The banner should be 56 feet long to fit the garage door.
What is the perimeter of rectangle?The perimeter of a rectangle is the total length of all the sides of the rectangle.
P = 2 (L + B)
P = perimeter of rectangle, L = Length of rectangle, B = Breadth of rectangle
Given length of garage door = 12 feet
Given breadth of garage door = 16 feet
P = 2 (L + B)
P = 2 ( 12 + 16)
P = 2 (28)
P = 56 feet
Hence, The total length of the banner should be 56 feet to cover the entire door.
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Objective: 1. To apply programming using while loops 2. To determine roots of functions using the bisection method Problem 1 Write a function taylorcosi ne that takes two arguments: the first argument is the angle in radians, and the second argument the relative percentage error, and has two return values: first return value is the Taylor approximation for the cosine of the angle entered and the second is the number of terms required in the Taylor series to reach this level of error. You must use while loops. The Taylor expansion of
f(x)=cosx
about
x=0
is given by
cosx=1− 2!
x 2
+ 4!
x 4
− 6!
x 6
+⋯
Suppose we want to find the approximate value of the function at
x= 3
π
with an error tolerance of
0.1%
. We should be able to call the function as follows:
{
val, nsteps
]=
taylorcosine
( 3
π
,1e−3)
. Note relative error is defined a: To find percentage relative error, multiply by 100. Write a function myBi section that takes three arguments: the first argument is a function handie, the second argument is an array containing the lower and upper limits of the starting interval, and the third argument is the maximum allowable relative error. The return value of the function is the estimate of the root. Error here is defined is the absolute value of the ratio of the difference between the old and the new estimates of the root and the new estimate of the root. i.e. error
=
x new
x nnw
−x eld
Test this function on examples we have done in class. For example,
f(x)=x 2
−3x+2
with an initial bracket of
[1.33.0]
and an error tolerance of
1%
The Taylor expansion of cos(x) around x=0 is [tex]cos(x) = 1 - (x^2/2!) + (x^4/4!) - (x^6/6!) +[/tex]......
We would use this expansion to calculate the cosine of a given angle with an error tolerance of 0.1%.
To do this, we must first write a function taylorcosine() which takes two arguments: the angle (in radians) and the relative percentage error. The function should then return two values: the Taylor approximation for the cosine of the angle, and the number of terms required in the Taylor series to reach this level of error.
For example, if we want to find the approximate value of cos(3π) with an error tolerance of 0.1%, we would call the function as follows:
[tex]val, nsteps = taylorcosine(3π, 1e-3)[/tex]
To find the percentage relative error, we must multiply the relative error by 100.
We can also use the bisection method to determine the roots of a function. To do this, we must write a function myBisection() which takes
three arguments: the function handle, an array containing the lower and upper limits of the starting interval, and the maximum allowable relative error. The return value of the function is the estimate of the root.
For example, if we want to find the root of f(x) = x^2 - 3x + 2, with an initial bracket of [1.3, 0] and an error tolerance of 1%, we would call the function as follows:
root = [tex]myBisection(f, [1.3, 0], 1%)[/tex]
The error is defined as the absolute value of the ratio of the difference between the old and the new estimates of the root and the new estimate of the root.
Error = [tex]|x_new/x_new - x_old|/x_new[/tex]
By writing the taylorcosine() and myBisection() functions, we can calculate the cosine of an angle with a given error tolerance, and determine the roots of a function with a given error tolerance, respectively.
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Find a vector function that represents the curve of intersection of the two surfaces: The cone z=sqrt(x^2 + y^2) and the plane z =1 + y.
Thus, a vector function that represents the curve of intersection of the cone and the plane is: [tex]r(t) = tcos(t), 1 +\sqrt{ (1 - t^2)}, 1 -\sqrt{ (1 - t^2)}, tsin(t)[/tex]
The vector function that represents the curve of intersection of a cone and a plane can be found by equating the equation of the cone and the equation of the plane, and then solving for x and y in terms of z.
