The linear function that represents the above scenario is given as follows:
y = 6 + 2.5x.
The number of days needed to run 41 miles is given as follows:
14 days.
How to define a linear function?The slope-intercept representation of a linear function is given by the equation presented as follows:
y = mx + b
The coefficients of the function and their meaning are described as follows:
m is the slope of the function, representing the rate of change.b is the y-intercept of the function, which is the initial value.The parameters in the context of the problem have the values given as follows:
m = 2.5, as each day, Juan runs 2.5 additional miles.b = 6, as Juan has already ran 6 miles.Hence the function is modeled as follows:
y = 2.5x + 6.
The number of days needed to run 41 miles is given as follows:
2.5x + 6 = 41
x = 35/2.5
x = 14 days.
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Find the square ropt of 6,57,55,881 by using division method.
The square root of 6,57,55,881 using long division method is 8563.
How to use long division?Group the digits starting from the units place into pairs of two, from right to left. If there are any remaining digits, add a zero to the left of them. So for 65755881:
65 | 75 | 58 | 81
Find the largest number whose square is less than or equal to the leftmost group (in this case, 65). The square of 8 is 64, so the first digit of the square root must be 8. Write 8 as the first digit of the answer and subtract 64 from 65 to get 1.
Bring down the next group (75) to the right of the remainder (1) to get 175.
Double the first digit of the current partial answer (which is 8) to get 16, and place a blank digit to its right. We will be filling in this blank digit with the next digit of the square root.
Find the largest digit d such that the number 16d, when multiplied by d and then by 10, is less than or equal to 175. To do this, we can start with d=9 and work downwards until we find a suitable value. We find that d=5 works, since 165510=8250 is less than 17500. So the next digit of the square root is 5.
Append the digit 5 to the partial answer, so we have 85 as the current partial answer.
Subtract 165 (the product of 16 and 5) from 175 to get the new remainder, which is 10.
Bring down the next group (58) to the right of the remainder (10) to get 1058.
Double the first digit of the current partial answer (which is 85) to get 170, and place a blank digit to its right.
Find the largest digit d such that the number 170d, when multiplied by d and then by 10, is less than or equal to 1058. To do this, we can start with d=9 and work downwards until we find a suitable value. We find that d=6 works, since 1706610=102360 is less than 105800. So the next digit of the square root is 6.
Append the digit 6 to the partial answer, so we have 856 as the current partial answer.
Subtract 1706 (the product of 170 and 6) from 1058 to get the new remainder, which is 402.
Bring down the last group (81) to the right of the remainder (402) to get 40281.
Double the first digit of the current partial answer (which is 856) to get 1712, and place a blank digit to its right.
Find the largest digit d such that the number 1712d, when multiplied by d, is less than or equal to 40281. To do this, we can start with d=9 and work downwards until we find a suitable value. We find that d=3 works, since 17123×3=51369 is less than 40281. So the next digit of the square root is 3.
Append the digit 3 to the partial answer, so we have 8563 as the final answer.
Therefore, the square root of 65755881 is 8563.
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Given the function I need to evaluate question a)
Answer:
a) p(-6) = 30
b) c = -2 ,1
Step-by-step explanation:
[tex]p(c)=c^2+c[/tex]
a) Evaluate p(-6)
This mean input -6 into the equation to solve for p(-6) =
[tex]p(-6)=(-6)^2+(-6)\\\\p(-6)=36-6\\\\p(-6)=30\\[/tex]
(b) Solve for p(c) = 2.
[tex]p(c)=c^2+c\\\\2=c^2+c\\\\c^2+c=2\\\\c^2+c-2=0\\\\Factoring\\(c+2)(c-1)=0\\(c+2)=0,(c-1)=0\\c = -2 , 1[/tex]
NEED HELP ASSIGNMENT DUE IN AN HOUR WOULD BE MUCH APPRECIATED!
