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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Math help. HEEEEEEEEEEELP.
The expression g(f(x)) simplifies to -6x + 6, and we can see that the coefficient of x is -6 and the constant term is 6.
What is a function f(x)?A function f(x) is a mathematical relationship that assigns a unique output value (or range value) for every input value (or domain value) from a specified set. In other words, a function takes one or more input values and produces a single output value based on a specific rule or set of rules.
According to question:To find g(f(x)), we need to substitute the expression for f(x) into g(x) wherever x appears, since g(x) is being evaluated at the value of f(x). That is, we need to substitute -2x+5 for x in the expression for g(x). This gives:
g(f(x)) = g(-2x+5)
= 3(-2x+5) - 9
= -6x + 15 - 9
= -6x + 6
So, g(f(x)) = -6x + 6.
Therefore, the expression g(f(x)) simplifies to -6x + 6, and we can see that the coefficient of x is -6 and the constant term is 6. Thus, we can express the response as follows:
g(f(x)) = -6x + 6
= [-6]x + [6]
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f a barometer were built using water instead of Hg, how high would the column of water be if the pressure were 1 atm, knowing that the density of water is 13.6 times lower than that of mercury?
The height of the water column would be 1033.6 cm if the pressure were 1 atm.
SOLUTION:
If a barometer were built using water instead of mercury, and the pressure were 1 atm, the height of the water column would be:
1. First, find the height of the mercury column at 1 atm. The standard height is 760 mm (or 76 cm) for mercury.
2. Since the density of water is 13.6 times lower than that of mercury, the water column needs to be 13.6 times higher than the mercury column to exert the same pressure.
3. Multiply the height of the mercury column (76 cm) by 13.6:
76 cm x 13.6 = 1033.6 cm.
So, the height of the water column would be 1033.6 cm if the pressure were 1 atm.
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calculate breakeven w/ hidden costs, and no sponsorship number of tickets needed to break even for a run 315 323 331 ticket receipts needed to break even $7,592 $7,784 $7,977 average number of tickets needed to break even per show 79 65 56 break-even occupancy 88% 72% 62%
As per the given average, the solution of the breakeven w/ hidden costs is 62% higher.
Let's assume that the costs associated with running a 315-ticket run are $7,592. This means that on average, each ticket needs to sell for $24.10 (($7,592/315) = $24.10) to break even.
Similarly, if we consider the other two runs, we can calculate the average number of tickets needed to break even per show as follows:
For the 323-ticket run, the average number of tickets needed to break even per show is 65. (($7,784/323) = $24.10)
For the 331-ticket run, the average number of tickets needed to break even per show is 56. (($7,977/331) = $24.10)
Furthermore, we can calculate the break-even occupancy percentage for each run, which is the percentage of tickets that need to be sold to break even. The break-even occupancy for each run is as follows:
For the 331-ticket run,
=> 56/331 = 0.17 or 17%,
=> 1-0.17 = 0.83 or 83%,
=> 0.83/0.17 = 4.88,
=> 4.88 x 100% = 488%,
=> 488% x 0.62 = 303%,
=> 303%/4.88 = 62%
Hence the break-even occupancy is 62%.
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How much plastic wrap will be needed to completly cover and ice cream cone with the slant height of 4. 25 inches and a diameter of 2 inches
The amount of plastic wrap required to cover the entire cone will be 16.575 square inches.
To calculate how much plastic wrap is required to completely cover an ice cream cone with a slant height of 4.25 inches and a diameter of 2 inches, we must use the surface area of the cone.
Here, the ice cream cone can be visualized as a cone-shaped object with an added circular base.
We must use the following formula to calculate the surface area:
Surface area = πr2 + πrl
Where r is the radius and l is the slant height of the cone.
As we know the diameter of the ice cream cone is 2 inches, and its radius can be calculated by dividing it by
2.r = d/2 = 2/2 = 1 inch.
Substitute the values of r and l in the formula, and then calculate the surface area of the cone.
π = 3.14r = 1 inchl = 4.25 inches
Surface area = πr2 + πrl
= 3.14 × 1² + 3.14 × 1 × 4.25
= 3.14 + 13.435
= 16.575 square inches
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if you deposit $4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, how much money will you have in the account in 20 years ? how much will you have if you make deposits for 40 years ?
If you deposit 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest, you will have 347,401.59 in the account in 20 years. You will have 2,545,025.81 if you make deposits for 40 years.