Given the cone [tex]z = \sqrt{(x^2 + y^2)}[/tex] and the plane [tex]z = 1 + y[/tex] , we have:
[tex]\sqrt{(x^2 + y^2) }= 1 + y[/tex]
Squaring both sides, we get:
[tex]x^2 + y^2 = (1 + y)^2 = 1 + 2y + y^2[/tex]
Solving for y, we get:
[tex]x^2 + y^2 - 2y = 1[/tex]
[tex]y^2 - 2y + x^2 - 1 = 0[/tex]
Using the quadratic formula, we get:
[tex]y = 1 + \sqrt{(1 - x^2)} , 1 + \sqrt{(1 - x^2)}[/tex]
Thus, a vector function that represents the curve of intersection of the cone and the plane is:
[tex]r(t) = tcos(t), 1 +\sqrt{ (1 - t^2)}, 1 -\sqrt{ (1 - t^2)}, tsin(t)[/tex]
where t varies between -1 and 1.
The resulting curve is a circle with center (0, 1, 0) and radius 1, which lies in the xy-plane and is perpendicular to the z-axis.
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please calculate the probability that a particle in a one-dimensional box of length a is found between 0 and a/2
The probability of finding a particle in a one-dimensional box of length a between 0 and a/2 is[tex](2/a)^3/3[/tex].
The probability of finding a particle in a one-dimensional box of length a between 0 and a/2 can be calculated using the equation [tex]P = (1/h)^3 * (∫0^a/2Ψ^2dx)[/tex]. The equation is derived from the equation of probability density of finding a particle in a given state which is given as [tex]P = (1/h)^3 * ∫Ψ^2dx[/tex]. In this equation, h is the Planck's constant, and Ψ is the wave function of the particle.
For a particle in a one-dimensional box of length a, the wavefunction can be written as [tex]Ψ(x) = (2/a)^1/2 * sin (nπx/a)[/tex]. Substituting this in the equation for probability density, the probability of finding a particle between 0 and a/2 is [tex]P = (1/h)^3 * (2/a)^3 * (1/3 - 0)[/tex]. Therefore, the probability of finding a particle in a one-dimensional box of length a between 0 and a/2 is [tex](2/a)^3/3[/tex].
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(FoF) (0) f(x) = 3x-2
The solution is (FoF) (0) = -8, when f(x) = 3x-2.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.
here, we have,
f(x) = 3x-2
i.e. fof(x)
=3(3x-2)-2
=9x-8
so. fof(0)
=9*0-8
= -8
Hence, The solution is (FoF) (0) = -8, when f(x) = 3x-2.
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PLEASE HELP 10 Points
Answer:
last option
number of students in class plus new students
select all the rates that are unit rates 2/4/5 3/4/1 3:4 9/1 10:1
Note that the rates that are unit rates are given as follows:
Note that a unit rate is a rate in which the second term equals 1. It represents a comparison of a quantity to 1.
Since:
Therefore, it is right or correct to state that 2/4, 9/1, and 10:1 are unit rates.
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Identify which of the following statements is true, with regards to the heap data structure and its role in sorting. Pick ONE-Heap sort functions in O(nlogn) asymptotic complexity and a heap of n elements may be constructed in O(n) asymptotic complexiy (i.e. linear time). -Heap sort functions in O(nlogn) time and a heap of n elements may be constructed in no better than O(nlogn) time -Heap sort functions in O(n ∧ 2) time and a heap of n elements may be constructed in no better than O(nlogn) time -None of the above are correct.
The time complexity of constructing a heap of n elements is no better than O(nlogn).
The correct statement is that heap sort functions in O(nlogn) time and a heap of n elements may be constructed in no better than O(nlogn) time.
Heap sort is an efficient sorting algorithm that uses a heap data structure to store the data elements. The heap is a complete binary tree structure where the root node is the largest element in the heap and each node contains a value that is less than or equal to its parent node. The heap is constructed in a bottom-up fashion, meaning that each leaf node is compared to its parent node and swapped if it is larger. This ensures that the root node is always the largest element in the heap.
The complexity of heap sort is O(nlogn), since the heap is constructed in O(n) time but the sorting operation requires O(nlogn) time. This is because, for each element in the heap, the sorting algorithm must compare it to its parent node and swap if necessary. Therefore, the overall time complexity of the algorithm is O(n) + O(nlogn) = O(nlogn).
The complexity of constructing a heap of n elements is also O(nlogn), since each element must be compared to its parent node and swapped if necessary. This process must be repeated for each element in the heap, so the time complexity is O(n) + O(nlogn) = O(nlogn). Therefore, the time complexity of constructing a heap of n elements is no better than O(nlogn).
