The orthogonal decomposition of vector [tex]\vec b = <9, 0, 0>[/tex] with respect to vector [tex]\vec a = <4, -5, 0>[/tex] is
[tex]b'=<\frac{16}{5},\frac{8}{5},0>[/tex]
From the Question we are told that
Vector [tex]\vec b = <9, 0, 0>[/tex]
Vector [tex]\vec a = <4, -5, 0>[/tex]
Generally in the orthogonal decomposition of b to a we have
[tex]\vec b=\vec b"+\vec b'[/tex]
Where
[tex]\vec b"=(\frac{\vec b*\vec a}{\vec *\vec a})*\vec a[/tex]
[tex]\vec b"=(\frac{ <9, 0, 0>*<4, -5, 0>}{<4, -5, 0>*<4, -5, 0>})*<4, -5, 0>[/tex]
[tex]\vec b"=<\frac{4}{5},\frac{-8}{5},0>[/tex]
Therefore
[tex]b'= \vec b- \vec b"\\\\b'=<4,0,0>-<\frac{4}{5},\frac{-8}{5},0>[/tex]
[tex]b'=<\frac{16}{5},\frac{8}{5},0>[/tex]
in Conclusion
The orthogonal decomposition of vector [tex]\vec b = <9, 0, 0>[/tex] with respect to vector [tex]\vec a = <4, -5, 0>[/tex] is
[tex]b'=<\frac{16}{5},\frac{8}{5},0>[/tex]
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If a^2+b^2=13 and ab =6 find the value of
(i)(2a+2b)
(ii)(2a-2b)
Answer:
I)
[tex]2a + 2b = -10\text{ or } 2a + 2b = 10[/tex]
II)
[tex]2a - 2b = -2 \text{ or } 2a-2b= 2[/tex]
Step-by-step explanation:
We are given that:
[tex]\displaytstyle a^2 + b^2 = 13 \text{ and } ab= 6[/tex]
I)
Recall the perfect square trinomial pattern:
[tex]\displaystyle (a+b)^2 = a^2 + 2ab + b^2[/tex]
Rewrite:
[tex]\displaystyle (a+b)^2 = (a^2 + b^2) + (2ab)[/tex]
Substitute:
[tex]\displaystyle (a+b)^2 = (13) + (12)[/tex]
Evaluate:
[tex]\displaystyle (a + b)^2 = 25[/tex]
Take the square root of both sides:
[tex]\displaystyle a + b = \pm\sqrt{25} = \pm5[/tex]
Hence:
[tex]\displaystyle 2a + 2b = \pm 10[/tex]
Therefore:
[tex]\displaystyle 2a + 2b = -10 \text{ or } 2a + 2b = 10[/tex]
II)
Likewise:
[tex]\displaystyle (a-b)^2 = a^2 - 2ab + b^2[/tex]
Substitute:
[tex]\displaystyle (a-b)^2 = (13) -(12)[/tex]
Solve:
[tex]\displaystyle \begin{aligned} (a-b)^2 &= 1 \\ a-b &= \pm \sqrt{1} \\ a-b &= \pm 1\\ 2a - 2b &= \pm 2\end{aligned}[/tex]
In conclusion:
[tex]2a - 2b = -2 \text{ or } 2a-2b= 2[/tex]
The scatterplot to the left shows the cost, C, in thousands of dollars, and living space, z, in square feet (ft) for several houses in a certain neighborhood. According to the data, which of the following best approximates the cost for an additional square foot of living space for homes in this neighborhood?
The best approximation of the cost for an additional square foot of living space for homes in this neighborhood is a decrease of $0.125 thousand, or $125, for every one additional square foot of living space.
Since we are looking for an approximation of the cost for an additional square foot of living space, we need to find the slope of the line of best fit for the given scatterplot. The slope of the line represents the change in the cost of the house for every one unit increase in the living space, which in this case is one square foot.
From the scatterplot, we can see that as the living space increases, the cost of the house also increases, indicating a positive linear relationship. We can also see that there is a line of best fit that closely approximates this relationship.
To find the slope of the line of best fit, we can choose any two points on the line and calculate the change in the y-coordinate (the cost) divided by the change in the x-coordinate (the living space). One way to do this is to choose the two points where the line intersects the y-axis and the x-axis. From the scatterplot, we can estimate these points to be approximately (0, 200) and (1600, 0), respectively.
Using these two points, the slope of the line of best fit is:
slope = (change in y) / (change in x)
slope = (200 - 0) / (0 - 1600)
slope = -0.125
Therefore, the best approximation of the cost for an additional square foot of living space for homes in this neighborhood is a decrease of $0.125 thousand, or $125, for every one additional square foot of living space.
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Given m||n, find the value of x.
