By definition of linear independence, the vectors in the set {a, b, c} are independent if
[tex]k_1\vec a+k_2\vec b+k_3\vec c=\vec0[/tex]
can only be obtained with the choice of k₁ = k₂ = k₃ = 0.
This vector equation corresponds to the system of linear equations
[tex]\begin{cases}k_1 - 2k_3 = 0 \\ 2k_1 + k_2 = 0 \\ k_1 + 2k_3 = 0\end{cases}[/tex]
The first equation says k₁ = 2 k₃, while the third one says k₁ = -2 k₃. This can only be possible if k₁ = k₃ = 0, and from the second equation it follows that k₂ = 0. So the given set is linearly independent (and *not* dependent).
WILL GIVE BRANLEST IF CORRECT
Which could be the dimensions of a rectangular prism whose surface area is greater than 140 square feet? SELECT 3 OPTIONS
A.) 6 feet by 2 feet by 3 feet
B.) 6 feet by 5 feet by 4 feet
C.) 0 7 feet by 6 feet by 4 feet
D.) 8 feet by 3 feet by 7 feet
E.) O 8 feet by 4 feet by 3 feet
Answer:
B or C
Step-by-step explanation:
B area = 2 ( 6 x5 + 5 x 4 + 4 x 6) = 148 square feet
C area = 2 ( 8x3 + 3x7 + 7x8) = 202 sq ft
Find two pairs of prime numbers less than 20 that differ by 4
Answer:
3 and 7,
7 and 11,
13 and 17
Step-by-step explanation:
Prime numbers have exactly two factors, the number itself and 1. This just means that nothing "goes into" these numbers. Example: 7. 7 is a prime number; the only number that goes into 7 is 7 (and 1)
First, find all the prime numbers that are less than 20:
2, 3, 5, 7, 11, 13, 17, 19
Next find the pairs that are 4 units apart. 3 and 7 works.
7 - 3 is 4
Also, 13 and 17 works, and 7 and 11.
What is the complex conjugate of 12i ?
[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]
The conjugate of given complex number is ~
[tex]\qquad \tt \dashrightarrow \: \overline{z} = - 12i[/tex]
Conjugate of a complex number is the same number with its imaginary part having opposite sign.
Eg. if z = a + i b
Then it's Conjugate = a - i b
Which set of data is represented by the box plot?
Answer:
Step-by-step explanation:
It looks like the solution is the first set of data
{1, 4, 6, 10, 12, 14, 19, 20, 25 }
because: median is 12, Q1 is 6, Q3 is 19, yet the range is from 1 to 25 while the range of the box and whisker plot is 1 to 24.
So theoretically none of those sets represents the box plot.
Can you find the area and explain how you got the area
Answer:
102cm^2 - hope this helps
Step-by-step explanation:
find the area of the rectangle first in the middle
which equals 6 x 13 = 78cm^2
then find the traingles on the side
(6 x 4) / 2 = 12
there are 2 traingles so it would be 12 + 12 = 24
so all together the area would be 78 + 24 = 102cm ^2
To number the pages of a book,2022 digits are used. How many pages are in the book?
Answer:
710
Step-by-step explanation:
Numeration of pages goes from 1.
9 pages with 1-digit numbers, from 1 to 9.
90 pages with 2-digit numbers, from 10 to 99.
So, 2*90 + 9 = 189 digits are just used to numerate 9 + 90 = 99 pages.
The rest of numbers are 3-digit.
2022-189/3 = 611 pages with 3-digit numbers.
Total pages = 9 + 90 + 611 = 710.
The number the pages of a book,2022 digits are used there are 8880 pages in the book.
Let's assume there are "x" pages in the book. Each page number requires a certain number of digits to represent. The number of digits required to represent a page number depends on the value of the page number itself.
For example:
Page numbers from 1 to 9 require 1 digit each.
Page numbers from 10 to 99 require 2 digits each.
Page numbers from 100 to 999 require 3 digits each.
And so on.
