads is:

(1/2) x (1/2) x (1/2) = 1/8

Similarly, the probability of getting all tails is also 1/8.

So, the probability of all three coins landing on the same side is:

1/8 + 1/8 = 2/8 = 1/4

Therefore, the probability that Matrix will flip 3 coins and all three coins will land on the same side is 1/8 or 0.125, which can also be written as a fraction or percentage.

After answering the prοvided questiοn, we can cοnclude that Rοunding equatiοn tο the nearest tenth οf a fοοt, we get the final answer οf apprοximately 205917.5 feet.

An equatiοn is a statement in mathematics that states the equality οf twο expressiοns. An equatiοn has twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the statement "2x + 3" equals the value "9". The gοal οf equatiοn sοlving is tο determine which variable(s) must be changed in οrder fοr the equatiοn tο be true. Simple οr cοmplicated equatiοns, regular οr nοnlinear equatiοns, and equatiοns with οne οr mοre factοrs are all feasible. In the equatiοn "x² + 2x - 3 = 0," fοr example, the variable x is raised tο the secοnd pοwer. Lines are used in a variety οf mathematical disciplines, including algebra, calculus, and geοmetry.

Let's first draw a diagram to visualize the problem:

              Lighthouse

                   |

                   |

                   |  13 degrees

            A    |-------------* 787 feet

                   |            /

                   |          /

                   |        /

                   |      /

                   |    /

                   |  /

                   |/

                 * B

                   2 degrees

From triangle ABL:

tan(13 degrees) = h/787 feet

where h is the height of the lighthouse above sea level.

[tex]$\begin{array}{l}{\rm{t a n(2^{\circ})=h/(787-x)f e e t}}\\ {{\rm h=787\ f e e t \times t a n(13^{\circ})162.0\ f e e t}}\\ {{\rm x=787 f e e t-h/t a n(2^{\circ})205\ fe e t}}\end{array}$[/tex]

Therefore, the distance between AA and BB is approximately:

[tex]$\begin{array}{l}\rm {\sqrt{(787\ f e e t)^{2}+x^{2})}\\\rm=205917.5\ f e e t\\\rm=39118.2\ m e t e r s \end{array}$[/tex]

Rounding to the nearest tenth of a foot, we get the final answer of approximately 205917.5 feet.

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Therefore, it would take about 3322 years for the Gregorian and tropical years to be out of step by exactly one day.

Length is a physical quantity that describes how long or how far apart two points or objects are from each other in space. It is typically measured in units such as meters, feet, or inches, and is one of the basic dimensions used to describe the size and position of objects in the physical world.

given by the question.

The difference between the length of the Gregorian year and the tropical year is:

365.242500 - 365.242199 = 0.000301

This means that every year, the Gregorian calendar gains 0.000301 days on the tropical year. To be out of step by exactly one day, the Gregorian calendar needs to gain one full day on the tropical year, which would take:

1 / 0.000301 = 3322.26 years.

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The width of the rectangular garden is 9.5 feet.

Given that the perimeter of a rectangular garden is 43.8 feet and its length is 12.4 feet.

Let's assume the width of the rectangular garden be "w".

Now we need to find the width of the garden.

Solution: Perimeter of a rectangular garden is given by the formula: P = 2(l + w)

where l = length and w = width.

Substituting the given values in the above formula,

we get43.8 = 2(12.4 + w)

We can solve for "w" by simplifying the above equation.

43.8 = 24.8 + 2w43.8 - 24.8 = 2w19 = 2w

Dividing both sides by 2,we get

w = 9.5 feet.

Therefore, the width of the rectangular garden is 9.5 feet.

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Answer: multiplied by 5 or squared

Step-by-step explanation:

If the number 5 goes in and 25 is the result, the rule could be multiplying by 5 or squaring the number that goes in (input).

5 x 5 = 25

5^2 = 25.

Answer:

First, we evaluate the expression inside the parentheses: 2⋅3 = 6.

Next, we evaluate the exponent: 6² = 36.

Finally, we subtract 5² = 25 from 36: 36 - 25 = 11.

Therefore, the value of the expression (2⋅3)² − 5² is 11.

