Using law of cosine, the distance from the wall at point A is approximately 21.32 feet.
What is the distance from the wall at point AWe can use the law of cosines to find the distance from the wall at point A. Let's call this distance d.
In the triangle formed by the center of the merry-go-round, point A, and the point where the merry-go-round touches the wall (let's call this point B), we know that:
Angle AOB (the central angle formed by the rotation of 130 degrees) is 130 degrees.Side OA (the radius of the merry-go-round) is 42 feet.Side AB (the distance we want to find) is d + 8 feet (since the merry-go-round is 8 feet away from the wall).Side OB (the distance from the center of the merry-go-round to the wall) is 8 feet.Using the law of cosines, we have:
(8)^2 = (42)^2 + (d + 8)^2 - 2(42)(d + 8)cos(130)
Simplifying and solving for d, we get:
d = sqrt[ (8)^2 - (42)^2 cos^2(130) ] - 8
Plugging in the values, we get:
d ≈ 21.32 feet
Therefore, the distance from the wall at point A is approximately 21.32 feet.
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What is |–6.5|?........................................................
Answer: 6.5
Step-by-step explanation:
[tex]|-6.5| = 6.5[/tex]
_________
9 How do Jaden's questions about the missing students influence the development of the plot?
Page 9
A
By causing the Puppetmaster to challenge her curiosity
B
By emphasizing the close connection between the players and the Puppetmaster
C
By persuading the teachers to begin a search for them
D By highlighting the entertainment value that the game provides each player
11133-feb 2017023 12:29 PM
00 ON
Jaden's questions about the missing students influence the development of the plot in many ways.
What is number?Number is a mathematical object used to count, measure, and label. It is one of the most fundamental concepts in mathematics and is used in all areas of mathematics, including algebra, geometry, calculus, and statistics. Numbers are used to represent quantities and can be represented in a variety of ways, such as numerals, symbols, words, and graphs. Numbers can be used to measure and compare objects, define relationships between objects, and help solve problems.
Firstly, they cause the Puppetmaster to challenge her curiosity. The mysterious disappearances of the students compel the Puppetmaster to find out why they have gone missing, and to take measures to ensure that no one else goes missing. This encourages the Puppetmaster to become more involved in the game, and creates tension between her and the other players.
Secondly, Jaden's questions emphasize the close connection between the players and the Puppetmaster. The players rely on the Puppetmaster for guidance and safety, and her actions in response to Jaden's questions demonstrate her commitment to the players' wellbeing. This serves to strengthen the bond between the players and the Puppetmaster.
Thirdly, Jaden's questions persuade the teachers to begin a search for the missing students. By raising awareness of the situation, Jaden encourages the teachers to take action to investigate the disappearances and to protect the remaining students.
Finally, Jaden's questions highlight the entertainment value that the game provides each player. Her questions demonstrate her enthusiasm for the game, which encourages the other players to play with greater enthusiasm. This serves to increase the intensity of the game, and to make the game more exciting for all involved.
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Even though the triangles are all different sizes,the decimal for each ratio are
Even though the triangles are all different sizes,the decimal for each ratio are equal.
What is ratio ?
Ratios are commonly used in many different fields, including finance, engineering, and science. They are used to compare quantities or values that are not necessarily in the same units or are not directly comparable.
If the ratios of the corresponding sides of different triangles are equal, then the triangles are said to be similar. In this case, if the ratios of the sides of the different triangles are equal and result in the same decimal value, then it means that the triangles are similar to each other.
When two triangles are similar, it means that their corresponding angles are equal, and the ratios of their corresponding sides are also equal. This is known as the "angle-angle" or "AA" similarity criterion.
Therefore, if the ratios of the sides of different triangles are equal.
