suppose ax=b has a solution. explain why the solution is unique precisely when ax=0 has only the trivial solution.
Answers
Translation of the Ax=0 solution set yields the Ax-b solution set since Ax-b is consistent. The Ax = b solution set is therefore a single vector if and only if the Ax = 0 solution set is a single vector, which occurs if and only if Ax 0 has only the trivial solution.
what is solution ?Finding the solution to an equation is like finding the solution to a puzzle. A mathematical equation proves the equality of two algebraic expressions. Determine the values of the variables that make the equation a true statement in order to solve an equation. An equation's solution is any value that causes the equation to be true.
given
Let's suppose that there is a solution to the equation ax = b.
Now, we want to demonstrate that the trivial solution exists for the equation ax = b when ax = 0.
Ax = 0 is homogeneous.
In the event that this equation was true for b, we define
To be a set of vectors with the form ax = b
w = m + gh
The subscript "h"
A solution to ax = 0 is gh.
Ax=b is in the form of w= m+gh based on the information we know had.
with
m = ax=solution b's
Soulution of gh = ax=0
Only a simple solution, ax = 0, exists.
gh = 0
where gh = 0
The relationship between ax=b and w=m
Ax = b thus has no alternative solutions.
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Related Questions
Use the equation below to answer the question.
(1/3) – ÷ 27 = x
Which equation could be solved to also find x?
A. –27 × 3 = x
B. –27 ÷ 3 = x
C. –1 ÷ (27 ÷ 3) = x
D. –1 ÷ (27 × 3) = x
Answers
Answer:
The given equation is:
(1/3) – ÷ 27 = x
We can simplify it as follows:
(1/3) - (1/27) = x
8/27 = x
So, the value of x is 8/27.
We can substitute this value of x in each equation to see which one gives a true statement.
A. -27 × 3 = -81 ≠ 8/27
B. -27 ÷ 3 = -9 ≠ 8/27
C. -1 ÷ (27 ÷ 3) = -1/9 ≠ 8/27
D. -1 ÷ (27 × 3) = -1/81 ≠ 8/27
Therefore, none of the given equations could be solved to find x.
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Draw the graphs of the lines below on the same grid to find the coordinates of the point of intersection. y=2x+3 y−1/2x−2
Answers
Answer:
(2, 2)
Step-by-step explanation:
The point of intersection is at (2, 2)
A linear equation is given by:
y = mx + b;
where y, x are variables, m is the slope of the line and b is the y intercept.
Given the line with equations:
y = 3 x − 4 and y = 1/ 2x + 1
Plotting the graphs using geogebra online tool, the point of intersection is at (2, 2)
-2 (x+3)= -2x-6 is this one solution, mutipule solution, or no solution if one of the 2 plz tell me what x epual
Answers
Answer:
no solution
x=0
Step-by-step explanation:
when you do the math it all equals 0 meaning there are no solutions.
I hope this helps
what is an angle measuring below 90 degrees called?
Answers
Answer:
acute angle
Step-by-step explanation:
what is an angle measuring below 90 degrees called?
The acute angle is the angle that has an amplitude of less than 90°. The obtuse angle, on the other hand, has a width greater than 90°. The right angle measures 90° and its sides are orthogonal.
Answer:
an angle less than 90° is an acute angle
Step-by-step explanation:
an angle less than 90° is an acute angle
an angle equal to 90° is a right angle
an angle greater than 90° but less than 180° is an obtuse angle
an angle greater than 180° is a reflex angle
What is the value of x?
Answers
Answer:
46°
Step-by-step explanation:
from large triangle:
let the third unknown angle be 'a'
then,
a+x+7+85=180
a=88-x
now,from small triangle,
let the third unknown angle be 'b'
then,
b+x+2x=180
b=180-3x
b=a (vertically opposite angles)
then,
180-3x=88-x
2x=92
x=46
Determine, to the nearest tenth, the perimeter of the triangle shown in the accompanying diagram.
This is a diagram of triangle ABC. Point A is located at (-9,6). Point B is located at (-3,10). Point C is located at (-2,2).