Since we're given that 2022 digits are used in total, we can set up an equation based on the above observations:
Number of 1-digit page numbers + Number of 2-digit page numbers + Number of 3-digit page numbers + ... = 2022
Now let's solve this equation to find the number of pages:
Number of 1-digit page numbers = 9 (from 1 to 9)
Number of 2-digit page numbers = 90 - 10 + 1 = 81 (from 10 to 99)
Number of 3-digit page numbers = 900 - 100 + 1 = 801 (from 100 to 999)
Substituting these values into the equation:
9 + 81 + 801 + ... = 2022
Now we need to find the number of terms in this sequence. Each term corresponds to a certain number of digits, and we want to find the smallest number of digits that will exceed 2022. We can try different numbers of digits until we find the correct one:
Number of 4-digit page numbers = 9000 - 1000 + 1 = 8001
Adding the terms up:
9 + 81 + 801 + 8001 = 8880
To know more about digits here
https://brainly.com/question/30142622
#SPJ3
Find the point on the line -5x + 7y - 4 = 0 which is closest to the point (2,3).
Answer:
(x, y) = (2 35/74, 2 25/74)
Step-by-step explanation:
The closest point on the line to the given point will be the point of intersection of the given line and a perpendicular through the given point.
__
A line perpendicular to ax+by+c=0 that goes through point (h, k) can be written as ...
b(x-h) -a(y-k) = 0
For the given line and point, the perpendicular line will be ...
7(x -2) +5(y -3) = 0
7x +5y -29 = 0
Using the cross-multiplication method, we can find the solutions to the system of equations consisting of these two lines. It will be ...
-5x +7y -4 = 07x +5y -29 = 0Δ = (-5)(5) -(7)(7) = -74
Δx = (7)(-29) -(5)(-4) = -183
Δy = (-4)(7) -(-29)(-5) = -173
x = Δx/Δ = -183/-74 = 2 35/74 ≈ 2.4730
y = Δy/Δ = -173/-74 = 2 25/74 ≈ 2.3378
__
For more on the cross multiplication method, you can read ...
https://brainly.com/question/26397343
PLEASE HELP PLEASE HELP PLEASE
Answer:
I think it's D.
Step-by-step explanation:
The grid is divided into 100 smaller squares, with 10 squares in each row. 25 squares out of 100 squares are shaded. 25% of the grid is shaded and 25% belongs to 20% so the grid that's 2/5 shaded it's D.
hey does anyone know the answer to this? please. i really don’t know what i’m doing and completely depend on the internet for answers. if yk an app or website that helps with these type of problems lmk
Answer:
I believe the answer is #3 c=kv because you need to find c and it varies based on k and v.
Step-by-step explanation:
Solve for x: −7 < x − 1 < 8
6 < x < 9
−6 > x > 9
6 > x > −9
−6 < x < 9
[Hello, blueface1728]
Answer:
[D] −6 < x < 9
Step-by-step explanation:
So, if a < u <b then a < u and u <b
-7 < x - 1 and x -1 < 8
Solving
-7 < x - 1 = x > -6
x - 1 < 8 = x < 9
Combine the intervals
-6 < x < 9
Now looking at the answer choice :
6 < x < 9
−6 > x > 9
6 > x > −9
−6 < x < 9
Thus, the answer is [D] −6 < x < 9
Kavinsky
The ceiling of Katie's living room is a square that is 15 ft long on each side. To decorate for a party, she plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Katie can buy rolls that each contain 20 ft of crepe paper. What is the minimum number of rolls she should buy? ( Show Your Work). Will Mark Brainliest if answered correctly and please do not reshare another students answer from brainly or any other websites to answer my question or you'll be reported. Thank you.
Answer:
The answer is 70
Step-by-step explanation
Add 15 by 15 for each side then add 20 by 20 for each other side
Can someone please teach me how to solve this question step-by-step?
Answer:
[tex]\frac{1}{12}[/tex]
Step-by-step explanation:
1) Construct a probability tree (check the attachment).
1.1) Change the given items/values into fractions. In this case, there are 3 entrees, each with a probability of [tex]\frac{1}{3}[/tex] because the probability of selecting a hamburger (an example that could be applied to other options too) is 1 out of the 3 options. Likewise is the case with sides and drinks; the probability of selecting fries (or vegetable) out of the two options is [tex]\frac{1}{2}[/tex], and the probability of selecting milk (or juice) out of the two options is [tex]\frac{1}{2}[/tex].
Which is a perfect square?
6 ^1
6 ^2
6 ^3
6 ^5
Answer:
B, because when you square 6 you get 36.
What is the domain and range!!
PLEASE HELP I WILL BE GIVING OUT MORE POINTD AND MARKED BRAINIST ONLY IF YOU ARE RIGHT THO I DO CHECK !!
