The measure of angle 2 is 140 and <3 is 20 degree.
What is Rhombus?A parallelogram is a particular instance of a rhombus. The opposing sides and angles in a rhombus are parallel and equal. A rhombus also has equal-length sides on each side, and its diagonals meet at right angles to form its shape. The rhombus is also referred to as a diamond or rhombus.
As, Rhombus have angles which are opposite to each other are equal.
So, <1 = <2 = 140
Also, Consecutive angles are equal to 180° which shows the angle between <1 and <2 measure
= 180- 140
= 40
and, <3 = 1/2 <1
<3 = 1/2(40)= 20
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Which point is located at -1 3/8?
Point C is located at -1 3/8
Hope that helps!
PLEASE HELP! LIMITED TIME! URGENT!
Part of Thor's job at a nonprofit organization, Rag Na Care, is to simply answer the phone to collect donations. The data collected shows a weak
negative linear relationship between the number of hours he worked each week, a, and the amount of donations in dollars, y, that the organization
collected each week.
a. What does it mean for the relationship between the variables when the correlation is weak in this context?
Answer:
Sure In this context, a weak negative linear relationship between the number of hours worked and the amount of donations collected means that as the number of hours worked by Thor each week increases, the amount of donations collected by the organization each week decreases, but the relationship is not very strong.
When we say that the correlation between two variables is weak, we mean that there is a low degree of association between them. In this case, the negative correlation suggests that there is a tendency for the amount of donations collected to decrease as the number of hours worked increases, but the relationship is not very strong, meaning that there is a lot of variability in the data and it is difficult to make strong predictions or conclusions based on this relationship alone.
It is important to note that correlation does not necessarily imply causation, so a weak negative linear relationship between the number of hours worked and the amount of donations collected does not necessarily mean that one variable causes the other. Other factors may be influencing the amount of donations collected by the organization each week, and further analysis would be required to determine the nature and strength of these relationships.
Step-by-step explanation:
1,629 ÷ (6 + 9 ÷ 3) simplify
Answer:
181
Step-by-step explanation:
To simplify this expression, we need to apply the order of operations (PEMDAS):
First, we evaluate the expression inside the parentheses: 9 ÷ 3 = 3.
Then, we add 6 + 3 = 9.
Finally, we divide 1,629 by 9 to get the answer:
1,629 ÷ 9 = 181.
Therefore, 1,629 ÷ (6 + 9 ÷ 3) simplifies to 181.
PLEASE HELP!
Over the course of 24 hours, the tides on Earth complete one full cycle from low tide to high tide and back down again. On one particular beach, the tide drops to 2 feet below sea level for low tide and reaches 4 feet above sea level for high tide. Write a possible trigonometric function that would model the tide situation for
this beach.
Answer:picture is not clear on my side, please re-upload thx!
Step-by-step explanation:
Just need help with this question..
Graph appears to intersect the X axis in between 20 and 22 and algebraically the estimate of zero is 21.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Given a linear function which represents the profit of Bethany, y after x hours of dog walking.
(a) From the graph, we have to estimate the zero.
The graph seems to intersect the X axis in between 20 and 22, approximately 21.
(b) To solve this algebraically, we have the profit function,
y = 23x - 480
When y = 0,
23x - 480 = 0
23x = 480
x = 20.87 ≈ 21
Hence the graphical method gives the same estimate as the algebraic method.
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GROUP 'D' (4×5=20) A person purchases a piece of land in Rs.80, 00,000 in 2075 B.S. At the same time of 2075 B.S. a house is constructed on a piece of land in Rs. 2,70,00,000. If the price of land increases at the rate of 20% per annum and the price of house depreciates at the rate 20% per annum. After how many years the price of land and the price of house will be equal? Find it. combined solid is formed with the combination of hemisphere and cone having radius
After 2.5 years the price of land and the price of house will be equal.
What is Simple interest?A quick and easy method of calculating the interest charge on a loan is called a Simple interest.
Given that;
A person purchases a piece of land in Rs.80, 00,000 in 2075 B.S.
And, At the same time of 2075 B.S. a house is constructed on a piece of land in Rs. 2,70,00,000.
Since, The price of land increases at the rate of 20% per annum.
Hence, We get;
A = 80,00,000 (1 + 20/100)ⁿ
And, The price of house depreciates at the rate 20% per annum.
Hence, We get;
A = 2,70,00,000 (1 - 20/100)ⁿ
Let after n years the price of land and the price of house will be equal.
Thus, We get;
80,00,000 (1 + 20/100)ⁿ = 2,70,00,000 (1 - 20/100)ⁿ
8 (120/100)ⁿ = 27 (80/100)ⁿ
8 (6/5)ⁿ = 27 (4/5)ⁿ
Take log both side,
log 8 + n (log 6 - log 5) = log 27 + n (log 4 - log 5)
0.9 + n × 0.8 = 1.4 + n × 0.6
0.9 + 0.8n = 1.4 + 0.6n
0.2n = 0.5
n = 2.5 years
Therefore, After 2.5 years the price of land and the price of house will be equal.
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Find the area of the blue-shaded region. Please help I need it asap. The answer is 20.0m squared I cannot figure out the work for it
The area of the blue-shaded region is 19.95 m²
What is area?Area is defined as the total space taken up by a flat (2-D) surface or shape of an object.
Given that, a rectangle with length 14 m, and diagonal 15.5 m, a parallelogram has been cut out of it, we need to find the area remaining,
Using the Pythagoras theorem,
15.5² = 14²+w² [width]
w² = 240.25-196
w² = 44.25
w = 6.65
Therefore, the width of the rectangle is 6.65 m
That mean, the height of the parallelogram is 6.65 m,
The area of the blue-shaded region, is calculated by subtracting the area of the parallelogram by the area of the rectangle,
Area of the remaining region = 14×6.65-11×6.65
= 6.65(14-11) = 6.65×3
= 19.95 m²
Hence, the area of the blue-shaded region is 19.95 m²
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Solve the equation |2x-3| =7
Smallest Solution:
Greatest Solution:
Answer:
5 or -2
Step-by-step explanation:
|2x-3| can equal either (2x-3) or -(2x-3) thus
(2x-3) = 7
2x = 10
x = 5
-(2x-3) = 7
-2x = 4
x = -2
Answer: it’s 5 or -2, |2x-3| can equal either (2x-3) or -(2x-3) thus(2x-3) = 72x = 10x = 5-(2x-3) = 7-2x = 4x = -2
Step-by-step explanation: hope this helps0^0
Which function is equivalent to y=x^2-8x+10
Therefore, a function equivalent to y = x² - 8x + 10 is: y = (x - 4)² + 4.
What is function?In mathematics, a function is a relation between a set of inputs (called the domain) and a set of possible outputs (called the range), with the property that each input is associated with exactly one output. Functions are often denoted using function notation, such as f(x) or g(y), where the letter in parentheses represents the input and the expression to the right of the parentheses represents the output. Functions are used in many areas of mathematics, science, and engineering to model real-world phenomena and to solve problems. They are essential tools for analyzing data, making predictions, and creating mathematical models of physical and natural systems.
Here,
The function y = x² - 8x + 10 is a quadratic function, which has a U-shaped graph. To find a function that is equivalent to this function, we can start by completing the square, which involves adding and subtracting a constant term to create a perfect square trinomial. We can then write the function in vertex form, which is y = a(x - h)² + k, where (h, k) is the vertex of the parabola.
Completing the square, we get:
y = x² - 8x + 10
= (x² - 8x + 16) - 6 + 10 // Add and subtract (8/2)² = 16 to create a perfect square
= (x - 4)² + 4
Now we can see that the vertex of the parabola is at (4, 4). We also see that the coefficient of the squared term is 1, which means the parabola opens upward.
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the sum of 106 and h
The sum of 106 and h can be written as an expression in the following way: 106 + h
This expression represents the sum of the two numbers, 106 and h. We can simplify this expression by combining like terms, but since h is a variable and 106 is a constant, we cannot combine them. Therefore, the expression remains as 106 + h.
