Solve for y y - 12 = -10

Find the area of a plane figure bounded by lines

natulia [17]

Answer: 4.5

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

First, find the points of intersection by solving the system.

y = x² + 2x + 4

y = x + 6

Solve by substitution:

x² + 2x + 4 = x + 6 ⇒ x² + x - 2 = 0 ⇒ (x + 2)(x - 1) = 0 ⇒ x = -2, x = 1

Now, integrate from x = -2 to x = 1

$\int\limits^1_2 {(x+6)-(x^{2}+2x+4) } \,$ <em>the bottom of the integral is -2 </em>

= $\int\limits^1_2 {x+6-x^{2}-2x-4 } \,$

= $\int\limits^1_2 {-x^{2}-x+2 } \,$

= $\frac{-x^{3}}{3} - \frac{x^{2}}{2}+2x\int\limits^1_2 {} \,$

= $(\frac{-1^{3}}{3} - \frac{1^{2}}{2}+2(1)) - (\frac{-(-2)^{3}}{3} - \frac{(-2)^{2}}{2}+2(-2))$

= $(\frac{-1}{3} - \frac{1}{2} +2) - (\frac{8}{3} -\frac{4}{2} -4)$

= $\frac{-9}{3} + \frac{3}{2} +6$

= -3 + 1.5 + 6

= 4.5

3 0

3 years ago

HI! I HAVE A TEST ON MONDAY AND IM TRYING TO STUDY, IM KINDA STUCK ON HOW TO DO THIS PROBLEM..

sergij07 [2.7K]

Answer: See below

Step-by-step explanation:

number of yellow pieces/number of blue pieces

= 14/24

= 7/12 --> 7 to 12 --> 7:12

The ratio that represents the number of yellow pieces to the total number of pieces is part-to-whole

number of yellow pieces/total number of pieces

= 14/100

= 7/50 --> 7 to 50 --> 7:50

The ratio that represents the number of blue pieces to the total number of pieces is part-to-whole

= 24/100

= 6/25 --> 6 to 25 --> 6:25

8 0

2 years ago

Sheila bought some rose plants and sunflower plants.There were 35 rose plants than sunflower plants.If the ratio of the rose pla

DENIUS [597]

So assuming that youmeans there were 35 MORE rose plants than sunflower seeds, then

Rose:Sunflower =8:3

rose=sunflower+35
therefor

8 units=rose
3 units=sunflowers

rose-35=sunflower
8unit-35=3unit
5unit-35=0
5unit=35
therefor
35=5unit
divide by 5
7=1unit

so 8 units of roses

7 times 8=56

3 units of sunflowers
3 times 7=21

rose=56
sunflower=21

6 0

3 years ago

Find the sum of 10 x 2 + 7 x + 6 10x 2 +7x+6 and 6 x + 5 6x+5.

dusya [7]

The sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

<h3>Sum of expressions</h3>

Expressions are equations separated by mathematical signs. This expressions are known to contains certain unknowns

Given the following expression

10x^2 +7x+6 and 6x + 5

We are to take the sum of both expression to have:

f(x) = 10x^2 +7x+6 + 6x + 5

Collect the like terms

f(x) = 10x^2 + 7x + 6x + 6 + 5

f(x) = 10x^2 + 13x + 11

Hence the sum of the given expression expressed as a quadratic equation is 10x^2 + 13x + 11

Learn more on sum of functions here: brainly.com/question/11602229

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8 0

2 years ago

Write the equation of each line using the given information.

Marat540 [252]

A. The equation of the line is y = -0.2 x + 1.9

B. The equation of the line is y = 4 x + 3

C. The equation of the line is y = -8

D. The equation of the line is y = 2 x + 4

Step-by-step explanation:

The slope-intercept form of the equation of a line is y = m x + b, where

m is the slope of the line and b is the y-intercept

The formula of the slope of a line which passes through points $(x_{1},y_{1})$ and $(x_{2},y_{2})$ is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$
The slope of a horizontal line whose equation y = b is zero
The y-intercept means the line intersect the y-axis at point (0 , b)

A.

∵ The line passes through points (2 , 1.5) and (-5 , 36.5)

∴ $x_{1}$ = 2 and $x_{2}$ = -5

∴ $y_{1}$ = 1.5 and $y_{2}$ = 36.5

∵ $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

∴ $m=\frac{-5-2}{36.5-1.5}=\frac{-7}{35}=\frac{-1}{5}$

∴ m = -0.2

∵ y = m x + b

∵ m = -0.2

∴ y = -0.2 x + b

- To find b substitute x and y in the equation by the coordinates of

one of the two given points

∵ x = 2 and y = 1.5

∴ 1.5 = -0.2(2) + b

∴ 1.5 = - 0.4 + b

- Add 0.4 to both sides

∴ 1.9 = b

∴ y = -0.2 x + 1.9

The equation of the line is y = -0.2 x + 1.9

B.

∵ m = 4

∵ y = m x + b

∴ y = 4 x + b

∵ Point (3 , 15) lies on the line

- To find b substitute x and y in the equation by the coordinates

of the given point

∵ x = 3 and y = 15

∴ 15 = 4(3) + b

∴ 15 = 12 + b

- Subtract 12 from both sides

∴ 3 = b

∴ y = 4 x + 3

The equation of the line is y = 4 x + 3

C.

∵ The line has the same slope of line y = 1

- The line whose equation y = 1 is a horizontal line

∵ The slope of the line y = 1 is zero because it is a horizontal line

∴ m = zero

∵ y = m x + b

∴ The equation of the line is y = (0)x + b

∴ y = b

∵ The line passes through point (3 , -8)

- In the horizontal line the y-coordinates of all point lie on the line

are equal

∴ The line intersect the y-axis at point (0 , -8)

∴ b = -8

∴ y = -8

The equation of the line is y = -8

D.

∵ m = 2

∵ y-intercept is at point (0 , 4)

∴ b = 4

∵ y = m x + b

∴ y = 2 x + 4

The equation of the line is y = 2 x + 4

Learn more:

You can learn more about the linear equations in brainly.com/question/4326955

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6 0

3 years ago