what are the imports and Exports for Segbana,Benin
We can see here that from the available information it is clear that imports of Benin were:
refined petrolrice, etcWhile the exports are:
cottonsheanutscashewsWhat is an export?A locally produced commodity or service that is sold to another nation is referred to as an export. To put it another way, it's a good or service that is sold or sent to another nation to be utilized or consumed there.
Exports may help a nation's economy expand by bringing in money and creating jobs.
Imports are actually known to be goods and services that are brought into a country/nation.
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The value 3pi/4 is a solution for the equation 3√2 sec theta +7 = 1.
A. True
B. False
Answer:
False
Step-by-step explanation:
3√2 sec(theta) + 7 = 1
3√2 sec(theta) = -6
sec(theta) = -2/√2
sec(theta) = -√2
theta = arcsec(-√2)
However, the range of secant function is [-∞, -1] U [1, ∞]. Since -√2 is not within this range, we cannot take the arcsecant of -√2. Therefore, there is no real value of theta that satisfies the equation, including 3π/4.
Therefore, the statement "The value 3π/4 is a solution for the equation 3√2 sec(theta) + 7 = 1" is False.
I hope it helps you
the simplest form of 4(3x+y)
An expression which is the simplest form of 4(3x + y) + (2x - 5y) + x² include the following: x² + 14x - 6y.
What is an expression?In Mathematics and Geometry, an expression simply refers to a type of mathematical equation which is typically used for illustrating the relationship that exist between two (2) or more variables and numerical quantities (number), without an equal to sign (symbol).
In this scenario and exercise, the simplest form of the given expression 4(3x + y) + (2x - 5y) + x² can be determined or calculated by simplifying it as follows;
4(3x + y) + (2x - 5y) + x²
12x + 4y + 2x - 5y + x²
14x + - y + x²
By rearranging, we have;
x² + 14x - 6y.
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Complete Question:
Which expression is the simplest form of 4(3x+y)+2x-5y)+x²
Im doing my math homework and i need helpp
the power tells you how many times the base is multiplied.
1) 3^4 = 3 x 3 x 3 x 3
= 81
21 is 28% of what number? Enter your answer in the box. HELPPP ME PLEASE!!! (40 POINTS)
Answer:
To find out what number 21 is 28% of, we can use the proportion:
21 / x = 28 / 100
where x is the unknown number we are trying to find.
We can solve for x by cross-multiplying and simplifying:
21 * 100 = 28 * x
2100 = 28x
x = 2100 / 28
x = 75
Therefore, 21 is 28% of 75.
Answer:
21 is 28 percent of 75
Step-by-step explanation:
Which function is undefined for x = 0?
O y=³√√x-2
y = √√√x-2
Oy=³√√x+2
O
y=√x+2
O
The function y = √x+2 is undefined for any value of x that makes the expression inside the square root negative, which in this case is x ≤ -2.
What is an inequality equation?
An inequality equation is a mathematical statement that compares two expressions using an inequality symbol such as < (less than), > (greater than), ≤ (less than or equal to), or ≥ (greater than or equal to).
The function that is undefined for x = 0 is y = √x+2.
When x = 0, we have:
y = √0+2
y = √2
Since there is no real number whose square is negative, the square root of a negative number is undefined in real numbers.
Therefore, the function y = √x+2 is undefined for any value of x that makes the expression inside the square root negative, which in this case is x ≤ -2.
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A total of 550 tickets were sold for a game for a total of $1950. If adult tickets sold for $7 each and child tickets cost $2 each, how many of each kind of ticket were sold?
In linear equation, 170 adult and 380 children's tickets were sold.
What is a linear equation in mathematics?
A linear equation in algebra is one that only contains a constant and a first-order (direct) element, such as y = mx b, where m is the pitch and b is the y-intercept.
Sometimes the following is referred to as a "direct equation of two variables," where y and x are the variables. Direct equations are those in which all of the variables are powers of one. In one example with just one variable, layoff b = 0, where a and b are real numbers and x is the variable, is used.
It usually works well to let a variable represent the higher-value item in the mix. Here, we can let 'a' represent the number of adult tickets sold. Then the total revenue is ...
7a + 2(550 -a) = $1950
7a + 1100 - 2a = 1950
5a = 1950 - 1100
5a = 850
a = 170
c = 550 - 170 = 380
170 adult and 380 children's tickets were sold.
