Students are measuring various objects around the classroom. A pencil measures 8 ⅜ inches while a pair of scissors measures 5 ½
1 answer:
The pencil is longer than the pair of scissors by inches.
A pencil measures inches.
A pair of scissors measures inches.
We need to find the difference between the measures of a pencil and the scissors.
We see that the pencil measure is greater than the pair of scissors.
<h3>What is a mix fraction?</h3>A fraction is a part of a whole number. It has two parts - numerator and denominator.
Example: If you cut a cake into three slices each slice is 1/3.
Where 1 = numerator and 3 = denominator.
Four types of fractions:
Unit fraction - when the numerator is 1.
Proper fraction - When the numerator is less than the denominator.
Improper fraction - When the numerator is greater than the denominator.
Mixed fraction - When the fraction contains a whole number with a proper fraction.
Example:
The given measure of the pen and the pair of scissors is in mix fraction.
The pencil measure is longer than the pair of scissors measure so,
We will subtract the measure of the pair of scissors from the measure of the pen.
We have,
=
We can write the mix fraction into an improper fraction.
We multiply the denominator with the whole number and add this product with the numerator to get our numerator of the improper fraction. The denominator will remain the same as the mix fraction in the improper fraction.
So,
= 67/8 - 11/2
= (67-44) / 8
= 23 / 8
Writing in mix fraction.
=
Thus the pencil is longer than the pair of scissors by inches.
Learn more about mix fraction here:
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where
are the coordinates of the first point
are the coordinates of the second point
Length of WZ:
We know form our graph that the coordinates of our first point, W, are (1,0) and the coordinates of the second point, Z, are (4,2). Using the distance formula:
We know that all the sides of a rhombus have the same length, so
Now, we just need to add the four sides to get the perimeter of our rhombus:
We can conclude that the perimeter of our rhombus is
square units.
2. To solve this, we are going to use the arc length formula:
where
is the length of the arc.
is the radius of the circle.
is the central angle in radians
We know form our problem that the length of arc PQ is
inches, so 
, and we can infer from our picture that 
. Lest replace the values in our formula to find the central angle POQ:
Since
, We can conclude that the measure of the central angle POQ is 
3. A cross section is the shape you get when you make a cut thought a 3 dimensional figure. A rectangular cross section is a cross section in the shape of a rectangle. To get a rectangular cross section of a particular 3 dimensional figure, you need to cut in an specific way. For example, a rectangular pyramid cut by a plane parallel to its base, will always give us a rectangular cross section.
We can conclude that the draw of our cross section is:
where
Length of WZ:
We know form our graph that the coordinates of our first point, W, are (1,0) and the coordinates of the second point, Z, are (4,2). Using the distance formula:
We know that all the sides of a rhombus have the same length, so
Now, we just need to add the four sides to get the perimeter of our rhombus:
We can conclude that the perimeter of our rhombus is
2. To solve this, we are going to use the arc length formula:
where
We know form our problem that the length of arc PQ is
Since
3. A cross section is the shape you get when you make a cut thought a 3 dimensional figure. A rectangular cross section is a cross section in the shape of a rectangle. To get a rectangular cross section of a particular 3 dimensional figure, you need to cut in an specific way. For example, a rectangular pyramid cut by a plane parallel to its base, will always give us a rectangular cross section.
We can conclude that the draw of our cross section is: