(5 points) Find the vector equation for the line of intersection of the planes 5x + 3y - 52 -1 and 52 + 2 = 0 r = ( ,0) + t(3, >
Answers
The given equations of the planes are:the vector equation for the line of intersection is: r = (0, 0, 0) + t(-104, -260, 10).
5x + 3y - 52z - 1 = 0
5x + 2y + 0z - 52 = 0
To find the line of intersection of these planes, we can set up a system of equations using the normal vectors of the planes:
Equation 1: 5x + 3y - 52z - 1 = 0
Equation 2: 5x + 2y + 0z - 52 = 0
The normal vectors of the planes are:
Normal vector of Plane 1: (5, 3, -52)
Normal vector of Plane 2: (5, 2, 0)
To find the direction vector of the line of intersection, we can take the cross product of the normal vectors:
Direction vector = (5, 3, -52) x (5, 2, 0)
Using the cross product formula, the direction vector is:
Direction vector = (3(0) - (-52)(2), -52(5) - 0(5), 5(2) - 5(3))
= (-104, -260, 10)
Now, we need to find a point on the line. Let's use the point (0, 0, 0) from the given r = (0, 0) + t(3, >) equation.
So, a point on the line of intersection is (0, 0, 0).
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Related Questions
In physics class, Paul used a ruler to find the length of a kernel of corn to be 0.140 in. long. How many significant digits are in his answer?
Answers
Answer:
3
Step-by-step explanation:
1 and 4 are non-zero digits, so they are siginificant. A zero to the right of non-zero digits and to the right of the decimal point is also significant.
Answer: 3
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Which diagram shows possible angle measures of a triangle?
A triangle has angle lengths 35 degrees, 115 degrees, and 25 degrees.
A triangle has angle lengths 32 degrees, 115 degrees, and 33 degrees.
A triangle has angle lengths 35 degrees, 120 degrees, and 35 degrees.
a triangle has angle lengths 30 degrees, 120 degrees, and 20 degrees.
Answers
Answer:
A triangle has nagle 35, 120 degrees, and 35 degrees
Step-by-step explanation:
Answer:
The Triangle that has 115 32 33 or B
Step-by-step explanation:
115+32+33=180 All triangle angles measure 180.
Express y in terms of x. 0.5y - 2 = 0.25x
Answers
Answer:
y = 0.5x + 4
Step-by-step explanation:
1. Move terms to one side of the equation
0.5y - 2= 0.25x +0
+2 +2
__________________
0.5y = 0.25x + 2
2. Divide the coefficient of y (0.5) to both sides of the equation
\(\frac{0.5y}{0.5} = \frac{0.25x}{0.5} + \frac{2}{0.5}\)
3. Solve and simifpy
\(y = 0.5x +4\)
in the market for a bag of socks, what happens if the price of cotton falls?
Answers
A decrease in the price of cotton can have positive effects on the affordability and availability of socks in the market, benefiting consumers by potentially offering lower prices and a wider range of choices.
If the price of cotton falls in the market for a bag of socks, it is likely to have an impact on the overall cost and availability of socks. Cotton is a common material used in the production of socks, and its price plays a significant role in determining the cost of manufacturing.
When the price of cotton falls, it reduces the cost of raw materials for sock manufacturers. As a result, manufacturers may experience lower production costs. This can lead to several outcomes:
1. Decrease in sock prices: With lower production costs, manufacturers have the option to reduce the prices of socks to attract customers. This can result in more affordable socks for consumers, making them more accessible.
2. Increase in sock supply: Lower production costs may incentivize manufacturers to increase their sock production. As a result, the supply of socks in the market could rise, leading to a greater availability of socks for consumers.
3. Potential for improved quality or additional features: Manufacturers may choose to invest the cost savings from lower cotton prices into enhancing the quality of socks or adding extra features. This can result in socks with improved durability, comfort, or design, providing more options for consumers.
It's important to note that the impact of falling cotton prices on sock prices and availability may also depend on other factors, such as production and distribution costs, market competition, and consumer demand. Additionally, the extent to which the price reduction in cotton translates into lower sock prices may vary among different brands and retailers.
Overall, a decrease in the price of cotton can have positive effects on the affordability and availability of socks in the market, benefiting consumers by potentially offering lower prices and a wider range of choices.
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an arithmetic sequence $2,5,8, 11, 14,\ldots$ is written in order in a book, one hundred numbers per page, beginning on page one. on which page will the number $11{,}111$ appear? if you are having trouble with this question, read problem 10.4 in the textbook.
Answers
The page where the number 110 appears will be 37.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
An arithmetic sequence 2, 5, 8, 11, 14,... is written in the order in a book. Then the first term is 2 and the common difference is 3. Then the number of terms if the nth term is 110. Then we have
110 = 2 + (n - 1) x 3
108 = (n - 1) x 3
n - 1 = 36
n = 37
The page where the number 110 appears will be 37.
