The missing angle measures are:
m2F = 50 degrees
m2H = 125 degrees
m2G = 5 degrees
m2C = 158 degrees
How to find the missing angle measures?
Since triangle ABC is similar to triangle FGH, the ratios of their corresponding angles are equal. Let's call the missing angles m2F, m2H, m2G, and m2C.
From the given information, we have:
m2F / mLA = m2H / mzB
So, we can find m2H by cross-multiplying and solving for m2H:
m2H = (mzB * m2F) / mLA
Since we don't know m2F, we can use the fact that the sum of the angles in a triangle is 180 degrees:
m2F + m2H + 75 = 180
So,
m2F + ((mzB * m2F) / mLA) + 75 = 180
Expanding and solving for m2F:
m2F + (75 * m2F / 22) + 75 = 180
(22 + 75) * m2F / 22 + 75 = 180
97 * m2F / 22 + 75 = 180
97 * m2F / 22 = 180 - 75
97 * m2F / 22 = 105
m2F = 105 * 22 / 97 = 50
So, the missing angle measures are:
m2F = 50 degrees
m2H = (75 * 50) / 22 = 125 degrees
m2G = 180 - 50 - 125 = 5 degrees
m2C = 180 - 22 = 158 degrees
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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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In a chemistry experiment, 50,000
independent samples need to be tested for the presence of a chemical compound. To decrease the amount of testing, 5 samples at a time are combined and tested together. A combined sample will result in a negative test only if each of the five component samples is negative for the chemical compound.
If the probability of an individual sample testing positive is 0.2, what is the probability that a combined sample tests positive?
Note that the probability that a combined sample tests positive is 0.67232 or 67.232%.
What is the rationale for the above response?Let P(pos) be the probability that an individual sample tests positive.
We know P(pos) = 0.2,
so the probability that an individual sample tests negative is:
P(neg) = 1 - P(pos) = 0.8.
Let P(combined_neg) be the probability that a combined sample tests negative (i.e., all five component samples are negative).
Since the component samples are independent, we can calculate
P(combined_neg) as the product of their individual probabilities:
P(combined_neg) = P(neg) x P(neg) x P(neg) x P(neg) x P(neg)
= 0.8⁵
= 0.32768
Therefore, the probability that a combined sample tests positive (i.e., at least one of the five component samples tests positive) is:
P(combined_pos) = 1 - P(combined_neg)
= 1 - 0.32768
P(combined_pos) = 0.67232
Thus, the probability that a combined sample tests positive is 0.67232 or 67.232%.
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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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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.
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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Find X. round to nearest tenth using law of cosines, please help!
Step-by-step explanation:
Using the modified picture attached to this answer;
Parameters
x = Angle X
8 = x
19 = y
14 = z
Therefore,
Using Cosine rule
x² = y² + z² - 2·y·z·cos X
Masking Cos X the subject of the formula,
Cos X = (y² + z² - x²) / (2·y·z)
Cos X = (19² + 14² - 8²) / (2·19·14)
Cos X = (361 + 196 - 64) / 532
Cos X = (557 -64) / 532
Cos X = 493 / 532
Cos X = 0.92669
But, since we are looking for angle X, we have to divide both sides by Cos, therefore having;
X = Cos-¹ [0.92669]
Since 1 / Cos = Cos-¹
Therefore,
X = 22.075
And since x, our unknown, is equal to angle X, then,
x = 22.1 (to the nearest tenth)
What is the minimum interior angle possible for Aregular polygon Why?
Answer:
Step-by-step explanation:
The minimum interior angle possible for a regular polygon is given by the formula:
interior angle = (180° * (n-2)) / n
where n is the number of sides in the polygon. The formula is based on the fact that the sum of the interior angles of a polygon with n sides is equal to (n-2) * 180°.
As n increases, the value of the interior angle decreases and approaches the minimum value of 180°. However, for a regular polygon, all interior angles must be equal, so the minimum possible value is given by the formula above.
For example, consider a regular hexagon (n=6). The minimum interior angle is given by:
interior angle = (180° * (6-2)) / 6 = 120°
So, the minimum interior angle possible for a regular polygon is 120°.
a
= 13 m,
b
= 9 m and
c
= 2 m for the triangle shown below.
Work out the value of
x
, giving your answer as an exact surd.
The diagram is not drawn accurately
Answer:
2√21
Step-by-step explanation:
let the sides of bigger triangle be a, b and d.
then,
a²= b² + d² [ by Pythagoras theorem]
13² = 9² + d²
d² = 13² - 9²
d²= 169 - 81
d² = 88
d = √88
Now, the sides of smaller triangle are c, x, and d
by Pythagoras theorem,
d² = c²+x²
(√88)² = 2² + x²
88 - 4 = x²
x² = 84
x = √84
x= 2x2x3x7
x = 2√21
Therefore, the value of x is 2√21
Hope it's helpful..
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 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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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 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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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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bro whats, solve the following system of linear equations by elimination
5x + y = 9
10x - 7y =-18
Answer:
x=1,y=4
Step-by-step explanation:
5x+y=9
5x=9-y
x=(9-y)/5
put it in 10x-7y=-18
10x((9-y)/5)-7y=-18
18-2y-7y=-18
-9y=-36
y=4
x=(9-4)/5=1
Answer:
x = 1
y = 4
Step-by-step explanation:
5x + y = 9
10x - 7y = -18
Time the first equation by -2
-10x - 2y = -18
10x - 7y = -18
-9y = -36
y = 4
Now put 4 in for y and solve for x
5x + y = 9
5x + 4 = 9
5x = 5
x = 1
Let's check
5(1) + 4 = 9
5 + 4 = 9
9 = 9
So, x = 1 and y = 4 is the correct answer.