In conclusion, the sum of 106 and h is represented by the expression 106 + h.
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You just got your first job and are planning on renting your own apartment. What steps should you follow to help make this process easier?
Answer:
Determine Your Budget.
Check Your Credit.
View Multiple Rentals.
Consider Roommates.
Consider a Cosigner.
Gather Your References.
Check Out the Neighborhood.
Check All the Websites.
Jim, an artist, plans to paint and sell some miniature paintings. He just bought some brushes
for $1, and paint and canvas for each painting costs $44; he will sell each painting for $45.
Once Jim sells a certain number of his paintings, he will be breaking even. How much will Jim
have earned? How many paintings will that be?
Answer:
Step-by-step explanation:
Let's begin by calculating Jim's total cost for creating one painting:
Cost of paint and canvas + Cost of brushes = $44 + $1 = $45
This means that Jim makes a profit of $45 - $45 = $0 per painting sold until he breaks even.
To determine how many paintings Jim needs to sell to break even, we can set up an equation:
Total Cost = Total Revenue
Let's say Jim sells x paintings. Then his total revenue would be:
Total Revenue = $45x
His total cost would be the cost of materials plus the cost of brushes multiplied by the number of paintings:
Total Cost = $45 + $1)x = $46x
Setting these equal, we get:
$46x = $45x
Solving for x, we get:
x = 45
So Jim needs to sell 45 paintings to break even.
Once he has sold 45 paintings, he will have earned:
Total Revenue = $45 x 45 = $2025
So Jim will have earned $2025 after selling 45 paintings.
Answer:
Step-by-step explanation:
To break even, Jim's total revenue from selling his paintings should be equal to his total cost of producing them, including the cost of materials and the cost of the brushes. Let's call the number of paintings he needs to sell to break even as "x".
The cost of producing each painting is $44 + $1 = $45.
The revenue from selling each painting is $45.
So, Jim's total revenue from selling x paintings would be:
Total revenue = Price per painting x Number of paintings sold
Total revenue = $45 x x
Total revenue = $45x
Jim's total cost of producing x paintings would be:
Total cost = Cost per painting x Number of paintings produced + Cost of brushes
Total cost = $45 x x + $1
Total cost = $45x + $1
For Jim to break even, his total revenue must equal his total cost:
Total revenue = Total cost
$45x = $45x + $1
Solving for x:
$45x - $45x = $1
0 = $1
This is a contradiction, meaning that the situation is impossible. It is impossible for Jim to break even by selling his paintings at the given prices. If he sells each painting at $45, which is the same price he paid to produce it, he will not make any profit. In fact, he will lose $1 for every painting he sells due to the cost of the brushes.
If Jim wants to break even or make a profit, he will need to increase the selling price of his paintings or find ways to reduce the cost of producing them.
-x^3-3x^2=6x+4 find all the zeros of the equation
This is consistent with the solutions for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 being x = 1 and x = 5.
What is equation?An equation is a mathematical statement that expresses the equality of two expressions. It consists of one or more terms, each of which contains one or more variables. The terms are separated by an equal sign (=) and are usually written in a standard form known as an algebraic equation. Equations can be used to model and solve problems in a wide variety of fields, from physics and chemistry to economics and finance.
The graph of the quadratic equation is a parabola that opens upward and intersects the x-axis at two points. The x-intercepts occur when the equation is equal to zero, so the x-intercepts for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 are the solutions for x. These solutions are x = 1 and x = 5.
The graph of the quadratic equation also shows that the two solutions of the equation, x = 1 and x = 5, are the x-intercepts of the parabola. This means that when x equals 1 or 5, the equation is equal to zero, so the x-intercepts are the solutions of the equation. This is consistent with the solutions for the equation [tex]x^{2}[/tex] - 6x + 5 = 0 being x = 1 and x = 5.
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Many fire stations handle emergency calls for medical assistance as well as calls requesting firefighting equipment. A particular station says that the probability that an incoming call is for medical assistance is 0.63. This can be expressed as
P(call is for medical assistance) = 0.63.
(b) What is the probability that a call is not for medical assistance?
