The vector has components +5 and +7 along the x- and y-axes respectively. along a set of axes rotated 90 degrees counterclockwise relative to the original axes, the vector's components are
Answers
After rotating 90 degrees counterclockwise,
Now, Vector components are +7 in x-axis & +5 in y-axis.
Let the coordinates of the rotated vector be (a,b).
From the Pythagorean theorem,
d = √(5² + 7²) = 8.6023
The angle θ is given by
tan θ = 7/5 = 1.4
θ = tan⁻¹ 1.4 = 54.46°
φ = 180 - (90 + 54.46) = 35.54°
The coordinates of the rotated vector are
a = - d cos φ = - 8.6023*cos(35.54) = 7
b = d sin φ = 8.6023*sin(35.54) = 5
Answer: (-7, 5)
Related Questions
If the area of a square room is 225 ft², what is the length of each side of the room? question 4 options: 56.25 ft 112.5 ft 15 ft 80 ft
Answers
The length of each side of the square room with an area 225 ft² is 15 ft.
What are the dimensions of a square?The area of a square is a product of it's any two sides or a product of diagonals divided by two. If side has a length a then diagonal is a√2.
The perimeter of a square is the sum of the lengths of all the sides.
Given, The area of a square room is 225 ft².
Assuming the length of each side is 'a' feet.
∴ The area of the square room is,
a×a = 225 ft².
a² = 225 ft².
a = ± 15 ft.
As length can not be negative +15 ft is the admissible value.
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There are 64 pretzels in a 16 ounce bag of chocolate covered pretzels. how many ounces does each pretzel way?
Answers
Simply Divide:
16/64 = 0.25
So, Each Pretzel Weighs 0.25 Ounces.
HELP ME WITH MATH PLEASEEEEEEEEEEEEE
Answers
(1^2x)/(2^2x) = 32
1^2x = 1
1/2^2x = 32
32 = 2^5
2^-2x = 2^5
take out the base, (since they are the same. You are left with...)
-2x = 5
-2x = 5 is your answer in this case
hope this helps :D
The area of a square boxing ring is 436 square feet. What is the approximate length, in feet, of one side of the boxing ring?
4ft
21ft
54ft
109ft
Answers
The area of the square is the square of the side thus the approximate length of the square will be 21 ft so option (B) will be correct.
What is a square?A square is a geometrical figure in which we have four sides each side must be equal and the angle between two adjacent sides must be 90 degrees.
Area of square = Side²
As per the given question,
The area of a square boxing ring is 436 square feet.
It is known that,
Area = Side²
Side² = 436
Take square root on both sides,
Side = √436 = 20.88 ≈ 21 ft
Hence "The area of the square is the square of the side thus the approximate length of the square will be 21 ft so option (B) will be correct".
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1.The state fair charges and entry fee plus $0.75 per ticket needed for the rides. Sally spent her money only on ride tickets and fair admission. The price of the fair admission is the same for everyone. Use y to represent the total cost and x to represent the number of ride tickets.
(a)Sally spent a total of $31.25 on the entry fee plus 25 ride tickets. How much did Sally pay for the entry fee?
Answer:
(b)Joe has $26 he can spend at the fair on the entry fee and tickets. How many tickets can Joe buy?
Answer:
(c)Let x represent the number of ride tickets purchased and y represent the total cost of fair entry fee and ride tickets. Write an equation to calculate the total cost of the entry fee and fair admission for a person who purchases x tickets.
Answer:
Answers
Final answer:
Sally paid a $12.50 entry fee to the fair. Joe can buy 18 tickets after paying the entry fee with his $26. The equation to represent the total cost of entry fee and tickets based on the number of tickets purchased is y = 12.50 + 0.75x.
Explanation:
(a) We are told Sally spent a total of $31.25 on the entry fee plus 25 ride tickets. Since each ticket costs $0.75, we can multiply 25 tickets by $0.75 to find the total cost of the tickets alone. That is 25 tickets × $0.75 per ticket = $18.75. Subtracting this amount from the total cost of $31.25 gives us the entry fee. The entry fee is $31.25 - $18.75 = $12.50.
(b) Joe has $26 to spend on the entry fee and tickets. We found out earlier that the entry fee is $12.50. Subtracting the entry fee from the total amount Joe has, we get $26 - $12.50 = $13.50. Now, divide this by the cost of one ticket, $0.75, to determine the number of tickets he can buy: $13.50 / $0.75 = 18 tickets.
