How do you find the determinant of a 4x4 matrix?
The determinant of a 4x4 matrix is calculated using the Laplace Expansion method, which involves expanding the determinant along one row or column.
The formula for the determinant of a 4x4 matrix is:det(A) =[tex]a11 * a22 * a33 * a44 – a11 * a22 * a34 * a43 + a11 * a23 * a34 * a42 – a11 * a23 * a32 * a44 + a12 * a23 * a32 * a44 – a12 * a23 * a34 * a41 + a12 * a21 * a34 * a43 – a12 * a21 * a33 * a44 + a13 * a21 * a33 * a44 – a13 * a21 * a34 * a42 + a13 * a22 * a34 * a41 – a13 * a22 * a31 * a44 + a14 * a22 * a31 * a43 – a14 * a22 * a33 * a41 + a14 * a23 * a33 * a42 – a14 * a23 * a31 * a42[/tex]To calculate the determinant of a 4x4 matrix, take the sum of the products of the elements in each row/column and its corresponding minor, then multiply each product by the sign of the term (+ or -). For example, if A is a 4x4 matrix, then the determinant is: det(A) =[tex]a11 * |A11| - a12 * |A12| + a13 * |A13| - a14 *[/tex]|A14|.The minors A11, A12, A13 and A14 are the 3x3 matrices obtained by deleting the first row and first column from A. The values of the minors are calculated by applying the Laplace Expansion method to each minor.
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1) Chelsea and Matt each improved their yards by planting daylilies and ivy. They bought their
supplies from the same store. Chelsea spent $81 on 1 daylily and 8 pots of ivy. Matt spent $189
on 10 daylilies and 11 pots of ivy. Find the cost of one daylily and the cost of one pot of ivy.
Answer:
One daylily costs $9, and one pot of ivy costs $9.
Step-by-step explanation:
Step 1: Write a System of Algebraic Equations
We are given 2 different variables, or "unknowns", that we need to find the value of here - the cost of one daylily, and the cost of one pot of ivy. We know that the cost of each plant remains constant (doesn't change), and we are given the following information:
1 daylily and 8 pots of ivy cost $81.10 daylilies and 11 pots of ivy cost $189.We can see that we have a system of equations in the making. The first thing to do when writing a system is assign letters to variables. Let's let the cost of one daylily be denoted as [tex]d[/tex], and the cost of one pot of ivy be denoted as [tex]i[/tex] (in dollars for each). From the above information, we can write the system:
[tex]d+8i=81 \hspace{0.8cm} (1)\\10d+11i=189 \hspace{0.1cm} (2)[/tex]
Step 2: Solve the System (with Substitution)
Now that we have a solution, let's use it to solve for the value of each variable. There are many ways to do this (addition, subtraction, etc), but it seems that the quickest way to solve this particular system is using the substitution method. This is where you write one variable in terms of the others by manipulating one equation, and then substituting that expression in for the isolated variable in the other equation. It's easy to do this here because we already have a [tex]d[/tex] in (1).
Isolating [tex]d[/tex] in (1) by subtracting [tex]8i[/tex] from both sides, we get:
[tex]d+8i=81\\d=81-8i\hspace{0.5cm} (3)[/tex]
Substituting (3) into (2) and solving for i, we get:
[tex]10d+11i=189\\10(81-8i)+11i=189\\810-80i+11i=189\\810-69i=189\\-69i=-621\\\bf i=9[/tex]
Substituting this value into (3), we get:
[tex]d=81-8i\\=81-8*9\\=81-72\\=\bf9[/tex]
Therefore, one daylily costs $9, and one pot of ivy costs $9.
PLEASE HELP
The regular price on a pair of jeans is $54.
The store advertises a back-to-school sale at 40% off the regular price of the jeans.
Two weeks later, the store advertises a sale at an additional off the sale price of
these jeans.
5
Two friends decide to purchase the jeans. Shannon says that the jeans are now 60%
off the regular price. Mary disagrees because she figures that the total discount is actually
less than 60%.
1. What is the cost of the jeans at the back-to-school sale?
2. What is the cost of the jeans dufing the additional " off sale? Justify your reasoning.
3. Shannon says, Calculating 86/9P isthe same as calculating A0% of, then 20% off of the new price:
Mary Disagrees and says, "Calculating 40% off, then 20% off is NOT the same as calculating 60% off."
