Bonus Problem. Solve the equation for x in terms of the other<br> variables.<br> x(a +z)=w

If the null space of A4×5 is exactly a two-dimensional plane, answer the following:

Hatshy [7]

Answer:

I.

A is a 4 x 5 matrix => A: U -> V, dim U = 5, dim V = 4

Null space is exactly two dimensional plane

dim null (A) = 2

II.

Rank A = dim U - dim Null A = 5 - 2 = 3

III.

Number of linearly Independent columns of A is the rank of A = 3

IV.

Yes, The system Ax = b has no solution sometimes as range of A \neq V

V.

Yes,Sometimes Ax = b has a unique solution

VI.

Yes, sometimes Ax = b has infinitely many solutions

8 0

2 years ago

The following graph represents the hourly commission of a home appliance salesperson, y, based on the number of salespeople that

grandymaker [24]

We have been given graph of a downward opening parabola with vertex at point $(6.5,42.25)$ . We are asked to write equation of the parabola in standard form.

We know that equation of parabola in standard form is $f(x)=ax^2+bx+c$ .

We will write our equation in vertex form and then convert it into standard form.

Vertex for of parabola is $y=a(x-h)^2+k$ , where point (h,k) represents vertex of parabola and a represents leading coefficient.

Since our parabola is downward opening so leading coefficient will be negative.

Upon substituting coordinates of vertex and point (0,0) in vertex form, we will get:

$0=-a(0-6.5)^2+42.25$

$0=-a(42.25)+42.25$

$-42.25=-a(42.25)+42.25-42.25$

$-42.25=-42.25a$

$a=1$ Divide both sides by $-42.25$

So our equation in vertex form would be $f(x)=-(x-6.5)^2+42.25$ .

Let us convert it in standard from.

$f(x)=-(x^2-13x+42.25)+42.25$

$f(x)=-x^2+13x-42.25+42.25$

$f(x)=-x^2+13x$

Therefore, the equation of function is standard form would be $f(x)=-x^2+13x$ .

3 0

3 years ago

Given congruent triangles name the corresponding sides and corresponding angles

Alborosie

Answer:

See explanation

Step-by-step explanation:

Given $\triangle ABC\cong \triangle ADC$

According to the order of the vertices,

side AB in triangle ABC (the first and the second vertices) is congruent to side AD in triangle ADC (the first and the second vertices);

side BC in triangle ABC (the second and the third vertices) is congruent to side DC in triangle ADC (the second and the third vertices);

side AC in triangle ABC (the first and the third vertices) is congruent to side AC in triangle ADC (the first and the third vertices);

angle BAC in triangle ABC is congruent to angle DAC in triangle ADC (the first vertex in each triangle is in the middle when naming the angles);

angle ABC in triangle ABC is congruent to angle ADC in triangle ADC (the second vertex in each triangle is in the middle when naming the angles);

angle BCA in triangle ABC is congruent to angle DCA in triangle ADC (the third vertex in each triangle is in the middle when naming the angles);

6 0

3 years ago

PLEASE HELP WITH MATHH

Scorpion4ik [409]

Answer:

i think the answer is 76cm im pretty sure it is

Step-by-step explanation:

if so mark this as brainliest answer!!!

5 0

2 years ago

The math club wants to order t-shirts to recognize students who improved their performances in algebra I. Hot shirt charges $12.

horsena [70]

Answer:

1000

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers

Bonus Problem. Solve the equation for x in terms of the other variables. x(a +z)=w