Answer: The correct option is (B).
True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.
Step-by-step explanation:
Given that;
If V₁ ....... V₄ are in R⁴ and V₃ = 2V₁ + V₂ then {V₁, V₂, V₃, V₄} is linearly dependent.
Lets {V₁, V₂, V₃, V₄} are linearly dependent
Then there exist a scalars C₁, C₂, C₃, C₄
So that C₁V₁ + C₂V₂ + C₃V₃ + C₄V₄ = 0
where at least one of the Ci ≠ 0.
Take C₃ ≠ 0 then we have V₃ = (C₁V₁ + C₂V₂ + C₄V₄) / C₃
V₃ is a linear combination of V₁, V₂ and V₄}
that is
Given V₃ = 2V₁ + V₂
⇒ 2V₁ + V₂ - V₃ = 0
⇒ 2V₁ + V₂ + V₃ + 0V₃ = 0
Here, C₁ = 1, C₂ = 1, C₃ = -1 and C₄ = 0
So that {V₁, V₂, V₃, V₄} is linearly dependent.
therefore option B id the right answer.
- True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and set is linearly dependent.
B is the correct option. True, The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others and the set is linearly dependent.
If V₁ ....... V₄ are in R⁴ and V₃ = 2V₁ + V₂ then {V₁, V₂, V₃, V₄} is linearly dependent.
What is meant by linearly dependent?A set of vectors is linearly dependent if some vector can be expressed as a linear combination of the others.
Let's consider {V₁, V₂, V₃, V₄} are linearly dependent
then there exist a scalars C₁, C₂, C₃, C₄
therefore, C₁V₁ + C₂V₂ + C₃V₃ + C₄V₄ = 0
where at least one of the Ci ≠ 0.
Lets C₃ ≠ 0 then we will get
V₃ = (C₁V₁ + C₂V₂ + C₄V₄) / C₃
V₃ is a linear combination of V₁, V₂, and V₄
which means V₃ = 2V₁ + V₂
2V₁ + V₂ - V₃ = 0
2V₁ + V₂ + V₃ + 0V₃ = 0
Here, C₁ = 1, C₂ = 1, C₃ = -1 and C₄ = 0
therefore, {V₁, V₂, V₃, V₄} is linearly dependent.
So, option B is correct here.
True. The vector V₃ is a linear combination of V₁ and V₂, so at least one of the vectors in the set is a linear combination of the others, and the set is linearly dependent.
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4.2540 centimeters are equal to how many inches?!
Answer: 1.6748031in
Step-by-step explanation:
6х + 15 = 3(2х + 5) How many solutions does the equation to the left have?
Answer:
Infinitely many solutions
Step-by-step explanation: You have to distribute 3(2x+5) which equals 6x+15 which is equal to the other equation. Same slope same y-intercept means (infinitely many solutions).
There are 110 calories per 177.4 grams of Cereal X. Find how many calories are in 233.5 grams of this cereal,
There are calories in 233.5 grams of this cereal.
(Round to the nearest whole number as needed.)
Answer:
145
Step-by-step explanation:
110÷177.4=.62 cal per gram
.62×233.5=145 rounded
The length of rectangle is 5 centimeters less than three times its width .It’s area is 12 square centimeters. Find the dimensions of the rectangle
Answer:
14
Step-by-step explanation:
Answer: The length is 4 the width is 3
Step-by-step explanation:
What is the other term for integers
I NEED A SERIOUS ANSWER. THANK YOU!!
I really hope this helped you. If it did, could u plz mark me as brainliest?
round 2.294 to nearest hundredth
Answer:
The answer is 2.29 !
Step-by-step explanation:
To round 2.294 to the nearest hundredth means to round the numbers so you only have two digits in the fractional part. We use the following rules to round 2.294 to the nearest hundredth: A) If the last digit in the fractional part of 2.294 is less than 5, then simply remove the last the digit of the fractional part
Find the x- and y-intercepts of the graph of the equation.
f(x) = 4x – 12
x-intercept
(x, y) =
y-intercept
(x, y) =
Answer:
x intercept is (3, 0). y intercept is (0, -12).
Step-by-step explanation:
x intercept is when y = 0. [f(x) = y] So 0 = 4x - 12. Solving for x gives you a value of 3. [12 = 4x; divide by 4]
y intercept is when x = 0. So y = 4(0) - 12. Solving for y gives you a value of -12. [y= 0 - 12; y = -12]
What is the slope of the line that passes through the points M(-3,5) and N (1,8)
Answer:
the answer is A. 3/4
Step-by-step explanation:
Try using Symbolab for future reference it works really well (it's what I use ALL the time)!
