Pj satisfies all three subspace properties, it is a subspace of Pk.
To show that Pj is a subspace of Pk, we need to show that it satisfies the three subspace properties:
Contains the zero vector: The zero polynomial of degree less than or equal to k is in Pj, since it is also a polynomial of degree less than or equal to j.
Closed under addition: Let p(x) and q(x) be polynomials in Pj. Then p(x) + q(x) is also a polynomial of degree less than or equal to j, since the sum of two polynomials of degree less than or equal to j is also a polynomial of degree less than or equal to j. Therefore, p(x) + q(x) is in Pj.
Closed under scalar multiplication: Let c be a scalar and p(x) be a polynomial in Pj. Then cp(x) is also a polynomial of degree less than or equal to j, since the product of a polynomial of degree less than or equal to j and a scalar is also a polynomial of degree less than or equal to j. Therefore, cp(x) is in Pj.
Since To show that Pj is a subspace of Pk, we need to show that it satisfies the three subspace properties:
Contains the zero vector: The zero polynomial of degree less than or equal to k is in Pj, since it is also a polynomial of degree less than or equal to j.
Closed under addition: Let p(x) and q(x) be polynomials in Pj. Then p(x) + q(x) is also a polynomial of degree less than or equal to j, since the sum of two polynomials of degree less than or equal to j is also a polynomial of degree less than or equal to j. Therefore, p(x) + q(x) is in Pj.
Closed under scalar multiplication: Let c be a scalar and p(x) be a polynomial in Pj. Then cp(x) is also a polynomial of degree less than or equal to j, since the product of a polynomial of degree less than or equal to j and a scalar is also a polynomial of degree less than or equal to j. Therefore, cp(x) is in Pj.
Since Pj satisfies all three subspace properties, it is a subspace of Pk.
Learn more about subspace here:
https://brainly.com/question/31691975
#SPJ11
Based on the polynomial remainder theorem, what is the value of the function when x=−5?
f(x)=x^4+12x^3+30x^2−12x+70
Answer:
5.
Step-by-step explanation:
f(x)=x^4+12x^3+30x^2−12x+70
The remainder theorem says that f(a) is the value of f(x) when f(x) is divided by (x - a).
So when a = -5 f(a) will be 5.
Answer is 5.
From Andys house to Billys hometown you can travel by 3 roads. And to get from Billys hometown to Willies's house you can travel by 5 roads. How many possible wats are there to travel from andys house to willies house?
3 roada andy to billy
5 road billy to willies
3×5 =15 it's the answer 15
Find the measure of the arc or angle indicated by the question mark.
Answer:
FP is 70 degrees 35 times 2 so PD is 180 half a turn minus 70 = 110 degrees
Step-by-step explanation:
In order to determine an interval for the mean of a population with unknown standard deviation, a sample of 24 items is selected. The mean of the sample is determined to be 23. The number of degrees of freedom for reading the t value is _____. Group of answer choices 21 22 23 24
If the sample size of population is 24 then the number of degrees of freedom for reading the t value is 23 which is option c.
Given sample size of 24,mean 23.
We have to determine the number of degrees of freedom which will be used to find the critical values of t.
Degree of freedom is the number of values in the final calculation of a statistic that are free to vary means that can change their values in the formula of calculating t.
t=(X-μ)/s/[tex]\sqrt{n}[/tex]
where X is sample mean ,
μ is hypothsised population mean
s is sample standard deviation
n is sample size.
Degree of freedom=n-1
In this question n is 24 so the degree of freedom =24-1=23.
Hence the number of degrees of freedom for reading the t value is 23.
Learn more about degree of freedom at https://brainly.com/question/17305237
#SPJ4
which of the following best describes this graph
x² - 4x + 4 is the graphed parabola, so the correct option is D.
Which equation is the graphed one?
On the graph, we can see a parabola that opens upwards (then the leading coefficient is positive), and has a vertex at the point (2, 0).
Also, we can see that the y-intercept is y = 4, that means that the constant term of the parabola is 4.
The only option with a constant term equal to 4 is the last option:
y = (x - 2)*(x - 2) = x² - 4x + 4
So that is the graphed parabola.
