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3 years ago

What is the correct equation for a line that has a slope of 1/3, and a y intercept of 4

Mathematics

1 answer:

Julli [10]3 years ago

8 0

Answer:

y=1/3x+4

Step-by-step explanation:

It should be correct as the gradient = 1/3

and the y-intercept = C

= +4

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Wha is the area of this

Korvikt [17]

Octagon, stop sign.

Eight isoscles triangles. It looks like we're told the side is 9.9 and the height to the side (also called the apothem) is 12.

So each isosceles triangle has area (1/2)(9.9)(12) and we have eight of them,

area = 8(1/2)(9.9)(12) = 475.2

Answer: 475.2

Usually we wouldn't be told 9.9 -- this is the baby version. We know each of those isoscles triangles has unique angle 360/8=45 degrees, so the apothem and half the side of the octagon are a right triangle with acute angle 22.5 degrees.

The area of the right triangle with long leg 12, short leg x,

tan 22.5 = x/12 or

x = 12 tan 22.5

Twice that is what we're told is 9.9; let's check:

2x = 24 tan 22.5 = 9.941125496954282

The area of the little right triangle is

(1/2) 12 × 12 tan 22.5

and there are 16 of these

16 (1/2) 12 × 12 tan 22.5 ≈ 477.174

6 0

3 years ago

What is 0.08 written as a percent

andrew11 [14]

0.08 can be written as 8%

3 0

2 years ago

Read 2 more answers

Describe and correct the error in solving the equation<br><br> 7 - 3x = 12<br> 4x = 12<br> x = 3

aev [14]

If x=3
Just replace the X with 3
So seven minus three equals four
If 3 is X than do 4 times 3 which that makes twelve.

3 0

2 years ago

What equation models the data in the table if d = number of days and c = cost?

Anit [1.1K]

C = 22d is the correct answer because for every day the cost increases by 22 so two days mean the cost is equal to 22 (2)

4 0

3 years ago

Read 2 more answers

An n × n matrix B has characteristic polynomial p(λ) = −λ(λ − 3) 3 (λ − 2) 2 (λ + 1). Which of the following statements is false

asambeis [7]

Answer:

Only d) is false.

Step-by-step explanation:

Let $p=p(\lambda)=\lambda(\lambda-3)^3 (\lambda-2)^2 (\lambda+1)$ be the characteristic polynomial of B.

a) We use the rank-nullity theorem. First, note that 0 is an eigenvalue of algebraic multiplicity 1. The null space of B is equal to the eigenspace generated by 0. The dimension of this space is the geometric multiplicity of 0, which can't exceed the algebraic multiplicity. Then Nul(B)≤1. It can't happen that Nul(B)=0, because eigenspaces have positive dimension, therfore Nul(B)=1 and by the rank-nullity theorem, rank(B)=7-nul(B)=6 (B has size 7, see part e)

b) Remember that $p(\lambda)=\det(B-\lambda I)$ . 0 is a root of p, so we have that $p(0)=\det(B-0 I)=\det B=0$ .

c) The matrix T must be a nxn matrix so that the product BTB is well defined. Therefore det(T) is defined and by part c) we have that det(BTB)=det(B)det(T)det(B)=0.

d) det(B)=0 by part c) so B is not invertible.

e) The degree of the characteristic polynomial p is equal to the size of the matrix B. Summing the multiplicities of each root, p has degree 7, therefore the size of B is n=7.

8 0

3 years ago