(c) Let x represent the number of ride tickets purchased and y represent the total cost of fair entry fee and ride tickets. The total cost is the sum of the fixed entry fee and the variable cost of x tickets at $0.75 each. The equation is y = 12.50 + 0.75x.
Multiply. 3 ⋅ 3/5 whats the answer
Answers
3/1 * 3/5
9/5
Hope this helps!
Identify the properties needed to prove n + n + n + 2n = 5n.
Answers
The properties needed to prove n + n + n + 2n = 5n are: Distributive Property of Multiplication, Associative Property of Addition, and Commutative Property of Addition.
What is Commutative Property of Addition?The commutative property of addition states that when two or more numbers are added, the order in which they are added does not affect the sum. In other words, for any two numbers a and b, a + b = b + a.
The properties required to prove n + n + n + 2n = 5n are as follows:
Distributive Property of Multiplication: This property states that a(b + c) = ab + ac. In this case, we can apply the distributive property to 2n, which gives us 2n = n + n.Associative Property of Addition: This property states that (a + b) + c = a + (b + c). We can use the associative property of addition to group the n's together and the 2n's together, which gives us (n + n + n) + (2n) = 5n.Commutative Property of Addition: This property states that a + b = b + a. We can use the commutative property of addition to rearrange the terms in the equation, which gives us (n + n + n + 2n) = (n + n + 2n + n) = 5n.Thus, these properties can be used.
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Final answer:
To prove n + n + n + 2n = 5n, we use the commutative and associative properties of addition to group and combine like terms, then apply the distributive property to show that the sum equals 5n.
Explanation:
To prove the equation n + n + n + 2n = 5n, we need to use properties of equality and algebraic manipulation. First, we apply the commutative property of addition, which allows us to rearrange the terms in any order without changing the sum.
This property isn't strictly necessary here, as all terms involve 'n', but it's a useful property in general for manipulating equations.
Next, we utilize the associative property of addition, which allows us to group numbers in any combination when adding. In this specific case, we group all the 'n' terms together:
(n + n + n) + 2n
Using the associative property, we can simplify the equation further by combining like terms:
3n + 2n = 5n
Lastly, we apply the distributive property, which in this case shows that multiplying the coefficient (being 1 for n in this example) by the number of times 'n' appears (3 for the first set and 2 for the second set), gives the same result as adding 'n' that many times.
when constructing inscribed polygons and parallel lines how are the steps different
Answers
What is the area of the polygon below
Answers
−3x^ 4−7x+17=0
2
3
4
5
How many complex roots does the polynomial equation have?
(Show work if possible)
Answers
There are two complex roots of the polynomial equation.
What is a polynomial?They are mathematical expressions involving variables raised with nonnegative integers and coefficients and constants with only operations of addition, subtraction, multiplication, and nonnegative exponentiation of variables involved.
We have been given a polynomial expression as;
[tex]-3x^ 4-7x+17=0[/tex]
Since the Degree of a polynomial is the highest power that its terms (for multi-variables, the power of the term is the addition of the power of variables in that term).
Therefore, the highest power of the given polynomial is 4.
Thus, the Maximum possible roots are 4 but; only 2 are real and 2 are complex.
Hence, There are two complex roots of the polynomial equation.
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Simplify m - {n - [p + (m + n - p)]}.
0
2m
-2m + 2p
Answers
= m - {n - [p + m + n - p]}
= m - {n - m - n}
= m + m
= 2m
answer
2m
Answer:To simplify the following expression, we first simplify the terms inside the parenthesis from inner going outer. The first one is [p - (m + n - p)] equal to p - m- n + p = 2p - m - n. Then, n +2p - m - n equal to 2p -m. Then, m - 2p + m equal to 2m -2p. Answer is B
Step-by-step explanation:
Write the equation of a line given two points kuta
Answers
Lillian wants to buy a digital camera for $143.00. She baby-sits for $2.75 an hour. So far she has worked a total of 30 hours. How many more hours does she need to work to have enough to buy the camera?
Answers
A color printer prints 15 pages in 8 minutes. how many pages does it print per minute
Answers
Suppose that 16-ounce bags of chocolate chip cookies are produced with weights that follow a normal distribution with mean weight 16.1 ounces and standard deviation 0.1 ounce. for the distribution, approximately what percent of the bags will likely be underweight (that is, less than 16 ounces)?