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a) Write a similarity statement.
b)lf BC = 2 and DC = 10. AD =
Step-by-step explanation:
a) BD/AD=AB/AC=AD/CD; BD/AB=AB/BC=AD/AC; AD/AB=AC/BC=CD/AC;
b) if BC=2 and DC=10, then it is possbile to write:
BD/AD=AB/AC=AD/10; BD/AB=AB/2=AD/AC; AD/AB=AC/2=10/AC, then
AC/2=10/AC and AC²=20. According to the Pyphagorean's theorem AD²=AC²+CD² and AD=√120≈10.96
Solve the given differential equation by variation of parameters. x2y'' − 3xy' + 3y = x^4'*e^x
Answer:
Step-by-step explanation:
To solve the differential equation x^2y'' − 3xy' + 3y = x^4e^x using variation of parameters, we can follow these steps:
Step 1: Find the complementary solution y_c by solving the homogeneous equation:
x^2y'' − 3xy' + 3y = 0
The characteristic equation is r(r-1) - 3r + 3 = 0, which simplifies to r^2 - 4r + 3 = 0. Factoring, we get (r-1)(r-3) = 0, so the roots are r=1 and r=3. Therefore, the complementary solution is:
y_c = c1x + c2x^3
where c1 and c2 are arbitrary constants.
Step 2: Find the particular solution y_p using variation of parameters. We assume that the particular solution has the form:
y_p = u1(x)*y1(x) + u2(x)*y2(x)
where y1 and y2 are solutions to the homogeneous equation (in this case, y1=x and y2=x^3) and u1 and u2 are functions to be determined.
We need to find the derivatives of y1 and y2:
y1' = 1, y1'' = 0
y2' = 3x^2, y2'' = 6x
Substituting into the differential equation and simplifying, we get:
x^2(u1''y1 + u2''y2) + x(u1'y1 + u2'y2) = x^4e^x
Plugging in y1 and y2 and simplifying, we get:
x^2(u1''*x + u2''*x^3) + x(u1'*1 + u2'*3x^2) = x^4e^x
We can write this equation in matrix form as:
[x^2x, x^2x^3] * [u1'', u2''] + [x1, x3x^2] * [u1', u2'] = [0, x^4e^x]
Taking the determinant of the coefficient matrix [x^2x, x^2x^3; x1, x3x^2], we get:
(x^2x)(x3x^2) - (x^2x^3)*x = 2x^4
Therefore, the inverse of the coefficient matrix is:
[3x, -x^3] / (2x^4)
Multiplying by the column vector [0, x^4e^x] gives:
[u1', u2'] = [3x, -x^3] * (1/(2x^4)) * [0, x^4e^x]
Simplifying, we get:
u1' = (3/2)*e^(-x), u2' = -(1/2)xe^(-x)
Integrating u1' and u2' with respect to x, we get:
u1 = -(3/2)*e^(-x), u2 = -(1/2)*xe^(-x) + C
where C is an arbitrary constant.
Therefore, the particular solution is:
y_p = -(3/2)xe^(-x) + Cx^3e^(-x)
where C is an arbitrary constant.
Step 3: The general solution of the differential equation is the sum of the complementary solution and the particular solution:
y = y_c + y_p
HI can someone please help me with these 2 questions!!
Option A is the correct answer as EF/QR = CE/SQ is not correct, as the triangles contain no vertex C.
What is properties of similar triangles?Triangles with the same shape but different sizes are said to be similar triangles. Squares with any side length and all equilateral triangles are examples of related objects. In other words, if two triangles are similar, their corresponding sides are proportionately equal and their corresponding angles are congruent.
Although having the same form, each might have different sizes.
There are no matching angles that are not equal.
Similar equivalent side ratios exist.
Given that, EFG and QRS are similar.
We know that for similar triangles the ratio of length of the segments of the corresponding triangle are equal.
Thus, EF/QR = CE/SQ is not correct, as the triangles contain no vertex C.
Hence, option A is the correct answer.
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30 people gathered to watch a baseball game. While talking, they realized that 11 of them were Toronto Blue Jays fans. What is the probability that a randomly selected person from the group is a Toronto Blue Jays fan?
Type the answer in simple fraction form.
The probability that a randomly selected person from the group is a Toronto Blue Jays fan is 11/30.
What is the probability?Probability refers to the chance or likelihood that an expected outcome, event, or success occurs when there are many possible outcomes, events, or successes.
Probability is a fractional value that lies between one and zero depending on the degree of certainty.
