for what values of h are the given vectors linearly dependent [-1 4 6], [5 2 -3], [6 2 6], [-24 -8 h]
Vectors are linearly dependent for all h Vectors are linearly dependent for h -24 Vectors are linearly independent for all h Vectors are linearly dependent for h = -24
Answers
The given vectors are linearly dependent for h = 90 or h = -2, and they are linearly independent for all other values of h. The correct answer is A.
The given vectors are linearly dependent if and only if there exist constants c1, c2, c3, and c4, not all zero, such that
c1[-1 4 6] + c2[5 2 -3] + c3[6 2 6] + c4[-24 -8 h] = [0 0 0]
This can be written as a system of linear equations:
c1 + 5c2 + 6c3 - 24c4 = 0
4c1 + 2c2 + 2c3 - 8c4 = 0
6c1 - 3c2 + 6c3 + hc4 = 0
To determine for what values of h the vectors are linearly dependent, we can use row reduction to put the augmented matrix of this system in row echelon form:
[ -1 5 6 -24 | 0 ]
[ 4 2 2 -8 | 0 ]
[ 6 -3 6 h | 0 ]
Adding row 1 to row 2, and subtracting 2 times row 1 from row 3, we get:
[ -1 5 6 -24 | 0 ]
[ 0 7 8 -40 | 0 ]
[ 0 -13 -6 h+48 | 0 ]
Adding 13 times row 2 to row 3, we get:
[ -1 5 6 -24 | 0 ]
[ 0 7 8 -40 | 0 ]
[ 0 0 90-h 88 | 0 ]
So, the vectors are linearly dependent if and only if the last row of the row echelon form is not of the form [0 0 0 0]. This occurs when h = 90 or h = -2. The correct answer is A.
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Related Questions
ind the limit of the sequence with the given nth term. an = (7n+5)/7n.
Answers
The limit of the sequence is 1. This means that as n gets larger and larger, the terms of the sequence get closer and closer to 1.
The limit of the sequence with the nth term an = (7n+5)/7n can be found by taking the limit as n approaches infinity.
To do this, we can divide both the numerator and denominator by n, which gives:
an = (7 + 5/n)/7
As n approaches infinity, 5/n approaches 0, and we are left with:
an = 7/7 = 1
Therefore, the limit of the sequence is 1. This means that as n gets larger and larger, the terms of the sequence get closer and closer to 1.
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unding decimals to the nearest whole number, Adam traveled a distance of about
miles.
Answers
In a case whereby Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles Adam traveled a distance of about 335 miles.
How can the distance be calculated?The distance traveled in a unit of time is called speed. It refers to a thing's rate of movement. The scalar quantity known as speed is the velocity vector's magnitude. It has no clear direction.
Speed = Distance/ time
speed =72.4 miles
time=4.62 hours
Distance =speed * time
= 72.4 *4.62
Distance = 334.488 miles
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complete question;
Adam traveled out of town for a regional basketball tournament. He drove at a steady speed of 72.4 miles per hour for 4.62 hours. The exact distance Adam traveled was miles. Rounding decimals to the nearest whole number, Adam traveled a distance of about miles.
c)
A bus drives for 3/2 hours at an average speed of 56 mph.
How far does the bus drive?
Answers
Answer:
The bus drives 84 miles
Step-by-step explanation:
The question relates to relationship between average speed and time
The given parameters are;
The time duration in which the bus drives = 3/2 hours = 1.5 hours
The average speed of the bus = 56 mph
The formula average speed is given as follows;
\(Average \ speed = \dfrac{The \ total \ distance \ driven}{The \ time \ duration \ of \ travel}\)
Therefore, we have;
The total distance driven = Average speed × The time duration of travel
The total distance driven = The distance the bus drives
Substituting the given values, gives;
The distance the bus drives = 56 miles/hour × 1.5 hours = 84 miles
The distance the bus drives = 84 miles.
Answer:
196 miles
Step-by-step explanation:
To find the distance that the bus drives, we can use the formula:
distance = rate x time
where rate is the average speed and time is the duration of the trip.