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please help ||||
_________________
Answer:
[tex] \color{grey}{ \boxed{\sf x < \frac{1}{2} }}[/tex]
Solve..
Let's solve your inequality step-by-step.
[tex] \sf{3(6x+10)<39} [/tex]
Step 1: Simplify both sides of the inequality.
[tex] \sf{18x+30<39}[/tex]
Step 2: Subtract 30 from both sides.
[tex] \sf18x+30−30<39−30 \\ \sf18x<9 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:[/tex]
Step 3: divide by 18
[tex] \sf{x <\frac{9}{18} = \frac{9 \times 1}{9 \times 2} } \\ \\ \sf x < \frac{1}{2} [/tex]
4. Calculate the estimated cost of constructing the following house in New
Orleans, Louisiana: a two-story home of 950 ft2 on the first floor and 800 ft²
on the second floor.
O A. $113,750
O B. $67,600
O C. $61,750
O D. $52,000
The estimated cost for constructing the house in New Orleans, Louisiana of the given square feet is option A. $113,750.
What is Multiplication?Multiplication of two numbers is defined as the addition of one of the number repeatedly until the times of the other number.
a × b means that a is added to itself b times or b is added to itself a times.
Given that, construction rate per square feet is $65.
We have to find the estimated cost for a two-story home of 950 ft2 on the first floor and 800 ft² on the second floor.
Total area of the plot = 950 ft² + 800 ft²
= 1750 ft²
Estimated cost can be calculated by multiplying total area with the construction rate per square feet.
Estimated cost = 1750 ft² × $65
= $113,750
Hence the estimated cost is $113,750.
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43. a system of linear equations with fewer equations than unknowns is sometimes called an underdetermined system
Yes, that is correct. A system of linear equations with fewer equations than unknowns is often referred to as an underdetermined system.
In this type of system, there are infinitely many solutions or no solutions, and it is not possible to determine a unique solution for the variables.
Because free variables will give infinitely many solutions by just keeping on changing the values of free variable. We can do it because it is a free variable, it can take any value.When a system of equations has more variables than the equation, therefore, it has fewer rules to curb the variables, giving the variables more freedom to take up values from their respective domain(Usually it is a set of real numbers), in such a condition the system of equations has infinite solutions. This kind of system is known as an underdetermined system.
Hence, the system of equations doesn't have a unique solution.
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Redondear 2,325 a la unidad de millar más cercana.
0
X
3
When 2, 325 is rounded to the nearest thousand, the result would be 2, 000.
How to round numbers to the nearest thousand ?To round a number to the nearest thousand, identify the place value of the rounding digit, which is the thousandth place (the third digit from the right).
Then, look at the digit to the right of the rounding digit. If this digit is 5 or greater, then round up the rounding digit by adding one to it. If the digit is less than 5, keep the rounding digit as it is.
The number 2, 325 would therefore be rounded to 2, 000 because the digit " 3 " is less than 5.
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In each of the following cases, either find an example that contradicts the statement showing that it is false, or explain why the statement is always true. (a) If {u, 12, 13} is a spanning set for R", then {uj, 12, 13, 14} is also a spanning set for R". What are all possible values of n for which three vectors un, U2, U3 can span Rn? (b) If {u, uy, us} is a spanning set for R", then {u, u, + u2, u, -u3} also spans RM (c) If u, uz, uz are linearly independent, then u,, uy, us, , are also linearly independent. (d) If ui, uy, us are linearly independent, then u, u, + uy, u, -u3 are also linearly independent. (e) If u, u, uz do not span R", then there is a plane P in R that contain all of them. (Bonus: how can we find this plane? Does the plane go through the origin?)
The statement is false, as it is possible for three vectors to not span Rn but still lie on the same plane, such as the three vectors (1,1,1), (2,2,2), and (3,3,3), which all lie on a plane that passes through the origin.
(a) In order for three vectors un, U2, U3 to span Rn, all possible values of n must be 3 or greater. This is because three vectors can only span a 3-dimensional space or higher. Therefore, any n greater than or equal to 3 will work.
(b) Since {u, uy, u3} is a spanning set for Rn, then {u, u, + u2, u, -u3} is also a spanning set for Rn. This is because adding or subtracting any of the vectors in the original set will still form a set of three vectors that span Rn.