Can someone help, I don't know why but this isn't clicking with me
Therefore, the solution to the system of linear equations is (x, y) = (-1, 4).
What is equation?In mathematics, an equation is a statement that two expressions are equal. It typically contains one or more variables (unknowns) and specifies a relationship between those variables. Equations are used to model real-world phenomena, solve problems, and make predictions. There are many types of equations in mathematics, including linear equations, quadratic equations, polynomial equations, exponential equations, trigonometric equations, and many more. Each type of equation has its own set of methods and techniques for solving it. Solving an equation means finding the values of the variables that satisfy the equation. This may involve manipulating the equation algebraically, using graphical methods, or employing numerical techniques such as iteration or approximation. Equations play a central role in many areas of mathematics and science, as well as in everyday life. They are used to model physical systems, optimize processes, design products, and analyze data, among many other applications.
Here,
We are given the system of linear equations:
17x + 4y = -1 ...(1)
y - 4x - 8 = 0 ...(2)
We can use the substitution method to solve this system. Solving equation (2) for y, we get:
y = 4x + 8
Substituting this expression for y into equation (1), we get:
17x + 4(4x + 8) = -1
Simplifying this equation, we get:
17x + 16x + 32 = -1
33x = -33
x = -1
Substituting x = -1 into equation (2), we get:
y - 4(-1) - 8 = 0
y + 4 - 8 = 0
y = 4
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if i had 1000 apples and gave 39 away
how many wouldd i have left
Answer:
1000-39=961
so 961 apples are left.
Gabriel’s father has a garden in the back yard. The dimension of the garden are shown here 7 3/4 and 2 2/3
The area of Gabriel's father's garden is 62/3 square units, which is approximately 20.67 square units.
The question's purpose is obscure. But, based on its measurements of 7 3/4 by 2 2/3, I'm assuming you're interested in learning how to locate the location of Gabriel's father's garden.
We must multiply the length by the breadth in order to determine the garden's area. To make the calculation simpler, we can convert the mixed values to improper fractions as follows:
7 3/4 = (7 × 4 + 3)/4 = 31/4
2 2/3 = (2 × 3 + 2)/3 = 8/3
The garden is thus 8/3 in width and 31/4 in length. We multiply these values to determine the area:
Area is equal to 31/4 x (8/3), or 62/3 square units.
The size of Gabriel's father's garden is therefore 62/3 square units, or roughly 20.67 square units.
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I will mark you brainiest!
If an exterior angle of a regular polygon is 21.2º, how many sides does the polygon have?
A) 11
B) 13
C) 15
D) 17
Answer:
for any regular polygon, the sum of the exterior angles is always 360 degrees. In a regular polygon, all exterior angles have the same measure, which is equal to 360 degrees divided by the number of sides.
Let n be the number of sides of the polygon. Then we have:
360/n = 21.2
To solve for n, we can cross-multiply and simplify:
360 = 21.2n
n = 360/21.2
n ≈ 16.98
Since n must be a whole number (the number of sides in a polygon must be a whole number), the closest option is D) 17. Therefore, the polygon has 17 sides.
Find each angle measure to the nearest degree.
Answer:
5) A = 70°
6) X = 55°
7) Y = 8°
8) A = 51°
Step-by-step explanation:
There really no way to explain. All you ahve to do is inverse function to solve for the angle. Use a calculator.
5) sin(A) = 0.9397
[tex]A=sin^-1(0.9397)\\\\A=69.701...\\\\A = 70\\[/tex]
6) cos(X) = 0.5763
[tex]X=cos^-1(0.5763)\\\\X=54.998...\\\\X=55\\[/tex]
7) tan(Y) = 0.1405
[tex]Y=tan^-1(0.1405)\\\\Y=7.997...\\\\Y = 8\\[/tex]
8) sin(A) = 0.7771
[tex]A=sin^-1(0.7771)\\\\A=50.995...\\\\A = 51\\[/tex]
The suspension cable that supports a footbridge hangs in the shape of a parabola. The height h, in feet, of the cable above the bridge is given by the function
h(x) = 0.25x ^ 2 - 0.8x + 30, 0 < x < 3.2
where x is the distance in feet measured from the left tower toward the right tower. What is the minimum height of the cable above the bridge? (Round your answer to two decimal places.)