Given that you deposited 4,500 at the end of each of the next 20 years into an account that is paying 9.7% interest. Now you have to find out how much money you will have in the account in 20 years and how much will you have if you make deposits for 40 years.
The formula to calculate the future value of an annuity due is:
[tex]FV = PMT \times [(1 + r)^{(n - 1)} / r] \times(1 + r)[/tex]
Where,
FV = Future Value
PMT = Payment (amount) each period
r = Interest Rate per period
n = Number of periods
To find the future value of an annuity due for 20 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(20 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{19} / 0.097] \times (1.097)\\FV = 4500 \times [(6.226)] \times (1.097)\\FV = 347,401.59[/tex]
To find the future value of an annuity due for 40 years:
[tex]FV = 4500 \times [(1 + 0.097)^{(40 - 1)} / 0.097] \times (1 + 0.097)\\FV = 4500 \times [(1.097)^{39} / 0.097] \times (1.097)\\FV = 4500 \times [(38.84)] \times (1.097)\\FV = 2,545,025.81[/tex]
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Let x represent the height of first graders in a class. This would be considered what type of variable:NonsensicalLaggingContinuousDiscrete
The height of first graders in a class, represented by x, would be considered a Continuous variable. Continuous variables can take on any value within a specified range and are often used to measure physical attributes, such as height.
Let x represent the height of first graders in a class. Discrete variables are those that can be measured using whole numbers, such as the number of people in a room, the number of items on a grocery list, or the number of pages in a book. Continuous variables, on the other hand, are those that can take on any value, such as height, weight, and time.Continuous variables are those that can take on any value between two points on a measurement scale. For example, the height of first graders in a class can be measured in inches or centimeters and can take on any value between the smallest and largest heights in the class.
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Let triangle ABC be similar to DEF. Find the missing side EF.
The length of the side EF is equal to 18 units since the triangle DEF and triangle ABC are similar and DEF is bigger than ABC in the margin of 3 times.
Given, two triangles ABC and DEF.
The length of AB = 8 units
The length of its concurrent side DE = 24 units
Also given that the length of BC = 6 units
Here we can see that:
As both triangles are similar, their corresponding sides are in proportion.
This means that:
[tex]\frac{BC}{EF} = \frac{AE}{DE} =\frac{AC}{DF}[/tex]
Length of AB * 3 = Length of DE
Now the length of the side EF will be 3 times more than the side BC.
Length of EF = Length of BC * 3
Length of EF = 6 * 3
Length of EF = 18 units.
Therefore, the length of the side EF is equal to 18 units.
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I need help with dis math
the concentration of a drug in a patient's bloodstream is monitored over 10-minute intervals for two hours. t (min) 0 10 20 30 40 50 60 70 80 90 100 110 120 c (mg) 0 2 17 37 55 72 89 103 111 113 113 103 68 a.) how fast is the concentration of the drug changing at 50 minutes? 1.7 mg/min b.) how fast is the concentration of the drug changing at 85 minutes? 1 mg/min c.) is the drug's concentration increasing or decreasing at 115 minutes? decreasing
a) The rate of change of the drug's concentration at 50 minutes is 1.7 mg/min.
b) The rate of change of the drug's concentration at 85 minutes is 0.2 mg/min.
c) The drug's concentration is decreasing at 115 minutes.
a) The central difference approach can be used to calculate the rate of medication change after 50 minutes.
f'(x) = (f(x+h) - f(x-h))/2 × h ....(1)
As per the question, we have h = 10 and x = 50
Substitute the values of h = 10 and x = 50 in (1),
f'(40) = (f(50+10) - f(50-10))/2 × 10
f'(40) = (89-55)/20
f'(40) = 1.7 mg/min
b) For the rate of change of concentration at 85 minutes:
Here, f(80) = 111 mg and f(90) = 113.
The concentration at 90 minutes is 113 mg.
Rate of change = (f(90) - f(80)) / h
= (113 - 111) /10
= 2 / 10
= 0.2 mg/min
c) Since the concentration at 120 minutes (68 mg) is lower than the concentration at 110 minutes (103 mg), the drug's concentration is decreasing.
Therefore, the drug's concentration is decreasing at 115 minutes.
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Mayte es una estudiante extranjera y recibe de
sus padres $977 por semana. Ella ahorra $200 y
el resto lo distribuye entre los 7 días de la semana,
¿cuánto dinero puede gastar diariamente?