Probabilities can be expressed as decimals, fractions, or percentages.
The total number of people who gathered to watch the baseball game = 30
The number of Toronto Blue Jays fans = 11
Thus, the probability of selecting a Toronto Blue Jay fan from the 30 spectators is 11/30.
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n the first week of July, a record 1,120 people went to the local swimming pool. In the second week, 125 fewer people went to the pool than in the first week. In the third week, 145 more people went to the pool than in the second week. In the fourth week, 132 fewer people went to the pool than in the third week. What is the percent decrease in the number of people who went to the pool over these four weeks?
First, we need to find the number of people who went to the pool in the second, third, and fourth weeks.
Number of people in second week = 1,120 - 125 = 995
Number of people in third week = 995 + 145 = 1,140
Number of people in fourth week = 1,140 - 132 = 1,008
To find the percent decrease, we need to find the difference between the number of people in the first week and the fourth week, and then divide by the number of people in the first week.
Difference between first and fourth weeks = 1,120 - 1,008 = 112
Percent decrease = (112/1,120) x 100% = 10%
Therefore, the percent decrease in the number of people who went to the pool over these four weeks is 10%.
Suppose your boss proposes an alternative form of payment. For the first day of each month, you’ll earn a penny. Thereafter, each workday your wages will double what they were the day before. If there are 20 workdays in a month, how much would you make for the month?
We will make ₹1,048,575 for the month. The solution has been obtained by using the arithmetic operations.
What are arithmetic operations?The four basic operations, often referred to as "arithmetic operations", are thought to be able to describe all real numbers. Divide, multiply, add, and subtract are the four mathematical operations that result in the quotient, product, sum, and difference.
We are given that for the first day of each month, a penny is earned. Thereafter, each workday wages will double what they were the day before.
Now, since there are 20 workdays in a month so, the total amount earned is as follows:
⇒ 1 + 2 + 4 + 8 + 16 + 32 + 64 + 128 + 256 + 512 + 1,024 + 2,048 + 4,096 + 8,192 + 16,384 + 32,768 + 65,536 + 131,072 + 262,144 + 524,288
⇒ ₹ 1,048,575
Hence, we will make ₹ 1,048,575 for the month.
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what is the answer?????????????????
Surface Area of cuboid = 2 (lb + bh + hl)
According to the question :
length = x, width = x-5, height = 0.5x
250 = 2 ( x × (x-5) + (x-5) × 0.5x + 0.5x × x )
250 = 2 ( x² - 5x + 0.5x² - 2.5x + 0.5x²)
250 = 2 ( x² - 5x + x² - 2.5x )
250 = 2 ( 2x² - 7.5x )
250 = 4x² - 15 x
4x² - 15x -250 = 0
44. A survey asked buyers whether color, size, or brand influenced their choice of cell phone. The results are below. How many people were influenced by brand?
5 only said color
8 only said size
16 only said brand
20 said only color and size
42 said only color and brand
53 said only size and brand
102 said all three
20 said none of these
222 people were influenced by brand.
What is Algebraic expression ?
Algebraic expression can be defined as combination of variables and constants.
To determine how many people were influenced by brand, we need to add up the number of people who said "brand" as one of their influencing factors. However, we need to be careful not to double-count those who selected multiple factors.
Let's start by creating a diagram of the data:
| Color | Size | Brand | Total
Only | 5 | 8 | 16 | 29
Color/Size| 20 | 0 | 42 | 62
Size/Brand| 0 | 53 | 42 | 95
All Three | 0 | 0 | 102 | 102
None | 20 | 20 | 20 | 60
Total | 45 | 81 | 222 | 348
From this table, we can see that 222 people said that brand influenced their choice of cell phone.
Therefore, 222 people were influenced by brand.
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Xander has a checking account at Smart Money Bank. He chose an overdraft protection option that costs $20.00 every time
he writes a check for an insufficient amount. He is charged a monthly service fee of $15.00 if his account falls below $100.00.
Debt card transactions are free. An ATM fee of $1.00 is charged if he uses a non-Smart Money ATM. The online bank
statement shows all of the latest transactions.