Step-by-step explanation:
The height of the cable above the bridge is given by the function:
h(x) = 0.25x^2 - 0.8x + 30
To find the minimum height of the cable above the bridge, we need to find the vertex of the parabola, which is the lowest point.
The x-coordinate of the vertex is given by:
x = -b / 2a
where a = 0.25 and b = -0.8. Substituting these values, we get:
x = -(-0.8) / 2(0.25) = 1.6
So the vertex is at x = 1.6.
To find the height of the cable at the vertex, we substitute x = 1.6 into the equation for h(x):
h(1.6) = 0.25(1.6)^2 - 0.8(1.6) + 30 = 29.48
Therefore, the minimum height of the cable above the bridge is approximately 29.48 feet (rounded to two decimal places).
PLEASE ITS MY DCP While Amy and Sherry are talking, Amy discovers her earring fell off somewhere in the room. Amy goes 11 feet in one direction to look for it and Sherry goes 15 feet in a different direction. What are all the possible values, d, of the distance between Sherry and Amy? (Drawing is not to scale) Amy Starting point 11 15 Sherry A 4 < d < 26 B4 < d < 15 C11 < d < 15 D11 < d < 26
This means that option A, "4 < d < 26," is the correct answer.
The triangle inequality can be used to calculate various distances between Sherry and Amy. The lengths of any two sides of a triangle must add up to more than the length of the third side in order for the triangle inequality to hold.
If we assume that d is the separation between Amy and Sherry in this instance, we can then create a triangle with sides that are 11, 15, and d in length. The inequality of the triangle indicates that:
11 + 15 > d
or
d < 26
and
15 + d > 11
or
d > 4
So, d might have any of the following values:
4 < d < 26
This indicates that "4 d 26" in option A is the right response.
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Al traveled to France on vacation. He wants to buy lunch at a cafe. He has $30.00 in US money, but in France they use the euro. About how many euro can Al spend on his lunch?
Conversion 1 US dollar = about 0.69 euro
A. 1 B. 18 C. 21 D. 60
Option C. Al spends approximately 21 euros on his lunch in France.
Define the term Conversion rate?Conversion rate is the percentage of website visitors or potential customers who take a desired action, such as making a purchase, signing up for a newsletter, or filling out a form. In other words, it is the rate at which website visitors are converted into customers or subscribers.
To convert US dollars to euros, we multiply the US dollar amount by the exchange rate of 0.69 euro per US dollar:
30.00 US dollars × 0.69 euro/US dollar = 20.70 euros ≅ 21 euros
Therefore, Al can spend approximately 21 euros on his lunch in France.
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3x(x-3)=12 How do you solve this
Step-by-step explanation:
3x squared -9 = 12
3x squared = 12 + 9
3x squared = 21
am i doing the wrong maths?
is it find what 3x squared is or....
The Sock Company buys hiking socks for $6 per pair and sells them for $10. Management budgets monthly fixed costs of $12,000 for sales volumes between 0 and 12,000 pairs of socks.
If the company sells more than 3,000 pairs of socks per month, it will make a profit.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To analyze the profit of the Sock Company, we need to consider the total cost and total revenue.
Let's start with the total cost:
The cost per pair of socks is $6.
If x is the number of pairs of socks sold, then the total cost is 6x.
There is also a fixed cost of $12,000 per month.
So, the total cost can be expressed as:
C(x) = 6x + 12,000
Now, let's move to the total revenue:
The selling price per pair of socks is $10.
If x is the number of pairs of socks sold, then the total revenue is 10x.