In this case, the average speed of the bus is 56 mph and the duration of the trip is 3 1/2 hours. However, it is easier to work with time in terms of a single unit, so let's convert 3 1/2 hours to 7/2 hours:
3 1/2 hours = (2 x 3) + 1/2 hours = 7/2 hours
Now we can plug in the values into the formula:
distance = rate x time
distance = 56 mph x 7/2 hours
We can simplify by multiplying 56 by 7 and then dividing by 2:
distance = (56 x 7) / 2 = 196 miles
Therefore, the bus drives 196 miles.
Angle a and b are complementary angle a measure 10x +10 and angle b measure 20 find the value of c
Answers
The measure of angle c is 70 degrees.
If angle a and angle b are complementary, it means that the sum of their measures is equal to 90 degrees.
Given:
Measure of angle a = 10x + 10
Measure of angle b = 20
We can set up the equation:
(10x + 10) + 20 = 90
Simplifying the equation:
10x + 30 = 90
Subtracting 30 from both sides:
10x = 60
Dividing both sides by 10:
x = 6
Now, we have found the value of x to be 6.
To find the measure of angle c, we can substitute the value of x into the equation for angle a:
Measure of angle a = 10x + 10
Measure of angle a = 10(6) + 10
Measure of angle a = 60 + 10
Measure of angle a = 70
As a result, angle c has a measure of 70 degrees.
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3.9 times 10 to the 20 power
Answers
Hope this helps!
Answer:
6.626621133E31 or
3.9e+20
Step-by-step explanation:
you can use a caclulator to do this
Determine which measure of center best represents the data?
Answers
Answer:
Step-by-step explanation:
There is one value 9 which is a lot less than the rest of the values.
I would the median is the best.
what is 1 as a percentage -2
Answers
Answer:
Step-by-step explanation:
percentage: 1%
decimal:0.01
fraction :1/100
Which polygon has an interior angle sum of 1080°?
Answers
Answer:
The polygon with an interior angle sum of 1080° is an octagon or a polygon with 8 sides. We are given that the interior angle sum of our polygon
Step-by-step explanation:
Sorry if it's wrong.
Answer:
Step-by-step explanation:
Remark
First of all, you need a regular polygon, otherwise the question can have all sorts of interior angles. The standard way to solve this is set up an equation that looks like this.
(n - 2)*180 = 1080 Divide by 180
(n - 2) = 1080/180
n - 2 = 6 Add 2 to both sides.
n = 6 + 2
n = 8
Conclusion
So an 8 sided figure has 8 interior angles that add up to 1080 if the 8 sided figure is regular.
Let P be the plane containing the point (-21, 2, 1) which is parallel to the plane 1+ 4y + 5z = -15 If P also contains the point (m, -1, -2), then what is m? 11
Answers
To find the value of m, we need to determine the equation of the plane P and then substitute the point (m, -1, -2) into the equation.
Given that P is parallel to the plane 1 + 4y + 5z = -15, we can see that the normal vector of P will be the same as the normal vector of the given plane, which is (0, 4, 5). Let's consider the general equation of a plane: Ax + By + Cz = D. Since the plane P contains the point (-21, 2, 1), we can substitute these values into the equation to obtain: 0*(-21) + 42 + 51 = D, 0 + 8 + 5 = D, D = 13
Therefore, the equation of the plane P is 0x + 4y + 5z = 13, which simplifies to 4y + 5z = 13. Now, we can substitute the coordinates (m, -1, -2) into the equation of the plane: 4*(-1) + 5*(-2) = 13, -4 - 10 = 13, -14 = 13
Since -14 is not equal to 13, the point (m, -1, -2) does not lie on the plane P. Therefore, there is no value of m that satisfies the given conditions.In conclusion, there is no value of m that would make the point (m, -1, -2) lie on the plane P.
