find all values of the scalar k for which the two vectors are orthogonal. (enter your answers as a comma-separated list.) u
Answers
Therefore, the value of the scalar k for which the two vectors are orthogonal is k =1/5.
What is vector ?In physics and mathematics, the term "vector" is used to refer, informally, to certain quantities that cannot be described by a single number or to certain constituents of vector spaces.
Here,
When the dot product of two vectors is zero, those two vectors are said to be orthogonal.
Dot product:
Let's assume we have the two vectors a and b.
a = (1,2) (1,2)
b = (2,3) (2,3)
Their dot item is:
a.b = (1,2). (1,2).
(2,3) = 1*2 + 2*3 = 8
Regarding this issue:
u = (2,3) (2,3)
(k + 1, k - 1) = v
So
u.v = (2,3). (2,3).
(k + 1, k - 1) = 2k + 1, 3k - 1, or 2k + 2, 3k - 3, or 5k - 1
The vectors must be orthogonal for the dot product to equal 0.
So:
=> 5k -1 =0
=> 5k =1
=> k =1/5
Therefore , the value of the scalar k for which the two vectors are orthogonal is k =1/5.
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Related Questions
Based on the graph, estimate (to one decimal place) the average rate of change f
Answers
The estimate (to one decimal place) of the average rate of change f is 1.7
How to estimate (to one decimal place) the average rate of change f?The interval is given as
x = 1 to x = 4
This can be represented as
(a, b) = (1, 4)
From the attached graph, we have
f(1) = 2
f(4) = 7
The estimate (to one decimal place) of the average rate of change f is
Rate = [f(b) - f(a)]/[b - a]
This gives
Rate = [f(4) - f(1)]/[4 - 1]
So, we have
Rate = [7 - 2]/[4 - 1]
Evaluate
Rate = 1.7
Hence, the estimate (to one decimal place) of the average rate of change f is 1.7
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3. It took Sandy two hours to jog 13 miles. She ran 17 miles in the first hour. How far did she run during the second hour?
Answers
Answer:
this doesn't amke sense
Step-by-step explanation:
she joged 13 miles in 2 hours. she ran 17 miles the 1st hour. 38? im not sure what your trying to do
Which inequality is equivalent to the given inequality? -4(x+7)< 3(x-2)
Answers
An equivalent inequality to the given \(-4(x + 7) < 3(x - 2)\) is \(7x > -22.\)
To find an equivalent inequality, we can start by simplifying the given inequality and then make adjustments to preserve its truth.
Let's simplify the given inequality step by step:
\(-4(x + 7) < 3(x - 2)\)
Expanding both sides:
\(-4x - 28 < 3x - 6\)
Grouping like terms:
\(-4x - 3x < -6 + 28\)
Simplifying:
\(-7x < 22\)
To maintain the direction of the inequality, we need to multiply both sides by -1.
However, when we multiply or divide both sides of an inequality by a negative number, the direction of the inequality is reversed.
Therefore, we need to flip the inequality sign:
\(7x > -22\)
Hence, an equivalent inequality to the given \(-4(x + 7) < 3(x - 2)\) is
\(7x > -22.\)
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How do I do this problem? My teacher isn’t good at explaining things...Thank you
Answers
Answer:
i cant read it cuz its sideways can you flip the picture plz i want to help
Step-by-step explanation:
Select the term that can be a list of values or numbers associated with context over an entire set of interest.
a.)
Frequency
b.)
Distribution
c.)
Variable
d.)
Data set
Answers
Answer: D
Step-by-step explanation:
What is the area of the shaded segment ?
Answers
9514 1404 393
Answer:
5.1 cm²
Step-by-step explanation:
The area of a segment is given by the formula ...
A = 1/2r²(α -sin(α)) . . . . . where α is the central angle in radians
For this segment, its area is ...
A = 1/2(6 cm)²(7π/18 -sin(70°)) ≈ 5.077 cm²
The area of the segment is about 5.1 square centimeters.
_____
The angle is converted to radians by multiplying by π/180°. Then a 70° angle is π(70°/180°) = 7π/18 radians.