So, the total revenue can be expressed as:
R(x) = 10x
The profit is the difference between the total revenue and total cost:
P(x) = R(x) - C(x) = 10x - (6x + 12,000) = 4x - 12,000
To find the range of x where the company makes a profit, we need to set P(x) greater than 0:
4x - 12,000 > 0
4x > 12,000
x > 3,000
Therefore, if the company sells more than 3,000 pairs of socks per month, it will make a profit.
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17. Write an equation of a circle that has
no x-intercepts, no y-intercepts, and a
radius of 5. Draw a sketch of your circle on
the grid provided.
Answer:
(x - 5)^2 + (y - 5)^2 = 25
Step-by-step explanation:
If a circle has no x-intercepts and no y-intercepts, it means that the circle does not intersect either the x-axis or the y-axis. In other words, the center of the circle must lie at some point (h, k) where h and k are not equal to zero.
The general equation of a circle with center (h, k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2
Since we know that the circle has a radius of 5, we can substitute r = 5 into the equation:
(x - h)^2 + (y - k)^2 = 25
Now, we need to find values for h and k such that the circle has no x-intercepts and no y-intercepts. Since the x-intercepts occur when y = 0 and the y-intercepts occur when x = 0, we need to make sure that neither of these values satisfies the equation.
Let's first consider the x-intercepts. We want to make sure that the circle does not intersect the x-axis, which means that the y-coordinate of the center must be equal to the radius. In other words, k = 5. Now, the equation becomes:
(x - h)^2 + (y - 5)^2 = 25
Next, we need to make sure that the circle does not intersect the y-axis, which means that the x-coordinate of the center must be equal to the radius. In other words, h = 5. Now, the equation becomes:
(x - 5)^2 + (y - 5)^2 = 25
Therefore, the equation of the circle that has no x-intercepts, no y-intercepts, and a radius of 5 is:
(x - 5)^2 + (y - 5)^2 = 25
Find a quadratic function that includes the set of values below.
(0,7), (2,17), (3,16)
The equation of the parabola is Y
Replace the by >, < 0o = to make the sentence -4/9* -5/9
The inequality to replace the symbol is > and the expression is -4/9 > -5/9.
How to determine the inequality to replace the symbolWe can utilize the following parameters in our calculation based on the question:
-4/9* -5/9
Represent the symbol * as a blank
This gives
-4/9 [ ] -5/9
Evaluate the quotients
-0.44444444444 [ ] -0.55555555555
By comparison, 0.44444444444 is greater than -0.55555555555
Using the above as a guide, we have the following:
-0.44444444444 [ > ] -0.55555555555
So, we have
-4/9 > -5/9
Hence, the inequality is >
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Which of the loans should you try to pay off first?
A. a loan for $3,400 at 16%
B. a loan for $3,500 at 15%
C. a loan for $3,600 at 14%
D. a loan for $3,700 at 13%
A loan for $3,400 at 16% should be paid first as it has the highest interest rate.
What is loan?A loan is a financial agreement in which one party (the lender) agrees to give money, property, or other assets to another party (the borrower) in exchange for the promise of repayment with interest or other charges. Loans are typically used by individuals, businesses, or governments to finance specific projects, make purchases, or cover expenses.
Assuming that all other factors such as minimum payments and penalties are the same, the loan that you should try to pay off first is the one with the highest interest rate, as it will be accruing interest at a faster rate than the others.
Based on this reasoning, the loan that you should try to pay off first is option A, which has a higher interest rate of 16%.
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What is the perimeter and area of a piece of land in the shape of a regular octagon with a side of 2 km, and an apothem of 2.4 km?
a) 16km and 21.9 km²
b) 16km and 19.2 km²
c) 16km and 29.1 km²
d) 61km and 19.2 km²
e) 16km and 12.9 km²
Answer:
the answer is b because 16km is resolved by 19.2
Given: AM = MC, BN = NC Prove: ΔABC ~ ΔMNC.
The prove to show that ΔABC is similar to ΔMNC is explained below.
How to prove that two triangles are similar?Similar triangles are triangles that have the same shape but are not necessarily the same size. More precisely, two triangles are similar if their corresponding angles are congruent and their corresponding sides are proportional.
Considering the given diagram, we can say:
AM = MC (Given)
BN = NC (Given)
BC = BN + NC (addition property of a line segment)
AC = AM + MC (addition property of a line segment)
NC/ BC = MC/ AC = constant
∠ACB = ∠MCN (Reflexive property)
Thus, ΔABC ~ ΔMNC (Side-Angle-Side theorem)
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Your firm purchases large shipments of a component, subject to the requirement that not more than 4% of a shipment may be defective. If a random sample of 200 parts from a new shipment reveals 12 defectives, can you reject this shipment as not meeting requirements, at the 5% level of significance?
Answer:
see the attachment
Step-by-step explanation:
Since the p-value is greater than the significance level of 0.05, we fail to reject the null hypothesis. Therefore, we do not have sufficient evidence to conclude that the shipment does not meet requirements.
What is the area of this trapezoid?
Enter your answer in the box.
Answer:
80
Step-by-step explanation:
Marilou,a buyer of lot,pays Php10,000 every month for ten years.If money is 8%compoundef annually,how much is the cash value of the lot?
Answer:1,200,000
Step-by-step explanation:
The road is 7m wide. The Corner is in the shape of a quarter of a Cude the inside radius of the Corner is 70m. Ali Walks round the Corner on the inside, from A to B, Obi walks round the Corner On Obe Outside from C Go D. How much further does Obi walk than Ali? use the Value 22 for To- 7
a teachers age is 6 years greater that 2 times a students age. a principles age is 10 years greater than 3 time times the students age. If x represents the students age in years, which expression represents how many years older the principal is than the teacher?
On solving the provided question we cans ay that As a result, x + 4 function denotes the number of years the principal is older than the instructor, where x is the student's age in years.
what is function?Mathematicians examine numbers with their modifications, equations and associated structures, forms and their locations, and feasible positions for these things. The term "function" indicates the connection between a collection of inputs, each of which has a corresponding output. A function is a connection of inputs and outputs where each supply leads to a specific, identifiable outcome. Each function is assigned a domain, a codomain, or a scope. The letter f is widely used to denote functions (x). The symbol for entry is an x. The four primary types of accessible capabilities are on functions, yet another skills, so multiple capabilities, in capabilities, and on operations.
Let's start by writing down the phrases from the problem:
• The teacher's age is six years older than the student's age: T = 2x + 6, where T is the age of the instructor.
• The principal's age is ten years older than the student's age: P = 3x + 10, where P is the age of the principal.
To determine how many years the principal is older than the instructor, subtract the teacher's age from the principal's age:
P - T = (3x + 10) - (2x + 6)
When we simplify the equation, we get:
P - T = x + 4
As a result, x + 4 denotes the number of years the principal is older than the instructor, where x is the student's age in years.
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6.5 practice the measure of the exterior of a triangle is equal to the sum of the remote interior angles?
Answer:
Step-by-step explanation:
Yes, that is correct. The measure of the exterior angle of a triangle is equal to the sum of the two remote interior angles. In other words, if you extend one side of a triangle to form an exterior angle, then the measure of that exterior angle is equal to the sum of the measures of the two interior angles that are not adjacent to the exterior angle. This property is known as the Exterior Angle Theorem.
Mathematically, we can express this as:
Exterior angle = Sum of remote interior angles
Or, in symbols:
∠ABC = ∠A + ∠C
where ∠ABC is the exterior angle formed by extending side BC of triangle ABC, and ∠A and ∠C are the two remote interior angles.