Answer:

759=165% of last quarters members so you could divide by 1.65(move the decimal place twice to the left) so you get 460 people were there last quarter

Step-by-step explanation:

Max's swim time during the triathlon would be 42 minutes.

Rather than being stated as a fraction, a percentage is a piece of a whole expressed as a number between 0 and 100. Nothing is zero percent; everything is 100 percent; half of something is 50 percent; and nothing is zero percent. You split the part of the whole by the whole and multiply the result by 100 to get the percentage.

To calculate this, we first need to find out how much Max's original swim time will decrease by 30%. We can do this by multiplying his original swim time by 0.3:

60 minutes x 0.3 = 18 minutes

This means that Max will decrease his original swim time by 18 minutes during the triathlon.

To find out Max's new swim time during the triathlon, we need to subtract the amount of time he will decrease from his original swim time:

60 minutes - 18 minutes = 42 minutes

Therefore, Max's swim time during the triathlon would be 42 minutes.

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Answer:

30 feet

Step-by-step explanation:

Coordinates of Ann: (-4,3)

Coordinates of bottle caps: (4,-10)

Distance from Ann to bottle caps can be found out using the distance formula:
[tex]x_2=4, x_1=-4\\y_2=-3,y_1=-10\\Distance=\sqrt{(x_{2}-x_{1})^2 + (y_{2}-y_{1})^2 } \\=\sqrt{(4-(-4))^2 + ((-10)-3)^2} \\=15.26\\15\text{ is the answer}[/tex]

Answer: 0.51

Step-by-step explanation:

To find the value of P(F|B), we need to use the formula:

P(F|B) = P(F and B) / P(B)

where P(F and B) is the probability that a student prefers brand B and their strongest stroke is freestyle, and P(B) is the probability that a student prefers brand B.

From the given table, we can see that:

P(F and B) = 26/95

P(B) = 51/95

Therefore, we can calculate

:P(F|B) = (26/95) / (51/95) = 26/51 ≈ 0.51

So, the correct value of P(F|B) is approximately 0.51, which can be interpreted as the probability that a student's strongest stroke is freestyle given that they prefer brand B.

The four points with y-coordinates half their x-coordinates are (0,0), (2,1), (4,2), and (6,3). These points do lie on a line, as they all satisfy the linear equation y = x/2.

To plot four points whose y-coordinates are half their x-coordinates, we can choose any four values of x and then compute the corresponding values of y using the equation y = x/2. For example

If x = 0, then y = 0/2 = 0, so the first point is (0,0).

If x = 2, then y = 2/2 = 1, so the second point is (2,1).

If x = 4, then y = 4/2 = 2, so the third point is (4,2).

If x = 6, then y = 6/2 = 3, so the fourth point is (6,3).

We can plot these points on a coordinate plane

As we can see from the plot, the four points do lie on a straight line. This is because the equation y = x/2 is the equation of a linear function with slope 1/2 and y-intercept 0. Therefore, any two points on this line will have a constant slope between them, and thus the four points will be collinear.

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the equation y = 4x - 3 is also not a solution for the ordered pairs y > -1/2x + 5 and y ≤ 3x - 2.

What is inequality?

Mathematical expressions with inequalities on both sides are known as inequalities. In an inequality, we compare two values as opposed to equations. In between, the equal sign is changed to a less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

To determine which equation is not a solution for the ordered pairs y > -1/2x + 5 and y ≤ 3x - 2, we can substitute different ordered pairs into the equations and see if they satisfy the inequalities.

For example, the ordered pair (0, 0) satisfies the inequality y > -1/2x + 5, since 0 > (-1/2)(0) + 5 = 5, and it satisfies the inequality y ≤ 3x - 2, since 0 ≤ 3(0) - 2 = -2.

Now, let's try the equations:

y = -x + 4

y = 4x - 3

Substituting (0, 0) into y = -x + 4, we get y = -0 + 4 = 4, which does not satisfy the inequality y > -1/2x + 5, since 4 is not greater than (-1/2)(0) + 5 = 5. Therefore, the equation y = -x + 4 is not a solution for the ordered pairs y > -1/2x + 5 and y ≤ 3x - 2.

On the other hand, substituting (0, 0) into y = 4x - 3, we get y = -3, which also does not satisfy the inequalities, since -3 is not greater than 5 or less than or equal to -2.