Recall that domain is in x axis
Thus from the graph we can see,
the domain is x ≥ -1 and x ≤ 3
Thus final domain: -1 ≤ x ≤ 3
Answer:
[tex]\textsf{domain:}\quad-1\leq x\leq 3[/tex]
[tex]\textsf{range:}\quad\dfrac{16}{3}\leq y\leq 27[/tex]
Step-by-step explanation:
Information
Domain of a function: set of all possible input values (x-values)
Range of a function: set of all possible output values (y-values)
Closed circle: less than or equal to and greater than or equal to (≤ or ≥).
Open circle: less than or greater than (< or >)
Domain
There is a closed dot at x = -1 and x = 3
Therefore, the domain is -1 ≤ x ≤ 3
Range
To calculate the exact range, we need to figure out the equation of the function (as it is difficult to read the exact value of y at x = -1).
From inspection of the graph, we can identify the following ordered pairs:
(1, 12) (2, 18) (3, 27)
General form of an exponential equation: [tex]y=ab^x[/tex]
Inputting the first two ordered pairs into the exponential equation:
[tex]\implies ab^1=12[/tex]
[tex]\implies ab^2=18[/tex]
Dividing the equations to find b:
[tex]\implies \dfrac{ab^2}{ab^1}=\dfrac{18}{12}[/tex]
[tex]\implies b=\dfrac32[/tex]
Inputting b into the first equation to find a:
[tex]\implies \dfrac32a=12[/tex]
[tex]\implies a=8[/tex]
Therefore, the equation of the function is: [tex]y=8\left(\dfrac32\right)^x[/tex]
Input [tex]x = -1[/tex] into the equation to find y:
[tex]\implies 8\left(\dfrac32\right)^{-1}=\dfrac{16}{3}[/tex]
Therefore, the range is [tex]\dfrac{16}{3}\leq y\leq 27[/tex]
The number of boys in a school is 120. If the ratio of boys to girls is 2:3, find the total number of students in the school.
Answer:
300
Step-by-step explanation:
For every two boys, there are three girls, so divide 120 by 2 = 60
Multiply 60 by 3 = 180
Total number of students in school: 120 + 180 = 300
Select the correct answer. If d=8, what is the value of the expression 4+d/2 ? A.4 B.6 C.8 D.12 E.14
Answer:
C
Step-by-step explanation:
4+(8/2)
Bidmas
4+4 = 8
Answer is C
Ask me for any questinosss
And brainliest would be appreciated :)
Answer:
d=8
8/2
4
4+4=8
the answer is (c) 8
The equations of three lines are given below.
Line 1: 3y - 2x+5
Line 2: 4x+6y= 2
Line 3:
+2
2
Answer:
Step-by-step explanation:
A team won 60% of the games they played. If the team lost 12 games, how many games did they win?
well, we know they won 60% of the games, meaning 100% - 60% = 40%, they lost 40% of the games, and we also know that that number is 12.
[tex]\begin{array}{ccll} \%&amount\\ \cline{1-2} 40 & 12\\ 60& x \end{array} \implies \cfrac{40}{60}=\cfrac{12}{x}\implies \cfrac{2}{3}=\cfrac{12}{x} \\\\\\ 2x=36\implies x=\cfrac{36}{2}\implies x=18[/tex]
Help help help help math math
Mr. Davis invested $8,000 in a savings account. The bank pays 4.5% annual compound
interest. Mr. Davis never withdrew nor deposited in the savings account. Which of the
following exponential graphs represents the money y that Mr. Davis has after x years
Answer:
Compound interest formula
[tex]\sf A=P(1+\frac{r}{n})^{nt}[/tex]
where:
A = final amountP = principalr = interest rate (in decimal form)n = number of times interest applied per time periodt = number of times periods elapsedGiven:
A = yP = $8,000r = 4.5% = 0.045n = 1t = xSubstitute given values into the equation:
[tex]\implies y=8000(1+\frac{0.045}{1})^x[/tex]
[tex]\implies y=8000(1.045)^x[/tex]
So the graph will have a y-intercept of (0, 8000)
The rectangle of the rectangle is shown 44m squared. Find out the missing length of x
Answer:
12 m
Step-by-step explanation:
3 ⅔
= 3 + 2/3
= 9/3 + 2/3 { LCM = 3 }
= ( 9 + 2 ) / 3
= 11/3
In the diagram,
Length ( l )= x m
Breadth ( b ) = 3 ⅔ m = 11/3 m
Given that area of the rectangle = 44 m²
Formula : -
Area of the rectangle = lb
lb = 44
x * 11/3 = 44
x = ( 44 * 3 ) / 11
x = 4 * 3
x = 12 m
Therefore,
the missing length = 12 m
if the Vertical angle of an isosceles triangle is equal to the sum of the base angle find the size of each angle
Answer:
I try my best to give you answer
Find the present value of the following future amount.