If you want to learn more about parabolas:
https://brainly.com/question/4061870
#SPJ1
What do these values indicate about a sample mean absolute deviation being used as an estimator of the mean absolute deviation of a population?
Because the sample statistic centers around a different value than the population parameter, the sample mean absolute deviation is a biased estimator of the population mean absolute deviation.
Reason Behind a Biased Estimator
The expected value (average) of all the sample absolute deviations must match the population absolute deviation in order for the absolute deviation to function as an unbiased estimator. It does not, however, which makes the values of sample mean absolute deviation behave as a biased estimator.
Brief Description of Sample Mean Absolute Deviation
The average of the absolute deviations from a central point makes up the average absolute deviation of a data collection. It is a statistical summary of statistical variability or dispersion.
Learn more about biased estimator here:
https://brainly.com/question/26415101
#SPJ4
In a 10-year period, Bakersfield, CA population grew from 558,000 to 718,000. What is the percentage of increase? (Round to the nearest tenth of a percent)
The percent increase to the nearest tenth is 22.2%
Calculating percent increasePercent increase is the percent it takes from a value to change from its initial value
Given the following
Initial value = 558,000
Final value = 718,000.
Determine the percent increase
% increase = (718,000-558000)/718,000 * 100
% increase = 160000/718000 * 100
% increase = 22.2%
Hence the percent increase to the nearest tenth is 22.2%
Learn more on percent increase here: https://brainly.com/question/11360390
#SPJ1
if m<0 and b>0,the graph of y=max+b does not pass through which quadrant
Answer:are u sure its not y=mx+b? And it doesn’t pass thru 1 im pretty sure
Step-by-step explanation:
Answer: Quadrant III
Explanation:
Let's pick example values for m and b
I'll go for m = -2 and b = 5. Anything works as long as m is negative and b is positive.
We go from y = mx+b to y = -2x+5
Plot this graph as shown below. The line passes through quadrants I, II, and IV. Only quadrant III is not touched at all.
How do you find the interior angle of a triangle given the external angle of 125°
Answer:
<x = 55 degrees
<y = 55 degrees
<z = 70 degrees
Step-by-step explanation:
The 125 degree angle and x are supplementary since they form a straight line, which means that their degrees add up to 180. To find x, the interior angle, we must subtract 125 from 180.
180 - 125 = 55
Angle x is 55 degrees. Since the sides opposite x and y are marked with lines, they are congruent, and since the sides are congruent, the angles must be, too. So, y is also 55 degrees.
Finally, the angles in any triangle add up to 180 degrees. To find z, we must subtract the values of x and y from 180.
180 - 55 - 55 = 70, so z is 70 degrees.
Brainliest, please :)
❄Hi there,
the external angle & the interior angle form a linear pair, which means, if you add these angles together, you'll arrive at 180°.
Using this knowledge let's set up an equation and find x:
[tex]\triangleright \ \sf{125+x=180}[/tex]. We let x be the desired angle.
[tex]\triangleright \ \sf{x=180-125=55}[/tex]
So the interior angle is [tex]\angle\sf{55}\textdegree[/tex].
❄
Micheal measured the distance around the circler swimming pool as apppoximly 108 feet which of the following represents the approximates radius of the circular swimming pool
The radius of the circular swimming pool is 17.20 feet.
What is the radius?The distance round the circular swimming pool is the circumference of the circle.
Radius = circumference / (pi x 2)
108 / (3.14 x2)
108 / 6.28 = 17.20 feet
To learn more about how to determine the circumference of a circle, please check: https://brainly.com/question/14351152
#SPJ1
8. What do you know about triangles PDX and triangle CRX? Justify your answer.
Answer:
The triangles are Congruent for the same reason as the answer above
Step-by-step explanation:
Make w subject of formula
C=(4+w)/(w+3)
Answer:
Step by Step Solution
More Icon
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
c-((4+w)/(w+3))=0
STEP
1
:
4 + w
Simplify —————
w + 3
Equation at the end of step
1
:
(w + 4)
c - ——————— = 0
w + 3
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using (w+3) as the denominator :
c c • (w + 3)
c = — = ———————————
1 (w + 3)
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
2.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
c • (w+3) - ((w+4)) cw + 3c - w - 4
——————————————————— = ———————————————
1 • (w+3) 1 • (w + 3)
Equation at the end of step
2
:
cw + 3c - w - 4
——————————————— = 0
w + 3
STEP
3
:
When a fraction equals zero :
3.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
cw+3c-w-4
————————— • w+3 = 0 • w+3
(w+3)
Now, on the left hand side, the w+3 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
cw+3c-w-4 = 0
Solving a Single Variable Equation:
3.2 Solve cw+3cw-4 = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
We shall not handle this type of equations at this time.