The amount of money Mayte can spend on a daily basis is given by $ 111 .
Sellers and purchasers of products and services both accept money as a form of payment. When we purchase goods like food, clothing, a house, groceries, etc., we provide money in exchange. We exchange money for everything we buy. This is a straightforward swap.
In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that can be made. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each. The division sign, "," or occasionally "/," is used in computer code.
Mayte get a total money of $977 from her parents so,
total = 977
She saves $200 for herself so now the remaining sum is
977 - 200 = 777
The rest she has to distribute in 7 days so, by using the simple dividation rule we get,
777/7 = 111
Therefore, much money can you spend daily is $111.
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Complete question:
Mayte is a foreign student and receives his parents $977 per week. She saves $200 and the rest is distributed among the 7 days of the week, How much money can you spend daily?
Pease help!!
Question below!
Answer: Line PQ is parallel to line LM
Step-by-step explanation:
We can check if they are of equal distance apart by checking if the ratios of the given lines are equal...in other words we must check if LP/PN=MQ/QN
We know that triangle PNQ is inscribed inside triangle LNM
Using the information we have we see that side LP is 18 units, PN is 16 units, MQ is 27, and QN is 24. With this information we can write out LP/PN=MQ/QN and see if it's true.
LP= 18, PN= 16, 18/16= 1.125
MQ= 27, QN=24, 27/24= 1.125
therefore, LP/PN=MQ/QN is true. Making line PQ and line LM parallel.
. Calculate the slope of the line that passes through (3, 2) and (-7, 4).
Answer:
-0.2
Step-by-step explanation:
[tex]\frac{y2-y1}{x2-x1}[/tex]
^This here is how I calculated the slope^
Y2=4
Y1= 2
4-2= 2
X2=-7
x1=3
-7-3=-10
2/-10
or -2/10
El precio de unos zapatos se ha disminuido en un 20% vendiéndose actualmente en 40,39e cual era el precio primitivo ?
Answer:15%
Step-by-step explanation:
help please!! i have no clue how to do this without the answer to DC
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For the given figure, can you conclude mlln? Explain.
Convert 330 litres per hour into millimeters per minute
330 litres per hour = 5489.64 millimeter³ per minute.
Given that330 litres per hour needs to be converted into millimeters per minute.
Conversion factor: 1 litre =1000 cubic centimeter 1 cubic centimeter =1 millimeter³
∴ 1 litre=1000 millimeter³
∴ 1 litre per hour=1000 millimeter³ per hour
Also, 1 hour = 60 minutes
∴ 1 hour = 60 × 60 seconds = 3600 seconds
∴ 1 second = 1/3600 hours=0.0002778 hours
Thus, 1 litre per hour =1000/3600 millimeter³ per second =0.2778 millimeter³ per second
Therefore, 330 litres per hour = 330 × 0.2778 millimeter³ per second=91.494 millimeter³ per second
Also, 1 minute =60 seconds
∴ 1 minute = 60 × 60 seconds=3600 seconds
∴ 1 second = 1/60 minutes=0.01667 minutes
Thus, 91.494 millimeter³ per second = 91.494/0.01667 millimeter³ per minute = 5489.64 millimeter³ per minute
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Write the equation of a circle with a center of (1, -5) and a radius of √5
Simplifying this equation gives: [tex](x - 1)^2+(y+5/8)^2=5[/tex].
What is the circle?A circle is a geometrical shape that consists of all the points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter. The circumference of a circle is the distance around the edge of the circle, and it is calculated as 2 times pi (π) times the radius. Circles are found in many areas of mathematics and the physical world, and they have important applications in geometry, trigonometry, calculus, physics, and engineering, among other fields.
The equation of a circle with center (a, b) and radius r is given by:
[tex](x - a)^2 + (y - b)^2 = r^2[/tex]
In this case, the center is (1, -5/8) and the radius is √5. So, the equation of the circle is:
[tex](x - 1)^2 + (y + 5/8)^2 = (\sqrt5)^2[/tex]
Simplifying this equation gives:
[tex](x - 1)^2+(y+5/8)^2=5[/tex]
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what value makes a expressions equivalent 5 11 15 30
The value that makes the expressions equivalent is 6, as 5+6=11, 11+6=15 and 15+6=30.