Here are two more examples that illustrate the Exterior Angle Theorem:
Example 1:
Consider a triangle ABC with angles A, B, and C as shown below. If we extend side AC to form an exterior angle, then we can label the exterior angle as ∠DCE. The remote interior angles are ∠B and ∠A.
css
Copy code
C
/ \
/ \
/ \
/ \
/ \
/______\
A B
D
According to the Exterior Angle Theorem, we have:
∠DCE = ∠B + ∠A
A certain element decays at a constant rate of 6% per year. If you start with 20 grams of the element, how long will it take before there are only four grams left?
Answer:
26.0 years
Step-by-step explanation:
It will take approximately 16.79 years (to the nearest hundredth) for the initial mass of 20 grams to decay to four grams, given a constant decay rate of 6% per year.
To determine how long it will take for the 20 grams of the element to decay to four grams, we need to calculate the time using the given decay rate.
Given:
Initial mass (M₀) = 20 grams
Decay rate: 6% per year
Let's set up an equation to represent the decay of the element:
M(t) = M₀ * (1 - r)^t
Here, M(t) represents the mass at time t in years, M₀ is the initial mass, r is the decay rate (expressed as a decimal), and t is the time in years.
We want to find the value of t when M(t) = 4 grams:
[tex]4 = 20 * (1 - 0.06)^t[/tex]
Dividing both sides by 20:
[tex]0.2 = (1 - 0.06)^t[/tex]
Taking the natural logarithm of both sides:
[tex]ln(0.2) = ln[(1 - 0.06)^t][/tex]
Using logarithmic properties, we can simplify further:
[tex]ln(0.2) = t * ln(1 - 0.06)[/tex]
Now, we can solve for t by dividing both sides of the equation by ln(1 - 0.06):
t =[tex]ln(0.2) / ln(1 - 0.06)[/tex]
Using a calculator, we find:
t ≈ 16.79 years
Therefore, it will take approximately 16.79 years (to the nearest hundredth) for the initial mass of 20 grams to decay to four grams, given a constant decay rate of 6% per year.
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The table below shows the grade and reading level for 5 students. Grade Reading Level Student 1 2 6 Student 2 6 14 Student 3 5 12 Student 4 4 10 Student 5 1 4 For grade, the mean is 3.6 and the standard deviation is 2.1. For reading level, the mean is 9.2 and the standard deviation is 4.1. Using the formula below or Excel, find the correlation coefficient, r, for this set of students. Answer choices are rounded to the nearest hundredth. r equals fraction numerator 1 over denominator n minus 1 end fraction sum from blank to blank of open parentheses fraction numerator x minus x with bar on top over denominator s subscript x end fraction close parentheses open parentheses fraction numerator y minus y with bar on top over denominator s subscript y end fraction close parentheses
The cοrrelatiοn cοefficient οf data is 1.
What is cοrrelatiοn cοefficient?A statistical measure knοwn as cοrrelatiοn expresses hοw clοsely twο variables are related linearly (meaning they change tοgether at a cοnstant rate).
The cοnstant cοefficient (οr cοnstant term) is the cοefficient nοt attached tο variables in an expressiοn. Fοr example, the cοnstant cοefficients οf the expressiοns abοve are the number 3 and the parameter c, respectively.
The cοefficient attached tο the highest degree οf the variable in a pοlynοmial is referred tο as the leading cοefficient. Fοr example, in the expressiοns abοve, the leading cοefficients are 2 and a, respectively.
In excel, use fοllοwing cοmmand tο find r
=>cοrrel(select data οf grade, select data οf Reading level)
press enter
=> 1
i.e. 1.00
The required cοrrelatiοn cοefficient r is 1.00
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If you ran this company, what is something that would concern you? (Make sure you
support your answer with quantities displayed in the graph)
Assume the numbers are in $1000s.
Marketing
HR
Developer
Budget Analysis
Customer Support
100
ol
Actual Spending
Finance
Admin
Allocated Budget
Sales
If I were to run this company, I would be concerned about the discrepancy between the allocated budget and the actual spending in the graph.