Answer:
w = (4 - 3C)/(C - 1).
Step-by-step explanation:
C=(4+w)/(w+3)
Multiply both sides of the formula by w+3:-
C(w + 3) = 4 + w
Cw + 3C = 4 + w
Cw - w = 4 - 3C
w(C - 1) = 4 - 3C
w = (4 - 3C)/(C - 1).
I know only one answer whats the other one help me image-
Answer:
A. 4(4a + 18)
B. 8(2a + 9)
Step-by-step explanation:
We know that :
16a = 4×4×a
72 = 4×18
Then
16a + 72 = 4×(4a) + 4×(18)
= 4 × (4a + 18)
On the other hand,
16a = 8×2×a
72 = 8×9
Then
16a + 72 = 8×(2a) + 8×(9)
= 8 × (2a + 9)
Quick algebra 1 question for 50 points!
Only answer if you know the answer, quick shout-out to Dinofish32, tysm for the help!
Scenario 1: Cameron works at a local grocery store after school. He is paid $8 for each hour he works.
Scenario 2: At a local bakery, one box of donuts costs $5. Two boxes of donuts cost $10.
Consider the two scenarios given above. Can you write an equation to represent each situation? What would the graphs of these equations look like? Can you think of a situation that would result in a similar equation?
Describe a scenario that would result in an equation similar to the equations for Scenarios 1 and 2. Post your scenario and the corresponding equation to the discussions area.
Answer:
Scenario 1: Cameron works at a local grocery store after school. He is paid $8 for each hour(h) he works. And ammount of money can be (m)
considering theres no like first hour pay or something then it would be
Equation: m = 8h
Scenario 2: At a local bakery, one box of doughnuts(b) costs $5(c). Two boxes of doughnuts cost $10.
Equation: c = 5b where b is the ammount of doughnut boxes and c is the cost
Scenario 1a: Jim goes to the gym for 10 hours(h) It costed him $20(c) for those 10 hours.
Equation: c = 2h
Scenario 1b: Kayla goes to a for a ride on her bike and traveled 15 miles(m) and was out for 30 minutes. (t)
Equation: t = 2m
I don’t get this either please save me from this ahhhhhh
Answer:
y=
[tex] - \frac{x {}^{2} + 8x + 16 }{2} - 7[/tex]
Step-by-step explanation:
calculate the product, use (a+b)^2=a^2+2ab+b^2
A cruise line ship left Port A and traveled 90 miles due west and then 400 miles due north. At this point, the ship docked at Port B What is the shortest distance between Port A and Port B?
Answer:
410 Miles
Step-by-step explanation:
Please refer to the photo attached. (Apologies for the legitimately terrible drawing)
The Shortest Distance between any 2 points is the distance thats connects the 2 points directly.
In this case, we can use Pythgoras's Theorem to find AB which is the shortest distance between A and B.
By Pythagoras's Theorem,
[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {ab}^{2} = {ac}^{2} + {cb}^{2} \\ {ab}^{2} = {90}^{2} + {400}^{2} \\ab = \sqrt{ {90}^{2} + {400}^{2} } \\ = 410 \: miles[/tex]
Wen Sam got a puppy from the shelter, it weighed 20.5Ibs. The puppy gain%30 of its original weight in the first month that Sam had him. How much did the puppy weight after the first month?
The weight of the puppy after the first month as described is; 26.65lbs.
What is the weight of the puppy?Since, it follows from the task content that the initial weight of the puppy is; 20.5lbs and it gained 30% of this after 1 month, it follows that the weight of the puppy after one month is;
Weight = 20.5lbs × 130% = 26.65lbs.