Answers
Answer:
23.3
Step-by-step explanation:
A 10-mile bike race is divided into 4 equal sections.
Which equation shows how to find the number of miles in each section?
Math item stem image
CLEAR CHECK
4÷10=410 mile
4÷10=104 miles
10÷4=410 mile
10÷4=104 miles
Answers
Answer:
Step-by-step explanation:
read the question it says
a 10 mile bike rade is DIVIDED into 4 equal sections
10 DIVIDED BY 4
10÷4=104 miles
Figure A is a scale image of figure B. Figure A maps to figure B with a scale factor of 0.80. What is the value of x?
Answers
Answer:
4
Step-by-step explanation:
x=5*0.8=4
Answer:
here is the answer
Step-by-step explanation:
we need to find x
therefore,
0.80*x=5 (since it is a factor of 0.80)
x= 5/0.80
x=6+1/4= 6.25 units
For the graph shown, identify a) the point(s) of inflection and b) the intervals where the function is concave up or concave down. 10 0 0 5 ilm EX m. mil -10 WO 110 a) The point(s) of inflection is/are (Type an ordered pair. Use a comma to separate answers as needed.)
Answers
Answer
a) Point of inflection is (3, 8)
b) The function is concave up in the interval where x < 4.
The function is convex down in the interval where x ≥ 2
Explanation
a) Points of Inflection
These are the points on the graph where concavity changes. That is, the graph changes from concave up form to convex down form or from convex down form to concave up form.
From this portion of the graph attached, we can see that this graph changes from concave to convex form around the point where
x = 3 and y = 8.
In ordered pair form, (3, 8)
b) Intervals where the function is concave up and intervals where the function is convex down.
We can see that the function is concave up at values of x less than 4. So, the interval where the graph is concave up is x < 4.
And we can see that the function is convex down from the point where x = 2 upwards. So, the function is convex down in the interval where x ≥ 2
Hope this Helps!!!
Leila wants to rent a boat and spend at most $93. The boat costs $8 per hour, and Leila has a discount coupon for $3 off. What are the possible numbers of
hours Leila could rent the boat?
Use t for the number of hours.
Write your answer as an inequality solved for t.
Answers
Answer:
0 ≤ t ≤ 18
Step-by-step explanation:
The cost of renting the boat without any discount is $8 per hour. However, Leila has a discount coupon for $3 off, so the effective cost per hour would be $8 - $3 = $5.
Let's assume Leila rents the boat for t hours. The total cost of renting the boat for t hours would be $5 multiplied by t, which is 5t.
According to the problem, Leila wants to spend at most $93. Therefore, we can set up the following inequality:
5t ≤ 93
This inequality represents the condition that the total cost of renting the boat (5t) should be less than or equal to $93.
Simplifying the inequality:
5t ≤ 93
Dividing both sides by 5 (since the coefficient of t is 5):
t ≤ 93/5
t ≤ 18.6
Since we cannot rent the boat for a fraction of an hour, we can round down the decimal value to the nearest whole number:
t ≤ 18
0 ≤ t ≤ 18
Answer: 0≤t≤12
Step-by-step explanation:
(I’m not sure if it’s 5 dollars off per hour, or total, but here’s what I did!)
If Leila has a $3 coupon, than she can spend +$3 because when you get a coupon, you can spend more, so 93+3 is equal to 96, now we just divide by 8 (because a boat costs $8 per hour) and we get 96/8=12.
Then, in inequality form it’s t≤12, because she can rent the boat for at most 12 hours, you could also do 0≤t≤12, because you can’t rent it for a negative amount of time, but either works.
What is the missing coefficient?
(15x^2 +11y^2 +8x)-(7x^2+5y2 +2x) =
?x^2+6y^2+6x
•4
•8
•10
•22
Answers
Answer:
8
Step-by-step explanation:
The missing coefficient in the expression is 8.
Option B is the correct answer.