How to find the probability of the complement of an event?
Use the Distributive Property to expand the expression -(u-v)
Answer:
(U+V) is the answer to the solution
Determine the quotient
Answer:
option 2: [tex]\large \frac{10}{12}[/tex]
Step-by-step explanation:
when dividing fractions, you can actually multiply them together by the reciprocal of the second one. (reciprocal is just flipping the fraction)
so, [tex]\frac{2}{3}[/tex] ÷ [tex]\frac{4}{5}[/tex]
becomes [tex]\frac{2}{3} * \frac{5}{4}[/tex]
to multiply fractions together, just multiply the top and bottom.
2 * 5 = 10
3 * 4 = 12
so the answer would be [tex]\frac{10}{12}[/tex]
Write the equation that represents the model above. Please help!
Answer:
2x + 30 = -2x + 2
Step-by-step explanation:
left side has 2 x's so u get 2x and it also has 3 10's so 2x+30
do the same on the right
2 -xs so -2x and 2 ones
-2x+2
These shapes below are mathematically
Answer:
x=30
Step-by-step explanation:
they are conqruent,
the proportion is 2.5 as we can find that by 20/8
2.5 times 12 is 30
Please help!! i cant fail math
Answer:
The scale factor is 2
Step-by-step explanation:
Which of the following quantities are inversely proportional? WILL GIVE BRAINLIEST AND 25 POINTS
a
The number of hours worked and the amount of money earned, assuming the worker is paid by the hour
b
The height of a rectangular fish tank and the area of its base, if the volume is constant
c
The amount of candy purchased for $25.50 and the price per pound
d
The time it takes to use a 5 lb bag of dry cat food and the number of cats, if each cat eats the same amount of food per same time interval.
Answer:
I believe the answer is D
Step-by-step explanation:
Inverse proportion occurs when one value increases and the other decreases
D is the answer because as each cat eats the same amount of dry cat food, there is less dry cat food in the bag; so this is why D best answers the question.
Hope this helps!
Answer:
a is false, B is true,
Step-by-step explanation:A is false because the more hours you work, the more money you get.
B is true because if the volume is constant, the bigger the length, the smaller the width, or vice versa.
The cost of Marianne's old bracelet is two-thirds
The cost of her new bracelet. The cost of her old
bracelet is $18. Need help what Is this solution
Answer:
the answer is $12
Step-by-step explanation:
to get the answer you would multiply 18 by 2/3 or you can divide by 3 then multiply what you get from dividing by 3 by 2.
version 1: 18(2/3) = ?
12
version 2: 18/3=?
6 you want to multiply by to because that is 1/3 of the original price
6(2) = 12
Either way you get the same answer. Hopes this helps
Anthony has saved $15 of the $140 he needs to purchase a new bicycle. He plans to save $15 each week w, until he has enough money to buy the bicycle. Write an equation to find the number of weeks it will take Anthony to save enough money to buy the bicycle.
Answer:
(140-15)÷15=W
Step-by-step explanation:
140-15=125
125 still needed. divide that by the amount that will be saved each week which is 15 a week and you get 8.3. If they want an actual answer you would say 9 weeks because if you only did 8 Anthony would be short $5 so hed have to wait an additional week to have enough to cover the purchase. So thats why the answer would be 9
Brainliest please!!!
calvin had 43 cents he found 14 more cents. how much money dose calvin have rounded to the nearest dime
Answer:
Calvin has 60 cents rounded to the nearest dime. without rounding he would only have 57
Helpp me plzzzzzZZzz
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
6x - 15y = 135
6x -15y = 135
-15y = 135 -6x
y = (135-6x)/-15
y = 2/5x + 9
Grade Math
Do Not Reproc
26. What is the solution to the equation 3(4x – 11) + 15 = -6(-x + 7)?
А
X=-30
B
x= -10
C X=-4
D
x= -1
make a list of all 3 digit numbers using the digit 5, 2, and 6
which equation show you how to find 13-6
Answer:
13-6=7
Step-by-step explanation:
lol
Answer:
it equals 7
Step-by-step explanation:
Trisha uses 3 cups of sugar for every 2 teaspoons of baking soda to make a batch of cookies. Which proportion could be solved to find X, the number of teaspoons of baking soda needed for 9 cups of sugar?
Answer:
Heres how to solve.
