Change each fraction to a decimal. If the division doesn’t end, round your answer to the nearest hundredth. a. 3⁄4 b. 7⁄16 d. 3⁄
1 answer:
You might be interested in
Answer:
900°
Step-by-step explanation:
The sum of interior angles of a polygon with sides is given by:
Sum =
Here, <u>the polygon has 7 sides</u>, so . Plugging this into the formula gives us:
Sum =
So the answer is the first choice, 900°.
<h3>Answer: 40</h3>
=======================================================
Explanation:
The inscribed angle 20 degrees doubles to 2*20 = 40 which is the measure of the central angle, and the arc in which the inscribed angle subtends (or cuts off). This is due to the aptly named inscribed angle theorem.
------------
A slightly longer alternative path would be to do this:
The triangle with interior angles 20 and c is isosceles. Note how the missing angle up top is one of the congruent base angles, so the missing angle is 20 degrees. That means angle c is...
20+20+c = 180
40+c = 180
c = 180-40
c = 140
Then angle b is supplementary to this
b+c = 180
b+140 = 180
b = 180-140
b = 40
This path leads to the same answer. It's slightly longer, but it's a path you can take if you aren't familiar with the inscribed angle theorem.
In fact, this line of thinking is effectively how the inscribed angle theorem is proved as shown in the diagram below.
Answer:
With Method I, they should plan to refinish 92 chairs and with Method II they should plan to refinish 70 chairs.
Step-by-step explanation:
This problem can be solved by means of a system of equations, that is to say a system that in this case will contain 2 linear equations with two variables: "x" and "y".
First you must define what your variables x and y are:
- x: Chairs refinished by method I.
- y: Chairs refinished by method II.
On the one hand, you know that between method I and method II they plan to work 151 hours. In method I, each chair takes 0.5 hours of work, this means that to obtain the total amount of time it takes to work in the "x" chairs by this method, 0.5 must be multiplied by the number of chairs. You can apply the same reasoning to calculate the total amount of time it takes to work on the "y" chairs by method II knowing that each chair takes 1.5 hours. Everything said above is represented by the equation:
<em> Equation (A)</em>
In the equation the values 0.5 and 1.5 are represented in the form of a fraction (1/2 and 3/2 respectively) to be able to solve more in a way how the system of equations.
On the other hand, to state the other equation of the system, it must be taken into account that by method I the material costs $ 9 for each chair and by method II the material costs $ 7 for each chair. To determine the value of the material in each method, multiply the value of each chair by the amount of chairs refinished in each case. And the sum of the value of the materials of both methods must be $ 1318. This is represented by the equation:
<em>9*x+7*y=1318 Equation (B)</em>
Having both equations, you can solve the system. There are several methods to solve it, but one of the easiest and most widely used methods is substitution. This consists of isolating one of the variables from one of the equations and replacing it in the other equation.
In this case you can choose to isolate the variable x from equation B, resulting in:
<em>Equation (C)</em>
It is always preferable to work in fractions for convenience to solve the calculations.
Now you replace the expression obtained from x in equation A, obtaining:
Now you have an equation with a variable, "y", which can be solved, that is, you can get the value of "y". So "y"=70
Remembering that the variable "y" is the number of chairs refinished by method II, <u><em>the value of "y" means that 70 chairs by that method were refinished</em></u>.
To calculate the value of "x", you simply replace the value of "y" in either of the two equations (A) or (B) of the system and solve the equation. Or you can replace the value of "y" in equation (C): Either way the result must be the same: "x"=92
Remembering that the variable "x" is the number of chairs refinished by method I, <u><em>the value of "x" means that 92 chairs by that method were refinished.</em></u>