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
Step2247 [10]
2 years ago
9

Find the gradient and the intercept shown by the straight line 2x + 3y = 6 ​

Mathematics
2 answers:
sveta [45]2 years ago
6 0

Answer:

\sf gradient =\dfrac{-2}{3}\\\\ y -intercept = 2

Step-by-step explanation:

<h2>Equation of the line in slope intercept form:</h2>

      \sf \boxed{\bf y = mx +b}

Here m is the slope or gradient and b is the y-intercept.

Write the given equation in slope-intercept form.

  2x + 3y = 6

          3y = -2x + 6

            \sf y =\dfrac{-2}{3}x +\dfrac{6}{3}\\\\     y = \dfrac{-2}{3}x + 2

\sf gradient =\dfrac{-2}{3}\\\\ y -intercept = 2

storchak [24]2 years ago
6 0

Answer:

The gradient is -\frac{2}{3} and the intercept is 2.

Step-by-step explanation:

First, transform the given equation into the slope-intercept form, y = mx + b. The variable m represents slope (gradient) and the variable b represents the intercept.

2x + 3y = 6

3y = -2x + 6

y = -\frac{2}{3}x + 2

The gradient is -\frac{2}{3} and the intercept is 2.

You might be interested in
PLEASE HELP ASAP!!! Actually help and answer them correctly.
SSSSS [86.1K]

Answer:

use wolfram alpha it helps :D

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Find the imaginary part of\[(\cos12^\circ+i\sin12^\circ+\cos48^\circ+i\sin48^\circ)^6.\]
iren [92.7K]

Answer:

The imaginary part is 0

Step-by-step explanation:

The number given is:

x=(\cos(12)+i\sin(12)+ \cos(48)+ i\sin(48))^6

First, we can expand this power using the binomial theorem:

(a+b)^k=\sum_{j=0}^{k}\binom{k}{j}a^{k-j}b^{j}

After that, we can apply De Moivre's theorem to expand each summand:(\cos(a)+i\sin(a))^k=\cos(ka)+i\sin(ka)

The final step is to find the common factor of i in the last expansion. Now:

x^6=((\cos(12)+i\sin(12))+(\cos(48)+ i\sin(48)))^6

=\binom{6}{0}(\cos(12)+i\sin(12))^6(\cos(48)+ i\sin(48))^0+\binom{6}{1}(\cos(12)+i\sin(12))^5(\cos(48)+ i\sin(48))^1+\binom{6}{2}(\cos(12)+i\sin(12))^4(\cos(48)+ i\sin(48))^2+\binom{6}{3}(\cos(12)+i\sin(12))^3(\cos(48)+ i\sin(48))^3+\binom{6}{4}(\cos(12)+i\sin(12))^2(\cos(48)+ i\sin(48))^4+\binom{6}{5}(\cos(12)+i\sin(12))^1(\cos(48)+ i\sin(48))^5+\binom{6}{6}(\cos(12)+i\sin(12))^0(\cos(48)+ i\sin(48))^6

=(\cos(72)+i\sin(72))+6(\cos(60)+i\sin(60))(\cos(48)+ i\sin(48))+15(\cos(48)+i\sin(48))(\cos(96)+ i\sin(96))+20(\cos(36)+i\sin(36))(\cos(144)+ i\sin(144))+15(\cos(24)+i\sin(24))(\cos(192)+ i\sin(192))+6(\cos(12)+i\sin(12))(\cos(240)+ i\sin(240))+(\cos(288)+ i\sin(288))

The last part is to multiply these factors and extract the imaginary part. This computation gives:

Re x^6=\cos 72+6cos 60\cos 48-6\sin 60\sin 48+15\cos 96\cos 48-15\sin 96\sin 48+20\cos 36\cos 144-20\sin 36\sin 144+15\cos 24\cos 192-15\sin 24\sin 192+6\cos 12\cos 240-6\sin 12\sin 240+\cos 288

Im x^6=\sin 72+6cos 60\sin 48+6\sin 60\cos 48+15\cos 96\sin 48+15\sin 96\cos 48+20\cos 36\sin 144+20\sin 36\cos 144+15\cos 24\sin 192+15\sin 24\cos 192+6\cos 12\sin 240+6\sin 12\cos 240+\sin 288

(It is not necessary to do a lengthy computation: the summands of the imaginary part are the products sin(a)cos(b) and cos(a)sin(b) as they involve exactly one i factor)

A calculator simplifies the imaginary part Im(x⁶) to 0

4 0
3 years ago
2(x + 1),<br> x = 5<br> Substitute
Vlada [557]

Answer:

12

Step-by-step explanation:

2(5+1) =

2(6) =

12

7 0
3 years ago
Math Vocabulary. Please Help.
solong [7]

Answer:

Algebraic Fraction for #9

Step-by-step explanation:

The fraction is Algebraic so it should instantly be a Algebraic Fraction.

6 0
3 years ago
100 points! Mhanifa please help! Look at the picture attached. I will mark brainliest. Random answers will be reported guys.
Natalija [7]

Steps by explanation:

for second one

centroid ={(1+3+5)/3,(2+4+0)/3}=(9/3,6/3)

=(3,2)

4 0
3 years ago
Read 2 more answers
Other questions:
  • Solve the system of equations.<br><br> y = x + 6<br> y = x^2 + 8x + 16
    6·1 answer
  • Can you please help me?l
    6·2 answers
  • I need help<br><img src="https://tex.z-dn.net/?f=%20-%203n%20%2B%207%20%2B%202n%20-%208" id="TexFormula1" title=" - 3n + 7 + 2n
    14·1 answer
  • How do find the inequality???
    15·1 answer
  • Marcus is 66 inches tall. This is 20 inches less than 2 times William's height.
    13·1 answer
  • The figure shows two semicircles with centers K &amp; M. The semicircles are tangent to each other at point J, and (QN) ⃗ is tan
    15·1 answer
  • What is the degree of 6x^5 - 4х^2+2x^3 - 3 + x<br> ОА. 6<br> Ов. 5<br> Ос. 2<br> OD. з
    9·2 answers
  • Help please!! i dont understand geometry
    13·1 answer
  • 1. Evaluate the following expression. Write your answer WITHOUT any exponents. (52)8 x 5-9​
    10·1 answer
  • It angle relationship and show work??
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!