(c) Assuming that successive calls are independent of one another, calculate the probability that two successive calls will both be for medical assistance.
(d) Still assuming independence, calculate the probability that for two successive calls, the first is for medical assistance and the second is not for medical assistance.
(e) Still assuming independence, calculate the probability that exactly one of the next two calls will be for medical assistance. (Hint: There are two different possibilities. The one call for medical assistance might be the first call, or it might be the second call.)
(b) The probability that the call is not for medical assistance = 0.37
(c) The probability that two successive calls will both be for medical assistance = 0.3969
(d) The probability that the first is for medical assistance and the second is not for medical assistance = 0.2331
(e) The probability that exactly one of the next two calls is going to be for medical assistance = 0.4662
Define Probability.The probability of an event is the proportion of favourable outcomes to all other possible outcomes. The symbol x can be used to denote how many successful outcomes there were in an experiment with 'n' outcomes. The formula below can be used to determine a given event's probability:
Probability (Event) = Positive Results/Total Results
= x/n
Given P (call for medical assistance) = 0.63
This means that out of all incoming calls to the fire station, the probability that the call is for medical assistance is 0.63 or 63%. The complement of this event, which is the probability that an incoming call is NOT for medical assistance, is:
P (Not Medical Assistance) = 1 - P (Medical Assistance)
= 1 - 0.63
= 0.37
Now, assuming that successive calls are independent of one another, the probability that two successive calls will both be for medical assistance will be:
P (2 calls for medical assistance)
= 0.63 × 0.63
= 0.3969
The probability that the first is for medical assistance and the second is not for medical assistance will be:
P (1st for medical assistance × 2nd for not medical assistance)
= 0.63 × 0.37
= 0.2331
The probability that exactly one of the next two calls is going to be for medical assistance will be:
P (Exactly 1 call for medical assistance)
= (0.63×0.37) + (0.63×0.37)
= 0.2331 + 0.2331
= 0.4662
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let $pqr$ be an equilateral triangle, centered at $o.$ a point $x$ is chosen at random inside the triangle. find the probability that $x$ is closer to $o$ than to any of the vertices. (in other words, find the probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$)
The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,
⇒ 1/3
What is mean by Probability?The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
Given that;
Let $pqr$ be an equilateral triangle, centered at $o$ a point $x$ is chosen at random inside the triangle.
Hence, The probability that $xo$ is shorter than $xp,$ $xq,$ and $xr.$ is,
⇒ 1/3
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You insure your home for $125,000. You want to be safe and add coverage on the contents, so you take 55% on the contents. How much coverage will you have on the contents of your home?
The amount of coverage that you will have on the contents of your home would be = $68,750
How to calculate the amount of coverage for contents of your home?The total amount of money that was insured for the house = $125,000
The percentage of insurance that was left for the contents of the house = 55% of insurance.
That is;
= 55/100 × $125,000
= 6875000/100
= $68,750.
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Use this table to answer the question. Round to 2 decimal places.
Car Plane Train Total
Green 120 250 500 870
Blue 150 350 750 1250
Yellow 170 200 450 820
Red 200 300 300 800
Brown 220 450 320 990
Total 860 1550 2320 4730
What percent of the total are made up of Yellow Trains?
Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.
It's unclear what the percentages mean.A percentage that corresponds to one tenth of an amount. One percent, represented by the symbol 1%, is equivalent to one hundredth of something; hence, 100 percent represents the complete object, and 200 percent represents twice the amount given.
According to the table:
The total number of Yellow Trains is 450.
The total number of all modes of transportation is 4730.
To calculate the percentage of the total that Yellow Trains make up, we can use the following formula:
percentage = (part/whole) x 100
Substituting the values we have:
percentage = (450/4730) x 100
percentage = 0.095 x 100
percentage = 9.5%
Therefore, Yellow Trains make up 9.5% of the total modes of transportation in the table.
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Help me I will mark brainliest!!!!
The area of a circle with a diameter of radius 14 inches is given as follows:
A = 153.86 inches².
What is the area of a circle?The area of a circle of radius r is given by π multiplied by the radius squared, as follows:
A = πr².