We have,
The given expression is:
(15x^2 + 11y^2 + 8x) - (7x^2 + 5y^2 + 2x)
Simplifying the expression by combining like terms, we get:
= 15x^2 + 11y^2 + 8x - 7x^2 - 5y^2 - 2x
= (15x^2 - 7x^2) + (11y^2 - 5y^2) + (8x - 2x)
= 8x^2 + 6y^2 + 6x
The coefficient of x^2 is 8.
Thus,
The missing coefficient is 8.
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Determine the domain on which the following function is decreasing.
Answers
Answer:
[3,10]
Step-by-step explanation:
Lmk if you need an explanation and I'll add one.
f(x)=x^3 −9x
What is the average rate of change of f over the interval [1,6] ?
Answers
Answer:34
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
Here [ a, b ] = [ 1, 6 ], thus
f(b) = f(6) = 6³ - 9(6) = 216 - 54 = 162
f(a) = f(1) = 1³ - 9(1) = 1 - 9 = - 8
average rate of change = = = 34
Sumaya's soccer coach randomly passes out three kinds
of fruit bars (strawberry, blueberry, and apple) after each
game. Sumaya has two games one morning. This table
lists the sample space of outcomes ( click the image i put to see it )
In the event SB, sumaya gets a strawberry bar after the game 1 and a blueberry bar after game 2
which outcome would be included in the event “ gets only one apple bar “
Answers
Answer:
D. AS
Step-by-step explanation:
In this event, only one apple bar may be included in the conclusion. In the instance of AS, only one apple bar is present.
Answer: AS
Step-by-step explanation:
In the event AS, Sumaya would get only one apple along with a strawberry bar. This is the only choice that has only one A in it, meaning that this is the correct answer.
is y = -x + 2 a function
A-yes, because it passes the vertical line test.
B-yes, because it fails the horizontal line test
C-no, because itpasses the horizontal line test.
D-no, because it fails the vertical line test.
Answers
The relation y = -x + 2 is a function because (a) yes, because it passes the vertical line test.
Checking if the relation y = -x + 2 is a functionFrom the question, we have the following parameters that can be used in our computation:
y = -x + 2
The above equation is a linear function
As a general rule of functions and relations
All linear functions are functions
This is because they pass the vertical line test
So, the true statement is (a)
Hence, the relation y = -x + 2 is a function because (a) yes, because it passes the vertical line test.
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Which of the following scores has the better relative position ( as measured by the z score) a. A score of 53 on a test for which the sample mean is 50. b. A score of 230 on a test for which the sample mean is 200. c. A score of 480 on a test for which the sample mean is 400. d. Cannot be determined with the information provided.
Answers
Answer:
d. Cannot be determined with the information provided.
Step-by-step explanation:
Z-score:
In a set with mean \(\mu\) and standard deviation \(\sigma\), the z-score of a measure X is given by:
\(Z = \frac{X - \mu}{\sigma}\)
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Finding the better relative position:
The score with the better relative position is the one with a higher z-score.
To find the z-score, the mean and the standard deviation is needed, and in this question, the standard deviation is not given, and thus, the correct answer is given by option d.
Solve 6x^2-2x+1=0 using any method.
Answers
Answer:
\(x=\frac{1-\sqrt{-5} }{6}\\x=\frac{1+\sqrt{-5} }{6}\)
There are no real roots.
Step-by-step explanation:
\(6x^2-2x+1=0\\x=\frac{2-\sqrt{2^2-4*6} }{2*6} \\x=\frac{2-\sqrt{-20} }{12}\\x=\frac{1-\sqrt{-5} }{6}\\x=\frac{1+\sqrt{-5} }{6}\)
A baker made 36 blueberry muffins on Monday. What percent of the total number of muffins were blueberry if the baker made 90 muffins?
Answers
The blueberry muffins made by baker on monday is 40% of the total muffins made by the baker .
What is Percentage ?A quantity or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. In order to determine the percentage of a number, divide it by its sum and then multiply the result by 100. The proportion thus refers to a component per 100. The word percent indicates a percentage of 100. The word "percent" denotes "per 100." The letter "%" stands for it.