+
mm
(6x-20)
(6x-4)
PLS HELP ASAP
Answer:
17°
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
Answer:
x=17
Step-by-step explanation:
The angles add to 180
6x-20 + 6x-4 = 180
Combine like terms
12x -24 =180
Add 24 to each side
12x = 180+24
12x = 204
12x/12 = 204/12
x =17
A certain forest covers an area of 4900 km². Suppose that each year this area decreases by 7%. What will the area be after 8 years?
Use the calculator provided and round your answer to the nearest square kilometer.
Answer:
area after 8 years is 2156km²
Step-by-step explanation:
Area of forest=4900 km²
decrease in area in 1 year=4900km² × 7%
decrease in area in 1 year= 343km²
decrease area in 8 years=343km² × 8
=2744km²
Remaining area= (4900-2744)km²
=2156km²
Note:If you have any question about it please ask.
3.1 = k - 1.9 solve for k
Find seven ordered pairs to the equation y=x^2-4
Answer:
(1,-3)
(2,0)
(3,5)
(4,12)
(0,-4)
(-1,-3)
(-2,0)
Select the correct answer.
What is the value of xin 2(5x) = 14?
Answer: x= 1.4 or x=7/5
Step-by-step explanation:
2(5x)=14
Divide both sides by 2
5x=7
divide again this time both sides by 5 to solve for x
x=7/5 or 1.4 as a decimal
y = –3x – 5 ???
(–11, –2)
(–2, –11)
(–2, 1)
(1, –2)
Answer:
option c (-2,1)
Step-by-step explanation:
hope it helps u
Pls help I’m having trouble
Answer:
find the area of each side of the shapes and add make sure it's in square centimeters
More help Pls (am also giving away points).
Answer:
Bot #11
Step-by-step explanation:
If you picked bot 12 in 5 second it produces 21 clicks which means if you add another 5 second it will be 10 second with 42 clicks. But, if you pick the bot with 17 clicks per 4 second, 8 seconds it will already be 34 clicks and 10 seconds half of 17 is 8/5 which in 10 seconds it produces 42.5 which shows the first bot produces more.
ruto is 12 years old.in three years time he will be ⅓ of his father present age.how old was his father 12 years ago
Answer:
He was 45 in present day. But 12 years ago, he was 33.
Step-by-step explanation:
12+3=15
15•3=45 (you multipply because if you use 1/3 you would have to divide 45 by 3.)
Hello :D
Ruto is currently 12 years old. In 3 years he will be 15. 1/3 is 15. 3/3 would be 45 years old. 45 - 12 = 33
Compare -3 and -5 using <,>, Or =
Please help asap thank you! I'll mark brainlyest
Answer:
3
Step-by-step explanation
add all of the numbers then divide by the amount the numbers you added
in this situation it is 1+2+3+4+5=15 divided by 5 equals 3. Hoped this helped. pls give brainliest
NEED ASAP DUE IN 1 HOUR
is x + 1 a factor of [tex]x^{4} +2x^{3} +2x^{2} -2x-3[/tex]?
Answer:
Yes.
Step-by-step explanation:
We want to determine if (x + 1) is a factor of the polynomial:
[tex]x^4 + 2x^3 + 2x^2 - 2x -3[/tex]
According to the Factor Theorem, if a binomial in the form (x - a) is a factor of a polynomial P(x), then P(a) must equal zero.
Our binomial factor is (x + 1) or (x - (-1)). Hence, a = -1.
Let our polynomial be P(x). Find P(-1):
[tex]\displaystyle\begin{aligned} P(-1) &= (-1)^4 + 2(-1)^3 +2(-1)^2 -2(-1) -3 \\&=0\end{aligned}[/tex]
Therefore, since the resulting value is indeed zero, (x + 1) is indeed a factor of the given polynomial.
In conclusion: yes.
You are offered an hourly job making $11per hour. If you are scheduled to work 45
hours per week. What would the weekly gross pay for this job be?
Answer:
$495
Step-by-step explanation:
This is because Gross income is the total amount without taxes or deductions
So all you have to do is 11x45 which gives you 495.
Can i have more details explanation about the ways to find the answers?
Answer:
I can't answer the B question, but I can answer the A question. First, you need to add 1/3, 1/4, and 5/8 by converting them into having the same denominators (24 is the best) and then subtracting them by 24/24 or the number of your choosing. That's how you find out how much he saves.
Step-by-step explanation:
Find the value of x and QR if Q is between P and R.
PQ=2x
QR=x + 2
PR= 5x -10
Answer:
2x+x+2=5x-10
3x+2=5x-10
-3x -3x
2=2x-10
+10 +10
12=2x
2x/2=x 12/2=6
x=6
QR=x+2
6+2=8
QR=8
The value of x is 6 and the value of QR will be 8 units.