What is value?Value is the worth of something in terms of the amount of other things for which it can be exchanged or in terms of some medium of exchange. It is also seen as a measure of the usefulness or desirability of something. Value is often subjective, based on personal opinion and preferences, and can change over time. Value can also be seen as an intangible quality of a product or service that makes it desirable, such as convenience, reliability, or customer service.
This is known as a linear sequence, where the difference between each number is the same. In this case, the difference is 6. To find the equivalent expression, you must add 6 to each number in the sequence.
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The value that makes the expressions equivalent is 6, as 5+6=11, 11+6=15 and 15+6=30.
What is value?Value is the worth of something in terms of the amount of other things for which it can be exchanged or in terms of some medium of exchange. It is also seen as a measure of the usefulness or desirability of something. Value is often subjective, based on personal opinion and preferences, and can change over time. Value can also be seen as an intangible quality of a product or service that makes it desirable, such as convenience, reliability, or customer service.
This is known as a linear sequence, where the difference between each number is the same. In this case, the difference is 6. To find the equivalent expression, you must add 6 to each number in the sequence.
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Complete questions as follows-
What value makes the expressions equivalent?
6(3x+5) and 15x+□+3x
A. 5
B.11
C.15
D.30
The number of minutes m you spend in line is 5 times the number of people p in line. Identify the independent and dependent variables. Then write and graph a function that describes the relationship between p and m.
Answer:The number of minutes m you spend in line is 5 times the number of people p in line. Identify the independent and dependent variables. Then write and graph a function that describes the relationship between p and m.
Step-by-step explanation:
4. Which of the following is the square of a binomial?
A. r² - 2rs +s²
B. c² + d²
C. 16x² - 25y²
D. d² - de + e²
The correct answer is (A) r² - 2rs +s² which is a square of a Binomial.
What exactly are binomials?
In algebra, a binomial is a polynomial which consists of two terms. The terms may be separated by a plus or minus sign. The general form of a binomial is:
ax + b
where "a" and "b" are constants and "x" is the variable. A binomial can be added, subtracted, multiplied, and divided using algebraic operations. Binomials are commonly used in algebra to represent and solve problems involving two quantities or variables.
Now,
The correct answer is (A) r² - 2rs +s².
This is a perfect square trinomial, which can be written as (r - s)².
Option (B) c² + d² is not a binomial, it is the sum of two squares.
Option (C) 16x² - 25y² is a difference of two squares, which can be written as (4x + 5y)(4x - 5y).
Option (D) d² - de + e² is also a perfect square trinomial, but it cannot be written as the square of a binomial.
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Complete the story problem so that it can be represented by the equation, and then solve. Aldo and Leola help their teacher, Ms. Krebs, put books on the bookshelves in her classroom. There are 2 times as many nonfiction books as fiction books. There are fiction books. They put the same number of books on each of the 7 bookshelves and put as many as they can on each shelf. Then, they put any remaining books on Ms. Krebs's desk. Aldo and Leola put books on each bookshelf. They put books on Ms. Krebs's desk
Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.
To represent the problem as an equation, we first need to define some variables. Let's let "f" represent the number of fiction books, and "n" represent the number of nonfiction books. We know from the problem that there are 2 times as many nonfiction books as fiction books, so we can write:
n = 2f
We also know that they put the same number of books on each of the 7 bookshelves and put as many as they can on each shelf. Let's call this number "s". We can then write an equation for the total number of books that can fit on the bookshelves:
7s = f + n
Since n = 2f, we can substitute 2f for n in the equation:
7s = f + 2f
Simplifying, we get:
7s = 3f
Finally, we know that any remaining books are put on Ms. Krebs's desk. Let's call this number "r". We can write an equation for the total number of books:
f + n = 7s + r
Substituting 2f for n, we get:
f + 2f = 7s + r
Simplifying, we get:
3f = 7s + r
Now we can solve for "f":
3f = 7s + r
f = (7s + r) / 3
We don't have enough information to solve for "s" or "r", but we can use this equation to find the number of fiction books. For example, if we know that there are a total of 70 books, we can write:
f + n = 70
f + 2f = 70
3f = 70
f = 23.33
Since we can't have a fractional number of books, we would round down to the nearest whole number and get:
f = 23
We could then use the equation f = (7s + r) / 3 to find the number of books on each shelf, assuming there are no books left over:
23 = (7s + 0) / 3
69 = 7s
s = 9.86
Since we can't have a fractional number of books on a shelf, we would round down to the nearest whole number and get:
s = 9
So Aldo and Leola would put 9 fiction books and 18 nonfiction books on each of the 7 bookshelves, for a total of 189 books on the shelves. They would then put the remaining 7 books on Ms. Krebs's desk.
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Helppppppppppppppppppppppppppp
Answer:
No.
Step-by-step explanation:
Line XY will be tangent to Circle W when XY is perpendicular to the radius XW. We can test if it is perpendicular by using Pythagoras theorem as it only works on right angled triangle. If the angle WXY is 90 degrees (XY ⊥ WX) then the theorem should work.
[tex](XY)^2=(WX)^2+(XY)^2\\R.H.S = 66^2+54^2 = 7272\\L.H.S = 87^2 = 7569\\R.H.S \neq L.H.S[/tex]
Thus the angle is not 90 degrees since the Pythagoras theorem doesn't work thus the line is not tangent since it is not at 90 degrees with the radius WX.
Answer:
not a tangent
Step-by-step explanation:
if XY is a tangent to the circle then ∠ WXY = 90°
using converse of Pythagoras' identity.
if the square of the longest side is equal to the sum of the squares on the other 2 sides , then the triangle is right.
longest side is WY
WY² = 87² = 7569
WX² + XY² = 66² + 54² = 4356 + 2916 = 7272
since WY² ≠ WX² + XY² , then Δ WXY is not right
then XY is not a tangent to the circle
ccording to this statement, government is held accountable by the - a king b church c laws d citizens next pageback
According to the given statement, the government is held accountable by the citizens. Citizens are the ones who elect the government and, thus, have the power to hold it accountable. This is a fundamental principle of democracy that ensures that those in power are serving the people's interests.In a democratic society, the government is accountable to the people.
This means that citizens have the right to hold elected officials accountable for their actions. This is achieved through various means such as free and fair elections, the rule of law, and the right to free speech and expression.Government officials are elected to serve the people and carry out their wishes. This means that they must be transparent and open to criticism. They must be willing to listen to citizens' concerns and take action to address them. This is why democratic societies have mechanisms in place to ensure that citizens can hold their government accountable, such as a free press and independent judiciary.In conclusion, citizens are the ones who hold the government accountable in a democratic society. They have the power to elect officials and the right to criticize them if they are not serving their interests. This ensures that those in power are always acting in the best interests of the people.
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What is the mean of this data set?
A line plot titled Height of Lilies. The bottom of the line plot is labeled height in inches. There is a number line showing whole numbers from 18 to 24. The line plot has one mark above the 18. There is one mark above 19. There are two marks above 20. There are two marks above 21. There are three marks above 22. There are zero marks above 23. There is one mark above 24.
20
20.9
21
22.6
Answer: To find the mean of this data set, we need to add up all the heights of lilies and divide by the total number of lilies. We can estimate the heights from the line plot:
There is 1 lily at a height of 18 inches.
There is 1 lily at a height of 19 inches.
There are 2 lilies at a height of 20 inches.
There are 2 lilies at a height of 21 inches.
There are 3 lilies at a height of 22 inches.
There are 0 lilies at a height of 23 inches.
There is 1 lily at a height of 24 inches.
To calculate the mean, we need to multiply each height by the number of lilies at that height, then add up these products, and divide by the total number of lilies:
(1 x 18) + (1 x 19) + (2 x 20) + (2 x 21) + (3 x 22) + (0 x 23) + (1 x 24)
markdown
Copy code
10
= (18 + 19 + 40 + 42 + 66 + 0 + 24) / 10
= 209 / 10
= 20.9
Therefore, the mean height of lilies in this data set is 20.9 inches. The answer is (B) 20.9.
Step-by-step explanation:
A rectangle has an area of 717. 8m2. One of the sides is 7. 4m in length. Work out the perimeter of the rectangle
The perimeter of the rectangle is approximately 208.9 meters.
To find the perimeter of the rectangle, we need to know the length of the other side.
Let's use the formula for the area of a rectangle:
area = length x width
We know that the area is 717.8 m^2 and one of the sides (width) is 7.4 m. So we can rearrange the formula to solve for the length:
length = area / width
length = 717.8 / 7.4
length ≈ 97.05 m
Now we have both the length and width of the rectangle, so we can find the perimeter:
perimeter = 2 x (length + width)
perimeter = 2 x (97.05 + 7.4)
perimeter = 2 x 104.45
perimeter = 208.9 m
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Find the measure of x.
