Evaluate the expression when y=1 <br> expression: 5y

A chain has a ribbon tied to it every 2/3 foot. If the chain is 10 2/3 feet long, how many ribbons are tied to the chain??

patriot [66]

Answer:

16 ribbons

Step-by-step explanation:

Given the length of the chain as 10 $\frac{2}{3}$ and there is a ribbon tied to it every $\frac{2}{3}$ , we can take the total length of the chain and divide by the measure of $\frac{2}{3}$ :

$10\frac{2}{3}=\frac{32}{3}$

$\frac{\frac{32}{3}}{\frac{2}{3}}=\frac{32}{3}*\frac{3}{2}=\frac{96}{6}=16$

When dividing with fractions, we use the rule of 'keep/change/flip' to keep the first fractions, change the operation to multiplication and flip the second fraction.

7 0

2 years ago

What is the area of the shaded region in the figure below ? Leave answer in terms of pi and in simplest radical form

ser-zykov [4K]

Answer:

Step-by-step explanation:

That shaded area is called a segment. To find the area of a segment within a circle, you first have to find the area of the pizza-shaped portion (called the sector), then subtract from it the area of the triangle (the sector without the shaded area forms a triangle as you can see). This difference will be the area of the segment.

The formula for the area of a sector of a circle is:

$A_s=\frac{\theta}{360}*\pi r^2$ where our theta is the central angle of the circle (60 degrees) and r is the radius (the square root of 3).

Filling in:

$A_s=\frac{60}{360}*\pi (\sqrt{3})^2$ which simplifies a bit to

$A_s=\frac{1}{6}*\pi(3)$ which simplifies a bit further to

$A_s=\frac{1}{2}\pi$ which of course is the same as

$A_s=\frac{\pi}{2}$

Now for tricky part...the area of the triangle.

We see that the central angle is 60 degrees. We also know, by the definition of a radius of a circle, that 2 of the sides of the triangle (formed by 2 radii of the circle) measure √3. If we pull that triangle out and set it to the side to work on it with the central angle at the top, we have an equilateral triangle. This is because of the Isosceles Triangle Theorem that says that if 2 sides of a triangle are congruent then the angles opposite those sides are also congruent. If the vertex angle (the angle at the top) is 60, then by the Triangle Angle-Sum theorem,

180 - 60 = 120, AND since the 2 other angles in the triangle are congruent by the Isosceles Triangle Theorem, they have to split that 120 evenly in order to be congruent. 120 / 2 = 60. This is a 60-60-60 triangle.

If we take that extracted equilateral triangle and split it straight down the middle from the vertex angle, we get a right triangle with the vertex angle half of what it was. It was 60, now it's 30. The base angles are now 90 and 60. The hypotenuse of this right triangle is the same as the radius of the circle, and the base of this right triangle is $\frac{\sqrt{3} }{2}$ . Remember that when we split that 60-60-60 triangle down the center we split the vertex angle in half but we also split the base in half.

Using Pythagorean's Theorem we can find the height of the triangle to fill in the area formula for a triangle which is

$A=\frac{1}{2}bh$ . There are other triangle area formulas but this is the only one that gives us the correct notation of the area so it matches one of your choices.

Finding the height value using Pythagorean's Theorem:

$(\sqrt{3})^2=h^2+(\frac{\sqrt{3} }{2})^2$ which simplifies to

$3=h^2+\frac{3}{4}$ and

$3-\frac{3}{4}=h^2$ and

$\frac{12}{4} -\frac{3}{4} =h^2$ and

$\frac{9}{4} =h^2$

Taking the square root of both the 9 and the 4 (which are both perfect squares, thankfully!), we get that the height is 3/2. Now we can finally fill in the area formula for the triangle!

$A=\frac{1}{2}(\sqrt{3})(\frac{3}{2})$ which simplifies to

$A=\frac{3\sqrt{3} }{4}$

Therefore, the area in terms of pi for that little segment is

$A_{seg}=\frac{\pi}{2}-\frac{3\sqrt{3} }{4}$ , choice A.

8 0

3 years ago

What is the value of x?

Karolina [17]

Answer:

14

Step-by-step explanation:

A triangle with 45 degrees on one corner and 90 degrees on another has 45 degrees on the third corner (180-side1-side2=side3). Therefore that’s an isosceles triangle, which has the same length on the two sides next to the right angle. To get the length of the third side, remember that for any right triangle, the longest side is equal to the square root of :(the first side squared)+(the second side squared). A^2+b^2=c^2 or c=sqrt(a^2+b^2). If you do the math, sqrt((7sqrt2)^2+(7sqrt2)^2)=14. That’s your third side length, x=14.

4 0

2 years ago

Read 2 more answers

A 176 inch pole is leaning up against a wall, but is sliding down the wall so that the vertical distance between the top of the

natta225 [31]

Answer:

... Wall, But Is Sliding Down The Wall So That The Vertical Distance Between The Top Of The Pole And The Floor Is Decreasing At A Rate Of 4 Inches Per Second. How Fast Is The Horizontal Distance Between The Bottom Of The Pole And ... A 176 inch pole is leaning up against a wall, but is sliding down the wall so that the ...

Step-by-step explanation:

3 0

2 years ago

Please I need help<br><br> Question: What are the solutions to this graph?

I am Lyosha [343]

Answer:

The solution to the graph are x = -2 and x = 2

Step-by-step explanation:

Here, we want to get the solution to the graph

As we can see, the graph is parabolic; which is a property of a quadratic polynomial

The solution refers to the value at which the graph plot crosses the x-axis

In other words, the solutions to the graph are represented by the point at which we have the graph crossing over the x-axis

We can see this happen at two points

These are the points x = -2 and x = 2

5 0

3 years ago

Evaluate the expression when y=1 expression: 5y​

Evaluate the expression when y=1 expression: 5y