The radius, representing the distance between the center and a point on the circumference of the circle, has the measure defined as half the diameter, hence it is given as follows:
r = 7 inches.
Hence the area of the circle with radius of 7 inches is given as follows:
A = 3.19 x 7²
A = 153.86 inches².
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Please help me my grade is suffering and I need slot of these questions to be correct I will try and ward brainliest
The length of ML in the line segment is 35 units.
How to find the line segment ML?The figure below has the following length as follows:
LN = 79 units
Let's find ML in the line segment as follows:
LM + MN = LN
Hence,
LM = 5y - 5
MN = 4y + 12
Therefore,
LN = 5y - 5 + 4y + 12
79 = 5y - 5 + 4y + 12
79 = 9y + 7
79 - 7 = 9y
72 = 9y
divide both sides by 9
y = 72 / 9
y = 8
Therefore,
ML = 5(8) -5
ML = 40 - 5
ML = 35 units
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In a population of 6000 cave-dwelling fish, eyesight is under selection. Fish that are homozygous for allele A1 have good eyesight, fish that are homozygous for A2 are blind and fish that are heterozygous have poor eyesight. In the dark caves that these fish live in, the cost of good eyesight is higher than the benefits and having good eyesight is thus deleterious. Blind fish have a selective advantage of 0.25, fish with poor eyesight have a selection coefficient of 0.05. Which statement is true?
I. Fish with good eyesight have a fitness W = 0
II. The trait blindness is likely to increase in this population
I
II
Both are false
Both are true
Answer: I am in high school so this may not be the best answer, but I would say that eventually eye sight would simply become useless to the fish because they live in a cave and don’t really need to see, there for I would say that the second answer is correct.
PLEASE HELPPPP
A student is graduating from college in six months but will need a loan in the amount of $3,725 for the last semester. The student may receive either an unsubsidized Stafford Loan or a PLUS Loan. The terms of each loan are: Unsubsidized Stafford Loan: annual interest rate of 4.65%, compounded monthly, with a balance of $3,901.95, at the time of repayment PLUS loan: annual interest rate of 5.65%, compounded monthly with payment deferred until graduation Which loan will have a lower balance and by how much at the time of repayment? The Stafford Loan will have a lower balance by $70.47 at the time of repayment. The PLUS Loan will have a lower balance by $70.47 at the time of repayment. The Stafford Loan will have a lower balance by $16.72 at the time of repayment. The PLUS Loan will have a lower balance by $16.72 at the time of repayment.
The loan that will have a lower balance is;
Option B: The PLUS Loan will have a lower balance by $70.47 at the time of repayment.
How to Identify the best loan offer?To determine which loan will have a lower balance at the time of repayment, we need to calculate the total amount of interest that will be accrued on each loan.
1) For the unsubsidized Stafford loan:
The loan amount is $3,725.
The annual interest rate is 4.65%, compounded monthly. This means the monthly interest rate is 4.65%/12 = 0.3875%.
The loan will be repaid in 6 months, so there will be 6 monthly compounding periods.
Using the formula for compound interest, the balance of the loan at the time of repayment will be:
balance = principal x (1 + monthly interest rate)^number of compounding periods
balance = $3,725 x (1 + 0.003875)^6
balance = $3,901.95
So the balance of the unsubsidized Stafford loan at the time of repayment will be $3,901.95.
2) For the PLUS loan:
The loan amount is $3,725.
The annual interest rate is 5.65%, compounded monthly. This means the monthly interest rate is 5.65%/12 = 0.4708%.
The loan will be deferred until graduation, which is in 6 months, so there will be 6 monthly compounding periods.
Using the formula for compound interest, the balance of the loan at the time of repayment will be:
balance = principal x (1 + monthly interest rate)^number of compounding periods
balance = $3,725 * (1 + 0.004708)^6
balance = $3831.47
So the balance of the PLUS loan at the time of repayment will be $3831.47
Difference in balance = $3,901.95 - $3831.47
= $70.47
Therefore, the PLUS loan will have a lower balance at the time of repayment, by an amount of $70.47
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The point (7,-9) lies on a circle. What is the length of the radius of this circle if the center is located at (5,-7)
I think the radius would be 2
A central angle is an angle whose vertex is at the center of a circle. Find the AOC
I. The correct statement is: m<AOB = m<BOC
The measures of the angles are:
II. m<BOC = 53 degrees.
III. m<AOC = 106 degrees.
How to Find the Measure of a Central Angle?When a segment bisects an angle, it forms two equal angles. Therefore, we have following which explains how to find the measure of the given central angle.
I. <AOC is bisected by segment OB into: AOB and BOC, which are equal. Therefore:
m<AOB = m<BOC
II. m<AOB = 53 degrees, therefore,
m<BOC = 53 degrees.
III. m<AOC = 2(53)
m<AOC = 106 degrees.
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Diameter(a) is 20 cm and diameter(b) is 5. What is the ratio of circumference(a) to circumference(b)?.
Answer:
5:1
Step-by-step explanation:
d_a = 20
d_b = 5
Equation for the circumference of a circle:
C = pi*d
C_a = pi * d_a
C_a = pi*20
C_b = pi * d_b
C_b = pi * 5
Ratio of C_a to C_b = C_a/C_b
C_a/C_b = (pi * 20)/(pi * 4) = 5:1
Fill in the blanks:
1) If tan x= -2.5, then tan (-x)= ___
2) If sin x= 0.4 then sin (-x)= ___
3) If cos x = 0.9 then cos (-x)= ___
4) If tan x = 1.5 then tan (pi+x)= ___
Trigonometric functions have some interesting symmetry properties
If tan x= -2.5, then tan (-x)= 2.5 and If sin x= 0.4 then sin (-x)= -0.4
If cos x = 0.9 then cos (-x)= 0.9 If tan x = 1.5 then tan (pi+x)= -1.5
Trigonometric Functions and Their Symmetry PropertiesTrigonometric functions are mathematical functions that are widely used in various fields, including mathematics, physics, and engineering. The most commonly used trigonometric functions are sine, cosine, and tangent, which are abbreviated as sin, cos, and tan, respectively.
Trigonometric functions have some interesting symmetry properties. For example, the sine and tangent functions are odd functions, which means that sin(-x) = -sin(x) and tan(-x) = -tan(x). On the other hand, the cosine function is an even function, which means that cos(-x) = cos(x).
These symmetry properties have important implications in many applications of trigonometric functions. For example, if we know the value of sin(x), we can immediately determine the value of sin(-x) by using the odd symmetry property. Similarly, if we know the value of cos(x), we can determine the value of cos(-x) by using the even symmetry property.
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Zachary invests $400 into an account that earns 3.5% simple interest for 5 years. He does not make any other deposits or withdrawals.
At the end of 5 years, Zachary invests the entire account balance into a different account that earns 5% simple interest. He leaves the money in the account for 2 years without making any additional deposits or withdrawals.
What is the new account balance at the end of 2 years?
The new account balance at the end of 2 years is $517.
Simple interest
5 yearsUsing this formula I= (P+r×t)
Where: I=Interest=?
P=Principal=$400
r=Interest rate=3.5%
t=Time=5 years
Hence: I= ($400×0.035 x 5) which makes I= $70
2 years
I=Interest=?
P=Principal=$470
r=Interest rate=5%
t=Time=2 years
I=($470+0.05×2) which makes I=$47
New balance:
New balance=$400+$70+$47
New balance=$517
Inconclusion the new account balance at the end of 2 years is $517.
1) Ryan buys a sofa for £2500 plus VAT at 20%
a) What is the total price of the sofa?
The total price of the sofa is £3000.
Step-by-step explanation:1. Calculate the amount to pay for VAT.To calculate this, multiply the given amount by "0.2", which equals "20%".
[tex]2500*0.2=500[/tex]
2. Add up the two number to find the total amount due.[tex]2500+500=3000[/tex]
3. Conclude.The total price of the sofa is £3000.
-------------------------------------------------------------------------------------------------------
Alternative (and also easier) method.So if we want to add 20% of any amount to said amount, we may multiply it by (1+0.2), which equals "1.20", and it'll give us the result immediately:
[tex]2500*(1+0.2)\\ \\2500*1.2=3000[/tex]
Now, working on the opposite way, let's say we want to reduce that same number (2500) by 25%, maybe because there's a discount on the product. In that case, we must multiply by (1-0.25), which equals 0.75:
[tex]2500*(1-0.25)\\ \\2500*(0.75)=1875.[/tex]
Given :-
Ryan buys a sofa for £2500 .VAT is 20% .To Find:-
Total price of the sofa.Solution:-
Here we are given that Ryan purchases a sofa for £2500 . In order to find the cost of sofa after VAT , find 20% of the price of the sofa,
20% of £2500
20/100 * £2500
£500
Now add this to the original price of the sofa,
£2500 + £500
£3000
Hence the cost of the sofa after VAT is £3000 .
My teacher gave me an extra credit assignment with 25 minutes left of class. It is extra credit, not a timed assessment.
need done as soon as possible
Answer: it will be square or rhombus
Step-by-step explanation:
Wurs 2/15-16: 10 Question Practice
7. An airplane pilot sights an airport runway at an
angle of depression of 18°. The airplane's altitude
is 1560 ft. What is the diagonal distance from
airplane to the runway?
The diagonal distance from the airplane to the runway is
▼
feet.
2 3 4 5 6
The diagonal distance from the airplane to the runway is approximately 5230.8 ft.
What is Trigonometry?Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems related to measurements of angles and distances.
The angle of depression of 18° is the angle between the airplane's line of sight and the horizontal line representing the runway. We can label the altitude of the airplane as 1560 ft:
Now we can use trigonometry to find the diagonal distance from the airplane to the runway. In particular, we can use the tangent function:
tan(18°) = opposite / adjacent
In this case, the opposite side is the altitude of the airplane (1560 ft), and the adjacent side is the diagonal distance we're trying to find (x). Therefore:
tan(18°) = 1560 / x
To solve for x, we can multiply both sides by x and then divide both sides by tan(18°):
x = 1560 / tan(18°)
Using a calculator, we find that:
x ≈ 5230.8 ft
Therefore, the diagonal distance from the airplane to the runway is approximately 5230.8 ft.
To learn more about Trigonometry from the given link
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fill in the entries of the row equivalent matrix formed by performing the indicated elementary row operation.
The solution to the matrix is x1 = (-555 - 356x3)/90, x2 = (138 + 89x3)/10 and x3 = free variable
What is the solution to the matrixTo find the solution to this matrix, we need to perform row operations to put it into row echelon form or reduced row echelon form. We can do this by adding multiples of one row to another row, multiplying a row by a nonzero scalar, and swapping two rows.
Here are the row operations we can use to put this matrix into row echelon form:
1. Add 5 times the first row to the third row to eliminate the 5 in the (3,1) entry:
0 0 -9 6
0 -1 -4 4
25 35 11 38
2. Multiply the second row by -1 to make the pivot in the second row, second column equal to 1:
0 0 -9 6
0 1 4 -4
25 35 11 38
3. Add 9 times the second row to the first row to eliminate the -9 in the (1,3) entry:
0 9 0 -30
0 1 4 -4
25 35 11 38
4. Add -25 times the second row to the third row to eliminate the 25 in the (3,1) entry:
0 9 0 -30
0 1 4 -4
0 10 -89 138
5. This matrix is now in row echelon form. We can solve for the variables by back-substitution. Starting with the last row:
0 10 -89 138 | x3
We have:
10x2 - 89x3 = 138
Solving for x2, we get:
x2 = (138 + 89x3)/10
Substituting this expression for x2 in the second row, we have:
Copy code
0 1 4 -4 | (138 + 89x3)/10
Solving for x1, we get:
9x1 + 4(138 + 89x3)/10 = -30
Simplifying and solving for x1, we get:
x1 = (-555 - 356x3)/90
So the solution to the matrix is:
x1 = (-555 - 356x3)/90
x2 = (138 + 89x3)/10
x3 = free variable
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