Therefore, the equation y = 4x - 3 is also not a solution for the ordered pairs y > -1/2x + 5 and y ≤ 3x - 2.

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Answer: 5.7 inches

Step-by-step explanation:

To find the width of the home in the scale drawing, we can use algebra to solve for w.

First, we can simplify the equation w/0.6 = 9.5 by multiplying both sides by 0.6:

w/0.6 * 0.6 = 9.5 * 0.6

w = 5.7 inches

Therefore, the width of the home in the scale drawing is 5.7 inches.

All of these are the combinations that might be made if a person chose a sandwich and a biscuit at random.

The possibilities of the result of any random event is known as probability. This phrase refers to determining the likelihood that any given occurrence will occur.

Turkey & cheese sandwiches and two varieties of cookies are available (coconut and oatmeal). As a result, there seem to be 2 x 2 = 4 different sandwich and biscuit combinations from which to pick.

The following four pairings are possible:

sandwich with turkey and a coconut biscuit

Oatmeal cookies and a turkey sandwich

Coconut cookies and a cheese sandwich

Oatmeal cookies with a cheese sandwich

So all of these are the combinations that might be made if a person chose a sandwich and a biscuit at random.

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If a car traveling at 40 mph requires 80 feet to stop, the stopping distance S of a car varies directly as the square of its speed v and is equal to 180 feet.


Given, the stopping distance S of a car varies directly as the square of its speed v. So the relation can be represented as,

S ∝ v2

Here, the constant of proportionality is k.

S = kv2 ——— (1)

Given, when the speed v = 40 mph, stopping distance s = 80 feet.

Therefore, from equation (1), we have

80 = k × 402

k = 80/1600

k = 0.05

Hence, the relation between the stopping distance S and the speed v of the car can be given as

S = 0.05v2

To find the stopping distance S of the car at speed v = 60 mph, substitute v = 60 in the above equation.

S = 0.05 × 602

S = 0.05 × 3600

S = 180 feet

Therefore, the stopping distance of a car traveling at 60 mph would be 180 feet.


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In this instance, the buoy forms the right corner of a triangle made up of the two ships and the buoy. To the closest tenth, the distance between the two ships is roughly  [tex]24.1[/tex] km.

To find the distance between the two ships, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the legs

(the sides that form the right angle) is equal to the square of the length of the hypotenuse (the side opposite the right angle).

In this case, the two ships and the buoy form a right triangle, with the buoy at the right angle.

Let d be the distance between the two ships, x be the distance of the northern ship to the buoy and y be the distance of the eastern ship to the buoy. Then we have:

[tex]d^2 = x^2 + y^2[/tex]

Substituting the given values, we get:

[tex]d^2 = (20 km)^2 + (13.5 km)^2[/tex]

[tex]d^2 = 400 km^2 + 182.25 km^2[/tex]

[tex]d^2 = 582.25 km^2[/tex]

[tex]d ≈ 24.1 km[/tex]

Therefore, the distance between the two ships is approximately 24.1 km, rounded to the nearest tenth.

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This connection makes smells particularly powerful in triggering memories and emotions.

The sense of smell is the most likely to call up mental images of specific sights, sounds, tastes, or smells. This is because the olfactory system, which is responsible for the sense of smell, is closely linked to the brain's limbic system, which is involved in emotions and memory. This connection makes smells particularly powerful in triggering memories and emotions.

The olfactory system, which is responsible for the sense of smell, is unique in its connection to the brain's limbic system, which is involved in processing emotions and memory. When we smell something, the odor molecules enter our nose and are processed by specialized sensory neurons in the olfactory epithelium. These neurons then send signals to the olfactory bulb, which is located in the brain and is the first site of olfactory processing.

From there, the olfactory information is sent to several brain regions, including the amygdala and hippocampus, which are both part of the limbic system. The amygdala is involved in processing emotions and is responsible for generating feelings of pleasure, disgust, or fear in response to smells. The hippocampus, on the other hand, is involved in forming new memories and is responsible for encoding information about the context in which a smell is experienced.

The strong connection between the olfactory system and the limbic system makes smells particularly powerful in triggering memories and emotions. For example, the scent of freshly baked bread may evoke memories of childhood mornings spent in the kitchen with a loved one, while the smell of a certain perfume may remind you of someone special. Additionally, certain smells may elicit strong emotional responses, such as the smell of smoke triggering feelings of panic and fear in someone who has experienced a fire.