Step-by-step explanation:
3 cups of sugar for every 2 teaspoons of baking soda.
So 6 cups of sugar for 4 teaspoons of baking soda.
And 9 cups of sugar for 6 teaspoons of baking soda.
Basically you just multiply by 3, 3×3=9 and 2*3=6
The number of teaspoons of baking soda Trisha needed will be 6.
It is given that Trisha uses 3 cups of sugar for every 2 teaspoon of baking soda.
We have to find out that what will be the number of teaspoons of baking soda needed for 9 cups of sugar.
If a car goes 10 km in two hours , how far will it go in one hour ?
The car will go, 10 ÷ 2 = 5 km in an hour.
As Trisha uses 3 cups of sugar for every 2 teaspoons of baking soda.
For 1 cup of sugar Trisha will have to use 2/3 teaspoons of baking soda .
For 9 cup of sugar Trisha will use ;
= (2/3) × 9 = 18 ÷ 3
= 6
So, Trisha will have to use 6 teaspoons of baking soda for 9 cups of sugar.
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Which of the following numbers would be an outlier if added to the data set below?
507, 586, 499, 542, 615, 600, 561, 519
Group of answer choices
610
487
535
380
Answer:
The answer is 380
Step-by-step explanation:
It is 380 because 610, 487, 535 will be fine in the group but 380 is different so it will be considered a Outlier
The value of m varies inversely as the square of n. When n = 3 m = 6.
What is the positive value of n when m = 13.5?
(I already know C. is wrong)
A. 18
B. 2
C. 9 XXXX
D. 4
Answer:
B.]2
Step-by-step explanation:
The required positive value of n is 2. Hence, option B is correct.
Important information:
m varies inversely as the square of n.Whem n = 3, then m = 6.Inverse proportion:It is given that m is inversely proportional to the square of n. So,
[tex]m\propto \dfrac{1}{n^2}[/tex]
[tex]m=\dfrac{k}{n^2}[/tex] ...(i)
Where, k is the constant of proportionality.
Substitute m = 6 and n = 3 in the above equation.
[tex]6=\dfrac{k}{3^2}[/tex]
[tex]6=\dfrac{k}{9}[/tex]
[tex]6\times 9=k[/tex]
[tex]54=k[/tex]
Substitute this value in (i).
[tex]m=\dfrac{54}{n^2}[/tex]
Substitute m = 13.5 in the above equation.
[tex]13.5=\dfrac{54}{n^2}[/tex]
[tex]n^2=\dfrac{54}{13.5}[/tex]
[tex]n=\pm \sqrt{4}[/tex]
[tex]n=\pm 2[/tex]
Therefore, the required positive value of n is 2. Hence, option B is correct.
Find out more about 'Inverse proportion' here:
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Mr. Nell is painting his coffee table. The micture that he adds to the paint is made of 5/6 cup
baking soda for every 5 tablespoons of water.
What is the rate in cups of baking soda per tablespoon of water?
Answer:
1/6 cups
Step-by-step explanation:
5/6 /5 = 5/6 divided by 5
= 5/6 x 1/5
= 1/6
so your answer is 1/6 cups of baking soda per tablespoon of water
yw ;)
The rate for cups of baking soda per tablespoon of water is 1/6.
What is Division method?Division method is used to distributing a group of things into equal parts. Division is just opposite of multiplications. For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
Given that;
The mixture that he adds to the paint is made of 5/6 cup baking soda for every 5 tablespoons of water.
Hence, The rate for cups of baking soda per tablespoon of water is,
⇒ 5/6 ÷ 5
⇒ 5/6 × 1/5
⇒ 1/6
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May you all help me.I need to find this answer to help me study for my midterm test.I will give Brainliest.
9514 1404 393
Answer:
x = 17y = 26Step-by-step explanation:
In the left problem, you use the fact that the sum of the segment lengths is equal to the overall length.
AC +CB = AB
(3x -4) +(x -2) = 62
4x -6 = 62 . . . . . collect terms
4x = 68 . . . . . . . add 6
x = 17 . . . . . . . . . . divide by 4
__
In the right problem, you use the fact that the sum of the angles is equal to the overall angle. Here, that overall angle is a linear angle, so measures 180°.
∠DFG +∠GFE = ∠DFE
(5y +3) +(2y -5) = 180
7y = 182 . . . . . . . . . . . . . . collect terms, add 2
y = 26 . . . . . . . . . . . . . . . .divide by 7
The standard unit for measurement for volume is
Answer:
I'm pretty sure it's cubic meters