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factorise 9x^2 + 3x^3
Answer:
[tex]9 {x}^{2} + 3 {x}^{3} [/tex]
[tex]3 {x}^{2} (3 + x)[/tex]
[tex]3 {x}^{2} (x + 3)[/tex]
Find the surface area of the following figure, if the diameter of the inner cylinder is 7 cm. The inner cylinder has been hollowed out of the outer cylinder. Round your final answer to the nearest tenth.
The surface area is 653.1 square centimeters.
What is surface area?
A three-dimensional object's surface area is the space it takes up when viewed from the outside.
Here the given inner cylinder diameter d = 7m then
Radius r= d/2 = 7/2 = 3.5m
Now outer cylinder diameter = 9 cm then
Radius R= d/2 = 9/2 = 4.5 cm.
Height h = 26 cm.
Now using surface area of cylinder formula then,
=> Surface area A = [tex]\pi (R^2-r^2)h[/tex] square unit.
=> A = [tex]3.14(4.5^2-1.5^2)26[/tex]
=> A = [tex]3.14\times(20.25-12.25)\times26[/tex]
=> A = 3.14×8×26
=> A = 653.1 square centimeters.
Hence the surface area is 653.1 square centimeters.
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The graph of a function f is shown below. findf(-1)
please be detailed
The function f of the line is f(x) = 2x - 2 and f(-1) = -4.
What is a slope of a line?The slope of a line determines the steepness of the line and is calculated by dividing the vertical change (rise) between any two points on the line by the horizontal change (run) between those same two points. The formula for slope is (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) represent any two points on the line. The slope can be positive, negative, zero or undefined, depending on the direction and steepness of the line. If the line moves up from left to right, it has a positive slope, while a line that moves down from left to right has a negative slope.
From the graph we can take two points on the line (1,0) and (0,-2). Now we can find the equation of the line passing through these points, for that we can use the point-slope form of the equation of a line:
y - y₁ = m(x - x₁)
where m is the slope of the line and (x₁, y₁) is one of the points on the line.
First, we can find the slope:
m = (y₂ - y₁) / (x₂ - x₁) = (-2 - 0) / (0 - 1) = -2/-1 = 2
Next, we can choose either point and substitute the values into the point-slope equation:
y - y₁ = m(x - x₁)
Using point (1,0):
y - 0 = 2(x - 1)
Simplifying:
y = 2x - 2
Therefore, the equation of the line passing through points (1,0) and (0,-2) is y = 2x - 2. That is f(x) = 2x - 2.
f(-1) = 2 × -1 - 2 = -2 -2 = -4.
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if you roll a number cube 20 times. which scenario is least likely?
a) you find the experimental probability of rolling a 1 or 2 to be 0.3.
b) you find the experimental probability of rolling a 3 or 4 to be 0.4.
c) you find the experimental probability of rolling a 5 or 6 to be 0.5.
d) you find the experimental probability of rolling a number divisible by 3 to be 0.35
The temperatures, in degrees F, at 7:00 a.m. for five days during one week are shown.
-3, 4, -1, 6, 7
The mean temperature for all 7 days of the week was 0°F.
What was the mean of the temperatures for the two missing days?
a. -13
b. -10.5
c. -6.5
d. 0
The value of the mean of the temperatures for the two missing days are,
= - 6.5
We have to given that;
The temperatures, in degrees F, at 7:00 a.m. for five days during one week are shown.
-3, 4, -1, 6, 7
And, The mean temperature for all 7 days of the week was 0°F.
Now, We can assume that,
Last two days temp. are x and y.
Hence, We get;
(- 3 + 4 + (-1) + 6 + 7 + x + y) / 7 = 0
- 3 + 4 - 1 + 6 + 7 + x + y = 0
x + y = - 13
Divide both side by 2;
(x + y)/2 = - 13/2
(x + y)/2 = - 6.5
Thus, The value of the mean of the temperatures for the two missing days are,
= - 6.5
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Verify directly that F is an antiderivative of f.
F(x) is an antiderivative of f(x) because F'(x) = f(x)
What is an antiderivative?An anti-derivative is the integral of a function
To verify that F is an antiderivative of f where
F(x) = √(3x² - 4) and f(x) = 3x/√(3x² - 4)
This means that F(x) = ∫f(x)
This implies that F'(x) = f(x)
So, we verify as follows
F(x) = √(3x² - 4)
Taking the derivative with respect to x, we have that
dF(x)/dx = d√(3x² - 4)/dx
Let u = 3x² - 4
So, dF(x)/dx = d√u/dx
= d√u/du × du/dx
= 1/(2√u) × du/dx
Now,du/dx = d(3x² - 4)/dx
= 6x
So,
dF(x)/dx = 1/(2√u) × du/dx
= 1/(2√(3x² - 4)) × 6x
= 1/(√(3x² - 4)) × 3x
= 3x/(√(3x² - 4))
= f(x)
So, F(x) is an antiderivative of f(x) because F'(x) = f(x)
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If r = 6 units and h = 8 units, what is the volume of the cylinder shown above? Use 3.14 for
Answer:
the volume of the cylinder is 904.32 m³
Step-by-step explanation:
Describe and compare the solution sets of x 1 plus 3 x 2 minus 2 x 3
equals0
and x 1 plus 3 x 2 minus 2 x 3
equalsminus6
.
Question content area bottom
Part 1
Describe the solution set, xequals
left bracket Start 3 By 1 Matrix 1st Row 1st Column x 1 2nd Row 1st Column x 2 3rd Row 1st Column x 3 EndMatrix right bracket,
of x 1 plus 3 x 2 minus 2 x 3
equals
0
in parametric vector form. Select the correct choice below and fill in the answer boxes within your choice.
(Type an integer or fraction for each matrix element.)
To the right of 1.61, 9.24, and 15.09, the area under the X² curve with five degrees of freedom is 0.078, 0.0001, and 0, respectively.
Describe area?A surface's area can be measured in two dimensions by multiplying its length by its breadth. It is employed to determine the size of a room or a plot of land. The size of a shape, like a circle or a square, can also be determined using area. Area is frequently expressed in square metres or square feet.
Here in the question,
(a)1.61
The following formula can be used to determine the area under the 1.61-degree curve with five degrees of freedom to the right:
Area = 1 - Φ(x; df)
Where df stands for the degrees of freedom and (x; df) is the cumulative distribution function of the chi-square distribution.
For df = 5, Φ(1.61; 5) = 0.922.
As a result, 1 - 0.922 = 0.078 represents the area under the 1.61-degree curve with 5 degrees of freedom to the right.
(b) 9.24
For df = 5, Φ(9.24; 5) = 0.9999.
As a result, 1 - 0.9999 = 0.0001 is the value of the area under the X² curve with 5 degrees of freedom to the right of 9.24.
(c) 15.09
For df = 5, Φ(15.09; 5) = 1.
As a result, 1 - 1 = 0 represents the area under the 15.09-based X² curve with 5 degrees of freedom to the right.
The area under the X² curve with five degrees of freedom to the right of 1.61, 9.24, and 15.09, respectively, is 0.078, 0.0001, and 0.
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1. The solution set can be written as:
{x = [t, s, (3/2)t + (3/2)s] : t, s ∈ R}
2. The solution set can be written as:
{x = [t, s, (3/2)t + (3/2)s - 3] : t, s ∈ R}
What is equation?A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("="). For illustration, 2x - 5 = 13. 2x - 5 and 13 are expressions in this case. These two expressions are joined together by the sign "=".
To find the solution set in parametric vector form for the equation x₁ + 3x₂ - 2x₃ = 0, we can write:
x₁ = t (arbitrarily setting x1 = t)
x₂ = s
x₃ = (3/2)t + (3/2)s
where t and s are arbitrary parameters.
Therefore, the solution set can be written as:
{x = [t, s, (3/2)t + (3/2)s] : t, s ∈ R}
This is a set of infinitely many vectors that lie on a plane in three-dimensional space.
Part 2
For the equation x₁ + 3x₂ - 2x₃ = -6, we can rewrite it as x₁ + 3x₂ - 2x₃ = 0 - 6, which is of the same form as the equation in Part 1, but with a constant on the right-hand side.
Using the same method as in Part 1, we can find the solution set as:
x₁ = t
x₂ = s
x₃ = (3/2)t + (3/2)s - 3
where t and s are arbitrary parameters.
Therefore, the solution set can be written as:
{x = [t, s, (3/2)t + (3/2)s - 3] : t, s ∈ R}
This is also a set of infinitely many vectors that lie on a different plane in three-dimensional space.
Comparing the two solution sets, we can see that they are both sets of infinitely many vectors and have a similar form (parametric vector form). However, they lie on different planes in three-dimensional space, and the second set is shifted downward by 3 units along the third axis.
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4. From a survey of the population of the United States, a circle graph
was created.