Who do you agree with and why? Defend your argument with mathematical reasoning.
We can conclude that -
The cost of the jeans at the back-to-school sale is $32.4.The cost of the jeans dufing the additional " off sale is $30.78.The conclusion made by Manny is correct.What are algebraic expressions?In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
Given is that the regular price on a pair of jeans is $54. The store advertises a back-to-school sale at 40% off the regular price of the jeans. Two weeks later, the store advertises a sale at an additional off the sale price of these jeans at 5%.
Original price -
$54
Cost after 40% discount -
54 - {40% of 54}
54 - {40/100 x 54}
54 - {2/5 x 54}
54 - 21.6
$32.4
Cost after 5% discount -
32.4 - {5% of 32.4}
32.4 - {5/100 x 32.4}
32.4 - 1.62
$30.78
{ 3 } -
Calculating 60% of new price -
60% of 30.78
(60/100) x 30.78
18.5
Calculating 40% of new price -
40% of 30.78
(40/100) x 30.78
12.4
So, 60% of new price is greater than calculating 40%.
So, Manny is correct.
Therefore, we can conclude that -
The cost of the jeans at the back-to-school sale is $32.4.The cost of the jeans dufing the additional " off sale is $30.78.The conclusion made by Manny is correct.To solve more questions on functions & expressions, visit the link below
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name the point of concurrency of the angle bisectors
The point of concurrency of the angle bisectors is called the incenter. The incenter is the center of the incircle of a triangle, which is the largest circle that can be inscribed within the triangle.
The center present in the largest circle that can be inscribed in the triangle is defined as incircle. It is in the equal distance from all the sides present in the triangle , which makes it unique comparing to others.
The line that bisects the angle which is also called as angle bisector is one of the method to find the incenter. It divide the entire triangle into three triangles of same area and length. The triangle includes three bisectors to each angle.
These bisectors are intersected at the same point in the triangle , which is also termed as incenter of the triangle. This is because the incenter is in equal distance from each of the every side of the triangle, and this makes the angle bisectors to divide the triangle into parts which makes the incenter equidistant from all three sides of the triangle.
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Less variables: What is the value of the expression 5a - 7b + c when a =5 , b =3, and c = 1?
3
24
5
39
Answer:
5
Step-by-step explanation:
5(5) - 7(3) + 1 = 5
Iker runs laps on the track each week and increases what he runs by the same amount each Saturday. He began by running 24 laps and on the next Saturday he ran 35. A) How many laps did he start running?
b) How many more laps did he run each week?
c) Write the equation for this situation that models this type of growth:
A) Iker started running 24 laps on the track each week. This is mentioned in the question.
B) Iker ran 11 more laps each week.
C) The equation for this situation would be: y = 11x + 24
Determine the number of lapsTo find out how many more laps he ran each week, we can subtract the number of laps he ran on the first week from the number of laps he ran on the second week: 35 - 24 = 11 So, Iker ran 11 more laps each week.
To write an equation that models this type of growth, we can use the following formula: y = mx + b
Where y is the number of laps he runs, m is the number of additional laps he runs each week, x is the number of weeks, and b is the number of laps he started running.
In this case, m = 11 (the number of additional laps he runs each week) and b = 24 (the number of laps he started running).
So the equation for this situation would be: y = 11x + 24 This equation shows that the number of laps Iker runs each week (y) is equal to 11 times the number of weeks (x) plus the number of laps he started running (24).
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what is the area of a kite calculator?
The area of the kite is 40 square meters, calculated by using the area of a kite formula.
To calculate the area of a kite, you need to know the lengths of both the diagonals. Once you have those values, you can use the following formula to find the area:
Area = (d1 x d2) / 2
where d1 and d2 are the lengths of the diagonals.
Here is an example of how to use this formula:
Let's say you have a kite with diagonals of 8 meters and 10 meters. To find the area, you would use the formula:
Area = (8 x 10) / 2
Area = 40 square meters
So the area of the kite is 40 square meters.
There are also many online calculators available that can help you find the area of a kite if you enter the values of the diagonals.