Now in the given question,
Total number of muffins baker made = 90
Blueberry Muffins made by baker on monday = 36
Prcentage of blueberry muffins out of total muffins \(=\frac{36*100}{90} = 40 %\)
So , the Blueberry Muffins were 40% of the total muffins baker made.
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Use the relationship between the angles in the figure to answer the question. Which equation can be used to find the value of x? O x = 52 x + 52 = 180 O x + 52 = 90 O 52 + 38 = x + 52⁰ хо 1 WHAT'S THE ANSWER
Answers
Based on the above, the equation that can be used to know the value of x is x =52. In the attached figure, the two angles are option A: x = 52.
What is the relationship between the angles ?Vertical angles theorem is one that is used to show the relationship between the angles. It implies that two opposite vertical angles are made if two lines intersect one another and are always equal to one another.
From the attached figure, two angles namely x° and 52° are said to be vertically opposite angles
Hence, x = 52
Therefore, based on the above, the equation that can be used to know the value of x is x = 52.
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See correct text below
Use the relationship between the angles in the figure to answer the question.
Which equation can be used to find the value of x?
x = 52
x + 52 = 180
x + 52 = 90
52 + 38 = x
Solve the equation below
Answers
Answer:
The answer is (-8,8).Step-by-step explanation:
We know that:
x = -8Work:
-3x - 5y = -16=> -3(-8) - 5y = -16=> 24 - 5y = -16=> 24 + 16 = 5y=> 40 = 5y=> y = 8Hence, the answer is (-8,8).
Hoped this helped.
\(BrainiacUser1357\)
Dewie Lifftum, Howe Moving Company has a loading ramp for their moving truck. The ramp connects to the truck 5 feet above the ground and the length of the ramp from the truck to the ground is 13 feet long what is the distance along the ground from the truck to the end of the ramp?
Answers
Answer:
the answer is 65
Step-by-step explanation:
13x5=65
12 feet is the distance along the ground from the truck to the end of the ramp.
What is Pythagorean Theorem?
For a right-angled triangle
(base)²+(height)²=(hypotenuse)².
How to solve the problem?The ramp makes a right-angled triangle with the truck and the ground refer to the supported diagram.
Let x be the distance along the ground from the truck to the end of the ramp. Then
x²+5²=13²
⇒x²=13²-5²
⇒x²=169-25=144=12²
Hence, 12 feet is the distance along the ground from the truck to the end of the ramp.
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For every £1.00 a company spends on advertising, it spends £0.75 on its website. Express the amount spent on advertising to the amount spent on its website as a ratio in its simplest form.
Answers
Answer:
4:3
Step-by-step explanation:
For every £1.00 a company spends on advertising, it spends £0.75 on its website.
From the above question:
The ratio is given as:
Amount spent on advertising : Amount spent on website
= £1.00 : £0.75
Convert ratio sign to division
= 1/0.75
Multiply Numerator and Denominator by 100
= 1 × 100 / 0.75 × 100
= 100/75
= 4/3
= 4 : 3
Therefore, the ratio in its simplest form = 4:3
9n + 2 = 47
What number does n represent?
(p.s show how you did it)
Answers
Answer:
'n' will represent the number 5.
Step-by-step explanation:
\(9n \: + 2 = 47 \\ 9n \: = 47 - 2 \\ 9n \: = 45 \\ n \: = 45 \div 9 \\ n \: = 5\)
How can you tell if data has outliers? Include the formula
Answers
Using interquartile ranges.
Interquartile range (IQR) indicates the middle half range of the data set. You can use IQR to create "fences" around your data and define outliers as values outside those fences.
This method is useful when you have some values on either end of your dataset, but you are not sure whether any of them should be considered outliers.
Interquartile range method Sort the data from lowest to highest Identify the first quartile (Q1), median, and third quartile (Q3). Calculate IQR = Q3 – Q1 Calculate Top Fence = Q3 + (1.5 * IQR) Calculate bottom fence = Q1 – (1.5 * IQR) Use fences to highlight outliers, values outside the fence.About outliers of dataOutliers are data that deviate too far from other data in a data set (outlier). The existence of these data outliers will make the analysis of a series of data biased, or not reflect the actual phenomenon. The term outliers is also often associated with extreme values, both large extremes and small extremes.