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Challenge Solve each of the given inequalities for z. Which of the inequalities has −8 as a solution?
Inequality 1:
4(1.2z+1.25)
<
19.4
Inequality 2:
2(1.1z+2.5)
≥
−3.8
Answers
-8 is the solution of inequality 4(1.2z+1.25)<19.4
What is Inequality?a relationship between two expressions or values that are not equal to each other is called 'inequality.
The given inequality 4(1.2z+1.25)<19.4
4.8z+5<19.4
4.8z<19.4-5
4.8z<14.4
z<3
-8 is the solution of 4(1.2z+1.25)<19.4
2(1.1z+2.5)≥−3.8
2.2z+5≥−3.8
2.2z≥−8.8
z≥-4
-8 is not the solution of 2(1.1z+2.5)≥−3.8
Hence, -8 is the solution of inequality 4(1.2z+1.25)<19.4
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please help ‼️‼️‼️‼️
Answers
The scale factors are given as follows:
Figure A to Figure B: 3/4.Figure B to Figure A: 4/3.What is a dilation?A dilation happens when the coordinates of the vertices of an image are multiplied by the scale factor, changing the side lengths of a figure.
Considering two equivalent side lengths, the scale factors are given as follows:
Figure A to Figure B: Side length B/Side length A = 18/24 = 3/4.Figure B to Figure A: Side length A/Side length B = 24/18 = 4/3.More can be learned about dilation at brainly.com/question/3457976
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In a sale, the price of a book is reduced by 25%.
The price of the book in the sale is £12
Work out the original price of the book
Answers
Question: In a sale, the price of a book is reduced by 25%. The price of the book in the sale is £12. Work out the original price of the book
Answer: £16
Step-by-step explanation:
To determine the original price of the book, we can use the fact that the sale price is 75% (100% - 25%) of the original price. Let's denote the original price as x.
75% of x = £12
To solve for x, we can set up the equation:
0.75x = £12
To isolate x, we divide both sides of the equation by 0.75:
x = £12 / 0.75
x = £16
Therefore, the original price of the book was £16.
True or False: For a given mass of rising air, the dry adiabatic rate will always be higher than the wet adiabatic rate.
Answers
Answer:
true
Step-by-step explanation:
because there's less humidity
Desmond's family watched 32 hours of TV last week this week they watched 75% more than that how many hours of TV did they watch this week( this is a question on irl.com L.11 percent of change: word problems )
Answers
175%/100=1.75
32x1.75=56
What percent is represented by the shaded area?
Answers
Answer:
1.91%
Step-by-step explanation:
8. The numbers 0 through 9 are used to create a 5-
digit security code to enter a building. If
numbers cannot be repeated, what is the
probability that the security code is
2-4-9-1-7?
A.
B.
1
252
1
6048
C.
D.
1
30,240
1
100,000
Answers
The probability of the given security code is as follows:
C. 1/30,240.
How to calculate a probability?The parameters that are needed to calculate a probability are listed as follows:
Number of desired outcomes in the context of a problem or experiment.Number of total outcomes in the context of a problem or experiment.Then the probability is then calculated as the division of the number of desired outcomes by the number of total outcomes.
5 digits are taken from a set of 10, and the order is relevant, hence the total number of passwords is given as follows:
P(10,5) = 10!/(10 - 5)! = 30240.
Hence the probability is given as follows:
C. 1/30,240.
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a 9 by 12 rectangular piece of paper is folded so that two opposite corners coincide. what is the length of the crease
Answers
The length of the crease is 15 cm.When a 9 by 12 rectangular piece of paper is folded so that two opposite corners coincide, the length of the crease is 15 cm. When we fold a rectangular paper so that the opposite corners meet, we get a crease that runs through the diagonal of the rectangle.
In this case, the 9 by 12 rectangle's diagonal can be determined using the Pythagorean Theorem which states that the square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides. In this case, the two sides are the length and width of the rectangle.
The length of the diagonal of the rectangle can be determined as follows:\(`(9^2 + 12^2)^(1/2)`\) = 15 cm. Therefore, the length of the crease is 15 cm.
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A certain forest covers an area of 3900 km^2. Suppose that each year this area decreases by 6.75%. What will the area be after 12 years
Answers
Answer:
1686
Step-by-step explanation:
Rate of reduction = 100 - 6.75 = 93.25%
After 12 years, the reduction in trees = 0.9325^12 = 0.432301
Area after 12 years = 3900 x 0.432301 = 1686
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Given the recursive formula for a geometric sequence find the common ratio, the first five terms, the term named in the problem, and the explicit formula.
Show work
Find f(9)
11) f(n) = f(n - 1) x 4
f(1) = 4
Answers
Answer:
No solution
Step-by-step explanation:
Use the given functions to set up and simplify f(9)
On Monday morning, Tyler deposited $345 into his checking account. Later that day he used his bank card to make a $398
purchase. Which expression can Tyler use to show the change in his bank account on Monday?
Answers
Answer:
x+345-398
Step-by-step explanation:
x+345-398
=x-53
where x is the amount of money he previously had on his account
2.
Turkey for sandwiches costs $7.75 per pound. What equation best represents
y, the total cost of x pounds of turkey?
a. X = 7.75 + y
b. X = 7.75y
C. Y = 7.75 + x
d. Y = 7.75x
Answers
d
Explanation:
Y=7.75x
1pound-$7.75x1
Xpound-$7.75xX
CC has the following beginning balances in its stockholders' equity accounts on January 1, 2012: Common Stock, $100,000; Additional Paid-in Capital, $4,100,000; and Retained Earnings, $3,000,000. Net income for the year ended December 31, 2012, is $800,000. Court Casuals has the following transactions affecting stockholders' equity in 2012:
May 18 Issues 25,000 additional shares of $1 par value common stock for $40 per share.
May 31 Repurchases 5,000 shares of treasury stock for $45 per share.
July 1 Declares a cash dividend of $1 per share to all stockholders of record on July 15. Hint: Dividends are not paid on treasury stock.
July 31 Pays the cash dividend declared on July 1.
August 10 Reissues 2,500 shares of treasury stock purchased on May 31 for $48 per share.
Taking into consideration all the entries described above, prepare the statement of stockholders' equity for the year ended December 31, 2012.
Answers
Total stockholders’ equity 7,800,000
Statement of stockholders’ equity for CC for the year ended December 31, 2012:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000
Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
Total stockholders’ equity 7,800,000
Explanation:The given information is as follows:Common Stock on January 1, 2012 = $100,000Additional Paid-in Capital on January 1, 2012 = $4,100,000
Retained Earnings on January 1, 2012 = $3,000,000Net Income for the year ended December 31, 2012 = $800,000Cash Dividend Declared on July 1 and paid on July 31 = $200,000
To prepare the statement of stockholders’ equity for the year ended December 31, 2012, we will begin by preparing the opening balances of each of the equity accounts. We will then add the net income to the retained earnings account.
The closing balance for retained earnings is then computed by subtracting the cash dividend declared and paid from the total retained earnings. Finally, the total stockholders' equity is calculated by adding the balances of all the equity accounts.
Calculations:Opening balance of common stock = $100,000
Opening balance of additional paid-in capital = $4,100,000
Opening balance of retained earnings = $3,000,000
Net Income for the year ended December 31, 2012 = $800,000
Retained earnings (Opening Balance) = $3,000,000
Add: Net Income for the year ended December 31, 2012 = $800,000
Total retained earnings = $3,800,000Less: Cash Dividend Declared on July 1 and paid on July 31 = $200,000Retained earnings (Closing balance) = $3,600,000
Total stockholders’ equity = Common Stock + Additional Paid-in Capital + Retained Earnings (Closing balance) = $100,000 + $4,100,000 + $3,600,000 = $7,800,000
Therefore, the statement of stockholders’ equity for CC for the year ended December 31, 2012, is as follows:Particulars Amount ($)
Common Stock 100,000
Additional Paid-in Capital 4,100,000
Retained Earnings (Opening Balance) 3,000,000
Add: Net Income for the year ended December 31, 2012 800,000
Total retained earnings 3,800,000
Less: Cash Dividend Declared on July 1 and paid on July 31 (200,000)
Retained earnings (Closing balance) 3,600,000
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Which of the following formulas is CORRECT for finding the present value of an investment
A) FV = PV/(1 + r)^n
B) PV = FV x (1 + r)n
C) PV = FVn x (1 + r)
D) PV = FV x 1/(1 + r)^n
Answers
The correct formula for finding the present value of an investment is given by option D) PV = FV x 1/(1 + r)^n.
The present value (PV) of an investment is the current value of future cash flows discounted at a specified rate. The formula for calculating the present value takes into account the future value (FV) of the investment, the interest rate (r), and the number of periods (n).
Option D) PV = FV x 1/(1 + r)^n represents the correct formula for finding the present value. It incorporates the concept of discounting future cash flows by dividing the future value by (1 + r)^n. This adjustment accounts for the time value of money, where the value of money decreases over time.
In contrast, options A), B), and C) do not accurately represent the present value formula and may lead to incorrect calculations.
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the values of λ such that a = 2 1 6 0 1 λ λ 0 4 is singular are
Answers
we set -46λ = 0. This gives usλ = 0Thus, the value of λ such that a = 2 1 6 0 1 λ λ 0 4 is singular is `λ = 0`.
To determine the values of λ such that a = 2 1 6 0 1 λ λ 0 4 is singular we need to calculate its determinant and set it equal to zero. We can solve this by using a long answer as follows:Long Answer:We need to evaluate the determinant of the matrix `a`. The determinant of `a` is given by|a| = 2 × | 1 λ | − 1 × | 6 0 |+ 4 × | 1 λ |⇒ |a| = 2[1 × λ − λ × 0] − 1[6 × λ − 0 × 1] + 4[1 × 0 − λ × 6]|a| = 2λ − 24λ - 24λ|a| = -46λTo make the determinant zero,
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Please explain how to solve this:
Answers
Answer:
x = 47
Step-by-step explanation:
Because the lines are parallel, we know that some angles are the same, see the images attached. That means that A and B in the image are the same angles. So we know that angle A totals to 78 degrees. And the angle outside the triangle is 35. So the angle inside the triangle is
78 - 35 = 43.
The interior angles of a triangle add up to 180. We know that one angle is 43 and another angle is 90 because of the indicating square angle marker. That means that
43 + 90 + x = 180.
Then we can simplify the equation:
133 + x = 180⇒
x = 180 - 133⇒
x = 47
The sides of parallelogram $MNPQ$ are represented by the expressions below. Find the perimeter of $MNPQ$ . $MQ=-2x+37$ $NP=x-5$ $QP=y+14$ $MN=4y+5$. Whar is the perimeter is units?
Answers
Answer: P=52
Step-by-step explanation:
sorry if wrong
Answer:p=52
Step-by-step explanation:
Whats the value of the 23 term in the sequence 10, 8, 6, 4
Answers
The 23rd term in the sequence 10, 8, 6, 4 is -34.
The given sequence is an arithmetic sequence with a common difference of -2, since each term is 2 less than the previous term. To find the 23rd term, we can use the formula for the nth term of an arithmetic sequence:
an = a1 + (n-1)d
where an is the nth term, a1 is the first term, d is the common difference, and n is the number of terms.
Substituting the values given, we get:
a23 = 10 + (23-1)(-2)
a23 = 10 + (-44)
a23 = -34
Therefore, the 23rd term in the sequence 10, 8, 6, 4 is -34.
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5-3x=2
What is x equals to?
Explain too please.
Answers
x=1
Explanation:
-3x+5=2 subtract 5 on both sides to get -3x=-3 divide -3 from -3 to get 1
A local restaurant owner can purchase tea for $16 per pound and coffee for $8 per pound. His budget does not allow him to spend more than $280 on coffee and tea. Which graph shows the possible combinations of pounds of tea, x, and pounds of coffee, y, that the restaurant owner can purchase?
Answers
Answer:
answer is 152
Step-by-step explanation:
i mutiplied $16 and $8 and got 128 the subtracted 128 and 280 and final answer is 152
I NEED HELP THIS IS DUE TOMMOROW i think is going easy for you smart people
Answers
Answer:
Time would be the independent variable and tiles that was installed would be the dependent variable.
Step-by-step explanation:
Hope this helps you!!
If you have any more questions feel free to ask.
Answer:
Time is the independent variable, and tiles installed is the dependent variable.
Step-by-step explanation:
The independent variable is considered the input variable.
The depended variable is considered the output variable.
So, in other words, when you input x amount of time, there will be y amount of tiles installed.
What number can be added to the expression -4 - 9 to make it 0
Answers
Answer:
+ 13
Step-by-step explanation:
- 4 - 9 = - 13 then
- 13 + 13 = 0
PLEASE HELP!!!! I NEED THIS IN 10 MINUTES!!!
Explain how to evaluate the expression 8x to the power of 2 + 25y, when x =3 and y=2
Answers
To evaluate the expression 8x^2 + 25y when x = 3 and y = 2, substitute the given values of x and y into the expression and perform the necessary calculations.
The expression 8x^2 + 25y represents a quadratic expression with terms involving x and y. To evaluate it when x = 3 and y = 2, replace x with 3 and y with 2 in the expression:
8(3)^2 + 25(2)
Simplifying the expression within parentheses:
8 * 9 + 25 * 2
Multiplying:
72 + 50
Adding:
122
Therefore, when x = 3 and y = 2, the expression 8x^2 + 25y evaluates to 122.
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Tell whether the equation has one solution, infinite many solutions, or no solutions. 5w - 6w = -w + 5
Answers
Answer:
No solution
Step-by-step explanation:
Answer:
simplified:
5w = 5w + 5
Therefore,
No Solutions
PLS HELP DUE IN 10 MIN WITH BOTH IF POSSIBLE
Answers
Answer:
Step-by-step explanation:
(12x + 19) + (22x - 9) = 180
34x + 10 = 180
34x = 170
x = 5