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Explain what each point on theâ least-squares regression line represents. Choose the correct answer below.A. Each point on theâ least-squares regression line represents theâ y-value of the data set at that corresponding value of x.B. Each point on theâ least-squares regression line represents theâ y-values that would be considered ideal at that corresponding value of x.C. Each point on theâ least-squares regression line represents the predictedâ y-value at the corresponding value of x.D. Each point on theâ least-squares regression line represents one of the points in the data set.
Each point on the least-squares regression line represents a predicted y-value at a given x-value, based on the relationship between the two variables determined through regression analysis.
Regression is a statistical method used to analyze and understand the relationship between two variables. The least-squares regression line is a line of best fit that helps predict the value of one variable based on the value of another.
The correct answer is C, each point on the least-squares regression line represents the predicted y-value at the corresponding value of x.
The line is created by minimizing the sum of the squared differences between the actual y-values and the predicted y-values.
In other words, the line is chosen such that the average difference between the actual and predicted y-values is as small as possible.
Mathematically, the regression line is represented by an equation of the form
=> y = b0 + b1x,
where b0 and b1 are coefficients determined by minimizing the sum of squared residuals.
The predicted y-value for a given x can then be found by plugging in the x-value into the equation.
Complete Question:
Explain what each point on the least-squares regression line represents.\
Choose the correct answer below.
A. Each point on the least-squares regression line represents the y-value of the data set at that corresponding value of x.
B. Each point on the least-squares regression line represents one of the points in the data set.
C. Each point on the least-squares regression line represents the predicted y-value at the corresponding value of x.
D. Each point on the least-squares regression line represents the y-values that would be considered ideal at that corresponding value of x.
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The length of a rectangle is three times its width.
If the perimeter of the rectangle is 80 find its length and width.
The length is 30 unit and width is 10 unit.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
length of a rectangle is three times its width.
Perimeter of the rectangle = 80
let the width be x then length = 3x
So, Perimeter of the rectangle = 80
2( x+ 3x) = 80
4x= 40
x= 10
Thus, the length is 30 unit and width is 10 unit.
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Write and evaluate an expression for the following number line
The expression shown on the number line is 0 - 2 + 4 which is equal to 2.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables using mathematical operations. An equation can be linear, quadratic, cubic and so on, depending on the degree of the variable.
Number line contains numbers equally placed at regular intervals. Negative is shown by moving left while positive is shown by moving right
From the number line shown. It initially starts at 0. It is then moved 2 units left, to get:
0 - 2
Thereafter it is moved 4 units right to get:
0 - 2 + 4
= 2
The expression is 0 - 2 + 4
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Question 9
Jamal's parents borrow $2900.00 from the bank for new appliances for their kitchen. The simple interest rate is 9% per year. How much
interest will they have to pay if it takes them 2 years and 3 months to repay the loan?
The amount of interest after 2 years and 3 months to repay the loan will be $587.25.
What is simple interest?Simple interest is the concept that is used in many companies such as banking, finance, automobile, and so on.
The formula for interest is written as,
I = (PRT)/100
Where P is the principal, R is the rate of interest, and T is the time.
Jamal's parents borrow $2900.00 from the bank for new appliances for their kitchen. The simple interest rate is 9% per year.
The amount of interest after 2 years and 3 months is given as,
I = [$2,900 x 9 x (2 + 3 / 12)] / 100
I = $2,900 x 0.09 x 2.25
I = $587.25
The amount of interest after 2 years and 3 months to repay the loan will be $587.25.
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[tex] \frac{y }{8} + \frac{y}{4} [/tex]
Simplify.
I don't know how to do this, could someone please explain this for me.
y/8 + y/4
Algebraic Fractions
The expression of fractions y/8 + y/4 can be simplify as 3y/8.
How can the expression be simplified?Given that the expression is y/8 + y/4
Then we can find the number number that both 8, and 4 can go in, which is 8. and this will serves as the LCM. then we will start from the first value, 8 will divide 8 in just one times, then times y( numerator) which equals to y. for the right hand side values, 4 will divide 8 in two times which is 2, then times y equalos 2y.
y +2y/8
=(y+2y)/8
= 3y/8
Hence the simplification is 3y/8
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there are 50 586 757 people in south Africa and 44% live in rural areas. How many people live in rural areas
The number of people that live in the rural areas is 22 258 173
What is Percentage?
Percentage is a number or ratio that can be expressed as a fraction of 100.
How to determine this
44% live rural areas when there are 50 586 757 people in South Africa
i.e 44/100 * 50 586 757
= 22 258 173.08
which is approximately 22 258 173 people live in rural areas of South Africa
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Assume that we have two events, A and B, that are mutually exclusive. Assume further that we know P(A) = 0.30 and P(B) =0.40.
1. What is P(A B)?
2. What is P(A | B)?
3. Is P(A | B) equal to P(A)?
4. A student in statistics argues that the concepts of mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent. Is this statement accurate?
5. What general conclusion would you make about mutually exclusive and independent events given the results of this problem?
1) The value of P(A∩B) = 0.
2) The value of P(A|B) = 0.
3) P(A|B) is not equal to P(A). A and B are independent events.
4) The statement "Mutually exclusive events and independent events are really the same, and that if events are mutually exclusive they must be independent." is not accurate.
5) We can conclude that mutually exclusive events have a probability of intersection of zero and are not independent.
1) Since A and B are mutually exclusive, they cannot occur at the same time, so P(A∩B) = 0.
2) The conditional probability of A given B is defined as the probability of A occurring given that B has occurred. Since A and B are mutually exclusive, if B has occurred, then A cannot occur. Therefore, P(A|B) = 0.
3) No, P(A|B) is not equal to P(A). Since B has occurred, the sample space has been reduced to only those outcomes in which B has occurred. Therefore, the probability of A given that B has occurred can only be determined from the portion of the sample space in which both A and B occur.
However, since A and B are mutually exclusive, this probability is zero. Therefore, P(A|B) ≠ P(A).
4) The statement is not accurate. Mutually exclusive events and independent events are different concepts. Two events are mutually exclusive if they cannot occur at the same time, whereas two events are independent if the occurrence of one event does not affect the probability of the other event.
If two events are mutually exclusive, they are not independent because the occurrence of one event precludes the occurrence of the other event.
5) Mutually exclusive events have a relationship where if one event occurs, the other cannot. In contrast, independent events are events where the occurrence of one event does not affect the probability of the other event occurring.
Therefore, we can conclude that mutually exclusive events and independent events are not the same concept, and we must be careful not to confuse them.
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⚠️PLEASE HELP⚠️ URGENT (all separate questions) (middle school math) not advanced I will give everyone who answers this everything good that you can possibly give⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️⚠️
. You get scores of 85 and 91 on two history tests. Write and solve an
inequality to find the scores you can get on your next history test to have
an average of at least 90.
. You and a group of friends wait hour to ride an amusement park ride. You
go on the ride a second time and wait hour. You want to go on a third
time. Write and solve an inequality to find how many minutes you can wait
for your average waiting time to be at most hour. (Hint: Convert the
waiting times to minutes.)
Write and solve an inequality to find the possible
values of x so that the rectangle has an area of more
than 130 square units.
The rectangle is 5 on the left side and
3x + 2 on the bottom
Answer:
8>x
Step-by-step explanation:
A>L×B
where A=area of rectangle,L=length,B=breath
A=>130,L=51,B=3x+2
130>(5)(3x+2)
130>15x+10
130-10>15x
120>15x
8>x
L=3(8)+2=24+2=26
Collin did the work to see if 10 is a solution to the equation StartFraction r Over 4 EndFraction = 2.5.
StartFraction r Over 4 EndFraction = 2.5. StartFraction 10 Over 4 EndFraction = 2.5. 2.5 = 2.5.
Is 10 a solution to the equation?
Yes, because 10 and 4 are both even.
Yes, because if you substitute 10 for r in the equation and simplify, you find that the equation is true.
No, because 10 is not divisable by 4.
No, because if you substitute 10 for r in the equation and simplify, you find that the equation is not true.
Answer:
Yes, because if you substitute 10 for are in the equation and simplify, you find that the equation is true.
Step-by-step explanation:
Yes, because if you substitute 10 for are in the equation and simplify, you find that the equation is true.