(c) This statement is always true. If three vectors ui, uy, u3 are linearly independent, then any linear combination of those three vectors (such as u,, u, + u2, u, -u3) will also be linearly independent.
(d) This statement is also always true. If three vectors ui, uy, u3 are linearly independent, then any linear combination of those three vectors (such as u,, u, + u2, u, -u3) will also be linearly independent.
(e) This statement is false. It is possible for three vectors ui, uy, u3 to not span Rn but still lie on the same plane. For example, the three vectors (1,1,1), (2,2,2), and (3,3,3) do not span R3, but they all lie on the same plane that passes through the origin (x+y+z=0).
The statement is false, as it is possible for three vectors to not span Rn but still lie on the same plane, such as the three vectors (1,1,1), (2,2,2), and (3,3,3), which all lie on a plane that passes through the origin.
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At the 2012 Summer Olympics, Jamaican athlete Usain Bolt won the gold medal in the men's 100-meter track event. He ran the distance at an average speed of 34.1 feet per second. Convert this speed to miles per hour.
The speed of Usain Bolt is given by the equation S = 23.25 miles per hour
What is an Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the equation be represented as S
Now , the value of S is
The speed at which Usain Bolt won the gold medal = 34.1 feet per second
So , the speed at which Usain Bolt won the gold medal in miles per hour is calculated by dividing the value by 1.467
Substituting the values in the equation , we get
The speed of Usain Bolt S = ( speed of Usain / 1.467 ) miles per hour
On simplifying the equation , we get
The speed of Usain Bolt S = 34.1 / 1.467
The speed of Usain Bolt S = 23.25 miles per hour
Therefore , the value of S is 23.25 mph
Hence , the equation is S = 23.25 miles per hour
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May I have help on This question
4(2y-6) and 8y-24 why are they equivalent
Because in the first expression 4 was factored out to make it 4(2y-6). Before 4 was factored out the expressions were the same.
The state education commission wants to estimate the fraction of tenth grade students that have reading skills at or below the eighth grade level. In an earlier study, the population proportion was estimated to be 0.17
.
How large a sample would be required in order to estimate the fraction of tenth graders reading at or below the eighth grade level at the 95%
confidence level with an error of at most 0.02
? Round your answer up to the next integer.
The sample size required to estimate the fraction of tenth graders reading at or below the eighth grade level at the 95% confidence level with an error of at most 0.02 is 685.
What is population?Population is the term typically used to refer to the number of people in a single area.
To estimate the fraction of tenth graders reading at or below the eighth grade level at the 95% confidence level with an error of at most 0.02.
we can use the formula for sample size in a proportion estimation problem:
n = (Z^2 * p * (1 - p)) / E^2
Where n is the sample size Z is the Z-score for the desired confidence level (1.96 for 95% confidence)P is the estimated population proportion (0.17), and E is the maximum error in the estimate (0.02).Plugging in the values:
n = (1.96^2 * 0.17 * (1 - 0.17)) / (0.02^2)
n = 684.2
Since n must be a whole number, we round up to the next integer:
n = 685
So, the sample size required to estimate the fraction of tenth graders reading at or below the eighth grade level at the 95% confidence level with an error of at most 0.02 is 685.
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three identical charges q form an equilateral triangle of side a , with two charges on the x -axis and one on the positive y -axis. part a part complete find an expression for the electric field at points on the y -axis above the uppermost charge. express your answers in terms of some or all of the variables q , a , x , y , and coulomb constant k . enter your answers separated by a comma. ex,ey
The electric field at points on the y-axis above the uppermost charge is given by [tex]E= kq/(a^{2}+y^{2} )^{(3/2)} ,ex=0, ey=kq/(a^{2}+y^{2} )^{(3/2)}[/tex].
The electric field at points on the y-axis above the uppermost charge can be calculated by finding the electric field due to each of the three charges and summing them. This calculation requires the use of Coulomb's law, which states that the force between two point charges is proportional to the product of the charges and inversely proportional to the square of the distance between them. The electric field due to a single charge is proportional to the charge and inversely proportional to the square of the distance from the charge to the point at which the field is being calculated.
By using the equations for the electric field due to each charge and the vector sum of their electric fields, an expression for the electric field at points on the y-axis above the uppermost charge can be obtained. The final expression would likely be a function of q, a, x, y, and the Coulomb constant k.