Population of the United States, 1990
White
80%
American Indian,
Eskimo, and Aleut
1%
Black
12%
Asian and
Pacific Islander
3%
Other Races
4%
The ratio of whites to blacks is 20 to 3 ( or 20/3) in United States in 1990.
From a survey of the population of the United States, a circle graph (or, pie chart) was created on the information,
Population of the United States in 1990 :
White consists of 80%
American Indian, Eskimo, and Aleut consists of 1%
Black consists of 12%
Asian and Pacific Islander consists of 3%
Other Races consists of 4%
Let say the total population of the United States in 1990 was x.
By applying the formula of percentage to numbers we get,
The number of people who were white in 1990 in United States = 80% of x
= [tex][\frac{80}{100} ]x[/tex] = [tex]\frac{4}{5} x[/tex]
The number of people who were black in 1990 in United States = 12% of x
= [tex][\frac{12}{100} ]x[/tex] = [tex]\frac{3}{25} x[/tex]
Thus, we can calculate ratio as,
Ratio of whites to blacks = [tex]\frac{\frac{4}{5} x}{\frac{3}{25} x}[/tex] = 20/3
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HELP RNRNNRNRNRNRNNRNRNRR
Answer:
Step-by-step explanation:
Area= pi times radius²
The radius in the last one is 7, so 7² is 49.
Multiply 3.14 by 49 and you get 153.86. Round it to the nearest tenth and you get 153.9 as the area
Hope this helps!
Janelle is planning to rent a car while on vacation. The equation C=0.32m+15 models the relation between the cost in dollars, C, per day and the number of miles, m, she drives in one day. Interpret the C-intercept of the equation.
The C-intercept of the equation means that she will have to pay $15 per day for renting the car.
Interpreting the C-intercept of the equation.From the question, we have the following parameters that can be used in our computation:
C=0.32m+15
In the equation C=0.32m+15, the C-intercept represents the fixed cost of renting a car per day, which is $15 in this case.
This means that regardless of how many miles Janelle drives, she will have to pay $15 per day for renting the car.
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In a company, 80% of the workers are women. If people work for the company who aren't women , how many workers are there in all?
There are a total of 2000 workers in all in the company
How many workers are there in all?From the question, we have the following parameters that can be used in our computation:
Women percentage = 80%
People not women = 400
Using the above as a guide, we have the following:
People not women percentage = 1 - 80%
Evaluate
People not women percentage = 20%
So, we have
People not women = People not women percentage * Total
substitute the known values in the above equation, so, we have the following representation
20% * Total = 400
Divide
Total = 2000
Hence. there are 2000 people in the company
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a twenty sided fair die is rolled, with the numbers 1 through 20 on its faces. what is the probability that you will roll a number that is NOT between 4 and 12?
The probability of rolling a number that is NOT between 4 and 12 is approximately 0.55 or 55%.
What is probability?Probability is the concept that describes the likelihood of an event occurring. In real life, we frequently have to make predictions about how things will turn out. We may be aware of the result of an occurrence or not. When this occurs, we state that there is a possibility that the event will occur.
The range between 4 and 12 inclusive contains 9 numbers (4, 5, 6, 7, 8, 9, 10, 11, and 12) out of 20.
To find the probability of rolling a number that is NOT between 4 and 12, we need to find the probability of rolling one of the 11 numbers that are outside of this range.
The probability of rolling any one of these 11 numbers is 11/20, since there are 11 favorable outcomes out of 20 possible outcomes.
Therefore, the probability of rolling a number that is NOT between 4 and 12 is:
P = 11/20 ≈ 0.55
So, the probability of rolling a number that is NOT between 4 and 12 is approximately 0.55 or 55%.
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A deli wraps its cylindrical containers of hot food items with plastic wrap. The containers have a diameter of 5.5 inches and a height of 3 inches. What is the minimum amount of plastic wrap needed to completely wrap 8 containers? Round your answer to the nearest tenth and approximate using π = 3.14.
Answer:
B
Step-by-step explanation:
Riley is saving up to buy a new television. She needs a total of $1,290.78. Riley has saved $200.73 already and earns $83.85 per
week at her job. How many weeks does Riley need to work to save enough money to buy the new television?