Answers
To solve this we use the z statistic. The formula for z score is:
z = (x – u) / s
where x is the sample value = less than 16, u is the sample mean = 16.1, s is standard dev = 0.1
z = (16 – 16.1) / 0.1
z = - 1
From the standard distribution tables at z = - 1,
P (z = -1) = 0.1587
So about 15.87% is underweight.
To find the percentage of bags that will likely be underweight (less than 16 ounces), we need to find the area under the normal distribution curve to the left of 16 ounces. The probability is approximately 15.87%.
Explanation:To find the percentage of bags that will likely be underweight (less than 16 ounces), we need to find the area under the normal distribution curve to the left of 16 ounces. We can use a Z-table or a calculator to find this probability. First, we need to standardize the value of 16 ounces using the formula Z = (X - μ) / σ, where X is the given value, μ is the mean, and σ is the standard deviation. Plugging in the values, we get Z = (16 - 16.1) / 0.1 = -1. This means that 16 ounces is 1 standard deviation below the mean.
Next, we can use the Z-table or a calculator to find the probability associated with a Z-score of -1. From the table or calculator, we find that the probability is approximately 0.1587 or 15.87%. Therefore, approximately 15.87% of the bags will likely be underweight (less than 16 ounces).
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How many ways are there to distribute n distinct balls into r boxes (a box can contain any number of balls, ranging from zero (none) all the way to all n balls)?
Answers
Suzanne has a student loan balance of $25,904 with an average interest rate of 6.8 percent. Use the student loan repayment calculator (Links to an external site.)Links to an external site. to determine how much her monthly payment be if she selects the standard repayment option.
Answers
Since the problem is requiring us to use the loan repayment calculator and here is what the calculator gave:
Loan Balance: $25,506.00
Adjusted Loan Balance: $25,506.00
Loan Interest Rate: 6.80%
Loan Fees: 0.00%
Loan Term: 10 years
Minimum Payment: $0.00
Monthly Loan Payment: $293.52
Number of Payments: 120 months
Cumulative Payments: $35,223.07
Total Interest Paid: $9,717.07
It is projected that you will need an annual salary of a minimum $35,222.40 to be capable to have enough money to repay this loan. This approximation assumes that 10% of your gross monthly income will be keen to repaying your student loans. This resembles to a debt-to-income ratio of 0.7. If you use 15% of your gross monthly income to repay the loan, you will need an annual salary of only $23,481.60, but you may experience some financial difficulty. This corresponds to a debt-to-income ratio of 1.1.
factor the trinomial x^2 - 3x - 40
(x-5)(x+8)
(x+5)(x-8)
(x+5)(x+8)
(x-5)(x-8)
Answers
Hope this helps
The answer is (x+5)(x-8)
What is the square root of sixty four
Answers
A quadratic factor that cannot be factored further as a product of linear factors containing real numbers is said to be
Answers
____________________________________
Please Help!!! :)
Ned currently has an account balance of $3,634.51. He opened the account 13 years ago with a deposit of $2,564.65. If the interest compounds twice a year, what is the interest rate on the account?
A. 4.7%
B. 5.4%
C. 2.7%
D. 1.4%
Leroy opened a savings account 18 years ago with a deposit of $2,651.43. The account has an interest rate of 2.8% compounded twice a year. How much interest has Leroy earned?
A. $4,373.68
B. $2,725.67
C. $4,358.69
D. $1,722.25
Answers
Your formula is r = n(ln(A/P)/(nt)) R being the interest rate of what your trying to find. So A= 3,634.51 P = 2,564.65 N is the number of times compounded per year.N= 2 and t is the number of years t= 13. Also while doing so use PEMDAS Let me know if you need any more help!
Compound interest formula is :
[tex]A=p(1+\frac{r}{n} )^{nt}[/tex]
1.
A = 3634.51
p = 2564.65
r = ?
n = 2
t = 13
Putting the values in formula, we get
[tex]3634.51=2564.65(1+\frac{r}{2} )^{2*13}[/tex]
=> [tex]3634.51=2564.65(1+\frac{r}{2} )^{26}[/tex]
=> [tex]\frac{3634.51}{2564.65}=(\frac{2+r}{2} )^{26}[/tex]
=> [tex]1.417=(\frac{2+r}{2} )^{26}[/tex]
We get [tex]\sqrt[26]{1.417}=\frac{2+r}{2}[/tex]
We get r = 0.02699 and r = -4.02699 (neglecting the negative value)
We get r = 0.027 (rounded)
And in percentage, it is 2.7%.