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Pls help answer in the attached image
QRST is a Rhombus, then:
RT bisects of QRS becauseQS is perpendicular of RT becauseQS bisects RT becauseRhombus is a parallelogram with all congruent sides. Rhombus' diagonals are perpendicular and bisects its angles. Rhombus has 4 congruent right angles created from its perpendicular diagonals and form 2 pairs of two congruent isosceles triangle.
RT bisects of QRS because every diagonals on rhombus bisect their repsective angles.
QS is perpendicular to RT because both QS and RT are rhombus' diagonals and diagonals in rhombus are perpendicular with each other.
QS bisects RT because QS divide rhombus QRST into 2 congruent triangles, QRS and QTS. Since both triangles' height are half of RT, then QS bisects RT.
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The populations P (in thousands) of a certain city from 2000 through 2007 can be modeled by P = 1657.5e^kt, where t represents the year, with t = 0 corresponding to 2000. In 2005, the
population of the city was about 1,940,000.
(a) Find the value of k. (Round your answer to five decimal places.)
(b) Use the model to find the populations of the city in 2010 and 2015.
2010
P=
2015
P=
(c) According to the model, during what year will the population reach 2.5 million?
The population will reach 2.5 million in
a)
The value of k is 0.61.
b)
The population in 2010 is 739013.
The population in 2015 is 15604434.
c)
In 5.2 years, the population will reach 2.5 million.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
We have,
P = 1657.5 [tex]e^{kt}[/tex]
P is the population in t years.
Now,
In 2000, t = 0,
a)
In 2005, t = 5 and P = 1940,000
So,
P = 1657.5 [tex]e^{kt}[/tex]
1,940,000 = 1657.5 [tex]e^{5k}[/tex]
1940000/1657.5 = [tex]e^{5k}[/tex]
1170.44 = [tex]e^{5k}[/tex]
Taking logs on both sides.
log 1170.44 = 5k
3.07 = 5k
k = 0.61
b)
In 2010, t = 10
So,
kt = 0.61 x 10 = 6.1
P = 1657.5 [tex]e^{6.1}[/tex]
P = 1657.5 x 445.86
P = 739012.95
P = 739013
In 2015, t = 15
So,
P = 1657.5 [tex]e^{9.15}[/tex]
P = 1657.5 x 9414.44
P = 15604434
c)
P = 2.5 million = 2,500,000
Now,
P = 1657.5 [tex]e^{6.1}[/tex]
Solve for t.
2,500,000 = 1657.5 [tex]e^{0.61t}[/tex]
2500000/1657.5 = [tex]e^{0.61t}[/tex]
1508 = [tex]e^{0.61t}[/tex]
Taking logs on both sides.
log 1508 = 0.61t
3.18 = 0.61t
t = 3.18/0.61
t = 5.21
t = 5.2
Thus,
a)
k = 0.61
b)
P = 739013 in 2010
P = 15604434 in 2015
c)
In 5.2 years, the population will reach 2.5 million.
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Please help asap!!
Try ur best <3
• will give u brainliest
The domain of the function is Domain: (-2, 2). The range is:
Range: (-2, 2). The given graph does not have exactly one output for one input value. Hence, the given is not a function.
What is a function?A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output. Each function has a range, codomain, and domain. The usual way to refer to a function is as f(x), where x is the input. A function is typically represented as y = f. (x).
The domain of the function are the input values or the x-coordinate of the graph. From the given graph the domain is:
Domain: (-2, 2)
The range of the function are the output values, or the y-coordinate of the graph. From the given graph the range is:
Range: (-2, 2)
We know that a function is a relationship between inputs where each input is related to exactly one output.
The given graph does not have exactly one output for one input value.
Hence, the given is not a function.
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10. A skateboarding company produced
10,200 longboards last month and
found that some were defective.
a. The company plans to make 125,000
longboards this year. Predict
approximately how many longboards
will be defective.
1 Month
1 Year
Number of
Longboards Produced
10,200
125,000
Number of Defective
Longboards
204
?
b. Another skateboarding company produced 11,500 longboards last month and found that
225 were defective. If they also plan on making 125,000 longboards this year, predict how many
will be defective. Then determine if this company will produce a product with fewer defects.