Answer:
13
Step-by-step explanation:
First of all riley saved 200.73$ she needs 1,290.78$ so,
1290.78$-200.73$=1090.95$
she earns 83.85$ a week
then, 1090.95÷83.85= 13
13 weeks
Altina Restaurant Flexible Budget for November 2010
A. What was Watson’s actual check average? Was this higher or lower than the original budget and flexible budget check average?
b. Were Watson’s actual food sales higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?
c. Was Watson’s actual food cost higher or lower than the original budget? Why do you think this is so?
d. Was Watson’s actual food cost higher or lower than the flexible budget? By how much? Was this favorable or unfavorable? How can Watson use this information in his report to his general manager?
e. Were Watson’s variable salaries, wages, and benefits higher or lower than the original budget?
f. Were Watson’s variable salaries, wages, and benefits higher or lower than the flexible budget? By looking at both the original budget and the flexible budget, what conclusion can you draw about Watson’s ability to control his labor costs?
g. Was Watson’s actual net income higher or lower than the flexible budget? By how much? Was this favorable or unfavorable?
h. Overall, how do you think Watson is doing at meeting the budget goals set by the general manager? How should he respond to his general manager’s claim that his department is operating at a “sub-par” performance level?
Walton's actual check average is $9.52
The actual food cost is lower than the flexible budget by $5020
What is Net Income?Net income, considered a vital financial metric of an organization, delineates the earned sum after deducting expenses and taxes from total revenue.
The measure is indicative of the profitability status of an entity, portraying cash flow left over subsequent to settling all obligations. To uncover net income, business expenditures spanning across areas such as salaries, interest payments and rents alongside taxations are subtracted from entire receipts.
Ascertaining net income facilitates assessing the fiscal robustness and future prospects of a company for interested investors.
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AB and BC are perpendicular lines
Fine the value of x
Answer:
25 + x + x = 90
2x = 65
x = 32.5°
The circumference of the smaller circle is 25% of the circumference of the larger circle. Find the circumference of the larger circle. Round your answer to the nearest tenth
The circumference of the larger circle is approximately 9.4 units.
What is circumference?The circumference is the distance around the edge or boundary of a closed two-dimensional shape, such as a circle or an ellipse.
According to question:Let C be the circumference of the larger circle. Then the circumference of the smaller circle is 0.25C, according to the given information.
We know that the circumference of a circle is given by the formula C = 2πr, where r is the radius of the circle. Therefore, we can write:
C = 2πr for the larger circle
0.25C = 2πr for the smaller circle
Dividing the second equation by 0.25, we get:
C = 8πr for the smaller circle
Now we can equate the two expressions for C and solve for r:
2πr = 8πr
6πr = C
r = C/(6π)
Finally, we can substitute this value of r into the expression for C in terms of r for the larger circle:
C = 2πr = 2π(C/(6π)) = (1/3)Cπ
Solving for C, we get:
C = (3/π)C
C = 3π ≈ 9.4 (rounded to the nearest tenth)
Therefore, the circumference of the larger circle is approximately 9.4 units.
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Use an integer to represent the situation. 800 ft gain in elevation
The integer number that represents an 800 ft gain in elevation is given as follows:
+800.
What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
For altitudes, the signs are given as follows:
Gain of altitude: positive integer.Loss of altitude: negative integer.Hence the integer number that represents an 800 ft gain in elevation is given as follows:
+800.
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A group of marketing researchers for a popular cell phone manufacturer collected the following information about young adults (aged 18–25): 1% use a cell phone that is 3 years or older, 2% use a cell phone that is 2–3 years old, 20% use a cell phone that is 1–2 years old, and 77% use a cell phone that is less than 1 year old. Suppose a young adult was selected at random. Let X equal the age of a randomly selected person’s cell phone. Which of the following is the probability distribution for the age of that person’s cell phone?
according to the question 77% population use a cell phone that is less than 1 year old.
What is probability?Probability theory, a subfield of mathematics, quantifies the likelihood that an event is going to happen or that a statement is true. The probability for an event is a number between 0 and 1, where 0 roughly denotes how probable the event is to occur and 1 denotes certainty. A probability is a numerical representation of the likelihood that a certain event will occur. In addition to numbers from 0 to 1, probability values can also be stated as percentages between 0% and 100%. the fraction of an entire set of equally likely possibilities that result in a certain occurrence out of all possible outcomes, expressed as a ratio.
given,
The probability distribution for the age of a randomly selected young adult's cell phone can be represented using a probability mass function (PMF) as follows:
P(X = 3) = 0.01 (1% use a cell phone that is 3 years or older)
P(2 ≤ X ≤ 3) = 0.02 (2% use a cell phone that is 2-3 years old)
P(1 ≤ X ≤ 2) = 0.20 (20% use a cell phone that is 1-2 years old)
P(X < 1) = 0.77 (77% use a cell phone that is less than 1 year old)
Note that the values of the PMF correspond to the probabilities of the different age categories for the cell phones of young adults. The PMF satisfies the two main properties of a probability distribution: 1) the probabilities are non-negative, and 2) the sum of the probabilities is equal to 1.
