All categories

2 years ago

18. Write an expression to represent the area of the shaded region in simplest form. Please help it's due tomorrow

Mathematics

1 answer:

IgorC [24]2 years ago

7 0

Answer:

(x^2 + 2x - 21) sq units

Step-by-step explanation:

Area of the shaded region = Area of the larger rectangle - Area of smaller rectangle

Area of the larger region = x(x+2)

Area of the larger region =x^2 + 2x

Area of the smaller rectangle = 3 * 7

Area of the smaller rectangle = 21 sq. units

Area of the shaded region = x^2 + 2x - 21

Hence the required expression is (x^2 + 2x - 21) sq units

You might be interested in

3+5i/-2+3i perform operation

melisa1 [442]

Answer:

$\dfrac{9}{13}-\dfrac{19}{13}i$

Step-by-step explanation:

Remember $i^2=-1$

You are given the fraction $\dfrac{3+5i}{-2+3i}$

First, multiply the numerator and the denominator by -2-3i:

$\dfrac{3+5i}{-2+3i}=\dfrac{(3+5i)(-2-3i)}{(-2+3i)(-2-3i)}=\dfrac{(3+5i)(-2-3i)}{(-2)^2-(3i)^2}=\dfrac{(3+5i)(-2-3i)}{4-9i^2}=\dfrac{(3+5i)(-2-3i)}{4+9}$

This gives you 13 in denominator, now multiply two complex numbers in numerator:

$(3+5i)(-2-3i)=-6-9i-10i-15i^2=-6-19i+15=9-19i$

Thus, the initial fraction is

$\dfrac{9-19i}{13}=\dfrac{9}{13}-\dfrac{19}{13}i$

4 0

2 years ago

Part A- Create a fourth degree polynomial in standard form. How do you know it is in standard form?

Alexeev081 [22]

Answer:

(a) $2x^4-9x^3+x^2+x-5$

Step-by-step explanation:

(a)The degree of a polynomial is the highest power of the unknown variable in the polynomial.

A polynomial is said to be in standard form when it is arranged in descending order/powers of x.

An example of a fourth degree polynomial is: $2x^4-9x^3+x^2+x-5$

We know the polynomial above is in standard form because it is arranged in such a way that the powers of x keeps decreasing.

(b)Polynomials are closed with respect to addition and subtraction. This is as a result of the fact that the powers do not change. Only the coefficients

change. This is illustrated by the two examples below:

$(2x^5-3x^2+x)+(3x^5-5x^2)\\=2x^5-3x^2+x+3x^5-5x^2\\=5x^5-8x^2+x\\$Similarly\\(2x^5-3x^2+x)-(3x^5-5x^2)\\=2x^5-3x^2+x-3x^5+5x^2\\=-x^5+2x^2+x$

The degrees do not change in the above operations. Only the number beside each variable changes. Therefore, the addition and subtraction of polynomials is closed.

7 0

2 years ago

Find the difference -11 - -5, 25 - (-3) ,-7 - (-2), 4 - 15, 6 - (-9)

Leviafan [203]

Answer:

-11-(-5)= -6

25-(-3)= 28

-7-(-2)= -5

4-15= -11

6-(-9)= 15

7 0

3 years ago

Which graph best represents the feasibility region for the system shown above? ( pics are in this)

zalisa [80]

Consider the system of inequalities

$\left\{ \begin{array}{l} y\ge 2 \\ x\le 6 \\ y\le 3x+2 \\ y\le -x+10. \end{array}\right.$

1. Plot all lines that are determined by equalities (see attached diagram)

$\left\{ \begin{array}{l} y=2 \text{ (red line)} \\ x= 6 \text{ (blue line)}\\ y=3x+2 \text{ (green line)} \\ y= -x+10 \text{ (orange line)}. \end{array}\right.$

2. Determine which bounded part of the plane you should select:

$y\ge 2$ means that you should take points with y-coordinates greater than or equal to 2 (top part of the coordinate plane that was formed by the red line);
$x\le 6$ means that you should take points with x-coordinates less than or equal to 6 (left part of the coordinate plane that was formed by the blue line);
for $y\le 3x+2$ you can check where the origin is placed. Since $0\le 3\cdot 0+2$ , the origin belongs to the needed part and you have to take the right part of the coordinate plane that was formed by green line.
for $y\le -x+10$ you can check where the origin is placed. Since $0\le -1\cdot 0+10$ , the origin belongs to the needed part and you have to take the bottom part of the coordinate plane that was formed by orange line.