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SOMEBODLY PLZ HELP ASAP! Find x
Answers
Answer:
x=4
Step-by-step explanation:
We can use the leg rule
hyp leg
------- = -----------------
leg part
2+6 x
------- = -----------------
x 2
Using cross products
8*2 = x^2
16 =x^2
Take the square root of each side
4 =x
I need help on this.. the first person with the correct answer gets A BRANLIST
Answers
Hope this helps <3
solve for x -48=6(x-3)
Answers
Answer:
\(\boxed{x = -6}\)
Step-by-step explanation:
\(x-48 = 6(x-3)\)
Resolving parenthesis
\(x - 48 = 6x-18\)
Adding 18 to both sides
\(x-48+18 = 6x\\x-30 = 6x\)
Subtracting x from both sides
\(-30 = 6x-x\\-30 = 5x\)
Dividing both sides by 5
\(-30/5 = x\)
\(-6 = x\\\)
OR
x = -6
Answer:
x = - 6Step-by-step explanation:
x - 48 = 6(x - 3)
Expand the terms in the bracket
That's
x - 48 = 6x - 18
Group the constants at the right side of the equation and the ones with variables at the left side
x - 6x = 48 - 18
- 5x = 30
Divide both sides by - 5
x = - 6Hope this helps you
Determine the coordinates of the y-intercept of the function shown in the graph.
A)(0, -1)
B)(2, 0)
C)(0, 2)
D)(-1, 0)
Answers
Explanation: Extend the line to cross the y axis and then find the point
The piston stroke depend on * offset
crank angle
B crank radius the crank angle value when the piston at TDC is...... 120 30 0*2pi B the maximum ratio of crank radius to connected length is *
4
0.25-0.3 0.25 0.3
Answers
The crank angle value when the piston is at Top Dead Center (TDC) is 0 radians or 0 degrees. The maximum ratio of the crank radius to the connected length is 0.3.
The crank angle value refers to the angle between the crankshaft and a reference point when measuring the position of the piston. When the piston is at Top Dead Center (TDC), it is at its highest point in the cylinder. The crankshaft is positioned such that the connecting rod is aligned with the crank radius and the piston is at the topmost position. This corresponds to a crank angle value of 0 radians or 0 degrees.
Regarding the maximum ratio of the crank radius to the connected length, this value is given as 0.3. The crank radius is the distance from the center of the crankshaft to the center of the crank pin, and the connected length is the distance from the center of the crank pin to the center of the piston pin. The maximum ratio of 0.3 indicates that the crank radius is 0.3 times the connected length.
It's important to note that these values are specific to the context of the problem statement provided. Different engines or mechanisms may have different values for the crank angle at TDC and the maximum ratio of crank radius to connected length.
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WILL MARK BRAINLIEST !!!! RIGHT ANSWERS ONLY PLSSSSS
Answers
Answer:
11
Step-by-step explanation:
Since ΔNOP is a traingle, all the angles added up together equal 180 degrees.
(5x-8) + (x-5) + (6x+1) = 180
Now simplify by adding like terms
12x-12 = 180
Solve for x by adding 12 to both sides and then dividing both sides by 12
12x=192
x=16
Once you solved for x, plug it into the angle you need to find.
m∠O=(x-5)
=(16-5)
=11
A committee consisting of 3 men and 5 women is selected from 5 men and 10 women. Find how many way, this committee can be formed
Answers
There are 2,520 ways to form a committee consisting of 3 men and 5 women from a group of 5 men and 10 women.
How to determine how many way, this committee can be formedThe combination formula gives the number of possibilities to choose a committee of three persons from a group of five:
C(5, 3) = 5! / (3! * 2!) = 10
Also, the number of ways to select a committee of 5 women from 10 women is given by:
C(10, 5) = 10! / (5! * 5!) = 252
The total number of ways to select a committee consisting of 3 men and 5 women: 10 * 252 = 2,520
Therefore, there are 2,520 ways to form a committee consisting of 3 men and 5 women from a group of 5 men and 10 women.
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Pleaseeee helpppp meeeeeeeeee with this ? Pleaseeee dontttt guesssssss
Answers
Answer:
D
Step-by-step explanation:
(3x+2) + (3x+2) + 2x + 2x
combine
10x+4
Answer:
D.) 10x+4
Step-by-step explanation:
perimeter= all the sides added together
3x+2+3x+2=6x+4
2x+2x=4x
6x+4+4x=10+4
Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
AB is parallel to CD, and EP is perpendicular to AB.
