Is it possible that all solutions of a homogeneous system of ten linear equations in twelve variables are multiples of one fixed nonzero solution

Answers

Answer 1

The answer is no, because the Rank Theorem tells us that rank A + dim Nul A = 12 . Since the rank can be at most 10, the null space has to have dimension at least two.


Related Questions

write the ratio as a fraction in simplest form

Answers

14/27. I have linked my working our down below make sure to have a look at it for a better understanding.

Hello I would really appreciate if someone could help me with this math question. I’m so confused

Answers

Answer:

  a. f = 17.5/c

  b. 8.75 N

Step-by-step explanation:

(a)

Inverse variation means one variable is proportional to the inverse of the other. The equation for that is ...

  f = k(1/c) . . . . . . force (f) is proportional to the inverse of distance (c)

We find the value of k using data given for a specific instance.

  3.5 N = k(1/(5 cm)) . . . . use the given values

  17.5 N·cm = k . . . . . . multiply by the denominator

Then the equation of interest is ...

  f = 17.5/c . . . . . . . where c is in cm, and f is in newtons

__

(b)

Using the above equation, we find the force to be ...

  f = 17.5/2 = 8.75 . . . . newtons

_____

Additional comment

We often look at several different kinds of proportionality:

y = kx . . . . directy = k(1/x) . . . . inversey = kx² . . . . proportional as the squarey = kx·z . . . . jointly proportional to x and z

and there are combinations of these, such as ...

y = kr²h . . . . jointly proportional to h and the square of r

You may have noticed that when x and y are inversely proportional, their product is a constant. y = k/x  ⇒  xy = k

__

We have left off the units of k in the problem above. Sometimes it is a good idea to retain them, or to pay close attention to what they are. This can avoid using the wrong measures for the variables.

  f = (17.5 N·cm)/(2 cm) = 8.75 N . . . . . units of cm cancel

Write an equation of the line that passes through (3, 1) and (0,10) .

y=

Answers

Answer:

Step-by-step explanation:

hello :

y = -3x+10

What is the median for the following set of data?

4, 4, 6, 10, 12, 13, 15, 16



a 12

b 10

c 11

d 16

Answers

Answer:

C

Step-by-step explanation:

The median is where we find the number that is in the middle of the data set. In this case, there cannot be a single number in the middle because the number of numbers in this data is even.

Knowing this, we need to add the two numbers that are in the middle (10 and 12). We add these two numbers and divide them by 2

[tex]\frac{10+12}{2} =\frac{22}{2} =11[/tex]

5>x/5
Show all work in steps

Answers

Answer:

[tex]\boxed{\sf{x < 25}}[/tex]

Step-by-step explanation:

To find the value of x, isolate it on one side of the equation.

5>x/5

First, you have to switch sides.

→ x/5<5

Then, you multiply by 5 from both sides.

→ 5x/5<5*5

Solve.

Multiply the numbers from left to right.

→ 5*5=25

→ x<25

Therefore, the solution is x<25, which is our answer.

I hope this helps you! Let me know if my answer is wrong or not.

Answer:

25 > x

Step-by-step explanation:

[tex]5 > \frac{x}{5}[/tex]

To find the value of x, you have to multiply both sides by 5.

[tex]5*5 > \frac{x}{5}* 5[/tex]

[tex]25 > \frac{5x}{5}[/tex]

[tex]25 > x[/tex]

Express 10/1,000 as a decimal​

Answers

answer: 0.01

just count how many zeroes are in 1000 (3) and then move 3 times to the left which gives you 0.01

Answer:

0.01

Step-by-step explanation:

hope this helps -_-

Which of the following values in the set below will make the equation 4x + 2 = 18 true?