What is Xander's ending balance?
O-$68.00
O $32.00
O $68.00
O-$32.00
Date
Transaction
Balance of $62.00
7/21
7/25 ATM withdrawal of $20 from Federal Credit Union
7/25 Online payment to Cell Phone Company of $42.00
7/28
Deposits his paycheck of $88.00
7/29 ATM withdrawal of $20 from Smart Money Bank
7/30
Check for $100 for rent
Xander's ending balance is -$68
What is Xander's ending balanceLet's start by calculating Xander's balance after each transaction:
7/21: Starting balance of $62.007/25: ATM withdrawal of $20.00 from Federal Credit Union, balance of $42.007/25: Online payment to Cell Phone Company of $42.00, balance of $0.007/28: Deposit of $88.00, balance of $88.007/29: ATM withdrawal of $20.00 from Smart Money Bank, balance of $68.007/30: Check for $100.00 for rent, balance of -$32.00Now let's consider the fees and charges:
Xander wrote a check for an insufficient amount, which triggered an overdraft protection fee of $20.00.His account fell below $100.00, which triggered a monthly service fee of $15.00.He used an ATM that is not a Smart Money ATM, which triggered an ATM fee of $1.00.So the total fees and charges are $20.00 + $15.00 + $1.00 = $36.00.
Therefore, Xander's ending balance is -$32.00 - $36.00 = -$68.00.
So the answer is -$68.00.
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Calculate the value of the expression 4+2(5+(-3))=
Answer:
8
Step-by-step explanation:
4 + 2 (5 - 3) = 8
hope this helps :))
Alan and Ben had collected 360 game cards altogether. They played three games using these cards. In the first game, Alan lost 2 /5 of his cards to Ben. In the second game, Alan won 1 /4 of Ben cards. In the last game, Alan lost 1 /6 of his cards to Ben. In the end, both boys had the same number of cards. How many game cards did each boy have at first?
Answer:
Alan had 272 cards initially and Ben had 88 cards initially.
Step-by-step explanation:
Let's start by assuming that Alan had x cards and Ben had y cards initially. We know that the sum of their cards is 360, so:
x + y = 360
In the first game, Alan lost 2/5 of his cards to Ben, so he gave away (2/5)x cards to Ben. Therefore, he was left with:
(3/5)x cards
Ben received (2/5)x cards from Alan and had y cards initially, so he had:
y + (2/5)x
cards after the first game.
In the second game, Alan won 1/4 of Ben's cards, so he received (1/4)(y + (2/5)x) cards. Therefore, he had:
(3/5)x + (1/4)(y + (2/5)x)
cards after the second game.
In the third game, Alan lost 1/6 of his cards to Ben, so he gave away (1/6)(3/5)x cards to Ben. Therefore, he was left with:
(2/3)(3/5)x = (2/5)x
cards.
Ben received (1/6)(3/5)x cards from Alan in the third game, and he had y + (2/5)x cards after the first game. Therefore, he had:
y + (2/5)x + (1/6)(3/5)x = y + (9/25)x
cards after the third game.
Since both boys ended up with the same number of cards, we can set the expressions for their final card counts equal to each other:
(3/5)x + (1/4)(y + (2/5)x) = y + (9/25)x
Multiplying both sides by 100 to get rid of the fractions, we get:
60x + 25y + 50x = 100y + 36x
Simplifying, we get:
24x = 75y
Since x + y = 360, we can use this equation to solve for one of the variables in terms of the other:
x = 360 - y
Substituting into the equation we just obtained, we get:
24(360 - y) = 75y
Simplifying, we get:
8640 - 24y = 75y
99y = 8640
y = 87.27
Since y must be a whole number (since it represents the number of cards that Ben had initially), we can round it up to 88. Substituting into the equation x + y = 360, we get:
x + 88 = 360
x = 272
Therefore, Alan had 272 cards initially and Ben had 88 cards initially.
To find the initial number of game cards Alan and Ben had, we can set up an equation and solve for a variable. The equation involves using the information about the games played and the number of cards lost and gained by Alan. The solution will give us the initial numbers of cards for both boys.
Explanation:To solve this problem, let's assume that Alan had x cards and Ben had y cards at the beginning. We are given that Alan lost 2/5 of his cards to Ben in the first game, so he had (3/5)x cards left and Ben had y + (2/5)x cards. In the second game, Alan won 1/4 of Ben's cards, so he gained (1/4)(y + (2/5)x) cards, leaving him with (3/5)x + (1/4)(y + (2/5)x) cards. In the last game, Alan lost 1/6 of his cards to Ben, so he had (5/6)((3/5)x + (1/4)(y + (2/5)x)) cards left. Since both boys had the same number of cards in the end, we can set up the equation: (5/6)((3/5)x + (1/4)(y + (2/5)x)) = y + (2/5)x. After simplifying and solving for y in terms of x, we can substitute back into the equation to find the value of x.
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√49is a
√50is a
V/127 is a non-perfect
125 is rational because it is equal to a
square and therefore
square and therefore
and therefore irrational.
number.
√49 is a rational number. √50 is an irrational number. √127 is an irrational number. 125 is a rational number because it is equal to a perfect cube of the whole number 5.
What does an irrational number look like?A real number is considered to be irrational if it cannot be written as a simple fraction. It cannot be described using a ratio. When p and q are numbers and q is not identical to 0, N is not equivalent to p/q if N is irrational. An illustration of this is the illogic of the integers
Why are certain numbers irrational?A actual number that's unable to be written as the ratio between two integers—that is, as p/q, where both p and q both are integers—is an irrational number.
√49 is a rational number because it is equal to 7, which is a whole number.
√50 is an irrational number because it cannot be expressed as a fraction of two integers and it is not a perfect square.
√127 is also an irrational number because it cannot be expressed as a fraction of two integers and it is not a perfect square.
125 is a rational number because it can be expressed as 5^3, which is a perfect cube of the whole number 5.
Therefore, the correct statements are:
√49 is a rational number.
√50 is an irrational number.
√127 is an irrational number.
125 is a rational number because it is equal to a perfect cube of the whole number 5.
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Plot the point (−312, 434) on the coordinate plane.
The graph of the point is on the image at the end.
How to plot the point on a coordinate plane?A coordinate plane has two axes, one is horizontal and the other is vertical.
A general point (x, y) has the value "x" in the horizontal axis and "y" in the vertical one, then to graph (-312, 434 ) in a coordinate plane, you need to find -312 in the horizontal axis and 434 in the vertical one.
The graph of the point is on the image at the end.
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guys pls give the correct answer quickly
The True statement is:
All the four function cut the y axis at (0, 3)
What is Intercept?The point at which the line or curve crosses the graph's axis is referred to as the intercept. When a point crosses the x-axis, it is referred to as the x-intercept. When a point crosses the y-axis, it is referred to as the y-intercept.
We have Four function
f(x) = 4[tex](2)^x[/tex] -1
g(x) = 3[tex](1/4)^x[/tex]
h(x) = [tex](1/2)^x[/tex] + 2
k(x) = -[tex]3^x[/tex] + 4
We have represented all the graph given below.
First, there is no function whose have negative y intercept.
Only f(x) have negative x intercept.
But all the four function cut the y axis at (0, 3)
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PLEASE HELPPPPP ITS A HUGE GRADE!!!!! WILL MARK BRAINLIEST!!!
The missing angles inscribed in the circle are
∠ C = 26 degrees∠ B = 26 degrees∠ BSD = 97 degrees∠ CSE = 97 degrees∠ E = 57 degreesHow to find the anglesThe angles are calculated using the inscribed angle theorem
Inscribed Angle Theorem: The measure of an inscribed angle is half the measure of the intercepted arc.
This is used as follows
∠ C = 52/2 degrees
∠ C = 26 degrees
∠ C = ∠ B = 26 degrees inscribed angle subtended by same arc are equal
∠ BSD + ∠ D + B = 180 degrees sum of angles in a triangle
∠ BSD + 57 + 26 = 180
∠ BSD = 180 - 57 - 26
∠ BSD = 97 degrees
∠ CSE = ∠ BSD vertical angles
∠ CSE = 97 degrees
∠ E = ∠ B = 57 degrees inscribed angle subtended by same arc are equal
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PRESENT AND FUTURE VALUES OF A CASH FLOW STREAMAn investment will pay $150 at the end of each of the next 3 years, $250 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal risk earn 11% annually, what is its present value? Its future value?
