Answer:
B: u = (1,5) and v = (-5,1)
Step-by-step explanation:
edge 2021
The pair of vectors which are orthogonal to each other will be u = ⟨1, 5⟩ and v = ⟨–5, 1⟩. Then the correct option is B.
What is a vector?The quantity which has magnitude, direction and follows the law of vector addition is called a vector.
For the orthogonal vector, the dot product of two vectors will be zero.
Check first option, we have
u·v = ⟨–3, 2⟩·⟨–2, 1⟩
u·v = 6 + 2 = 8 (incorrect)
Check second option, we have
u·v = ⟨1, 5⟩·⟨–5, 1⟩
u·v = –5 + 5 = 0 (correct)
Check third option, we have
u·v = ⟨2, 1⟩·⟨–4, 3⟩
u·v = –8 + 3 = –5 (incorrect)
Check fourth option, we have
u·v = ⟨2, 3⟩·⟨3, 1⟩
u·v = 6 + 3 = 9 (incorrect)
Then the correct option is B.
More about the vector link is given below.
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Three equal squares are superimposed as indicated in the figure. The areas of the overlapping zones are 2 cm², 5 cm², and 8 cm², respectively. The total area of the non-overlapping area of the squares is 117 cm². What is the length of the side of each square?
Answer: The square side lengths are 1 cm, 5 cm, and 11 cm.
===========================================================
Explanation:
Refer to the diagram below.
Define the following areas
A,B,C = non-overlapped regionsD,E,F = overlapped regionsIt doesn't really matter how you set up the labels, or what letters you pick, as long as you stay consistent.
We're told that "The areas of the overlapping zones are 2 cm², 5 cm², and 8 cm²", so let's make
D = 2E = 5F = 8Furthermore, we are told that "The total area of the non-overlapping area of the squares is 117 cm²" which means A+B+C = 117
---------------------------------------
Refer to the diagram. For now, focus on the upper right square. It has regions A, E, and F. The area of this square is A+E+F
Similarly, the area of the left-most square is D+B+E
The area of the bottom-most square is C+F+D
Add up the expressions we found and we get
(A+E+F)+(D+B+E)+(C+F+D) = A+B+C+2D+2E+2F
This represents the sum of all three square areas even if we peeled the squares apart to not overlap.
----------------------------------------
Let's plug in A+B+C = 117
We get
A+B+C+2D+2E+2F
117+2D+2E+2F
Now plug in D = 2, E = 5, and F = 8
117+2(2)+2(5)+2(8)
117+4+10+16
117+30
147
The sum of the three square areas is 147 square cm.
----------------------------------------
Now we have to do a bit of trial and error. We're looking for ways to break up 147 such that it is a sum of three squares.
In other words, we want to find integers m,n,p such that m^2+n^2+p^2 = 147
Let's try subtracting off 121
147-121 = 26
I picked 121 since it's the largest perfect square just smaller than 147
Repeat this process, but do so for 25 since 25 is smaller than 26
26-25 = 1
We can see that
1 + 25 + 121 = 147
1^2 + 5^2 + 11^2 = 147
One solution is m = 1, n = 5, p = 11. There may be other solutions. Keep in mind that m,n,p are positive whole numbers.
So we got a bit lucky with our trial and error process. If we didn't find such a triple, we'd have to try other possible combos of squares until we get the right match.
Because 1^2 + 5^2 + 11^2 = 147, this means the squares' side lengths are 1, 5, and 11.
A typical tip in a restaurant is 15% of the total bill. If the bill is $160, what would the typical tip be?
Answer:
24$
Step-by-step explanation:
15%=0.15
160*0.15=24
How many blueberries on the on cake roof
Answer:
say what
Step-by-step explanation:
Find the slope of the line graphed below.
Answer:
-3/5
Step-by-step explanation:
So first, you have to find out the two points :
(-1,-1), and (4,-4)
Next, you have to put into this formula:
y1-y2/x1-x2
The y values in our points are -4 and -1, and our x values are 4 and -1. Lets now substitute:
-4-(-1)/4-(-1)
Now simplify: -4+1/4+1, and solve and you will get -3/5 as the slope
If you liked it, please give me a good rating and please mark me as the brainliest... Thanks!
Hope you do well on your assignment!
Which of the following is the most likely the next step in the series ?
