Six friends want to play enough games of chess to be sure every one plays everyone else. How many games will they have to play

A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter. The central angle formed by the peach co

Vsevolod [243]

Answer:

D. 5 inches

Step-by-step explanation:

Given:

A frozen dinner is divided into 3 sections on a circular plate with a 12-inch diameter.

That means complete angle having 360° is divided into 3 section.

The central angle formed by the peach cobbler is 105 degrees.

The central angle formed by the pasta is 203 degrees.

Question asked:

What is the approximate length of the arc of the section containing the peas?

Solution:

The central angle formed by the peas = 360° - 105° - 203°

= 52°

$Ridius,r=\frac{Dameter}{2} =\frac{12}{2} =6\ inches$

As we know:

$Length\ of\ arc=2\pi r\times\frac{\Theta }{360}$

$=2\times\frac{22}{7} \times6\times\frac{52}{360} \\ \\ =\frac{13728}{2520} \\ \\ =5.44\ inches$

Therefore, the approximate length of the arc of the section containing the peas are 5 inches.

6 0

3 years ago

Cassidy wrote the linear equation y=5x+4. Then she wrote the equation of the line that is parallel to y=5x+ and that passes thro

Vera_Pavlovna [14]

Answer:

The value of b is -42

Step-by-step explanation:

Parallel equations have identical or equal slopes. Given the form of the equation; y=5x+b and the point it passes through (8,-2) we determine the unknown value b by substituting x with 8 and y with -2. We solve the equation; -2 =5(8)+b to obtain b = -42

5 0

3 years ago

Write a unit rate for the situation.

tamaranim1 [39]

Answer:

50 dollors

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

Find the points on the cone z2 = x2 + y2 that are closest to the point (6, 2, 0).

aliya0001 [1]

Answer:

The closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

Step-by-step explanation:

Let B(x, y, z) denote a point on the cone.

Therefore, the distance between the points (6, 2, 0) and B(x, y, z) is;

d = √[(x - 6)² + (y - 2)² + (z - 0)²]

d = √[(x - 6)² + (y - 2)² + z²]

Since we are given that z² = x² + y², we now have;

d = √[(x - 6)² + (y - 2)² + x² + y²]

Taking the square of both sides gives;

d² = [(x - 6)² + (y - 2)² + x² + y²]

x² is an increasing function. Thus, minimizing d is also the same as to minimize f (x, y) = d²

Thus, f' = 0. So;

df/dx = 2(x - 6) + 2x = 0

2x - 12 + 2x = 0

4x = 12

x = 12/4

x = 3

Similarly,

df/dy = 2(y - 2) + 2y = 0

2y - 4 + 2y = 0

4y - 4 = 0

4y = 4

y = 4/4

y = 1

Now,from earlier;

z² = x² + y²

Thus;

z = ±√(3² + 1²)

z = ±√10

Thus, the closest points on the cone are;

(6, 2, -√10) and (6, 2, √10)

7 0

3 years ago

Sajia has 30 Books in her library. she sold 9 books at the thrift store on Saturday. Write and solve and inequality to determine

ELEN [110]

Sajia can sell 21 books she can sell if she comes back on sunday and the required inequality is $9 + x \leq 30$

Solution:

Given that Sajia has 30 Books in her library

She sold 9 books at the thrift store on Saturday

To find: We have to write and solve an inequality to determine number of more books she can sell if she comes back on sunday

Let "x" be the number of more books she can sell if she comes back on sunday

We can write a inequality as:

$\text{ books already sold } + \text{ number of books remaining } \leq \text{ total number of books she has }$

$9 + x \leq 30$

Now moving 9 from L.H.S to R.H.S we get,

$x \leq 30 - 9$

On solving 30 - 9 = 21,

$x \leq 21$

So Sajia can sell 21 books she can sell if she comes back on sunday

6 0

3 years ago