Answer:
Step-by-step explanation:
To calculate the present value (PV) and future value (FV) of the cash flow stream, we can use the following steps:
Calculate the present value of each cash flow using the formula:
PV = CF / (1 + r)^n
where CF is the cash flow, r is the annual interest rate, and n is the number of years until the cash flow is received.
For the first three cash flows of $150 at the end of each of the next 3 years, assuming a starting point of Year 0, we have:
PV1 = $150 / (1 + 0.11)^1 = $134.59 (Year 1)
PV2 = $150 / (1 + 0.11)^2 = $120.75 (Year 2)
PV3 = $150 / (1 + 0.11)^3 = $107.99 (Year 3)
For the cash flow of $250 at the end of Year 4:
PV4 = $250 / (1 + 0.11)^4 = $165.14
For the cash flow of $300 at the end of Year 5:
PV5 = $300 / (1 + 0.11)^5 = $179.34
For the cash flow of $500 at the end of Year 6:
PV6 = $500 / (1 + 0.11)^6 = $277.12
Add up the present values of each cash flow to find the present value of the entire stream:
PV = PV1 + PV2 + PV3 + PV4 + PV5 + PV6
PV = $134.59 + $120.75 + $107.99 + $165.14 + $179.34 + $277.12
PV = $985.93
Therefore, the present value of the cash flow stream is $985.93.
To find the future value of the cash flow stream, we can simply add up the cash flows and then apply the future value formula:
FV = CF x [(1 + r)^n - 1] / r
where CF is the sum of the cash flows, r is the annual interest rate, and n is the number of years from the present until the future value is calculated.
CF = $150 x 3 + $250 + $300 + $500 = $1,100
n = 6 (assuming a starting point of Year 0)
FV = $1,100 x [(1 + 0.11)^6 - 1] / 0.11
FV = $2,525.72
Therefore, the future value of the cash flow stream is $2,525.72.
Shawn's coin collection contained 25 quarters, 20 dimes, 50 pennies, and 5 nickels. What was the
ratio of quarters to the total number of coins?
1. 04:1
2. 100 to 25
3. 1/4
4. 25: 1,000
The ratio of quarters to the total number of coins is 25:100, or simplified to 1:4.
What is the ratio and proportion ?
A ratio is an ordered pair of numbers a and b, written a / b where b does not equal 0. A proportion is an equation in which two ratios are set equal to each other. For example, if there is 1 boy and 3 girls you could write the ratio as 1 : 3 (for every one boy there are 3 girls).
To find the ratio of quarters to the total number of coins, we need to first calculate the total number of coins.
Total number of coins = number of quarters + number of dimes + number of pennies + number of nickels
Total number of coins = 25 + 20 + 50 + 5
Total number of coins = 100
Therefore, the total number of coins is 100.
The ratio of quarters to the total number of coins is:
Quarters : Total number of coins
= 25 : 100
= 1 : 4
Hence, the answer is option 3. 1/4.
Therefore, the ratio of quarters to the total number of coins is 25:100, or simplified to 1:4.
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Identify the solution for the system of equations and explain its meaning using the context from the real-world problem.
I GOT THE ANSWER BUT I NEED THE EXPLANATION
The linear equation in this situation is y=20x which will have its solution as per the values of 'x'.
Explain about the System of Linear Equations?A collection of more that two linear equations is known as a system of linear equations. It's possible for a linear equation to have a number of variables.There are numerous uses for a system of linear equations. Real-world problem like assessing cost, distance, lifespan, profit, etc., as an example. Every unknown quantity can be found for a given quantity by using it.For instance, the cost of a good for a certain amount can be determined using a linear equation.
If a unit of a single product costs $20, the equation would be y=20x.In this case, x is the quantity of items and y is the price.The linear equation in this situation is y=20x.
