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2 years ago

A triangle is cut from a rectangle. Find the area of the shaded region.

Mathematics

1 answer:

KATRIN_1 [288]2 years ago

4 0

The area of rectangle:

11 ft · 6 ft = 66 ft²

The area of triangle:

6 ft · 4 ft/2 = 6 ft · 2 ft = 12 ft²

The area of the shaded region:

66 ft² - 12 ft² = 54 ft²

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GUYSSSSS!!!! PLEASE I NEED HELP RIGHT NOWW!!! HELP PLEASE!

nikdorinn [45]

Answer:

$\angle ABC=20^{\circ}$

Step-by-step explanation:

Since each side of a line is 180 degrees, we can write the following system of equations:

$\begin{cases}2x+12y+x+2y=180,\\x+2y+8y-4x=180\end{cases},\\\begin{cases}3x+14y=180,\\-3x+10y=180\end{cases}$

Add both equations to solve for $y$ :

$24y=360,\\y=\frac{360}{24}=15$

Now substitute $y=15$ into $3x+14y=180$ to solve for $x$ :

$3x+14(15)=180,\\3x=-30,\\x=-10$

Finish by substituting both variables to solve for $\angle ABC$ :

$\angle ABC=x+2y,\\\angle ABC=-10+2(15),\\\angle ABC=-10+30=\boxed{20^{\circ}}$

7 0

2 years ago

Find the factors of 4x2-16x-9.

zzz [600]

Answer:

Step-by-step explanation:

$4x^2-16x-9.\\Writ -16x - as -a -difference\\ 4x^2 +2x-18x -9 \\Factor -out- common- terms\\2x(2x+1)-9(2x+1)\\ Factor -out (2x+1)\\(2x+1)(2x-9)$

I Hope It Helps :)

5 0

2 years ago

Read 2 more answers

After all the taxes are withheld, Jamie's paycheck is about 80% of his total

Andreyy89

Answer:

Explanation down below.

Step-by-step explanation:

10% of 91.25 = 9.125.

20% of 91.25 = 18.250.

30% of 91.25 = 27.375.

40% of 91.25 = 36.500.

36.500 × 2 = 73.

B, 70 dollars.

8 0

2 years ago

A solution to a system of equations is at the point of intersection.

solniwko [45]

Answer:

true

Step-by-step explanation:

i dont have an explanation its just true

7 0

2 years ago

Find the absolute maximum and absolute minimum for f (x )equals x cubed minus 2 x squared minus 4 x plus 2 on the interval 0 les

sineoko [7]

9514 1404 393

Answer:

maximum: 2
minimum: -6

Step-by-step explanation:

The extrema will be at the ends of the interval or at a critical point within the interval.

The derivative of the function is ...

f'(x) = 3x² -4x -4 = (x -2)(3x +2)

It is zero at x=-2/3 and at x=2. Only the latter critical point is in the interval. Since the leading coefficient of this cubic is positive, the right-most critical point is a local minimum. The coordinates of interest in this interval are ...

f(0) = 2

f(2) = ((2 -2)(2) -4)(2) +2 = -8 +2 = -6

f(3) = ((3 -2)(3) -4)(3) +2 = -3 +2 = -1

The absolute maximum on the interval is f(0) = 2.

The absolute minimum on the interval is f(2) = -6.

8 0

2 years ago