4. A triangle with base (2x+2) and height (x-2) is cut out of a rectangular sheet of paper that is (3x+4) by (2x+3) what is the area of the paper that remains?

Answers

Answer 1

Answer: so what we do is
area that remains=total area-triangle area that was cut out

we need to find 2 things
total area
triangle area

total area=rectange=base times height
area=(3x+4) times (2x+3)
FOIL or distribute
6x^2+8x+9x+12=6x^2+17x+12

triangle area=1/2 times base times height
triangle area=1/2 times (2x+2) times (x-2)=
(x+2) times (x-2)=x^2+2x-2x-4=x^2-4

so
total area=6x^2+17x+12
triangle area=x^2-4

subtract
area that remains=total area-triangle area that was cut out
area that remains=6x^2+17x+12-(x^2-4)=
6x^2+17x+12-x^2+4=
6x^2-x^2+17x+12+4=
5x^2+17x+16

area that remains is 5x^2+17x+16

D = b² - 4 a c

From the value of Discriminant , we know how many solutions the equation has by condition :

D < 0 → No Real Roots

D = 0 → One Real Root

D > 0 → Two Real Roots

Let us now tackle the problem!

An axis of symmetry of quadratic equation y = ax² + bx + c is :

$\large {\boxed {x = (-b)/(2a) } }$

Given:

$f(x) = - (x + 9)(x - 21)$

$f(x) = - (x^2 - 21x + 9x - 189)$

$f(x) = - (x^2 - 12x - 189)$

$f(x) = -x^2 + 12x + 189$

The axis of symmetry is

$x = (-b)/(2a)$

$x = (-12)/(2(-1))$

$x = (-12)/(-2)$

$\large {\boxed {x = 6} }$

Learn more

Solving Quadratic Equations by Factoring : brainly.com/question/12182022
Determine the Discriminant : brainly.com/question/4600943
Formula of Quadratic Equations : brainly.com/question/3776858

Answer details

Grade: High School

Subject: Mathematics

Chapter: Quadratic Equations

Keywords: Quadratic , Equation , Discriminant , Real , Number , Axis , Symmetry , Function

the ski team has a race in 3 hours and it is 120 miles away. the team drives 50 miles each hour. will they arrive at the same time?

Answers

They won't arrive exactly when the race starts, but they will arrive before the race starts because, assuming they leave exactly three hours before the race, they can drive a total of 150 miles in three hours (3h*50mi/h). Because they only need to drive 120 miles, they will make it to the race before it starts.

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Answers

debt means negative ballance

greater than 20 and less than 30
means owes more than -20 and less than -30
-20>x>-30

-24 is answer

Mrs. Klein surveyed 240 men and 285 women about their vehicles. Of those surveyed, 155 men and 70 women said they own a red vehicle. I g a person is chosen at random from surveyed, what is the probability of choosing a women or a person who does not own a red vehicle?