{0, 1, 2, 3,4}
^^ those are the input numbers

Answers

Answer:

4

Step-by-step explanation:

subtract 2 on both sides you will get 4x=16 because 18-2=16 then divide both sides by 4 to get ×=4

4x+2=18

-2. -2

4×=16

4. 4

x=4

The length of a rectangle is 8 more than the width. The area is 65 square centimeters. Find the length and width of the rectangle.

Answers

Answer: The width of the rectangle is 5 cm and the length is 13 cm

Step-by-step explanation:

Let the width be x cm

Let the length be (x+8) cm

Area = 65cm²

[tex]\Rightarrow x(x+8)=65 \ [\because$ Area of rectangle $=$ length $\times$ width $]$ \\$\Rightarrow x^{2}+8 x-65=0 \Rightarrow x^{2}+13 x-5 x-65=0$ \\$\Rightarrow x(x+13)-5(x+13)=0 \Rightarrow(x+13)(x-5)=0$ \\$\Rightarrow x=-13$ or $x=5$ \\But width car't be negative. so $x=5$ \\[/tex]

Therefore:

Width = 5 cm

Length = 5 + 8 = 13 cm

A chemist has three different acid solutions.
The first solution contains 15 % acid, the second contains 30 % acid, and the third contains 50 %
acid,
She created 78 liters of a 35 % acid mixture, using all three solutions. The number of liters of 50 %
solution used is 3 times the number of liters of 30 % solution used.
How many liters of each solution was used?

Answers

Answer:

Its 50 and it can reach 60

Question 8
1 pts
What is the best way to describe the central tendency of residential real estate prices in Westwood?
Hint: Westwood real estate is highly skewed. You are able to find houses that are $600,000 to
$69,000,000 with an average price of $1,020,000.
O Median
O Mean

Answers

The best way to describe the central tendency of residential real estate prices in Westwood is mean.

What are measures of central tendency?

A measure of central tendency attempts to describe a data set by determining the central value of the data set. Measures of central tendency are mean, median and mode

Mean is the average of a set of numbers.

Mean = sum of the numbers / total number

To learn more about mean, please check: https://brainly.com/question/25842202

Joanne earns $3,000 per month at her job at the department store. If her taxes are 28 percent of her pay, what is her monthly take-home pay?

Answers

Joanne her earns 3000$ I’m which she gives 28 percent of it to taxes
So 28 percent of 3000$ is
3000*28/100 where 3000*28 is equal to
84000/100
840$ is 28 percent of 3000$
So to fine the remaining amount of money after she pays that amount is
3000$-840$
Which is equal to 2160$

What are the sum of the interior angles in an irregular octagon?

Answers

Answer:

1080

Step-by-step explanation:

Use formula

Sum of in. angle=(n-2)*180

Answer:

1080°

Step-by-step explanation:

To find the sum of interior angles, use the formula: 180(n-2). Input '8' as 'n'.

180(8-2)

180(6)

1080°

Therefore, the sum of interior angles of an irregular octagon is 1080

So can someone explain how the heck does 4 x 4 x 4 = 64??
Cause I keep on getting 12 so like wth??

Answers

Answer:

it is more like, 4x4=16

16x4=64

Step-by-step explanation:

I know it can be confusing, but you will eventually get it :)

i think you were adding 4+4+4=12, but that is not what you are supposed to do here.

Hope i helped :)

+3=17
x
+
3
y
=
17

−+2=8

x
+
2
y
=
8



Step 1: Find the LCM to eliminate the x.

Step 2: Write the new equation.

Step 3: Divide to solve for y.

Answers

Answer:

1

Step-by-step explanation:

Solve using the square root property.X^2=-12

Answers

Answer:

x = ± 2i[tex]\sqrt{3}[/tex]

Step-by-step explanation:

note that [tex]\sqrt{-1}[/tex] = i

x² = - 12 ( take square root of both sides )

x = ± [tex]\sqrt{-12}[/tex] = ± [tex]\sqrt{4(3)(-1)}[/tex] = ± 2i[tex]\sqrt{3}[/tex]

I need help with a math problem.