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Solve the simultaneous equations
x^2+y^2=9
x+y=2
Give your answers correct to 2 decimal places
The two solutions to the simultaneous equations are; y1 = -0.87 and y2 = 2.87. x1 = 2.87, x2 = -0.87
How do you solve the simultaneous equations?To solve these simultaneous equations, we can use the method of substitution. We can rearrange the second equation to isolate one of the variables, for example, y:
y = 2 - x
Now, substitute this expression for y into the first equation:
x^2 + (2 - x)^2 = 9
Expand the equation:
x^2 + (4 - 4x + x^2) = 9
Combine like terms:
2x^2 - 4x + 4 = 9
Move all terms to one side to set the equation to equal zero:
2x^2 - 4x - 5 = 0
Now, we can solve this quadratic equation using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
In our equation, a = 2, b = -4, and c = -5:
x = (4 ± √((-4)^2 - 4(2)(-5))) / (2 x 2)
x = (4 ± √(16 + 40)) / 4
x = (4 ± √56) / 4
The two possible values for x are:
x1 ≈ (4 + 7.48) / 4 = 2.87
x2 ≈ (4 - 7.48) / 4 = -0.87
Now, we'll find the corresponding y values using the equation y = 2 - x:
For x1 ≈ 2.87:
y1 ≈ 2 - 2.87 ≈ -0.87
For x2 ≈ -0.87:
y2 ≈ 2 - (-0.87) ≈ 2.87
So, the two solutions to the simultaneous equations are approximately (2.87, -0.87) and (-0.87, 2.87), both correct to 2 decimal places.
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The lengths of two sides of a triangle are shown.
Side 1: 3x² - 4x-1
Side 2: 4x-x² +5
The perimeter of the triangle is 5x³ - 2x² + 3x - 8.
Part A: What is the total length of the two sides, 1 and 2, of the triangle? Show your work.
Part B: What is the length of the third side of the triangle? Show your work.
Part C: Do the answers for Part A and Part B show that the polynomials are closed under addition and subtraction? Justify your answer.
Answer:
Part A:
To find the total length of the two sides of the triangle, we need to add Side 1 and Side 2:
Side 1: 3x² - 4x - 1
Side 2: 4x - x² + 5
Total length: (3x² - 4x - 1) + (4x - x² + 5)
Simplifying and combining like terms, we get:
Total length: -x² + 7x + 4
Therefore, the total length of the two sides of the triangle is -x² + 7x + 4.
Part B:
To find the length of the third side of the triangle, we need to subtract the sum of Side 1 and Side 2 from the perimeter of the triangle:
Length of Side 3 = Perimeter - (Side 1 + Side 2)
Length of Side 3 = (5x³ - 2x² + 3x - 8) - (3x² - 4x - 1 + 4x - x² + 5)
Simplifying and combining like terms, we get:
Length of Side 3 = 2x³ - 2x² + 7x - 12
Therefore, the length of the third side of the triangle is 2x³ - 2x² + 7x - 12.
Part C:
The answers for Part A and Part B show that the polynomials are closed under addition and subtraction. The sum of Side 1 and Side 2 is a polynomial (-x² + 7x + 4), and the difference between the perimeter of the triangle and the sum of Side 1 and Side 2 is also a polynomial (2x³ - 2x² + 7x - 12). In both cases, the result is a polynomial, which means that the set of polynomials is closed under addition and subtraction.
Show that sin^2x+cos^2x=1 by using the unit circle.Hint:start with the equation of the circle and finish labeled the circle
Proof that cos²(x) + sin²(x) = 1 using the unit circle shows that this equation represents a circle with radius 1
How to prove the unit of a circle?The equation of the unit circle is given by:
x² + y² = 1
where x and y are the coordinates of any point on the circle. Let us assume that the point P on the circle makes an angle of x with the positive x-axis. Then, the coordinates of P are given by:
x = cos(x)
y = sin(x)
Substituting these values in the equation of the circlet:
cos²(x) + sin²(x) = 1
Therefore, we have shown that sin²(x) + cos²(x) = 1 using the unit circle.
Graphically, this equation represents a circle with radius 1 centered at the origin, and any point (cos(x), sin(x)) on the circle will satisfy this equation.
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