$2000 at 12% compounded annually for 25 years
The present value is $ _____
(Round to the nearest cent as needed.)
Answer:
$ 39,576.93
Step-by-step explanation:
Beau's suitcase weighs 40 pounds. which is NOT a reasonable prediction for the number of items he packed?
A. 39
B.45
C. 31
D. 42
Answer:
B
Step-by-step explanation:
45 items is not a reasonable number, as the suitcase itself probably weighs about 20 pounds, and the likeliness of each item weighing about 1/2 a pound is unreasonable.
Answer:
The answer is 31.
Step-by-step explanation:
Since Beau's suitcase weighs 40 pounds he packed at least 35 items. Anything less than 35 items couldn't be possible.
See attachment. I got it right on my quiz:)
A conveyor belt drops gravel to create a pile in the shape of a right circular cone. The cone is formed from 3,200 ft^3 of gravel. If the height of the cone is 24ft, what is the radius, in feet, of the base cone? Round your answer to the nearest tenth of a foot.
Answer:
11.3 ft
Step-by-step explanation:
[tex]V_{gravel}=3,200\: ft^3\\\\height \:(h) =24\: ft\\\\ To \: find:\: radius\:(r)[/tex]
Since, gravel is in the shape of right circular cone.
[tex]\implies V_{gravel}= \frac{1}{3}\pi r^2 h\\\\\implies 3,200= \frac{1}{3}(3.14) r^2 (24)\\\\\implies r^2=\frac{3,200\times 3}{3.14\times 24}\\\\\implies r^2=\frac{9,600}{75.36}\\\\\implies r^2=127.388535\\\\\implies r=\pm\sqrt{127.388535}\\\\\implies r=\pm 11.286653\\radius\: can't\: be\: negative\\\\\implies r=11.286653\\\\\implies r \approx 11.3 \: ft[/tex]
Integrate the expression below
[tex]\displaystyle\int~4t(5t^2-1)^6 dt \\\\[-0.35em] ~\dotfill\\\\ u=5t^2-1\implies \cfrac{du}{dt}=10t~\hspace{10em} \cfrac{du}{10t}=dt \\\\[-0.35em] ~\dotfill\\\\ \displaystyle\int~4t~u^6\cdot \cfrac{du}{10t}\implies \int~\cfrac{4t~u^6}{10t}\cdot du\implies \int~\cfrac{2~u^6}{5}du\implies \cfrac{2}{5}\int~u^6\cdot du \\\\\\ \cfrac{2}{5}\cdot \cfrac{u^7}{7}\implies \cfrac{2(5t^2-1)^7}{35}[/tex]
Colleen found this decorative cookie tin to use for sending cookies to her grandfather what is the volume of the cookies tin
*NEED HELP I WILL GIVE BRAINLIEST FOR BEST ANSWER PLEASE HELP ME*
A cylinder has a height of 9 meters and a diameter of 36 meters. What is its volume? Use ≈ 3.14 and round your answer to the nearest hundredth.
______cubic meters
Answer:
0.15 cubic meters
Step-by-step explanation:
Formula volume = π x radius² x height
Answer
πr2h
Step-by-step explanation:
What do 12y and 8y represent? You can look up the formula for the volume of a cylinder pir^2h and plug in your dimensions.
Can someone help me please
Answer:
59.55555555555556
Step-by-step explanation:
Rosie went on a hiking trip. The first day she walked 18 kilometers. Each day since she walked 90% of what she walked the day before. What is the total distance Rosie has traveled by the end of the 10th day?
Answer:
Rosie has walked 163.8 kilometers by the 10th day,
Step-by-step explanation:
We know that the first day is 18 kilometers.
90% = 0.9
0.9 x 18 = 16.2
There are 9 more days
16.2 x 9 = 145.8
Now we add the first day
145.8 + 18= 163.8