The number of longboards that will be defective based on the defective longboards in the month can be predicted to be 2, 500 longboards.
The number of longboards that would be defective for the other skateboarding company is 2, 446 longboards.
How to find the defective items ?To find the defective longboards, first find the percentage of the longboards that were produced in the month. Then multiply this result with the number of longboards to be produced :
= 204 / 10, 200 x 125, 000
= 2 % x 125, 000
= 2, 500 longboards
The same procedure can be used for the other skateboarding company to find the defective products to be:
= 225 / 11, 500 x 125, 000
= 2, 446 longboards
The product for the second company therefore has fewer defects.
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Write an equation that represent the sum of the angle measures of the triangle. The equations are 3x-5y=-22 and 2y-18+x. What are the values of x and y?
The solutions to the equations of the triangle is given by x = 86 and the value of y = 56
What is a Triangle?A triangle is a plane figure or polygon with three sides and three angles.
A Triangle has three vertices and the sum of the interior angles add up to 180°
Let the Triangle be ΔABC , such that
∠A + ∠B + ∠C = 180°
The area of the triangle = ( 1/2 ) x Length x Base
For a right angle triangle
From the Pythagoras Theorem , The hypotenuse² = base² + height²
if a² + b² = c² , it is a right triangle
if a² + b² < c² , it is an obtuse triangle
if a² + b² > c² , it is an acute triangle
Given data ,
Let the triangle be represented as ABC
Now , the equation is
3x - 5y = -22 be equation (1)
Now , the measure of ∠A = ( y - 18 )°
The measure of ∠B = y°
The measure of ∠C = x°
Now , for a triangle
∠A + ∠B + ∠C = 180°
Substituting the values in the equation , we get
y - 18 + y + x = 180
On simplifying the equation , we get
2y + x = 198 be equation (2)
Multiply equation (2) by -3 , we get
-6y - 3x = -594 be equation (3)
Adding equation (3) and equation (1) , we get
-5y - 6y = -594 - 22
-11y = -616
Divide by -11 on both sides of the equation , we get
y = 56
Substitute the value of y in equation (2) , we get
2 ( 56 ) + x = 198
x + 112 = 198
Subtracting 112 on both sides of the equation , we get
x = 86
Hence , the solution to the equation is ( 86 , 56 )
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3. Is the relation a function ?
Answer:
yes
Step-by-step explanation:
the following pair of triangles are similar. find the value of x 10 x x+2 x+14
The numerical value of x in the similar pair of triangle is 10.
What is the numerical value of x?A ratio is simply the relation between two amounts showing how many times a value is contained within another value.
From the diagram,
Side A of the small triangle = 10
Side B of the small triangle = x + 2
Side A of the Big triangle = 10 + x
Side B of the big triangle = x + 14
Hence;
Ratio of Side A to Side B of the small triangle = 10 / x + 2
Ratio of Side A to Side B of the Big triangle = 10 + x / x + 14
Since the triangle area similar, equate the two ratio and solve for x.
10 / ( x + 2 ) = ( 10 + x ) / ( x + 14 )
Cross multiply
10( x + 14 ) = ( 10 + x )( x + 2 )
Expand using FOIL method
10x + 140 = 10x + 20 + x² + 2x
10x + 140 = x² + 12x + 20
x² + 12x + 20 = 10x + 140
x² + 12x + 20 - 10x - 140 = 0
x² + 2x - 120 = 0
Factor the left side of the equation
( x - 10 )( x + 12 ) = 0
Hence;
x - 10 = 0 and x + 12 = 0
x = 10 and x = -12
Since the dimension of the triangle cannot be negative,
x = 10
Therefore, the value of x is 10.
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P(-3,-1), Q(-1,-1), R (1, 1) are three of the four vertices of a parallelogram PQRS and S is the opposite vertex of Q. Plot these vertices in graph paper and find: (i) the coordinates of the vertex S. (ii) the coordinates of the point of intersection of the diagonals PR and QS.
(i) the coordinates of the vertex S = Q + QS = (-1, -1) + (2, 2) = (1, 1).
(ii) the coordinates of the point of intersection of the diagonals PR and QQS is point (-1, 0).