Read more on percentages;
https://brainly.com/question/16865197
#SPJ1
Line a is purpendicular to line b. if the slope of line a is 7 than what is the slope of line b
The slope of the perpendicular line b is -1/7 if the slope of the perpendicular line a is 7.
According to the question,
Line 'a' is perpendicular to the line 'b'. If the slope of the line 'a' is 7.
The condition of slopes if two lines are perpendicular m₁ m₂ = -1
(7)(m₂) = -1
m₂ = -1/7
Hence, the slope of the perpendicular line b is -1/7 if the slope of the perpendicular line a is 7.
Learn more about perpendicular lines here
https://brainly.com/question/2505127
#SPJ4
Which of the following matches the graph of f (x) = 2(x + 1)2(x – 1)(x – 2)?
The graph that matches the function f(x) = 2(x – 1)2(x + 1)(x + 2) is shown in the attached file
How to draw the graph of a Polynomial?A function assigns the value of each element of one set to the other specific element of another set.
We want to draw the graph of the function f(x) = 2(x – 1)2(x + 1)(x + 2). Using relevant coordinates input into the function and the generated output, the graph of the given function is as attached below.
Read more about Graph of polynomial at; https://brainly.com/question/14625910
#SPJ1
An airplane rises at an angle of 12 degrees with the ground. About how high, in feet will the plane be above the ground when it has traveled 500 yards fromt he airport horizontally? Round your answer to the nearest foot.
please help solve for n. 5/15 = n/21 a. n = 35 b. n = 7 c. n = 5 d. n = 90
Answer:
b. n = 7
Step-by-step explanation:
You want to solve the proportion ...
5/15 = n/21
This is most easily done by multiplying by the inverse of the coefficient of the variable:
(21/1)(5/15) = (21/1)(n/21)
7 = n . . . . . . . . . simplify
__
Additional comment
The math is a little easier if you simplify 5/15 to 1/3. Then, n = 21/3 = 7.
The sixth grade band students are selling magazines to raise money for new instruments. As a reward for selling, the students earn points to spend on prizes. Each student gets 25 points to start with, and then they earn an additional 5 points for each magazine they sell. If m represents the number of magazines a student sells, write an expression to represent the total number of points the student has.
WRITER
Answer:
okay he's saying that each student gets 25 points to start with and then they get five more like 25 / 25 * 5 or like 25 + 5 or 25 - 5 like represent those numbers and like get the number or something like that
Solve for X if possible:
5x -4y = 24
x =
Answer:
x=6 because if you multiple 4x6 you get 24
not exactly sure but try
Answer:
it is not possible
Step-by-step explanation:
there are two different variables in one equation, so you cannot solve for one. You would need a system of equations to do that.
you can solve for x in terms of y, which is x = (24+4y)/5 but i dont think thats what the question is asking so the answer is probably just that its not possible
A family is having a pool built in their backyard. If their yard is rectangular and measures 10x by 10x and the pool is circular with a radius of 2x how much of the yard will be left over after the pool is built
Answer:
[tex]100x^2-4\pi x^2[/tex]
Also can be said as:
[tex]4x^2(25-\pi )[/tex]
Step-by-step explanation:
The scenario:The question is asking you, "how much is left over."
In this scenario, you're going to have to subtract the area of the pool (P) from the total area of the backyard (B), which will leave you with the remaining area of the backyard (x).
This means your equation to solve this question is:
[tex]x=B-P[/tex]
Step 1:The value of B is the area of the backyard.
We are told that the backyard is a rectangular shape. So, we can use the formula of finding the area of a rectangle.
The formula is [tex]B=L*W[/tex], where L is the length and W is the width.
Both the length and width are 10x, so we must plug that into this equation.
We end up getting:
[tex]B=10x*10x[/tex]
Which can be simplified to:
[tex]B=100x^2[/tex]
Step 2:The value of P is the area of the pool.
The pool is a circular shape. So, to get the area of it, we must use the formula of finding the area of a circle.
The formula is [tex]P=\pi r^2[/tex], where r is the radius.