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Fill in the sentence below with the description that most specifically applies to the quadrilateral below.
The quadrilateral is most specifically a D. square, because C. all sides are congruent.
What is a square?
A quadrilateral with four equal edges is called a square. There are numerous items in our environment that have a square form. Equal sides and interior angles that are both 90 degrees distinguish each square form.
A square is a quadrilateral where all sides are congruent and all angles are right angles.
This matches the given description of the figure with 4 vertices, where the diagonal angles are same and all the sides are equal.
Therefore, the correct option for the first blank is D, and the correct options for the second blank is C.
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Answer:
The quadrilateral is most specifically a rhombus because all sides are congruent.
Step-by-step explanation:
From inspection of the given quadrilateral, we can see that:
All 4 sides are of equal length.Opposite angles are congruent, but adjacent angles are different.(This is denoted by the same number of tick marks on each congruent line segment and each congruent angle).
All sides of a square and a rectangle meet at right angles, i.e. their interior angles are congruent. Since the interior angles of the given quadrilateral are not all equal, the figure cannot be a square or a rectangle.
All sides of a rhombus are equal in length, and its opposite angles are congruent. This description matches the given shape. Therefore, the quadrilateral is a rhombus.
the number of cars in a parking lot are no more than 7.
Let c be the number of cars in the parking lot
Answer: C is less than or equal to 7
Step-by-step explanation: because the numbers of cars are not less nor greater than 7
If each quadrilateral below is a rectangle, find the missing measures.
Please helpppp
The measures of the angles are JKN = 27 degrees and JNK = 126
How to determine the measures of the anglesThe complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
The rectangle
On the rectangle, we have
JKN = NJK
Using the above as a guide, we have the following:
JKN = 27 degrees
Next, we use the sum of angles in a triangle theorem
The sum of angles in a triangle is 180
Mathematically, this is represented as
J + N + K = 180
So, we have the following representation
JNK = 180 - 27 * 2
Evaluate
JNK = 126
Hence, the measure of the angle JNK is 126 degrees
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find the vertex, y intercept, and x intercept to this quadratic function "y = x^2 + 2x - 3" pls show you work!
I need help fast, PLS HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:hunger
Step-by-step explanation:
i hungry
A city’s population has been growing linearly. In 2008, the population was 28,200. By 2012, the population was 36,800. Assume this trend continues. Let p(x) = population, and x = years since 2012. Answer the questions. -Expected Population in year 2014 =
- Predicted year when population will reach 54000 =
- The rate of population changes = ?
- The number of years for the population doubled since 2008 =
Using the equation, we found the following:
1) Expected Population in the year 2014 = 41100
2) Predicted year when the population will reach 54000 = 2020
3) The rate of population changes = 2150
4) The number of years for the population doubled since 2008 =9.12
What is a linear equation?
A mathematical equation is a formula that uses the equals sign to represent the equality of two expressions. An equation is said to be linear if the maximum power of the variable is consistently 1. Another name for it is a one-degree equation. A linear equation with one variable has the conventional form Ax + B = 0. In this case, the variables x and A are variables, while B is a constant.
Given,
the population in 2008 = 28,200
the population in 2012 = 36,800
The population is growing linearly.
Assume a linear equation,
p(x) = 36800 + kx
where,
p(x) = population
x = years since 2012.
k = increase in population
p(0) = 36800
p(-4) = 36800 - 4k
28200= 36800 -4k
4k = 36800 - 28200
k = 2150
Then the linear equation becomes,
p(x) = 36800 + 2150x
1) Population in 2014
x = 2014 - 2012 = 2
From the equation,
p(2) = 36800 + 2150 * 2 = 41100
2) x when p(x) = 54000
From the equation,
54000 = 36800 + 2150x
2150x = 17200
x = 8
Year = 2012 + 8 = 2020
3) Rate of population change = (population in 2012 - population in 2008) / number of years = 36800-28200 / 4 = 2150
4) Population doubled since 2008
p(x) = 2 * 28200 = 56400
We have to find x , when p(x) = 56400
Using the linear equation,
56400 = 36800 + 2150x
x = 9.12
Therefore using the equation, we found the following:
1) Expected Population in the year 2014 = 41100
2) Predicted year when the population will reach 54000 = 2020
3) The rate of population changes = 2150
4) The number of years for the population doubled since 2008 =9.12
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A farmer uses 162 pounds of fertilizer on 4 acres of crops. Each acre receives the same amount of fertilizer how much fertilizer does the farmer use on each acre of crops
Answer:
We can start by dividing the total amount of fertilizer by the number of acres:
162 pounds / 4 acres = 40.5 pounds per acre
Therefore, the farmer uses 40.5 pounds of fertilizer on each acre of crops.
