What is the perimeter of a rectangle (6in and 4in)

A5cm x 11 cm rectangle sits inside a circle with radius of 12 cm.

never [62]

Answer:

397.16 cm²

Step-by-step explanation:

Area of the circle = πr²

3.14 * 144 = 452.16

452.16 - (11 x 5 ) = area shaded region

452.16 - 55 = 397.16

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5 0

3 years ago

Twice the smallest of three consecutive odd integers is nine more than the largest. find the integers.

polet [3.4K]

let x x +2 x+4 three consecutive odd integers

2x =9+ x+4 Twice the smallest is nine more than the largest
2x - x= 13

x= 13 the first
the second integer 15 the third 17

7 0

2 years ago

Which expression equals 6x − 5y + 2 − 8x + 3( y + 5)? A) 3x − 2y + 17 B) −3x + 2y + 17 C) −2x − 2y + 17 D) −2x − 2y − 17

inysia [295]

Answer:

C) −2x − 2y + 17

Step-by-step explanation (PEMDAS):

First, we do 3 (y + 5) because of the parenthesis:

6x − 5y + 2 − 8x + 3y + 15

Since there are no exponents, multiplication ,or division, we will add and subtract. But we have to make sure we combine like terms. X with X's, Y with Y's and constants with constants. And ALWAYS go from left to right

6x − 5y + 2 − 8x + 3y + 15

−2x − 5y + 2 + 3y + 15

−2x − 2y + 2 + 15

−2x − 2y + 17.

8 0

3 years ago

If a = pi +3j - 7k, b = pi - pj +4k and the angle between a and is acute then the possible values for p are given by

PIT_PIT [208]

Answer:

The family of possible values for $p$ are:

$(-\infty, -4) \,\cup \,(7, +\infty)$

Step-by-step explanation:

By Linear Algebra, we can calculate the angle by definition of dot product:

$\cos \theta = \frac{\vec a\,\bullet\,\vec b}{\|\vec a\|\cdot \|\vec b\|}$ (1)

Where:

$\theta$ - Angle between vectors, in sexagesimal degrees.

$\|\vec a\|, \|\vec b \|$ - Norms of vectors $\vec {a}$ and $\vec{b}$

If $\theta$ is acute, then the cosine function is bounded between 0 a 1 and if we know that $\vec {a} = (p, 3, -7)$ and $\vec {b} = (p, -p, 4)$ , then the possible values for $p$ are:

Minimum ( $\cos \theta = 0$ )

$\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} > 0$

Maximum ( $\cos \theta = 1$ )

$\frac{p^{2}-3\cdot p -28}{\sqrt{p^{2}+58}\cdot \sqrt{2\cdot p^{2}+16}} < 1$

With the help of a graphing tool we get the family of possible values for $p$ are:

$(-\infty, -4) \,\cup \,(7, +\infty)$

7 0

2 years ago

The ages of the people in attendance at the showing of an award-winning foreign film are shown below.

guapka [62]

Definition: A histogram visualises the distribution of data over a continuous interval or certain time period. Each bar in a histogram represents the tabulated frequency at each interval.

According to the given histogram,

0-20 years occur 15 times,

21-40 years occur 40 times,

41-60 years occur 40 times,

61-80 years occur 15 times.

This shows that the data is symmetrical and the majority of the attendees were between the ages of 21 and 60 (40 times).

Answer: correct choice is B.

5 0

3 years ago

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