Overall, the sense of smell is closely linked to our emotional and memory centers, making it a powerful tool for triggering mental images of specific sights, sounds, tastes, or smells.

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The correct option is c: 46lb x (16 oz / 1lb). Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.

The same attribute is expressed using a unit conversion, but in a different measurement unit. For example say, time can be mentioned in minutes rather than hours, and distance can be expressed in kilometres, feet, or any other measurement unit instead of miles.

Measurements are frequently offered in one set of measurements, like feet, but are required in another set, like chains. A conversion factor is a mathematical equation that facilitates an equal exchange of feet for chains.

Given data:

ratio of ounces to pounds = 16:1

16 ounce / 1 pound

Let the weight of dog in ounce be 'x'.

weight of dog in pounds = 46 pounds.

ratio : x ounce /  46 pounds

Equating both ratios:

16 ounce / 1 pound = x ounce /  46 pounds

Cross multiplying:

x = 16*46  ounce

x = 736 ounce

The correct option is c: 46lb x (16 oz / 1lb)

Thus, amount of medicine given for the weight of dog in ounce is 736 ounce.

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Complete question is-

The ratio of ounces to pounds is 16:1. A veterinarian is treating a dog that weighs 46 pounds. To calculate the correct amount of medicine, the vet must convert the dog's weight

ounces. Which ratio shows the conversion to ounces?

The full question is attached.

The trade balance must be negative.

If Canada imports more goods and services than it exports, the trade balance must be negative.

Here's a step-by-step explanation of why this is true and why options A and E are wrong:

1. The trade balance is calculated as the value of exports minus the value of imports. If imports are greater than exports, the trade balance will be negative (C). This m that Canada is seen spending more on goods and services from other countries than it is receiving from the sale of its own goods and services to other countries.

2. The current account balance includes the trade balance, but also considers other transactions such as income from investments and transfers like foreign aid. While it is possible that a negative trade balance could be offset by other positive inflows, we do not have enough information to determine whether the current account balance must be negative (A) or positive (B). Therefore, we cannot definitively say that A or B is true.

3. The financial account (formerly called capital account) balance records the net change in ownership of financial assets, such as stocks and bonds, between a country and the rest of the world. A negative financial account balance means that a country's residents are purchasing more foreign assets than foreign residents are purchasing of that country's assets. A positive financial account balance means the opposite. Since we only have information about the trade balance and not the financial transactions, we cannot determine whether the financial account balance must be negative (D) or positive (E).

Based on the information given, we can only conclude that the trade balance must be negative (C) if Canada imports more goods and services than it exports.

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Answer:

a. To find the volume when the width is 5 inches, we plug in w=5 into the equation:

V = 2w³ - 7w² + 3w

V = 2(5)³ - 7(5)² + 3(5)

V = 250 - 175 + 15

V = 90

Therefore, the volume is 90 cubic inches.

b. To factor the polynomial, we can first factor out a w:

V = w(2w² - 7w + 3)

Then we can factor the quadratic expression in parentheses:

V = w(2w - 1)(w - 3)

Each factor represents a dimension of the rectangular prism:

w is the width

2w - 1 is the length

w - 3 is the height

c. If the width is 5 inches, we can use the factorization from part b to find the other dimensions:

length = 2w - 1 = 2(5) - 1 = 9 inches

height = w - 3 = 5 - 3 = 2 inches

This means that the rectangular prism has dimensions 5 inches by 9 inches by 2 inches. We can also use the dimensions to calculate the volume:

V = 5 × 9 × 2 = 90 cubic inches

This is the same as the answer from part a.

d. The graph of the polynomial is:

Graph of the polynomial

The x-intercepts are approximately 0.5 and 3. These correspond to the widths at which the volume is 0, which means the rectangular prism has zero volume. In other words, the x-intercepts represent the points where the rectangular prism collapses into a flat shape.

e. The domain of the function is all real numbers, since we can plug in any width w and get a corresponding volume. The range of the function is also all real numbers, since the volume can be any positive or negative value depending on the width. Specifically, the range is (-∞, ∞).

Answer: h=4

Step-by-step explanation:

According to the equation, Mia has 7 books if Tyler has 21 books and Mia has 6 books if Tyler has 18 books.

What is equation?

An equation is a mathematical statement that indicates the equality of two expressions. It typically consists of two parts: the left-hand side and the right-hand side, separated by an equal sign (=).

a. If Tyler has 15 books, we can set up the equation:

Tyler = 3 x Mia

15 = 3 x Mia

Dividing both sides by 3, we get:

Mia = 5

Therefore, Mia has 5 books if Tyler has 15 books.

If Tyler has 21 books, we can set up the same equation:

Tyler = 3 x Mia

21 = 3 x Mia

Dividing both sides by 3, we get:

Mia = 7

Therefore, Mia has 7 books if Tyler has 21 books.

If Tyler has x books, the equation would be:

Tyler = 3 x Mia

x = 3 x Mia

Dividing both sides by 3, we get:

Mia = x/3

Therefore, Mia has x/3 books if Tyler has x books.

b. If Tyler has 18 books, we can set up the equation:

Tyler = 3 x Mia

18 = 3 x Mia

Dividing both sides by 3, we get:

Mia = 6

Therefore, Mia has 6 books if Tyler has 18 books.

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Answer:

Step-by-step explanation:

big cheeze

Answer: 3/8

The given information is as follows: Out of the last 16 people, 6 people won a prize. We need to calculate the experimental probability of the next person winning the prize. To calculate experimental probability, we use the formula of experimental probability is given as: Experimental probability = Number of favorable outcomes / Total number of outcomes.

The given information tells us that out of the last 16 people, 6 people won a prize. It means that the number of favorable outcomes is 6. So, the experimental probability of winning a prize = Number of favorable outcomes / Total number of outcomes. Total number of outcomes is 16.

Therefore, Experimental probability = 6 / 16. Let's simplify this fraction. We can divide the numerator and denominator by 2.6/16 = 3/8Therefore, the experimental probability of the next person winning a prize is 3/8.

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Answer:

3,984.375 tons

Step-by-step explanation:

First, let's convert the weight of one box from ounces to tons:

0.51 oz = 0.51/16 = 0.031875 lbs

1 lb = 0.0005 tons (since 1 ton = 2000 lbs)

0.031875 lbs = 0.031875 x 0.0005 = 0.0000159375 tons

Next, let's calculate the total weight of cardboard needed for 250 million boxes:

Total weight of cardboard = weight of one box x number of boxes

Total weight of cardboard = 0.0000159375 tons x 250,000,000

Total weight of cardboard = 3,984.375 tons

As a question-answering bot, I cannot provide the solution of this question as it requires the use of MATLAB software which cannot be done in this platform. However, I can provide a general overview and steps that can be followed to solve the problem.  List all maximal orthogonal subsets of the above set. That is, group the vectors v, w, x, y, and z in as many ways as possible so that all the vectors in your group are orthogonal to each other and none of the vectors outside the group are orthogonal to all the vectors in the group. The maximal orthogonal subsets of the above set are: {v, y}, {w, x}, {z}b. Take the largest orthogonal subset and normalize all the vectors in that set as follows: >> V-v/norm(v) This code replaces v with itself divided by its size-so we get a vector pointing in the same direction but with length 1. The above code normalizes v, so you'll have to normalize the other vectors in your orthogonal subset as well, replacing v with the appropriate letter. Store the resulting vectors in MATLAB as columns of a matrix W. Enter them in alphabetical order from left to right.The largest orthogonal subset is {w, x}. The normalized vectors are w/norm(w) and x/norm(x). Store the resulting vectors in MATLAB as columns of a matrix W and enter them in alphabetical order from left to right. The resulting matrix would be: W = [1/√19 6/√19; 3/√19 1/√19; 0 -3/√19]Note: This solution is based on the assumption that the vectors are given in column form.

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the total cost of 4 nonmember tickets and 2 member tickets would be $116.

Why it is and what is financial literacy?

The expression to find the total cost of 4 nonmember tickets and 2 member tickets would be:

4($24) + 2($10)

This expression represents the cost of 4 nonmember tickets at $24 each, and 2 member tickets at $10 each.

To find the total cost, we simply need to evaluate this expression using basic arithmetic:

4($24) + 2($10) = $96 + $20 = $116

Therefore, the total cost of 4 nonmember tickets and 2 member tickets would be $116.

Financial literacy is the knowledge and skills required to manage one's personal finances effectively. It encompasses a range of topics, including budgeting, saving, investing, managing debt, understanding financial products such as credit cards and loans, and planning for retirement. Financial literacy also involves an understanding of financial concepts such as interest rates, inflation, and risk management.

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The answer of the given question are, (3)  the speed of the plane in still air is 135 km/h and the speed of the wind is 23 km/h. (4)   the price of a senior citizen ticket is $8 and the price of a child ticket is $14. (5) the number is 43. (6) the speed of the boat in still water is 12 mph and the speed of the current is 9 mph.

In mathematics, variable is symbol or letter that represents value that can change or vary in  given context or problem. Variables are often used in mathematical equations and formulas to express relationships between different quantities or to describe patterns and trends.

3). assume the speed of plane in still air "p" and speed of the wind "w". We can set up two equations based on the given information:

p + w = 158 (since the plane is flying with the wind)

p - w = 112 (since the plane is flying against the wind)

Adding the two equations together eliminates the w variable:

2p = 270

So p = 135 km/h. To find w, we can substitute this value into one of the original equations:

135 + w = 158

w = 23 km/h

Therefore,  speed of  plane in still air is 135 km/h and speed of the wind is 23 km/h.

4).  Let's call the price of a senior citizen ticket "s" and the price of a child ticket "c". We can set up two equations based on the given information:

3s + 1c = 38

3s + 2c = 52

Subtracting first equation from the second eliminates the s variable:

c = 14

Substituting the value into first equation gives:

3s + 1(14) = 38

So 3s = 24 and s = 8

Therefore, the price of a senior citizen ticket is $8 and the price of a child ticket is $14.

5).  Let's call the tens digit of the number "t" and the ones digit "u". We know that:

t + u = 7 (since the sum of the digits is 7)

10u + t - (10t + u) = 9 (since reversing the digits increases the number by 9)

Simplifying the second equation gives:

9u - 9t = 9

Dividing by 9 gives:

u - t = 1

Now we can solve for t in terms of u:

t = u - 1

Substituting the into first equation we get:

u - 1 + u = 7

So 2u = 8 and u = 4

Therefore, the number is 43.

6).  Let's call the speed of the boat in still water "b" and the speed of the current "c". We know that:

b + c = 210/10 = 21 (since distance = rate × time)

b - c = 210/70 = 3 (since distance = rate × time)

Adding the two equations eliminates the c variable:

2b = 24

So b = 12 mph. Substituting the value into one of  original equations gives:

12 + c = 21

So c = 9 mph.

Therefore, the speed of the boat in still water is 12 mph and the speed of the current is 9 mph.

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Thus, the vertices of the larger square have the following coordinates: (-6, 7),  (1, 7),(1, 0), and  (-6 ,0).

The ratio of the scale of an original thing to a new object that is a representation of it but of a variable size is known as a scale factor (bigger or smaller).

The procedures below can be used to increase form A by a scale factor of 3.5 with the centre of enlargement at (8,-7).

Transform the square so that its origin is where the centre of enlargement is (0,0).

To do this, we deduct each vertex's coordinates from the centre of enlargement (8,-7):

A = (4 - 8, -3+ 7) = (-4, 4)

B = (6 -8, -3 + 7) = (-2, 4)

C = (6 - 8, -5 + 7) = (-2, 2)

D = (4 - 8, -5 + 7) = (-4, 2)

Multiply the coordinates of the each vertex by the scaling factor (3.5) to enlarge the translated square:

A = (-14, 14)

B = (-7, 14)

C = (-7, 7)

D = (-14, 7)

By adding those coordinates of the centre of the enlargement (8,-7) to each vertex, move the square from its larger state back to its original one:

A = (-14 + 8, 14-7) = (-6, 7)

B = (-7 + 8, 14-7) = (1, 7)

C = (-7 + 8, 7-7) = (1, 0)

D = (-14 + 8, 7-7) = (-6 ,0)

As a result, the vertices of the larger square have the following coordinates: (-6, 7),  (1, 7),(1, 0), and  (-6 ,0).

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