-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
Simplify.
68.6³ = 61²]
65
I need someone to answer this please.
The equations of the functions are C(x) = 2.5x + 60, R(x) = 10x and P(x) = 7.5x - 60
How to determine the equationsDefining the variables, we have
x: the number of tie-dye T-shirts produced and soldP(x), C(x) and R(x) as the functionsFor the equation of the money they spend:
The cost of materials is $2.50 per T-shirtThe fixed cost for dyeing materials is $60So, the equation for the total money spent can be written as:
C(x) = 2.5x + 60
For the equation of the money they collect:
The cost of selling is $10 per T-shirtNo fixed costSo, the equation for the total money collected can be written as:
R(x) = 10x
To calculate the profit from selling, we subtract the cost from the revenue
So, we have
P(x) = 10x - 2.5x - 60
Simplifying this equation, we get:
P(x) = 7.5x - 60
Hence, the profit equation is P(x) = 7.5x - 60
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What is operationalization of variable in research?
Operationalization of variables in research involves defining a concept in a way that it can be measured or observed.
It is the process of taking abstract concepts, such as attitudes, beliefs, or behaviors, and defining them in a way that they can be measured using empirical methods. This is done by creating a set of specific and concrete indicators or measures that represent the concept being studied. The operationalization of variables is a critical step in the research process, as it ensures that the data collected is both reliable and valid, and can be used to draw meaningful conclusions and make predictions.
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Use the bar graph to find the experimental probability of rolling a 5.
Times rolled
25
20
10
Rolling a Number Cube
16 15
1 2
19 20
3
Number rolled
456
The experimental probability is
The experimental probability of rolling a 5 is 25/56, or 0.446.
What is Probability?Probability is a field of mathematics that deals with the chance of certain events happening. It is used to calculate the likelihood of different outcomes in a given situation. Probability helps to make decisions for a variety of real-world applications, such as predicting the weather, deciding whether to invest in stocks and calculating insurance rates. Probability is based on the idea that all outcomes are equally likely, and can be expressed as a number between 0 and 1, where 0 means something is impossible and 1 means something is certain.
The experimental probability is calculated by taking the total number of times a number was rolled and dividing it by the total number of rolls. In this case, the total number of times a 5 was rolled is 25, and the total number of rolls is 56. Therefore, the experimental probability of rolling a 5 is 25/56, or 0.446.
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Can anyone help me on this?
Answer:
A = 80ft^2
Step-by-step explanation:
Area of trapezoid = (a + b/2) x h
A = ((6 + 10)/2) x 10
A = (16/2) x 10
A = 8 x 10
A = 80ft^2
Answer:
Area is 80 square feet
Step-by-step explanation:
The shape of the bedroom is a trapezoid
h = perpendicular height of trapezoid
Area of a trapezoid:
[tex]\frac{1}{2}[/tex]×(Sum of parallel sides)× h
= [tex]\frac{1}{2}[/tex] × [(10 + 6) feet] × (10 feet)
= [tex]\frac{1}{2}[/tex] × (16 feet) × (10 feet)
∴ Area of Skylar’s Bedroom = 80 square feet
= [tex]80 ft^{2}[/tex]
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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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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f(x) = 2x + 1 value of f(5)
Answer:
[tex]\huge\boxed{\sf f(5) = 11}[/tex]
Step-by-step explanation:
Given function:f(x) = 2x + 1
Put x = 5
So,
f(5) = 2(5) + 1
f(5) = 10 + 1
f(5) = 11[tex]\rule[225]{225}{2}[/tex]
A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4. The correct answer is:
Slope: 2y-intercept: (0,1) What is intercept?In Math's, an intercept is a point on the y-axis, through which the slope of the line passes. It is y-coordinate of a point where a straight line or a curve intersects the y-axis. This is represented when we write the equation for a line, y = mx+c, where m is slope and c is the y-intercept. There are basically two intercepts, x-intercept and y-intercept.
Rewrite the function as an equation:
→ y = 2x + 1
Use the slope-intercept form to find the slope and y-intercept.
The slope-intercept form is y = mx + b where m is the slope of b is the y-intercept:
→ y = mx + b
Find the values of m and b using the form y = mx + b:
→ m = 2
→ b = 1
Therefore, A mathematical symbol, or combination of symbols, representing a value, or relation. Example: 2 + 2 = 4. The correct answer is:
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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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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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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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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)
I need help with the question ASAP
Answer:
3. d
4.b
5.a
6. is 15
Step-by-step explanation:
mn=5
no=5
op=10
pq=10
describe the characteristics of each parabola without graphing
f (x) = -3x^2
A. compression by 3, reflected over x-axis
B. stretch by 3, reflected over x-axis
C. stretch by 3, reflected over y-axis
D. compression by 3, reflected over y-axis
The characteristics of the given parabola f(x) = -3x² are, A. Compression by 3, reflected over the x-axis.
What is a parabola?A parabola is a cross-section cut out of the cone and represented by an equation.
Here,
The general form of a parabola is f(x) = ax² + bx + c, where a, b, and c are constants. In this case, the given equation is f(x) = -3x², which means that a = -3, b = 0, and c = 0.
The sign of "a" determines the direction of the parabola. When "a" is negative, the parabola opens downward, and when "a" is positive, the parabola opens upward. In this case, a = -3, which means the parabola opens downward.
If a parabola is reflected over the x-axis, the sign of "a" remains the same. If it is reflected over the y-axis, the sign of "a" changes. In this case, the parabola is reflected over the x-axis, which means the sign of "a" remains negative.
Therefore, the characteristics of the given parabola f(x) = -3x² are, A. Compression by 3, reflected over the x-axis.
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