Step-by-step explanation:
An
18
inch pizza from Pizza Pi has
12
servings and
1
,
725
calories. Kayla has enough pizza for each person to eat one slice. If Kayla has
8
,
625
calories worth of pizza, how many people does she feed?
Answer:
60Step-by-step explanation:
We need to divide 8625/1725
I used calculator and got 5.
Kayla has 5 pizzas.
Each pizza has 12 slices so we multiply 5x12.
That is 60.
FAQ:
Why do we multiply 5 by 12?
Answer: Each pizza has 12 slices. If we want to know how many slices 2 pizzas have, we would multiply 12 by 2. The ratio of pizza to slice is 12:1.
Pizza is 12x bigger than individual slice
(I want pizza now)
PLEASE HELP QUICK
Is X=[2 -1
6 -4] the inverse of A=[1/2 1/4
-2 -1/2]?
Select answers from the drop-down menus to correctly complete the statements.
The product of the matrices
(a - is b - is not)
the identity matrix. Therefore, X and A
(a - are b - are not)
inverses of each other.
Answer:
The product of the matrices A and X is the identity matrix. Therefore, X and A are inverses of each other.
Step-by-step explanation:
Five years ago, Castles in the Sand Inc. issued bonds at a face value of $1,000 at a yield to maturity of 4%. Now, with eight years left until the maturity of the bonds, the company has run into hard times, and the yield to maturity on the bonds has increased to 11%.
1). What is the price of the bond now? (Assume semiannual coupon payments.)
2). Suppose that investors believe that Castles can make good on the promised coupon payments but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 50% of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive?
A. The price of the bond is $556.25.
B. The yield to maturity expected by investors is 20.36%.
What is YTM?Yield to maturity (YTM) is the total rate of return that will have been earned by a bond when it makes all interest payments and repays the original principal.
here, we have,
A. The price of the bond is calculated using the formula:
P = C × (1 − (1 + YTM/2)−2T ) ÷ (YTM/2) + (1 + YTM/2)−2T
Here, C is the coupon payment, YTM is the yield to maturity and T is the time to maturity in years.
Face value = $1,000
YTM = 8.2%
Time to maturity = 7 years
Coupon payment = 8.2% × $1,000 = $82
Substituting these values in the formula, we get:
P = $82 × (1 − (1 + 0.082/2)−14 ) ÷ (0.082/2) + (1 + 0.082/2)−14
P = $82 × (1 − 0.6774) ÷ 0.041 + 0.6774
P = $556.25
B. The yield to maturity expected by investors is calculated using the formula:
YTM = 2 × (C × (1 + YTM/2)−2T + (FV − P) × (1 + YTM/2)−2T ) ÷ P
Here, C is the coupon payment, YTM is the yield to maturity, FV is the face value of the bond and P is the price of the bond.
Expected face value at maturity = 85% × $1,000 = $850
Substituting these values in the formula, we get:
YTM = 2 × ($82 × (1 + YTM/2)−14 + ($850 − $556.25) × (1 + YTM/2)−14 ) ÷ $556.25
YTM = 2 × ($82 × (1 + YTM/2)−14 + ($293.75) × (1 + YTM/2)−14 ) ÷ $556.25
YTM = 2 × ($82 × 0.6774 + ($293.75) × 0.6774) ÷ $556.25
YTM = 2 × ($55.35 + ($198.57) ) ÷ $556.25
YTM = 2 × $253.92 ÷ $556.25
YTM = 0.2036 = 20.36%
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