So, option C is the answer.
2.
p = 2651.43
r = 2.8% or 0.028
n = 2
t = 18
Putting the values in formula we get;
[tex]A=2651.43(1+\frac{0.028}{2} )^{2*18}[/tex]
=> [tex]A=2651.43(1.014)^{36}[/tex]
A = $4373.67
So, interest earned = [tex]4373.67-2651.43=1722.24[/tex] dollars
Hence, option D. $1,722.25 is the answer.
Write the expression 36+4 as a product using the greatest common factor and the distributive property.
Answers
(4 * 9) + (4 * 1) =
4(9 + 1) <==
The expression 36 + 4 can be written as a product using the greatest common factor and the distributive law is 4(9 + 1).
What are basic math properties?There are three basic math properties they are commutative property which states a + b = b + a, associative property which states
a + (b + c) = (a + b) + c and distributive property which states a(b+c) = ab + ac.
We know distributive property states a(b + c) = ab + ac.
Given 36 + 4, the here greatest common factor of 36 and 4 is 4.
∴ The expression 36 + 4 can be written as,
4(9 + 1).
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Drive-in movies were popular in the 1930s and 1940s. In 1933, there were 100 drive-in theater in the U.S by 1945 there were 2200. What was the percent of increase from 1933 to 1945?
Answers
To find the percent of increase in the number of drive-in theaters from 1933 to 1945, subtract the initial number from the final number, divide by the initial number, and multiply by 100, resulting in a 2100% increase.
Explanation:The question asks how to calculate the percent of increase in the number of drive-in theaters in the U.S. from 1933 to 1945. To find the percent of increase you subtract the original number from the new number divide by the original number, and then multiply by 100 to convert to a percentage.
Original number (1933) = 100 drive-in theatersNew number (1945) = 2200 drive-in theatersPercent of increase = ((2200 - 100) ÷ 100) × 100Percent of increase = ((2100) ÷ 100) × 100 = 2100%Therefore, the percent of increase from 1933 to 1945 was 2100%.
3x + 2 = 14 which number makes the equation true?a)1b)2c)4d)6
Answers
3X = 14- 2
3X = 12
X= 12/3
X=4
Answer:
X=4
Step-by-step explanation:
3 * 4 = 12 + 2 = 14.That means your answer is C) 4.
Hope this helps! :')
Given the slope of 6 and a y-intercept of 2, write the equation in slope intercept form.
Answers
Answer:
The equation of the line would be y = 6x + 2
Step-by-step explanation:
Since we have a slope (6) and a point (0,2) we can use them in point slope form. The slope goes in for m and the point goes in for (x1, y1).
y - y1 = m(x - x1)
y - 2 = 6(x - 0)
y - 2 = 6x
y = 6x + 2
What is the mean of the set of numbers?
-11, 22, -2, -3
Answers
add all the numbers and then divide by how many there are in the set to find the mean so
-11+22+-2+-3=6
6÷4=1.5
so 1.5 would be the mean
Hope this helps!
Hope this helped!
2,) What is the solution of the system?
Use the substitution method.
y+6=4x
8x−2y=14
A) The only solution is (14, 12)
B)The only solution is (12, 14)
C)There are an infinite number of solutions.
D)There is no solution.
Answers
Given the function f(x) = 2(x + 6), find x if f(x) = 22. PLEASE ANSWER DONT PLAY I REPORT NO GAME PLAYING PLEASE
Answers
x + 6 = 11
x = 5
check
f(5) = 2(5 + 6) = 2(11) = 22
Answer:
The correct answer is 5
Step-by-step explanation:
Jamal is driving in Europe and finds that he has to drive 56 kilometers until he arrives at his destination. If 1 km = 0.62137 mi, about how many miles does Jamal have left on his journey?
Answers
Jamal has to drive 56 kilometers until he arrives at his destination, so he needs to drive 56*0.62137 = 34.7967 mi.
So Jamal have 34.7967 miles left.
Hope this helps! :)
Kate has 6 more dimes than she has nickels. She has a total of $3.60. How many coins does she have in all?