How did we get the value?(i) The coordinates of the vertex S can be found by shifting the vector PQ to QS. The vector PQ is given by Q - P = (-1 - (-3), -1 - (-1)) = (2, 0). The vector QS can be found by shifting PQ by 2 units vertically, so QS = (2, 2). To find the coordinates of S, we add the vector QS to the point Q: S = Q + QS = (-1, -1) + (2, 2) = (1, 1).
(ii) The point of intersection of the diagonals PR and QS can be found by finding the midpoint of each diagonal and checking if they are equal. The midpoint of PR is given by ( (1 + -3)/2 , (1 + -1)/2 ) = (-1, 0). The midpoint of QS is given by ( (1 + -1)/2 , (1 + 1)/2 ) = (0, 1). Since the midpoints are equal, the diagonals PR and QS intersect at the point (-1, 0).
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need help fast please help me
What are the answers for
The correct options are a) ∠ R corresponds to ∠ P'QQ' and d) side RQ corresponds to QQ'
What is dilation?Dilation means changing the size of an object without changing its shape. The size of the object may be increased or decreased based on the scale factor.
Given that, a triangle PQR is being dilated to form a new triangle P'Q'Q following a rule: (x, y) → (2x, 2y)
This show that, the scale factor is 2 and the dilation is an enlargement,
We know that, dilation transformation makes similar figures, and in similar figures, the corresponding angles and ratio of corresponding sides are equal,
Here, the corresponding angles are:
∠ P = ∠ P'
∠ PQR = ∠ P'Q'Q
∠ R = ∠ P'QQ'
And, the corresponding side:
P'Q'/PQ = P'Q/PR = Q'Q/QR
Therefore, true statements are;
a) ∠ R corresponds to ∠ P'QQ'
d) side RQ corresponds to QQ'
Hence, the correct options are a) ∠ R corresponds to ∠ P'QQ' and d) side RQ corresponds to QQ'
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a point on the terminal side of an angle u in standard position is given. find the exact value of each of the six trigonometric functions of u.
The value of all trigonometric functions can be found with the help of a triangle,
from the diagram of the point and reference triangle needed to answer the problem.
Plot the point (2,-3) which is in quadrant 4
Draw a right triangle such that one leg is resting on the x axis and the other leg is perpendicular to the x axis. The hypotenuse goes from (0,0) to (2,-3).
The horizontal leg is 2 units long. So a = 2
The vertical leg is 3 units long. So b = 3
The hypotenuse is unknown but we can use the pythagorean theorem to find it. We'll call it c for now
Use the Pythagorean theorem to find c
[tex]a^2+b^2=c^2\\\\2^2+3^2=c^2\\\\c=\sqrt{13}\\[/tex]
The hypotenuse is sqrt(13) which is shown in the attached image (Fi
Using figure 1, now refer to figure 2 to compute the ratios for sine, cosine, and tangent
Figure 3 shows how to compute the ratios for cosecant, sectant, and cotangent
With figure 1, the leg furthest from angle theta is the opposite side (in this case -3). The leg closest to the angle theta is 2 units long.
[tex]Sin\theta=\frac{3}{\sqrt{13}}\\\\cos\theta = 2/\sqrt{13}\\\\tan\theta=3/2\\\\same\ as,\\cot\theta=2/3\\sec\theta=\sqrt{13}/2\\cosec\theta=\sqrt{13}/3[/tex]
The complete question is -
A point on the terminal side of an angle in standard position is given. Find the exact value of each of the six trigonometric functions of θ.
Point given: (2,-3)
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3(w-2) ≥10 3w 212 w24
Answer:
Step-by-step explanation:
3 (w - 2) ≥ 10
3w - 6 ≥ 10
3w ≥ 16
w ≥ 16/3
(5x + 1) (12x - 8) =
The multiplication of the expression given is 60x² - 28x - 8.
What are Expressions?Expressions are mathematical statements which consist of two or more terms and terms are connected to each other using mathematical operators like addition, multiplication, subtraction and so on.
The given expression is (5x + 1) (12x - 8).
We have to multiply the expressions and simplify.
For any numbers or algebraic expressions, a, b, c and d,
(a + b) (c + d) = ac + ad + bc + bd
(5x + 1) (12x - 8) = (5x × 12x) + (1 × 12x) + (5x × -8) + (1 × -8)
= 60x² + 12x - 40x - 8
= 60x² - 28x - 8
Hence the multiplication of the given expression gives 60x² - 28x - 8.
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