A bag has 6 blue cubes, 3 red cubes, and 3 green cubes. If you draw a cube and replace it in the bag 120 times, which of the following amounts would you expect to pull? Select all that apply. A) Pull a red cube 80 times B) Pull more red cubes than blue cubes C) Pull the same number of red and green cubes D) Pull two times as many blue cubes as red cubes E) Pull a blue cube 60 times
Answer: I Don't Know.
Step-by-step explanation: Add a picture.
what is the equation i need to write
The rate of change is $3 per mile and y=3x is the equation which represents the total cost to travel x miles.
What is Slope of Line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.
The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is
m=y₂-y₁/x₂-x₁
From the given table the rate of change or slope is m=8-5/2-1
m=3
The ride cost $3 per mile.
The equation which show the total cost to travel x miles is y=3x.
Hence, the rate of change is $3 per mile and y=3x is the equation which represents the total cost to travel x miles.
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Function (f) is defined by the equation f(x)=3x-7. Find the value of c so that f(c) =20 is true.
The required value of c is 9 so that [tex]f(c) =20[/tex] is true, where the function is defined by the equation f(x)=3x-7.
What is the solution to the equation?A solution to an equation is a number that can be substituted for the variable to provide a true number statement.
To determine the value of c such that [tex]f(c) = 20[/tex], we can simply substitute in the given equation and solve for c.
So, we have:
[tex]f(c) = 3c - 7[/tex]
And, we know that [tex]f(c) = 20[/tex], so we can substitute to get:
20 = 3c - 7
Adding 7 to both sides, we get:
27 = 3c
Dividing both sides by 3, we get:
c = 9
Therefore, the value of c that satisfies the equation [tex]f(c) = 20[/tex] is 9.
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find the size of the angle xyz
give you answer to 1 decimal point
hypotenuse is 15cm and the adjacent is 6
Answer:
Step-by-step explanation:
no
Solve for a.
Set up your equation using the
Pythagorean Theorem.
a² + b² = c²
a² + [?]²=
12
Hint: Plug in the given leg
length for b.
12
a
9
Enter help
Answer: a²+ 9² = 12² (look at the image for the solution)
Step-by-step explanation:
-1/6 divided by 2/3(9 - 3/4) - 1/2
Answer:
-1/30
Step-by-step explanation:
-1/6 divided by 2/3(9 - 3/4) - 1/2
2/3(9 - 3/4) - 1/2
= 18/3 - 6/12 - 1/2
= 72/12 - 6/12 - 6/12
= 60/12
= 5
We have
-1/6 ÷ 5
= -1/6 x 1/5
= -1/30
what is 150 kilos in pounds?
1 kilogram is equal 2.2046 pounds.
Therefore, 150 kilograms is equal to 330.693 pound.
Pound:
A pound (commonly abbreviated lb, plural lbs) is a unit used to measure the mass of something. It is used in the imperial system and the US trade system. There are various definitions. The most commonly used group of definitions today is the International Pound Sterling. This is equal to 0.45359237 kilograms, divided into 16 avoirdupois ounces.
Kilogram:
The kilogram is the unit of mass in the International System of Units (SI), expressed as kg. A unit of measurement widely used worldwide in science, technology and commerce, colloquially referred to simply as the kilogram. It means "a thousand grams."
Kilograms are defined in seconds and meters based on basic physical constants. This allows suitably equipped metrology laboratories to calibrate mass measuring instruments such as Kibble balances as a basic standard for determining accurate mass in kilograms.
Converting 150 kg to US pounds. We'll convert the formula in two different versions.
First one:
kilograms * 2.20462262 = 330.69339300 pounds.
The first version of the formula gives the most accurate result.
Sometimes even the smallest differences can matter. So, if you need accurate results, this formula will be the best option for figuring out how many pounds are in 150 kg.
Now,
we can also go to the second version of the formula and calculate how many pounds is 150 kg.
For the second version of the formula below:
This may be the best option if you want to quickly convert 150 kg to pounds, for example while shopping. It is important to remember that the results are imprecise.
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The point G( – 5, – 1) is rotated 180° counterclockwise around the origin. What are the coordinates of the resulting point, G'?
Answer:
the coordinates of the resulting point G' are (5, 1).
Step-by-step explanation:
When a point is rotated 180° counterclockwise around the origin, it is reflected across the x-axis and y-axis. This means that the x-coordinate and y-coordinate of the point are both negated.