Jacey has 40 pizzas to sell in the concession
stand at a basketball game. Each pizza has
been cut into 8 slices of equivalent size. In the
first hour, Jacey sold 16 3/8 pizzas. In the second
hour, she sold 18 3/4 pizzas. How many pizzas
does Jacey have left to sell?
Plz help
Answers
Answer:
the answer is 16.6 Pizzas
Step-by-step explanation:
16% of 40 is 6.4 that means she sold 6 full pizzas and 0.4 parts of one pizza
add that to 18 is 24.4 pizzas sold and 16.6 to go.
The cost of 10 pencils is Rs.15 more than the cost of such 7 pencils. What is the cost of a pencil ?
Answers
Let the cost of 7 pencils be 'x' & the cost of 10 pencils be (7x + 15)/10
According to the Question,
⇒(7x + 15)/10 = x
⇒7x + 15 = x × 10
⇒7x + 15 = 10x
⇒7x - 10x = 15
⇒3x = 15
⇒x = 15/3
⇒x = 5
∴ The cost of a pencil is ₹5Find each missing measurement of the angle, and determine the name of the angle
Answers
Answer:
the first one is 101 degrees
the second one is 106 degrees
the third one is 106 degrees
Step-by-step explanation:
Answer:
1. x = 101, x is an opposite interior angle
2. x = 106, x is an opposite interior angle
3. x = 106, x is a same-side interior angle
The figures below are similar with a scale factor of 3:2. Find the perimeter of figure B.
Answers
Answer:
Not 100% sure but I think it might be 28.8
If it is not this then it is 19.2
Step-by-step explanation:
Please let me know whether either of these are correct :)
Kon'nichiwa, everyone! just to make sure you are correct if you answer this question make sure you have a explaination, and a good one with that.
ex; you took the test and have proof you took it.
ex; explaining how you got your answer
also if you happen to need this "⎯⎯" you can just copy paste that and put it in the answer
that's all, thanks for reading this :D
Answers
Answer:
Hey there i see that you are doing scientific notation things well i will help you
Step-by-step explanation:
so 5.2 X 10 to the 5th power = 520000
3.9 X 10 to the 8th power = 390000000
and 4.7 X 10 to the 5th power = 470000
so on that info the answer is
4.7 x 10(5), 5.2 x 10(5), 3.9 x 10(8)
hope you have a nice day
Answer and work is all shown in the provided screenshot! I hope this helps! :)
Find the next two terms in this sequence:
16,8,4,2,1,__,__
They should be fractions but if anyone could help me that would be great!
Answers
Answer:
16,8,4,2,1,1/2,1/4
Step-by-step explanation: this is very straightforward, everytime the sequence is getting lower, its dividing by half! understand?
Five times the sum of 8u and eight gives one hundred sixty
Answers
Answer:
u=3
Step-by-step explanation:
(8u + 8)5 = 160
40u + 40 = 160
40u = 120
u = 3
Simplify the expression 2^5 +5^4
Answers
Therefore
\(2^5+5^4=657\)General form of
Y= 1/3x +3 and has an x intercept of 3
Answers
Answer:
Step-by-step explanation:
y
=
1
3
x
−
3
Use the slope-intercept form to find the slope and y-intercept
Slope:
1
3
y-intercept:
(
0
,
−
3
)
Any line can be graphed using two points. Select two
x
values, and plug them into the equation to find the corresponding
y
values.
x
y
0
−
3
3
−
2
Graph the line using the slope and the y-intercept, or the points.
Slope:
1
3
y-intercept:
(
0
,
−
3
)
x
y
0
−
3
3
−
2
image of graph
is 6(3x + 1) and 9x + 6 + 9x equivalent
Answers
Answer:
The expressions are equivalent.
Step-by-step explanation:
Let's simplify each expression.
6(3x + 1) = 18x + 6
9x + 6 + 9x = 18x + 6
Both expressions are equal to 18x + 6, so they are equivalent.
Answer: The expressions are equivalent.
HI PLEASE HELP ON QUESTION ASAP USING AVERAGE (MEAN) TO ANSWER QUESTION! IF UR ANSWER AND EXPLAINATION IS CORRECT ILL RATE YOU FIVE STARS, A THANKS AND MAYBE EVEN BRAINLIEST. PLEASE MAKE SURE YOU ANSWER MY QUESTION USING AVERAGES.