Answer:
I believe the likely awnser is c because it is adding one more side on each step.
Please help me with 4-6 ASAP I will give 30 points
Answer:
i did that paper made 100 but i was looking for it to help u and when i got it i tripped with my enchaladas im tryna clean it to get the answers
Step-by-step explanation:
Determine the value of x.
Question 8 options:
A)
2.2
B)
4.4
C)
2
D)
8.8
Answer:
The answer is: B) 4.4
Step-by-step explanation:
Complete the first step in the solution
4x= 24 4x/ = 24/
4x6=24. i hope this helps if not im sorry
What’s the quotient ? I’m helping out with my sisters homework once again and I don’t wanna explain it to her. Please help me ;-;
Answer:
quotient is the answer to division. So if 7/2=3 with a remainder of 1, then the quotient is 3
Use special right triangle ratios to find the length of the hypotenuse.
45°
18
457
A. 18V3
B. 1872
Answer:
Step-by-step explanation:
The length of the hypotenuse is 18√2.
What is hypotenuse?The longest side of the triangle is called as the hypotenuse.
In a right angled triangle, sin 45° = perpendicular /hypotenuse
here, perpendicular side P = 18 units and the hypotenuse H is unknown.
sin 45° = 18 /H
H = 18√2
Thus, the hypotenuse is 18√2.
Learn more about hypotenuse.
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PLEASEEEEE HELLLPPP MEEE
Answer:
100
Step-by-step explanation:
please help i will give brainliest what is 50-(20)
Answer:
30
Step-by-step explanation:
Answer:I believe its 30
Step-by-step explanation:
help one question! but pls show work
Answer:
5
Step-by-step explanation:
cant show work i need to draw then
Answer:
-28k^4
Step-by-step explanation:
I NEED HELP W 36
pls pls pls pls help help!
Answer:
1
Step-by-step explanation:
When you substitute the inside of f(g(2)), you get g(x)=2-4. Then you substitute that answer of -2 and plug it into f(x)=2x+5. Since f(-2)=2(-2)+5 equals to 1, that should be your answer.
Grades are due and I NEED THIS TO PASS
Create an equation with one solution of x = −9.
7x − (x − 26) = 2x − ( + x)
1 Remove parentheses.
7x-x+26=2x−x
2 Cancel -x on both sides.
7x+26=2x
3 Subtract 7x from both sides.
26=2x−7x
4 Simplify 2x-7x to -5x.
26=−5x
5 Divide both sides by -5.
26/-5=x
6 Switch sides.
x=26/-5
7 Simplify.
x=-5.2
find m
right anwser gets brainliest
Answer:
The measure of <FDE is 18°
Can anyone help me out solving this?
Answer: 25
Step-by-step explanation: When you divide exponents with the same base, you can subtract the exponents. It becomes 5^4-2, which is 5^2, which is 25
Which polynomial is in standard form?
N
O 26x5 + 12x7-8x3 + 6x
O 3x5 +x-6x2 + 5
11x5-6x2-9x+12
5x2 + 18x3 - 12x4 +4x7
Answer:
i am pretty sure it is D
Step-by-step explanation:
Answer:
Its C.) 11x^5 - 6x^2 - 9x + 12
Step-by-step explanation:
ejenuwitee
=D
=P
Lisa is a fitness instructor. For one month, she recorded the number of people who attended her aerobics class. She then used her data to make the box-and-whisker plot shown. Lisa’s data set includes a single outlier and no duplicate data values.
Which statement describes the effect on the range and interquartile range of Lisa’s data set when the outlier is removed?
---
A The interquartile range increases but the range decreases.
B The range and interquartile range both decrease, but the interquartile range
decreases more.
C The range decreases but the interquartile range increases.
D The range and interquartile range both decrease, but the range decreases more.
Help please! I need an explanation but I dont understand this!!!!!!!
Answer:
its to small
Step-by-step explanation:
What is the answer to 1112÷1/3
Answer:
3336
Step-by-step explanation:
pls give brainliest
Answer:
3336
Step-by-step explanation:
1112 divided by 1/3 is 1112 times 3/1=
3336
[tex]4 - \frac{2}{3} x = \frac{x - 6 }{5} [/tex]
Answer:
Step-by-step explanation:
60-10x=3x-18
78=13x
x=6
What is the Domain and range of y=(x-1)^2-4
The median age of the science teachers at Mike's school is the same as the median age of the math teachers, but the
ages of the math teachers show greater variability. Which statement most likely describes the data sets?