What is graph?Graph is a mathematical structure used to represent relationships between objects. It consists of vertices (also known as nodes) which represent the objects and edges (also known as arcs) which represent the relationships between the objects. Graphs are often used to represent networks, such as social networks, transportation networks, and communication networks. Graphs can also be used to represent data structures, such as trees and linked lists.
In particular, the finance, admin, marketing, HR, and developer departments all have allocated budgets that are greater than their actual spending. This could be a sign that the company is not utilizing its resources efficiently, since it is not spending up to its allocated budget. The discrepancy between allocated budget and actual spending could also indicate that the company is wasting money on unnecessary projects, or that its budget is not allocated correctly.
Furthermore, the customer support department has allocated budget of $100k, yet its actual spending is only $50k. This could indicate that the company is not providing adequate customer support, which could lead to customer dissatisfaction and a decrease in customer loyalty. It could also mean that the company is not taking advantage of its resources and not utilizing them to their fullest potential.
Overall, the discrepancy between the allocated budget and the actual spending could be a sign of inefficiencies and mismanagement within the company. As the company’s leader, I would be concerned about the implications of this discrepancy and would take steps to ensure that the company is utilizing its resources correctly and efficiently.
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Without using a calculator, compute the sine and cosine of by using the reference angle.
The sine of 5π/4 is [tex]\frac{-1}{\sqrt{2} }[/tex] , the cosine of 5π/4 is [tex]\frac{-1}{\sqrt{2} }[/tex] and the angle lies in the third quadrant.
What is the reference angle?
A reference angle is an acute angle formed between the terminal side of an angle in standard position and the x-axis. In other words, it is the smallest angle that can be formed between the terminal side of the angle and the x-axis.
To find the sine and cosine of 5π/4 using the reference angle, we first need to identify the reference angle.
In this case, 5π/4 is in the third quadrant, which means that the terminal side of the angle passes through the point (-1, -1) on the unit circle.
To find the reference angle, we draw a line from (-1, -1) to the x-axis, which forms a right triangle with sides of length 1, 1, and √2
The reference angle θ is the angle formed between the x-axis and the adjacent side of the triangle. By applying the trigonometric functions to this reference angle, we can find the sine and cosine of 5π/4.
sin(θ) = opposite/hypotenuse = [tex]\frac{1}{\sqrt{2} }[/tex]
cos(θ) = adjacent/hypotenuse = [tex]\frac{-1}{\sqrt{2} }[/tex]
Since sine is positive in the third quadrant and cosine is negative, we need to take the negative of the sine value and keep the negative sign for the cosine value:
sin(5π/4) = -sin(θ) = [tex]\frac{-1}{\sqrt{2} }[/tex]
cos(5π/4) = cos(θ) = [tex]\frac{-1}{\sqrt{2} }[/tex]
Therefore, the sine of 5π/4 is [tex]\frac{-1}{\sqrt{2} }[/tex], and the cosine of 5π/4 is [tex]\frac{-1}{\sqrt{2} }[/tex] .
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Find the length of side � x in simplest radical form with a rational denominator. 30° 60° x 2
The length οf side x can be any value, as lοng as it is nοt 0.
We can use the trigοnοmetric ratiοs fοr 30°-60°-90° triangles tο sοlve fοr the value οf x.
In a 30°-60°-90° triangle, the sides are in the ratiο:
1 : √3 : 2
In this case, we have the side οppοsite the 60° angle (which is the lοnger leg) equal tο x√3 and the side οppοsite the 30° angle (which is the shοrter leg) equal tο x.
Sο we can set up the fοllοwing equatiοn:
x√3 = 2x sin 60°
Simplifying the right side:
sin 60° = √3/2
2x sin 60° = 2x(√3/2) = x√3
Substituting back intο the equatiοn:
x√3 = x√3
This is true fοr any value οf x, as lοng as x is nοt equal tο 0. Therefοre, the length οf side x can be any value, as lοng as it is nοt 0.
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