Plugging in the radius of 2x, we get:
[tex]P=\pi (2x)^2[/tex]
By solving this out, we end up with:
[tex]P=4\pi x^2[/tex]
Step 3:From the scenario, we have the equation:
[tex]x=B-P[/tex]
And from steps 1 and 2, we have the values:
[tex]B=100x^2[/tex] and [tex]P=4\pi x^2[/tex]
Now we just plug those values in to get:
[tex]x=100x^2-4\pi x^2[/tex]
And finally, the amount of the backyard remaining is:
[tex]100x^2-4\pi x^2[/tex]
Different format:This answer may be simplified to:
[tex]4x^2(25-\pi )[/tex]
what is the area for the green square?
PLEASE HELP!!!!
Determine if the conclusion is valid. Give a thorough explanation of your answer.
D
B
Given: AB || DC, AD || BC, AB BC
Conclusion: ABCD is a rhombus.
Answer: Correct
Step-by-step explanation:
The conclusion is valid. Since [tex]\overline{AB} \parallel \overline{DC}[/tex] and [tex]\overline{AD} \parallel \overline{BC}[/tex], we know that ABCD is a parallelogram because it has two pairs of parallel sides. Also, since [tex]\overline{AB} \cong \overline{BC}[/tex], we know that ABCD is a parallelogram with a pair of consecutive congruent sides, making it a rhombus.
Can some please help
Number of rooms left excluding a quarter of 140 is: 105 rooms.
What is a Quarter of a Number?A quarter is one-fourth. A quarter of a number is therefore, one-fourth of that number or 1/4 part of the number.
Therefore, number of rooms cleaned = 1/4(140) = 35.
A quarter of the 140 rooms is: 35.
Number of rooms left for cleaning in the afternoon = 140 - 35
Number of rooms left for cleaning in the afternoon = 105 rooms.
Learn more about a quarter on:
https://brainly.com/question/334801
#SPJ1
8.8÷4=8, point, 8, divided by, 4, equals
\text{ tenths}\div 4 tenths÷4start text, space, t, e, n, t, h, s, end text, divided by, 4
8.8 \div 4 =8.8÷4=8, point, 8, divided by, 4, equals
\text{ tenths} tenthsstart text, space, t, e, n, t, h, s, end text
8.8 \div 4 =8.8÷4=8, point, 8, divided by, 4, equals
The results of the given task 8.8 ÷ 4 is 2.2.
Division of Decimal8.8 ÷ 4
= 2.2
Therefore, 8.8 ÷ 4 = 2.2
Learn more about division:
https://brainly.com/question/1622425
#SPJ1
Diane is filling a candle order for a wedding. She needs 6 large arrangements and 13 small arrangements .The large arrangements each contain 25 candles. The small arrangements each contain 12 candles. How many candles does diane need in all?
Answer:
406 candles in all.
Step-by-step explanation:
She needs 6 large arrangements with 25 candles in each arrangement.
Multiply 25 and 6 to find how much candles for all large arrangements combined.
25*6=150
She also needs 13 small arrangements with 12 candles in each arrangement.
Multiply 13 and 12 to find how much candles for all the small arrangements combined.
13*12=156
Add the answers together to find how many candles in all.
156+150=406.
She needs 406 candles in all.
Hope this helps!
Answer:
306
Step-by-step explanation:
First we find the number of candles needed for each size of arrangement.
Large Arrangements:
6 large arrangements with 25 candles each:
25 × 6 = 150
Small Arrangements:
13 small arrangements with 12 candles each:
13 × 12 = 156
Now we add the results above to find a grand total:
total = 150 + 156 = 306
The function G(x) = 2-sin(x) is the result of the application of
transformations on the original function F(x) = cos(x). Which of the following options correctly describes the transformations applied to F(x)?
The transformations applied to F(x) is a vertical shift of 2 and a phase shift of π/2.
What are transformations?When a function is transformed, the graph's curve either "moves to the left/right/up/down," "expands or compresses," or "reflects."
Function transformations are highly useful for graphing functions without having to start from scratch because they allow you to move, extend, compress, or reflect the curve.
The graph of the parent function is either "moved," "resized," or "reflected" by a function transformation. The three primary categories of function transformations are as follows:Translation,Dilation and Reflection.
The given function F(x)=cos x is transformed to G(x)=2-sin x, by applying a vertical shift of 2 units upwards and a phase shift of π/2.
Learn more about transformations here:
https://brainly.com/question/1548871
#SPJ1