29°
X
3.7
x = [?]
X
Round to the nearest hundredth.
Answer:
x ≈ 3.24
Step-by-step explanation:
using the cosine ratio in the right triangle
cos29° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{3.7}[/tex] ( multiply both sides by 3.7 )
3.7 × cos29° = x , then
x ≈ 3.24 ( to the nearest hundredth )
I need help with this math assignment, specifically #3
The solution to the system of equations are (-4, 5), (2, 7), (3, -1), no solution, (-5, 8) and (7, -3)
How to solve system of equation by substitution method?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Question 1 and 2
See attachment for the graphs, where we have the solutions to be
System 1: (-4, 5)
System 2: (2, 7)
Question 3 and 4
Here, we solve the system of equation by substitution method.
So, we have
2x - 7y = 13
3x + y = 8
Make y the subject in (2)
y = -3x + 8
Let's substitute the value of y in equation (i)
2x - 7(-3x + 8) = 13
2x + 21x - 56 = 13
23x = 13 + 56
23x = 69
Divide both sides by 23
x = 69 / 23
x = 3
Let's find y
y = -3(3) + 8
y = -9 + 8
y = -1
For system (4), we have
x - 3y = 2
2x - 6y = 6
So, we have
x = 2 + 3y
By substitution, we have
2(2 + 3y) - 6y = 6
4 + 6y - 6y = 6
4 = 6
The system has no solution
Question 5 and 6
Here, we have
x + y = 3
x - 3y = -29
By eliminating x, we have
4y = 32
So, we have
y = 8
This means that
x + 8 = 3
x = -5
So, the solution is (-5, 8)
For system 6, we have
3y = 26 - 5x
6x + 7y = 21
So, we have
5x + 3y = 26
6x + 7y = 21
This gives
30x + 18y = 156
30x + 35y = 105
By elimination, we have
17y = -51
y = -3
This means that
6x + 7(-3) = 21
6x = 42
So, we have
x = 7
So, the solution is (7, -3)
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Corey spies a bald eagle in a tall tree. He was able to measure the angle of elevation to the bird from where he stands at 62°. The leaves on the tree make it difficult for Corey to watch the bird, so he moves 10 feet further away from the tree to get a better view. Now his angle of elevation is 56°.
What is the height of the tree? Round your answer to the nearest foot.
pls help
The height of the tree is approximately 76 feet.
What is the angle of elevation?
The angle of elevation is the angle created between the line of sight and the horizontal. The angle created is an angle of elevation if the line of sight is upward from the horizontal line.
We can use tangent to set up the following two equations based on the given angles of elevation:
tan(62°) = h/x
tan(56°) = h/(x+10)
We can rearrange the first equation to solve for "h":
h = x * tan(62°)
tan(56°) = (x * tan(62°)) / (x+10)
We can solve for "x" by multiplying both sides by (x+10) and rearranging:
x = 10 * (tan(62°) - tan(56°)))
Now we can substitute this value for "x" into either of the two equations we set up earlier to find the height of the tree "h". Using the first equation, we get:
h = x * tan(62°) ≈ 76 feet
Therefore, the height of the tree is approximately 76 feet.
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13. The area of the kite is 30 m². What is the value
of x? Explain.
4m
xm
6 m
xm
14.
Answer:
answer is 3
Step-by-step explanation:
MODELING REAL LIFE You deposit $5000 in an account earning 7. 5% simple interest per year. How long will it take for the balance of the account to be $6500?
We use the formula I = Prt where I is the interest earned, P is the principal, r is the interest rate per year, and t is the time in years. Substituting the values, we find that it will take 4 years for a $5000 balance to reach $6500 with a 7.5% simple interest rate.
To solve this problem, we can use the formula for simple interest:
I = Prt
Where I is the interest earned, P is the principal (initial amount), r is the interest rate per year (as a decimal), and t is the time in years.
In this case, we know that the principal is $5000, the interest rate is 7.5% or 0.075, and we want to find the time required for the balance to reach $6500.
Substituting these values into the formula, we get:
I = $6500 - $5000 = $1500
P = $5000
r = 0.075
t = ?
Solving for t, we get:
$1500 = $5000 * 0.075 * t
t = $1500 / ($5000 * 0.075)
t = 4
Therefore, it will take 4 years for the balance of the account to be $6500 with a 7.5% simple interest rate.
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