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3 years ago

6x+y=4x+11y solve for y

Mathematics

1 answer:

seropon [69]3 years ago

4 0

Answer:

$y= \frac{1}{5} x$

Step-by-step explanation:

$6x + y = 4x + 11y$

put all the y's onto one side, and the x's onto another

$6x - 4x = 11y - y$

$2x = 10y$

$10y = 2x$

now divide both sides by 2

$y= \frac{1}{5} x$

and there you go!

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What number has exactly 6 factors

RoseWind [281]

The factors of 12 are 1, 2, 3, 4, 6, and 12 .

The factors of 32 are 1, 2, 4, 8, 16, and 32 .

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3 years ago

Read 2 more answers

Write an equation to match each statement. Then solve. #1) 8 less than a number x is -12. #2) 15 more than a number k is 2. #3)

guajiro [1.7K]

#1) x-8= -12
#2) 15+k= 2
#3) x/-7= -20
#4) (5/8)(x)= -20

The / in #2 means to divide and the ( ) mean to multiply

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4 years ago

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3 years ago

Find the slope of the line through each pair of points (6, -10) , (-15 , 15)

dem82 [27]

<h3>Answer:</h3>

$\boxed{\boxed{\pink{\bf \leadsto The \ slope \ of \ the \ line \ is \ \dfrac{-25}{21}.}}}$

<h3>Step-by-step explanation:</h3>

Two points are given to us and we need to find the slope of the line . The slope of the line passing through points $\bf (x_1,y_1 ) \ \& \ (x_2,y_2)$ is given by ,

$\qquad\boxed{\red{\bf Slope = tan\theta=\dfrac{y_2-y_1}{x_2-x_1}}}$

Here , the points are ,

( 6 , -10 )
( -15 , 15 )

$\bf\implies Slope = \dfrac{y_2-y_1}{x_2-x_1} \\\\\bf\implies Slope =\dfrac{15-(-10)}{-15-6} \\\\\bf\implies Slope = \dfrac{15+10}{-21}\\\\\bf\implies Slope =\dfrac{-1(25)}{-1(-21)}\\\\ \bf\implies\boxed{\red{\bf Slope =\dfrac{-25}{21}}}$

<h3>★ Hence the slope of the line joining the two points is -25/21 .</h3>

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3 years ago

What are the last three terms of the binomial expansion 32x³ + 80x'y + 80x³y² +

Gnesinka [82]

The last three terms of the given binomial expansion are 40x²y³ + 10xy⁴ + y⁵

<h3>Binomial expansion</h3>

From the question, we are to determine the last three terms of the binomial expansion 32x⁵ + 80x⁴y + 80x³y² + __ + __ + __

The highest power of the expansion is 5

Using the binomial expansion theorem

(m +n)⁵ = m⁵ + 5m⁴n + 10m³n² + 10m²n³ + 5mn⁴ + n⁵

Now, we will determine the values of m and n by comparison

By comparison,

m⁵ = 32x⁵

m⁵ = (2x)⁵

∴ m = 2x

Also,

5m⁴n = 80x⁴y

Divide both sides by 5, to get

m⁴n = 16x⁴y

Put m = 2x into the equation

(2x)⁴n = 16x⁴y

16x⁴n = 16x⁴y

∴ n = y

Thus, the expression being expanded is (2x + y)⁵

By binomial expansion, the expansion of (2x + y)⁵ is

(2x + y)⁵ = (2x)⁵ + 5(2x)⁴y + 10(2x)³(y)² + 10(2x)²(y)³ + 5(2x)(y)⁴ + y⁵

(2x + y)⁵ = 32x⁵ + (5×16)x⁴y + (10×8)x³(y)² + (10×4)x²(y)³ + (5×2)x(y)⁴ + y⁵

(2x + y)⁵ = 32x⁵ + 80x⁴y + 80x³y² + 40x²y³ + 10xy⁴ + y⁵

Hence, the last three terms of the given binomial expansion are 40x²y³ + 10xy⁴ + y⁵

Learn more on Binomial expansion here: brainly.com/question/13602562

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2 years ago