So, for the point G(-5, -1), the x-coordinate becomes -(-5) = 5 and the y-coordinate becomes -(-1) = 1.
Answer:
(5,1)
Step-by-step explanation:
Rotating 180 degrees about the origin means that there is a reflection against the y-axis and x-axis. Therefore, the x and y values will change their signs.
Hence, the new coordinate would be (5,1)
HELPPP PLEASE WILL GIVE BRAINLIEST
Answer: look at the images for the answers and solutions
Step-by-step explanation:
What are the first four terms of an arithmetic. Sequence if the first term is -3 and the common difference is 7
The first four terms of the arithmetic sequence are -3, 4, 11, 18.
How to find the termsIf the first term of an arithmetic sequence is -3 and the common difference is 7, then we can use this formula to find the nth term of the sequence:
Un = a + (n - 1)d
Where
Un is the nth term
a is the first term
d is the common difference, and
n is the position of the term in the sequence.
To find the first four terms of the sequence, we can substitute n = 1, 2, 3, 4 into the formula and solve for Un:
n = 1:
U1 = -3 + (1 - 1)7 = -3
n = 2
U2 = -3 + (2 - 1)7 = 4
n = 3
U3 = -3 + (3 - 1)7 = 11
n = 4
U4 = -3 + (4 - 1)7 = 18
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find the surface area of a Sphere of diameter
36 cm. tak x=22 7
Answer: The surface area of a sphere can be calculated using the formula:
A = 4 * π * r^2
Where r is the radius of the sphere.
The diameter of the sphere is 36 cm, so the radius can be found by dividing the diameter by 2:
r = 36 cm / 2 = 18 cm
Now that we have the radius, we can plug it into the formula:
A = 4 * π * r^2 = 4 * π * (18 cm)^2 = 4 * π * 324 cm^2 = 1296 * π cm^2
Since π is approximately equal to 3.14, we can get an approximate answer:
A ≈ 1296 * 3.14 = 4071.84 cm^2
So the surface area of the sphere with a diameter of 36 cm is approximately 4071.84 square centimeters.
Step-by-step explanation:
what is 1 usd to thai baht?
Answer: 1 usd to thai baht is 33.44 thai baht or 33 thai baht
Step-by-step explanation:
There's no need for an explanation for this as you can just search this on the internet.
Two friends shop for fresh fruit. Elena buys a watermelon for 7.45 and 5 pounds of cheeries. Taniy buys a pineapple for 4.35 and 4 pounds of cheeries. Use the variable p to represent the price, in dollars, per pound of cheeries.
The expression that represents how much more Elena spent is $3.2 + p
What is an expression?An expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them. In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
here, we have,
The variable p represents the price, in dollars, per pound of cherries.
Elena buys a watermelon for $ 6.35 and 5 pounds of cherries.
So, the price of the cherries bought by Elena will be = 5*p
Then the total amount spent by Elena during her purchase of fresh fruits is:
$6.35 + 5*p
On the other hand, Tania buys a pineapple for $ 3.15 and 4 pounds of cherries. So, the price of the cherries bought by Tania will be 4*p
Therefore, the total amount spent by Tania during her purchase of fresh fruits is:
$3.15 + 4*p
You want to determine an expression to represent how much more Elena spent. That is, you want to determine the difference between the money spent by Elena and the money spent by Tania, which represents how much more Elena spent:
Total amount spent by Elena on fresh fruits - Total amount spent by Tania on fresh fruits
$6.35 + 5*p - ($3.15 + 4*p)
Solving:
$6.35 + 5*p - $3.15 - 4*p
($6.35 - $3.15) + (5*p - 4*p)
$3.2 + p
The expression that represents how much more Elena spent is $3.2 + p
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I've been having trouble figuring out trigonometry and I really could use somebody who knows this kind of stuff to help me out. Can anyone answer this by showing me how to do it and what the answer would be?
Answer: The positive acute angle between the x-axis and the angle's terminal side, or the angle's terminal side wherever it is, measured so that the reference angle is positive and less than 90° (or 2) is known as the reference angle for a given angle in trigonometry.
This is all I know I don't have a class like this sorry hope this helps you!