1) a meal for 6 cost £12 per person. as it is one of the diners birthday , the other 5 decided to pay for his meal. how much do each of the five friends need to pay?
Answers
Each of the five friends needs to pay £14.40 to cover the cost of the birthday person's meal.
To calculate how much each of the five friends needs to pay, we can use the concept of averages or mean.
The total cost of the meal for 6 people is £12 per person. This means that the total cost of the meal is 6 * £12 = £72.
Since the other five friends have decided to pay for the birthday person's meal, they will evenly divide the total cost of £72 among themselves.
To find the average amount each friend needs to pay, we divide the total cost by the number of friends paying, which is 5:
£72 / 5 = £14.40
Using the concept of averaging or finding the mean allows us to distribute the cost equally among the friends, ensuring fairness in sharing the expenses.
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270 is 54% of what number
Answers
Answer:
500
Step-by-step explanation:
54%=0.54
0.54x=270
x=270/0.54
x=500
Answer : 500
Whole : ?
Part : 270
Percentage : 54
100 : 100
How to find the Whole of a Part . . . Part x 100 / Percent
270 x 100 = 27,000 / 54 = 500
270 is 54% of 500
a computer that normally cost 500 dolars was on sale for 200 dollars. what is the percent decrease. please show work for brainlist
Answers
Answer:
(100/500) *200 =40%
Step-by-step explanation:
3 Jack walk from Santa Clara to Polo Allo. Il took I hour 25 min to walk from Santa Clot to Los Altos. Than it took 25 minute of wal from los altos to Palo buto. He arrived in Palo alto at 2:45 P.M. of what time die Santa Clara ? he leave Santa clara
Answers
The time Jack left Santa Clara is 1 : 55 pm
What is word problem?A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.
The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.
Therefore, the total time he spent is
25mins + 25 mins = 50 mins
He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;
2:45 pm = 14 :45
= 14:45 - 50mins
= 13:55
= 1 : 55pm
Therefore he left at 1:55 pm
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Henrieta drove 250 miles in 4 hours. How much miles did she drive in 10 minutes?
Answers
Answer:
625 miles
Step-by-step explanation:
250/4=62.5
62.5*10 = 625
Answer:
Below.
Step-by-step explanation:
There are 6 * 10 minutes in 1 hour and 4*6 = 24 10minutes in 4 hours.
So in 10 minutes she travels 250 / 24
= 10.417 miles to nearest thousandth.
Which expression is equivalent to 4^7/8
4^1/4?
Answers
According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table:
Month
Average Maximum Monthly Temperature
Jan
48.1
Feb
50.9
Mar
62.4
Apr
67.0
May
76.5
Jun
83.9
Jul
86.8
Aug
88.1
Sep
79.2
Oct
69.9
Nov
59.5
Dec
49.6
Let x represent the months and y represent the average maximum monthly temperature.
Plot the data on a scatterplot. Choose the plot that best represents the data.
a.
On a coordinate plane, points are at (1, 48.1), (2, 50.9), (3, 62.4), (4, 67), (5, 76.5), (6, 83.9), (7, 86.8), (8, 88.1), (9, 79.2), (10, 69.9), (11, 59.5), (12, 49.6).
b.
On a coordinate plane, points are around (5, 85), (6, 90), (7, 80), (8, 70), (9, 60), (10, 50), (48, 1), (50, 3), (62, 4), (66, 4), (76, 5), (82, 8).
c.
On a coordinate plane, points are around (0, 49), (1, 52), (2, 62), (3, 68), (4, 78), (5, 85), (50, 12), (60, 10), (70, 10), (80, 9), (88, 8), (87, 9), (89, 9).
d.
On a coordinate plane, points are around (0, 48), (2, 52), (13, 50).
Please select the best answer from the choices provided
Answers
a) On a coordinate plane, points are at (1, 48.1), (2, 50.9), (3, 62.4), (4, 67), (5, 76.5), (6, 83.9), (7, 86.8), (8, 88.1), (9, 79.2), (10, 69.9), (11, 59.5), (12, 49.6) best represents the data.
This is because the data represents a set of paired values, with the months as the independent variable (x) and the average maximum monthly temperature as the dependent variable (y). A scatter plot is the appropriate graph for displaying this type of data.