As an illustration, if there are four students, the first student has a monthly allowance of Rp. 500 thousand, second students Rp. 600 thousand, third student Rp. 700 thousand, and the fourth student because he is the son of a rich man (sultan), has a monthly allowance of up to Rp. 5 million. At a glance it appears that the value of 5 million is relatively far compared to the pocket money of the other three students.
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Help me ASAP I have a 67% I math the girlie needs help
Answers
Answer:
x=28
Step-by-step explanation:
4(x-5)=92
4x-20=92
add 20 to both sides
4x=112
divide 4 on both sides
x=28
Answer:
The value of x is 28
Step-by-step explanation:
4(x - 5) = 92
4x - 20 = 92
4x = 92 + 20
4x = 112
x = 112 ÷ 4
x = 28
Thus, The value of x is 28
-TheUnknownScientist
An isosceles triangle has base angles that each measure 23 degrees. Which equation can be used to find x, the measure of third angle of this isosceles triangle in degrees?
Answers
Answer:
since a triangle measures up to 180 degrees getting the value of x will be all angles added together equals to 180.
(base angles) + x = 180°
46° + x = 180°
this is what I think good luck
The measure of third angle of this isosceles triangle is 134 degrees.
What is Angle Sum Property?According to the triangle's "angle sum property," a triangle's interior angles add up to 180°.
S = (n-2)*180° is the angle sum property formula for any polygon, where 'n' represents the number of sides in the polygon.
Given:
Two Base angles is 23 degree.
and third angle is x.
Using Angle Sum property
x + 23+ 23 =180
x +46 =180
x= 180- 46
x= 134
Hence, the third angle is 134 degree.
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A survey was conducted that asked 1060 people how many books they had read in the past year. Results indicated that x=14.5 books and s=16.8 books. Construct a 90% confidence interval for the mean number of books people read. Interpret the interval.
Answers
The confidence interval is (13.653, 15.347). This means that we are 90% confident that the true mean number of books people read in the past year falls within this range.
Based on a survey of 1,060 people, the mean number of books people read in the past year was estimated to be 14.5 books, with a standard deviation of 16.8 books. Using these values, a 90% confidence interval for the mean number of books can be constructed.
To construct a confidence interval, we can use the formula:
CI = x ± z * (s / sqrt(n))
Where:
CI = Confidence interval
x = Sample mean
z = Z-score corresponding to the desired confidence level (90% confidence corresponds to a z-score of approximately 1.645)
s = Sample standard deviation
n = Sample size
Plugging in the given values:
x = 14.5
s = 16.8
n = 1,060
Calculating the confidence interval:
CI = 14.5 ± 1.645 * (16.8 / sqrt(1,060))
CI = 14.5 ± 1.645 * 0.515
CI = 14.5 ± 0.847
In other words, if we were to repeat the survey multiple times, we would expect the true mean to be within this interval in approximately 90% of the cases.
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HELPP ME PLEASE ITS DUE TODAY!!!!
Answers
Answer:
b=-12.5
Step-by-step explanation:
\( - 9 - b = 3.5 \\ - b = 3.5 + 9 \\ - b = 12.5 \\ b = - 12.5\)
Goldfish care manuals recommend that you have only 12 goldfish per 10 gallons of water. If Alex owns a 40 gallon tank that has a population density of 1.75 goldfish/gallon, is Alex meeting the recommendations?
Answers
Answer:
Pretty sure he is..
Step-by-step explanation:
Cus yes
epicly
I don't under stand how to do it
Answers
F: 2=x and -6=y
G: 8=x and -5=y
Answer:
They are points on a graph. Just put the points on a graph. There's no math to it, really.
Step-by-step explanation:
F(2, -6)
F(x, -y)
and
G(8, -5)
G(x, -y)