The number of 90° angles formed by the intersections of EP and the two parallel lines AB and CD is
Answers
Answer:
8 right angles
Step-by-step explanation:
1. If two lines are perpendicular then we know they form 4 right angles, so EP and AB from 4 right angles.
2. The question states that AB and CD are parallel. Since we know EP is intersecting AB and CD, we can say that EP is perpendicular to CD as well because of a theorem that states, "...that if there are two parallel lines in the same plane and there is a line perpendicular to one of them, then it is also perpendicular to the other one."
3. So because of that theroem, we can add another 4 right angles from the intersection of EP and CD.
4. When you add all the right angles together, you get 8 right angles in total.
Answer:
ype the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar.
AB is parallel to CD, and EP is perpendicular to AB.
The number of 90° angles formed by the intersections of EP and the two parallel lines AB and CD isStep-by-step explanation:
(Q2) The set of line segments _____ meet the requirements to form a triangle.8 cm4 cm3 cm
Answers
To form a triangle, the set of line segments must satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Therefore, we need to check if the given line segments 8 cm, 4 cm, and 3 cm meet this requirement.
We can start by checking if the sum of the two smaller sides (3 cm and 4 cm) is greater than the largest side (8 cm). 3 cm + 4 cm = 7 cm, which is less than 8 cm. Therefore, these three line segments cannot form a triangle.
In general, for a set of line segments to form a triangle, the largest side must be smaller than the sum of the other two sides. In this case, the line segment of 8 cm is too long compared to the other two sides, which makes it impossible to form a triangle.
In conclusion, there are no line segments that meet the requirements to form a triangle with lengths of 8 cm, 4 cm, and 3 cm.
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please help!! i'm very confused
Answers
Answer:
Count the squares if the squares are half then add them until they make a whole then add up the remainder of what can't be whole
Step-by-step explanation:
O
-200
Is the√8 a rational or irrational number?
irrational, because
its decimal
rational, because all
expansion does not radicals are rational
repeat
rational, because its
decimal expansion
eventually repeats
Sod
3980 207
irrational, because
all radicals are
irrational
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Dec 15
Answers
The square root of 8 is an irrational number, because it is not an exact square root.
What are rational and irrational numbers?The rational numbers are composed by the set of all numbers that can be represented by fractions, such as whole numbers, terminating decimals, or repeating decimals.
The irrational numbers, conversely, are composed by the set of numbers that cannot be represented by fractions, such as non-exact roots and non-terminating decimals.
The square root of 8 is non-exact, hence it is an irrational number, as the square root is then a non-terminating and non-repeating decimal.
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The histogram shows the number of classes missed by students in a class during the school year. What percent of the class missed three or fewer days?
Answers
Answer:
36%
Step-by-step explanation:
9/(9+12+3) × 100%
= 9/25 × 100% = 36%
__________
What is the domain of y=3/(x-2)^2 -4?
Answers
Given:
\(y=\frac{3}{(x-2)^2}-4\)Required:
To find the domain of the given function.
Explanation:
Consider
\(y=\frac{3}{(x-2)^}-4\)Here when x =2, the y value becomes infinet.
Therefore the domain of the function is set of all real numbers, except 2.
\(D=\lbrace x\in R:x\ne2\rbrace\)In interval notation :
\((-\infty,2)\cup(2,\infty)\)Final Answer:
The domain is
\(D=\lbrace x\in R:x\ne2\rbrace\)A rocket is traveling at a speed 1500 m/s. How far will the rocket travel in 8 seconds?
Answers
Answer:
12,000m
Step-by-step explanation:
distance=speed×time
1500×8=12000m
Answer:
12,000
Step-by-step explanation:
1500m\s
8s
1500×8
= 12,000
A state park charges $6.00 entry fee plus $7.50 per night of camping. Write an algebra expression for the cost in dollars of entering the park and the camping for n night
Answers
Answer:
C=$7.50n + $6
Step-by-step explanation:
graph the image of V (3,–7) after a rotation 180° clockwise around the origin.
Answers
Answer and Step-by-step explanation:
It is in the screenshot.
The point is (-3, 7), and would be noted as V'.
#teamtrees #WAP (Water And Plant)
Image of the point V is V' = (-3, 7) as shown in the graph below.
What is Coordinate Geometry?One of the most intriguing ideas in mathematics is called coordinate geometry. By using graphs with curves and lines, coordinate geometry (also known as the analytic geometry) explains how geometry and algebra are related. They can answer geometrical problems because it gives them geometrical aspects of algebra. In this area of geometry, a pair of ordered numbers is used to describe the location of points on a plane.
As per the given data:
Coordinates of point V = (3, -7)
Rotation to be given = 180° (clockwise)
For drawing the image of point V (3, -7):
Step 1: Draw a line passing through the origin and V (3, -7) extending through 2nd and 4th quadrant.
Step 2: Change sign of x and y coordinates as rotation is of 180° and mark the point in the 2nd quadrant.
Image of the point V is V' = (-3, 7) as shown in the graph below.
Hence, the image of the point V is V' = (-3, 7).
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If N=m/x + q , find the value of q when N = 1whole 4/5 ,m=9 and x =2
please help asap
Answers
Answer:
The value of q is -2.7
Step-by-step explanation:
Given;N = m ÷ x + q
To Find;q = ?
when,
N = 1⅘ = 9/5
m = 9
x = 2
Now,
N = m ÷ x + q
9/5 = 9/2 + q
q = 9/5 – 9/2
q = 1.8 – 4.5
q = -2.7
Thus, The value of q is -2.7
-TheUnknownScientist 72
Answer:
N=m/x + q
First turn the mixed fraction into improper fraction.
1 4/5 in improper fraction is 9/5. So,
9/5= 9/2 + q
1.8 = 4.5 + q
q= 1.8 - 4.5
q= -2.7
two cheeseburgers and one small order of fries contain a total of 1350 calories. three cheeseburgers and two small orders of fries contain a total of 2140 calories. find the caloric content of each item.
Answers
Two cheeseburgers contain a total of 1120 calories (2 x 560) and one small order of fries contains 230 calories. And three cheeseburgers contain a total of 1680 calories (3 x 560) and two small orders of fries contain a total of 460 calories (2 x 230).
Let's use a system of equations to solve for the caloric content of each item.
Let x be the number of calories in one cheeseburger and y be the number of calories in one small order of fries.
From the first statement, we know that:
2x + y = 1350
From the second statement, we know that:
3x + 2y = 2140
We can use these two equations to solve for x and y. First, we'll solve for y in terms of x by rearranging the first equation:
y = 1350 - 2x
Now we can substitute thisn expression for y into the second equation:
3x + 2(1350 - 2x) = 2140
Simplifying this equation, we get:
3x + 2700 - 4x = 2140
-x = -560
x = 560
So one cheeseburger contains 560 calories. We can plug this value back into either of the original equations to solve for y:
2(560) + y = 1350
y = 230
So one small order of fries contains 230 calories.
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Use the following compound interest formula to complete the problem. a = p (1 startfraction r over n endfraction) superscript n superscript t rodney owes $1,541.05 on his credit card. his card has an apr of 16.29%, compounded monthly. assuming that he makes no payments and no purchases, how much will he owe after one year? a. $1,561.97 b. $1,811.70 c. $1,792.09 d. $1,541.05
Answers
The amount that he owes after one year is 1792.09 dollars. Then the correct option is C.
What is the percentage?The amount of something is expressed as if it is a part of the total which is a hundred. The ratio can be expressed as a fraction of 100. The word percent means per 100. It is represented by the symbol ‘%’.
Rodney owes $1,541.05 on his credit card.
His card has an APR of 16.29%, compounded monthly.
Assuming that he makes no payments and no purchases.
He owes after one year will be
Amount = 1541.05 × 1.1629
Amount = 1792.087 ≅ 1792.09
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Answer:
B.
Step-by-step explanation:
$1811.70
Need help please...........
Answers
Answer:
49 is the missing angle.
Step-by-step explanation:
just add the other angles then subtract by 180 to get your answer! have a nice day!