1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Fofino [41]
3 years ago
6

Write these expressions as simply as possible

Mathematics
2 answers:
harkovskaia [24]3 years ago
7 0
So it is asking you to group like term so
x terms can be grouped/added/subtracted to other x terms, but not to x^2 or x^3 terms
x^2 terms to x^2 and so on so

1.  9-3k+5k=
9+(5k-3k)=
9+2k

2.  k^2+2k+4k=
k^2+(2k+4k)=
k^2+6k=
Archy [21]3 years ago
4 0
1)\ 9-3k+5k=9+2k\\\\2)\ k^2+2k+4k=k^2+6k=k(k+6)
You might be interested in
Anna is selling boxes of chocolate chip cookies (c) for $6 each and boxes of peanut butter cookies (b) for $7 each. She must
Georgia [21]

Answer:

x+y\geq30

6c+7b\geq175

Step-by-step explanation:

Given : Let c represents the number of boxes of chocolate chip cookies and b represents the boxes for butter cookies.

Anna is selling boxes of chocolate chip cookies (c) for $6 each and boxes of peanut butter cookies (b) for $7 each.

i.e. Cost of 'c' chocolate chip cookies = 6c

Cost of b butter cookies = 7b

She must  sell at least 30 boxes of cookies and at least $175 worth of cookies.

i.e. x+y\geq30

6c+7b\geq175

Thus , the system of inequalities models this situation :

x+y\geq30

6c+7b\geq175

7 0
3 years ago
(a) Find the unit tangent and unit normal vectors T(t) and N(t).
andrey2020 [161]

Answer:

a. i. (i + tj + 2tk)/√(1 + 5t²)

ii.  (-5ti + j + 2k)/√[25t² + 5]

b. √5/[√(1 + 5t²)]³

Step-by-step explanation:

a. The unit tangent

The unit tangent T(t) = r'(t)/|r'(t)| where |r'(t)| = magnitude of r'(t)

r(t) = (t, t²/2, t²)

r'(t) = dr(t)/dt = d(t, t²/2, t²)/dt = (1, t, 2t)

|r'(t)| = √[1² + t² + (2t)²] = √[1² + t² + 4t²] = √(1 + 5t²)

So, T(t) = r'(t)/|r'(t)| = (1, t, 2t)/√(1 + 5t²)  = (i + tj + 2tk)/√(1 + 5t²)

ii. The unit normal

The unit normal N(t) = T'(t)/|T'(t)|

T'(t) = dT(t)/dt = d[ (i + tj + 2tk)/√(1 + 5t²)]/dt

= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + [-10tk/√(1 + 5t²)⁻³]

= -5ti/√(1 + 5t²)⁻³ + [-5t²j/√(1 + 5t²)⁻³] + j/√(1 + 5t²)+ [-10t²k/√(1 + 5t²)⁻³] + 2k/√(1 + 5t²)

= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) - 10t²k/[√(1 + 5t²)]⁻³ + 2k/√(1 + 5t²)

= -5ti/√(1 + 5t²)⁻³ - 5t²j/[√(1 + 5t²)]⁻³ - 10t²k/[√(1 + 5t²)]⁻³ + j/√(1 + 5t²) + 2k/√(1 + 5t²)

= -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + (j + 2k)/√(1 + 5t²)

We multiply by the L.C.M [√(1 + 5t²)]³  to simplify it further

= [√(1 + 5t²)]³ × -(i + tj + 2tk)5t/[√(1 + 5t²)]⁻³ + [√(1 + 5t²)]³ × (j + 2k)/√(1 + 5t²)

= -(i + tj + 2tk)5t + (j + 2k)(1 + 5t²)

= -5ti - 5²tj - 10t²k + j + 5t²j + 2k + 10t²k

= -5ti + j + 2k

So, the magnitude of T'(t) = |T'(t)| = √[(-5t)² + 1² + 2²] = √[25t² + 1 + 4] = √[25t² + 5]

So, the normal vector N(t) = T'(t)/|T'(t)| = (-5ti + j + 2k)/√[25t² + 5]

(b) Use Formula 9 to find the curvature.

The curvature κ = |r'(t) × r"(t)|/|r'(t)|³

since r'(t) = (1, t, 2t), r"(t) = dr'/dt = d(1, t, 2t)/dt  = (0, 1, 2)

r'(t) = i + tj + 2tk and r"(t) = j + 2k

r'(t) × r"(t) =  (i + tj + 2tk) × (j + 2k)

= i × j + i × 2k + tj × j + tj × 2k + 2tk × j + 2tk × k

= k - 2j + 0 + 2ti - 2ti + 0

= -2j + k

So magnitude r'(t) × r"(t) = |r'(t) × r"(t)| = √[(-2)² + 1²] = √(4 + 1) = √5

magnitude of r'(t) = |r'(t)| = √(1 + 5t²)

|r'(t)|³ = [√(1 + 5t²)]³

κ = |r'(t) × r"(t)|/|r'(t)|³ = √5/[√(1 + 5t²)]³

8 0
2 years ago
Is the following relation a function. <br><br> A) yes<br> B) no
dmitriy555 [2]

Answer:

yes

Step-by-step explanation:

A relation is a function in which for each input there is only one output.

In a relation, y is a function of x.

Now we look at the mapping

For input 6, -1 is the output

for input -1, 2 is the output

for input 4, 3 is the output

for input 0, 3 is the output

For each input , there is an output. Input is not repeating. Input is occurring only once.

So this relation is a function.

4 0
3 years ago
6.1712 rounded to the nearest tenth
anygoal [31]

Answer:

6.2

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
How far did we jump to go from 17 to 20<br>r=26-17<br>17+r=26​
BabaBlast [244]

Answer:

Both are correct!

Step-by-step explanation:

if R = 26 - 17 = 9

now the next one

17 + R = 26

Same thing as R = 26 - 17 = 9

5 0
2 years ago
Read 2 more answers
Other questions:
  • Who can help me out
    6·2 answers
  • Solve 2/3x &gt;8 or 2/3x&lt;4
    5·2 answers
  • What is the sum of the solutions for 6x^2 − x − 2 = 0?
    8·1 answer
  • The radius of one sphere measures twice the length of another. The ratio of their surface areas is
    8·2 answers
  • PLEASE!!!!!!!
    9·1 answer
  • Will give brainiest
    9·2 answers
  • Find the general solution and find the specific solutions over the interval [0,4pi]
    11·1 answer
  • Could someone verify this answer if you don’t know the answer don’t say anything I don’t want to download the answer if you can’
    10·2 answers
  • Classify the pair of angles, (complementary, supplementary, or vertical), then find the value of X.
    13·1 answer
  • Obtain the length of a ladder leaning against a wall 4.33 m high and forming an angle of 60 ° with respect to the floor of the
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!