O The difference in ages between the oldest and youngest math teachers is greater than the difference in ages
between the oldest and youngest science teachers.
There are more math teachers than science teachers at Mike's school.
The average age of the math teachers at Mike's school is greater than the average age of the science teachers.
The oldest teacher in Mike's school is a mathematics teacher.
dyit
Answer:
A
Step-by-step explanation:
THe guy above me explained
The difference in ages between the oldest and youngest math teachers is greater than the difference in ages between the oldest and youngest science teachers. Option A is correct.
What is the median?When a dataset is ordered, the median is the value that is exactly in the middle. It is a measure of central tendency that distinguishes between the lowest and top 50% of data.
Here,
The age gap between the oldest and youngest math teachers is larger than the age gap between the oldest and youngest science teachers. Option A is a true statement, while all other options are invalid.
Thus, the difference in ages between the oldest and youngest math teachers is greater than the difference in ages between the oldest and youngest science teachers. Option A is correct.
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Angela is planting flowers in her flowerbed. She wants the ratio of tulips to roses to be 5 to 2. If a total of 63 flowers are planted, how many tulips should there be?
Answer:
45 Tulips
Step-by-step explanation:
63/7=9
Tulips: Roses=5:2
Tulips=9x5=45
Roses=9x2=18
Find an ordered pair (x,y) that is a solution to the equation
3x-y=6
Answer:
2,0
Step-by-step explanation:
Solve the following equation with rational coefficients
0.8x = 6
y’all really should help me .
Answer:
I think its x=48
Step-by-step explanation:
Answer:
X = 7.5
Step-by-step explanation:
0.8x = 6
x = 6/0.8
x = 7.5
solve the simultaneous equations
5x + 6y = 3
2x - 3y = 12
Answer: x =3; y = -2
[tex]\left \{ {{5x+6y=3} \atop {2x-3y=12}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {2x-3y=12}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {2.\frac{3-6y}{5}-3y =12}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {6-12y-15y=12.5}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {17y=6-60=-54}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {y=-54/27}} \right.\\\\\\ <=>\left \{ {{x=\frac{3-6y}{5} } \atop {y=-2}} \right.\\\\<=>\left \{ {{x=3} \atop {y=-2}} \right.[/tex]
Step-by-step explanation:
Answer:
x = 3, y = -2.
Step-by-step explanation:
5x + 6y = 3
2x - 3y = 12 Multiply this by 2:
4x - 6y = 24 Now add this to the first equation:
9x = 27
x = 3.
Substitute x = 3 in the second equation:
2(3) - 3y = 12
-3y = 12 - 6 = 6
y = 6 / -3
y = -2.
A recursive rule for a sequence is given. Find the first four terms of the sequence.
f(1) = 2
f(n) = 4. f(n – 1), where n is an integer and n > 2.
Answer:
So...
a0 = -2
a1 = (a0)2 - 4 = 4 - 4 = 0
a2 = (a1)2 - 4 = ((a0)2-4)2 - 4 =...= 02 - 4 = -4
For an+1, you may use the previous term (an) if you have just calculated it, rather than calculating it recursively again
a3 = (-4)2 - 4 = 12
The first four terms in the sequence are -2, 0, -4, 12.
Step-by-step explanation:
This recursive sequence is defined as follows:
a0 = -2 [the first term]
an+1 = an2 - 4 [for all other terms, n≥0; note that you cannot find a0 using this line]
Note that this is not "BASE" for a number base, but it is "SUB" for subscript, indicating the term. Sometimes, sequences are written with the first term being a1 and sometimes sequences are written with the first term being a0. This is because there are situations that make one or the other more convenient (for example, starting with elapsed time t=0 makes sense).
To find the value of later terms, a recursive definition requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, which requires that you find the value of the previous term, ... which requires that use the value of the first term.
That's why (joke) that the dictionary definition of "recursive" is "see recursive."
What is the simple interest earned when the principal is $500 at a rate of 10% held in the ban for 8 months?
S.I= PRT /100
where,
P = price $500
R = rate 10%
T = time =8months
= $500*10*8/100
= $40,000/100
S.I = $400