Option a shows the correct placement of the data points on a scatter plot, with the x-axis representing the months and the y-axis representing the average maximum monthly temperature. The points are clearly organized in a sequence from January to December, with an upward trend in temperature from the winter months to the summer months, followed by a gradual decrease in temperature in the fall and winter months.
Option b has the correct range of temperatures, but the points are not arranged in a logical sequence and are scattered randomly across the graph. Option c also has a similar issue with random placement of points and does not reflect the actual values in the data set. Option d only has three points and does not represent the complete data set.
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58.74% as a decimal due today
Answers
Answer:
0.5874
Step-by-step explanation:
Answer:
0.5874
Step-by-step explanation:
Getting 58.74 percent of a number is the same as multiplying the number 0.5874
Casey inherited $70000, and decided to invest some of the money in a savings account earning 1% interest per year, and the rest in a certificate of deposit earning 2% interest per year. If the interest from the certificate of deposit was $800 more than the interest from the savings account, how much did Casey invest in each account?
Savings:
Certificate of Deposit:
Answers
The amount that Casey invested in the savings account is $10,000 and the amount Casey invested in the certificate of deposit is $60,000.
How much was invested in the savings account and the certificate of deposit?0.01c - 0.02s = $800 equation 1
c + s = $70,000 equation 2
Where:
c = amount invested in the certificate of deposit s = amount invested in the savings accountMultiply equation 2 by 0.01:
0.01c + 0.01s = 700 equation 3
Subtract equation 3 from equation 1:
0.01s = 100
Divide both sides of the equation by 0.01:
s = 100 / 0.01
s = 10,000
Substitute for s in equation 2:
c + 10,000 = 70,000
c = 70,000 - 10,000
c = 60,000
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Which graph shows a proportional relationship?
A. B. C D.
Answers
Answer:
B
Step-by-step explanation:
a proportional relationship must have a straight line when graphed and it must go through the origin (0,0)
Right off the bat we can eliminate answer choice C because the line is not straight
the answer is not a nor d
the line may be straight but it does not go through the origin therefore it is not a proportional relationship
B makes a straight line and the line goes through the origin therefore B is the answer
Question
Henry has collected data to find that the
typing speeds for the students in a typing
class has a normal distribution. What is the
probability that a randomly selected student
has a typing speed of less than 51 words per
minute if the mean (u) is 47 words per
minute and the standard deviation (o) is 4
words per minute? Use the empirical rule.
• Provide the final answer as a percent.
Provide your answer below:
%
Answers
The probability that a randomly selected student has a typing speed of less than 51 words per minute if the mean (u) is 47 words per minute and the standard deviation (o) is 4 words per minute is; 68%
How to use empirical formula in statistics?The empirical rule in statistics states that for normal distributions, 68% of observed data points will lie inside one standard deviation of the mean, 95% will fall within two standard deviations, and 99.7% will occur within three standard deviations.
The formula for z-score is;
z = (x' - μ)/σ
where;
x' is sample mean
μ is population mean
σ is standard deviation
We are given;
x' = 51
μ = 47
σ = 4
Thus;
z = (51 - 47)/4
z = 1
From empirical formula at 1 standard deviation above the means, the probability is 68%.
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Calculate the area of a circle with a radius of 5 meters
Answers
Ans: pi (5)^2 = 78.5( cor. to 3 sig. fig)/ 25 pi
21 cm 1.2.1 Calculate the perimeter of the A4 paper. Explain the meaning of the given scale. 1.2.2 1.2.3 What type of scale is shown on the drawing 1+1
Answers
The given scale is not provided, so it is impossible to explain its meaning.
The type of scale shown on the drawing is not provided, so it is impossible to determine whether it is a linear or a non-linear scale.
Find the missing angle according to the Triangle Sum Theorem.
Answers
Answer:
k = 140 degrees.
The missing INTERIOR angle is 40 degrees.
Step-by-step explanation:
The missing interior angle would be 40.
Triangle angle sum theorem states the 3 interior angles of a triangle sum to 180.
64+76+40 = 180
The exterior angle theorem states the exterior angle of a triangle is equal to the sum of the two remote interior angles of the triangle.
Exterior angle k = 64+76
k= 140