All categories

2 years ago

When using the given diagram to determine the area of the pentagon by decomposition, which statements are correct?:

Mathematics

1 answer:

pogonyaev2 years ago

6 0

Answer:

Options (B) and (E)

Step-by-step explanation:

Area of ΔABC = $\frac{1}{2}(\text{Base})(\text{Height})$

= $\frac{1}{2}(14)(6)$

= 42 in²

Area of trapezoid ADEC = $\frac{1}{2}(b_1+b_2)h$

[Here, $b_1$ and $b_2$ are the parallel sides and 'h' is the height of the isosceles trapezoid given]

= $\frac{1}{2}(10+14)(8)$

= 96 in²

Area of the pentagon = Area of triangle ABC + Area of trapezoid ADEC

= 42 + 96

= 138 in²

Therefore, Options (B) and (E) are the correct options.

You might be interested in

What write a fraction that is a multiple of 4/5

ahrayia [7]

Its 8/10 or 12/15 because 4 times 2 is 8 and 5 times 2 is ten

5 0

2 years ago

Read 2 more answers

Solve for x:a(a²+b²)x²+b²x-a

m_a_m_a [10]

Answer:

x = a/(a² + b²) or x = -1/a

Step-by-step explanation:

a(a²+ b²)x² + b²x - a =0

Use the quadratic equation formula:

$x = \dfrac{-b\pm\sqrt{b^2-4ac}}{2a} =\dfrac{-b\pm\sqrt{D}}{2a}$

1. Evaluate the discriminant D

D = b² - 4ac = b⁴ - 4a(a² + b²)(-a) = b⁴ + 4a⁴ + 4a²b² = (b² + 2a²)²

2. Solve for x

$\begin{array}{rcl}x & = & \dfrac{-b\pm\sqrt{D}}{2a}\\\\ & = & \dfrac{-b^{2}\pm\sqrt{(b^{2}+2a^{2})^{2}}}{2a(a^{2} + b^{2})}\\\\ & = & \dfrac{-b^{2}\pm(b^{2}+ 2a^{2})}{2a(a^{2} + b^{2})}\\\\x = \dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}\\\\x =\dfrac{-b^{2}+(b^{2} + 2a^{2})}{2a(a^{2} + b^{2})}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\\end{array}$

$\begin{array}{rcl}x = \large \boxed{\mathbf{\dfrac{a}{a^{2} + b^{2}}}}&\qquad& x =\dfrac{-b^{2}-(b^{2} +2a^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2b^{2}- 2a^{2}}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\dfrac{-2(a^{2}+ b^{2})}{2a(a^{2} + b^{2})}\\\\&\qquad& x =\large \boxed{\mathbf{-\dfrac{1}{a}}}\\\\\end{array}$

5 0

3 years ago

A number plus 1/3 of the number can be expressed as:

nirvana33 [79]

Answer:

n+n/3

Step-by-step explanation:

n+1/3 n=n+n/3=4n/3

Please mark as Brainliest! :)

Have a nice day.

6 0

3 years ago

One survey estimates that,on average, the retail value of a mid sized car decreases by8% annually.if the retail value of a car i

Scrat [10]

Percentage by which the average value of mid sized car decreases each year = 8%
Retail value of a car today = v dollars
Amount of decrease in the value of the car after 1 year = (8/100) * v
   = 2v/25 dollars
Then
The equation that represents the value of the car after 1 year = v - (2v/25) dollars
   = (25v - 2v)/25 dollars
   = 23v/25 dollars
So following this expression the value of the mid sized car can be easily determined after 1 year. I hope this is the answer you were looking for and the procedure is also clear to you.

5 0

3 years ago

Read 2 more answers

Leona [35]

Given:

The inequality is:

$y>5x+3$

To find:

The y-intercept, slope and type of line (solid or dotted).

Solution:

The slope intercept form of a line is:

$y=mx+b$ ...(i)

Where, m is the slope and b is the y-intercept.

We have,

$y>5x+3$

The relation equation is:

$y=5x+3$ ...(ii)

On comparing (i) and (ii), we get

$m=5$

$b=3$

It means the slope is 5 and the y-intercept is 3.

The sign of the inequality in the given inequality is ">". It means the boundary line is not included in the solution set. So, the boundary line is a dotted line.

Therefore, the slope is 5, the y-intercept is 3 and the line is a dotted line.

7 0

2 years ago