Answers

Answer:

where is the problem?

You should post question for us to answer

100 apples in total, 65% are green, and 21% of the green apples have worms. how many apples have worms?

Answers

Answer:

14 apples are green with worms.

Step-by-step explanation:

100 apples right

65% are green

21% are green with worms

Imma pretend the first time you meant red ok....

sooo to solve this

.65*100=65 are red

.21*65=13.65 are green with worms

A,B,C,D are points on the circumference of a circle centre o
ed is a tangent to the circle
angle odb = 25
work out angle bad

Answers

The points A,B,C,D make up the circumference of the circle

The measure of angle BAD is 65 degrees

How to determine the measure of angle BAD?

The measure of angle ODB is given as:

ODB = 25 degrees

Considering the triangle BOD, we have:

ODB + BOD + DBO = 180

Where:

ODB = DBO = 25

So, we have:

25 + BOD + 25 = 180

Solve for BOD

BOD = 130 degrees

The angle at an arc is twice the angle at the circumference.

So, we have:

BOD = 2 * BAD

Substitute 130 for BOD

130 = 2 * BAD

Divide both sides by 2

65 = BAD

Hence, the measure of angle BAD is 65 degrees

Read more about angle measures at:

https://brainly.com/question/17972372

Three neighbors plan to complete fencing projects this spring. As shown in the diagrams below, Neighbor A plans to fence in his rectangular backyard with a 6-foot tall wooden privacy fence. Neighbor B plans to construct a circular chain link fence around his pool. And, Neighbor C is putting a vinyl fence around three side of his front yard. Note: Diagrams are not drawn to scale. Intended fences are marked with a dashed line.
Neighbor A:

Neighbor B:

Neighbor C:

Neighbor A can put up three 8 foot sections of wood fencing in two hours.
Neighbor B can put up 15 feet of chain link fencing each hour.
Neighbor C can put up 1 yard of vinyl fencing in half an hour.

Which neighbor's fencing project will take the least amount of time to complete?
Which neighbor's fencing project will take the most amount of time to complete?

Answers

Answer:

i think c

Step-by-step explanation:

Answer:

Neighbor C will take the least amount of time and Neighbor B will take the most amount of time.  Let me know if i'm right!

Step-by-step explanation:

I hope this helps! Have a good weekend!! :)

Help I don't understand this math. Whoever gets the right answer gets Brainlist! :)

Find the equation using this graph.​

Answers

Answer:

the slope is 2

y=2x-1

Step-by-step explanation:

y(2)-y(1)/x(2)-x(1) is the formula for slope

-1-0/0-0.5=-1/0.5=2

however, it is looking for the equation

y=mx+b

(b=y intercept)

m=slope

y=2x-1

Answer:

Step-by-step explanation:

The equation of a line is y = m*x + b

So plug in the numbers...

the slope is the change in y over the change in x or (y - y₁)/(x - x₁)

(-1 - 0)/(0 - 0.5) = 2

so... m = 2

and b is the y-intercept which is -1

therefore the answer is: y = 2x - 1

PLEASE RATE!! I hope this helps!!

If you have any questions comment below

( I have verified my answer on an online calculator)

What is 8 cm enlarged by a scale factor of 6.5

Answers

Answer:

8cm enlarged by a scale factor of 6.5 is 52cm I believe.

Step-by-step explanation:

8 times 6.5= 52cm

convert y = -0.5(x + 4)^2 - 2 standard form

Answers

Answer:

I think the answer is: y = 0.5x^2 + 4x + 6, <3

Step-by-step explanation:

GIVING BRAINLIEST!! need this rlly soon thank you so much!

Answers

Answer:

Large - PR - 15 and QR - 9 Missing degrees is P - 37

Small - Missing degree is 53

They are similar because they have the exca same degrees and if you divided by 3 on each side of the larger triangle you get the small triangle.