What is a line segment?A line segment in geometry is a section of a line that has two clearly defined endpoints and contains every point on the line that lies within its confines.
Given that the value of x and QR if Q is between P and R.
PQ=2x
QR=x + 2
PR= 5x -10
The value of x will be calculated as below:-
2x+x+2=5x-10
3x+2=5x-10
2=2x-10
12=2x
x = 12 / 2
x =6
The value of QR will be calculated as below:-
QR=x+2
6+2=8
Therefore, the value of x is 6 and the value of QR will be 8 units.
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A 10 1/2-inch candle burns down in 7 hours. If b represents how much of the candle, in inches, has burned away at any time given in hours, t, write a proportional equation for b in terms of t that matches the context.
The proportional formula for b is 3/2 in terms of t.
What is proportional equation?The equation y = kx represents a proportionate relationship between two quantities y and x that have the same proportionality constant, k. If an equation in another form can be rewritten as in the example above, then the relationship is proportional.Assume that b = kt is the equation.In light of the statement 10 1/2 = k.7So, k = 10 1/2 /7 =21/2 /7 => 3/2Therefore, the equation is b = 3/2t, where t is the proportionality factor.y = k x, where is the proportionality constant, is the equation that depicts a proportional relationship, or a line. Find k and create the equation by using k = y x from a table or graph. Tables, graphs, and equations can all be used to represent proportional relationships.To learn more about proportional equation refer to:
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-11+x(-7) when x= 4
Please help ASAP
Step-by-step explanation:
-11+x(-7)
when x= 4, then
-11+x(-7)
-11+4(-7)
-11+(-28)
-11-28
-39
what does equal
(27/64)-2/3=
how to Round 342.296269789 to 2 decimal places.
Answer:
342.30.
Step-by-step explanation:
The third decimal place is 6 so we round up the previous 2 dec places by 1
29 -->> 30 so it is 342.30.
(We round up if the next decimal place is 5 6 7 8 or 9)
simplify 6^2n+1x9^nx4^2n÷18^nx2^nx12^2n please help ..Thank you
Answer:
[tex]2^{-4 n}\times3^{-2 n} + 3^{-2 n}\times4^{-n}[/tex]
Step-by-step explanation:
Assuming you meant [tex]\frac{6^{2n}+1*9^n*4^{2n}}{18^n*2^n*12^{2n}}[/tex], the answer is [tex]2^{-4 n}\times3^{-2 n} + 3^{-2 n}\times4^{-n}[/tex].
1. Gracie read "Burnt Norton," but not to the sounds of a Duke Ellington piano plece.
2. "East Coker" (which wasn't read by Devon) wasn't accompanied by either Duke
Ellington or Bela Bartok music.
3. The reading of "Little Gidding" was accompanied by Gregorian chants.
4. Cathy didn't read “East Coker" or "The Dry Salvages."
Answer:
Is this a story hmm mm i think
write each fraction number as a decimal 33/40
Answer:
0.825
Step-by-step explanation:
In order to make the denominator 100, we must multiply both the numerator and denominator by 2.5
33*2.5 = 66 + 16.5 = 82.5
33/40 = 82.5/100
Now we solve, 82.5/100 = 0.825
ANYONE KNOW HOW TO DO THIS IM BEGGING
- Is this a function? Why or why not?
Independent
Variable
Dependent
Variable
3
6
4
15
+8
12
14
agen 20
22
11
asking for
9514 1404 393
Answer:
a) yes (a function)
b) no (not a function)
Step-by-step explanation:
A functional relationship will have only one value of dependent variable for each value of independent variable. That is, the column on the left can only have one arrow tail per item.
__
a) is a function. Each independent variable maps to one dependent value
b) not a function. Independent variable values 7 and 30 map to two values each.
can someone explain this better?
Answer:
i would say transitive which is what u put because well i would say translate because it translates n2 different parts of the letter
Step-by-step explanation:
3t + 4y + 5t
Anyone?
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\text{3t + 4y + 5t}[/tex]
[tex]\huge\textsf{COMBINE the LIKE TERMS}[/tex]
[tex]\huge\text{(3t + 5t) + 4y}[/tex]
[tex]\huge\text{= 8t + 4y}[/tex]
[tex]\huge\text{Answer: \textsf{8t + 4y}}[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Answer:
8t + 4y
Step-by-step explanation:
First, we have to combine LIKE TERMS giving us (3t + 5t) + 4y.
We know that 3 + 5 = 8 so 3t + 5t must be 8t.
We still have the 4y left over so we get 8t + 4y. We cannot simplify this expression anymore
So, the answer is [tex]8t + 4y[/tex] as our answer.
(Hope this helped you!)
Convert 99000 milligrams into pounds. Round your answer to the nearest hundredth.
Answer:
0.22
Step-by-step explanation: