MATHEMATICS COLLEGE

Find the length of the indicated segments of each trapezoid.

Answers

Answer 1

Answer:

Answer:

BC = 16

EF = 23

AD = 30

Step-by-step explanation:

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Find the amount of the discount on a $120 bicycle that is on sale for 25% off.

C^2 + 5c =3 Tell if this factors or not? And show how it factors or does not factor? And if it factors what are the roots?

Answers

The answer to your questions is that it depends on how we view the polynomial. In particular,

$c^2+5c=3\implies c^2+5c-3=0$

If the left hand side were factorizable, then we would be able to write it in the form

$(c-r_1)(c-r_2)=c^2+5c-3=0$

If we expand the leftmost expression, we'd get

$c^2-(r_1+r_2)c+r_1r_2=c^2+5c-3=0$

and so for the two polynomials to be the same, the coefficients must match. In other words, the unknowns $r_1,r_2$ would have to satisfy

$\begin{cases}-(r_1+r_2)=5\nr_1r_2=-3\end{cases}$

Suppose that, moreover, we want integer solutions for $r_1,r_2$ . For this to happen, they must be factor pairs of the constant term.

-3 only has two factor pairs. Either $r_1=-1$ and $r_2=3$ , or $r_1=1$ and $r_2=-3$ . In the first case, we'd get a linear coefficient of $-(-1+3)=-2\neq5$ , while in the second, we'd get $-(1-3)=2\neq5$ .

There is no integer solution for this system, so the original quadratic is not factorizable - but only so over the integers.

If we change the scope of the coefficients, i.e. allow for any real numbers/complex numbers to appear in the factorization, then we always factorize a quadratic. The above system is easy to solve.

$r_1r_2=-3\implies r_2=-\frac3{r_1}$
$\implies-\left(r_1-\frac3{r_1}\right)=5$
$\implies{r_1}^2+5r_1-3=0$
$\implies r_1=\frac{-5\pm√(37)}2$

$\implies c^2+5c-3=\left(c+\frac{5-√(37)}2\right)\left(c+\frac{5+√(37)}2\right)$

so the original quadratic is factorizable over the reals.

Isaac works a job that pays him based oncommission. He earns 5% commission on all
sales after the first $5000. To determine the
amount of sales he earns commission on, he
uses the function f(x) = x - 5000. Then he uses
a different equation to determine how much
commission he actually earns, g(x) = 0.05x. He
wants to create a composite that includes
both. What is the composite function?
-
=

Answers

Answer: 1000000

Step-by-step explanation:

5x100

If A= (-4 -4 1) (1 4 7) (2 3 3) and B= (2 9 -9) (8 8 -2) (4 10 1), find -4A + 8B

Answers

C. Because (-4*-4) +(8*2)= 32 And c os the only one with it

Simplify x
${x}^(2) + 6x - 12$

Answers

Answer: x=8

Step-by-step explanation:

What's the vertex for 6x^2-48x-54=0?

Answers

it would be 4,-25 becuase of in the first place i in and the other imp in cams was the

A rectangle is inscribed in a circle.Calculate the area of the circle. Use 3.14 for π. Round to the nearest hundredth.

1___ Square centimeters

2 Calculate the area of the rectangle.

3. Calculate the area of the shaded region. Use 3.14 for π. Round to the nearest hundredth.

Answers

Answer:

1. The area of the circle is 132.67 square centimeters

2. The area of the rectangle is 60 square centimeters

3. The area of the shaded region is 72.67 square centimeters

Step-by-step explanation:

* Lets explain how to solve the problem

- A rectangle is inscribed in a circle, that means the vertices of the

rectangle lie on the circumference of the circle

∴ The diagonal of the rectangle = the diameter of the circle

- From the attached figure

∵ The diameter of the circle = 13 cm

∵ The radius of the circle is half the diameter

∴ The radius of the circle = 1/2 (13) = 6.5 cm

- The area of the circle = πr²

∵ π = 3.14

∴ The area of the circle = 3.14 × (6.5)² = 132.67 cm²

1. The area of the circle is 132.67 square centimeters

- The area of any rectangle = length × width

∵ The length of the rectangle is 12 cm

∵ The width of the rectangle is 5 cm

∴ The area of the rectangle = 12 × 5 = 60 cm²

2. The area of the rectangle is 60 square centimeters

- The area of the shaded region is the difference between the

area of the circle and the area of the rectangle

∵ The area of the circle = 132.67 cm²

∵ The area of the rectangle = 60 cm²

∵ The area of the shaded region = area of circle - area of rectangle

∴ The area of the shaded region = 132.67 - 60 = 72.67 cm²

3. The area of the shaded region is 72.67 square centimeters

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