Step-by-step explanation:

Pythagorean theorem

I WILL GIVE 20 POINTS TO THOSE WHO ANSWER THIS QUESTION RIGHT NOOOO SCAMS AND EXPLAIN WHY THAT IS THE ANSWER

Answers

Step-by-step explanation:

y - x = 4x (vertically opposite angles)

y = 5x

4x+ y+x = 180

5x+5x = 180

x = 18

y = 90

Graph the line with slope
2.
passing through the point (-3, 3).
3
1
?
13

Answers

The graph of the line with the given slope that passes through (-3, 3) is shown in the image attached below.

What is the Equation of a Line in Slope-intercept Form?

The equation in slope-intercept form of a line, is y = mx + b, where:

b = y-intercept

m = slope = change in y/change in x.

Given a line with slope = 2 and passes through (-3, 3), plug in m = 2 and (a, b) = (-3, 3) into y - b = m(x - a) to write the equation of the line

y - 3 = 2(x - (-3))

Rewrite in slope-intercept form

y - 3 = 2x + 6

y = 2x + 6 - 3

y = 2x + 3

Therefore, the graph of the line with the given slope that passes through (-3, 3) is shown in the image attached below.

Learn more about slope-intercept form on:

https://brainly.com/question/1884491

Use the proof above to answer the question: What reason can be used to prove that the triangles are congruent?
A. AAS B. ASA C. AAA D. SAS E. SSS

Answers

Answer:

E. SSS

Step-by-step explanation:

AB=BC (Given)

AD=CD (Midpoint)

BD=BD (common)

Therefore answer is : SSS

How many metres are there in 2 kilometres?

Answers

First i want you to find how many meters are in one kilometer then you multiply that by two

Answer:

2000 metres

Step-by-step explanation:

1000 metres = 1 km

therefore, (1000×2) metres = 2 km

2000 metres = 2km

Which coordinates best represents the vertex of the graph first correct answer gets Brianliest

Answers

Answer:

The vertex of the graph is:

the minimum point for a parabola that opens upwardsthe maximum point for a parabola that opens downwards

As this parabola opens upwards, the vertex is the minimum point.

From inspection of the graph, vertex = (-3, -1)

Equation of the graph

From inspection we can see that the x-intercepts are when
x = -4 and x = -2

[tex]\sf x = -4 \implies x+4=0[/tex]

[tex]\sf x = -2 \implies x+2=0[/tex]

Therefore:

[tex]\sf y=(x+4)(x+2)[/tex]

Expand:

[tex]\sf \implies y=x^2+6x+8[/tex]

Answer:

[tex]B)f(x) = {x}^{2} + 6x + 8[/tex]

Step-by-step explanation:

Let [tex] f(x)=x^2[/tex] be the parent function. With transformation of function, firstly,we know that,

We can move it up or down by adding a constant to the y-value

algebraically

g(x)=x²+C

Clearly, The parabola is moved down by 1 unit thus, C is -1. Therefore our function transforms to

f(x)=-1

secondly, we know that,

We can move it left or right by adding a constant to the x-value

algebraically,

g(x)=(x+C)²

in case,

C is positive, g(x) moves to the left and vise versa

Since the parabola is moved left by 3 unit, C is +3, and hence Our function eventually becomes

[tex]f(x) = (x + 3 {)}^{2} - 1[/tex]

simplifying it yields:

[tex]\implies \boxed{f(x) = {x}^{2} + 6x + 8}[/tex]

Hence,B is our required answer

I NEED HELP ON THIS QUESTION (I will give a Brainlist to the best one no links please.)

Answers

Answer:

1. 84.7

2. 24

3. 47.5

4. 57.5

Step-by-step explanation:

your welcome and mark as brainliest pls

I need to know the answer now please and thank you

Answers

Answer: D. f(-4)=g(-4)
When the y-value of the f line is -4 the y-value of the g line is -4
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