Answer:
Inches
Gallons
Kilometers
Yards
Step-by-step explanation:
We are to proffer the appropriate unit of measurement for each scenario given below :
a. My foot is 21 inches long. (unit for measuring length which are usually small such a a person's foot)
b. My large aquarium holds 55 gallons of water. (volume measurement of liquid in a large container)
c. My dad drives 27 kilometers to work each day. (distance measurement which are moderately long)
d. I just bought 12 yards of carpet to cover my family room floor. (length measurement used for materials such as cloth, carpet, rugs e.t.c).
Two million, nine hundred forty seven
2,000,000+900+40+7
The size of angle BAJ in the given regular polygons is 84⁰.
The given parameters;
- regular hexagon = ABCDEF = 6 sides
- regular pentagon = AJFGH = 5 sides
Each interior angles of a regular hexagon is calculated as follows;
![= \frac{(6-2) \times 180}{6} \\\\= 120^0](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%286-2%29%20%5Ctimes%20180%7D%7B6%7D%20%5C%5C%5C%5C%3D%20120%5E0)
Each interior angles of a regular pentagon is calculated as follows;
![= \frac{(5 -2)\times 180}{5} \\\\= 108^0](https://tex.z-dn.net/?f=%3D%20%5Cfrac%7B%285%20-2%29%5Ctimes%20180%7D%7B5%7D%20%5C%5C%5C%5C%3D%20108%5E0)
The size of angle BAJ is calculated as follows;
![JAF + BAJ = 120 \ \ ----- (1)\\\\JAF + JFA + 108 = 180 \ (sum \ of \ angles\ in \ \Delta\ AJF)\\\\|AJ| = |JF| \\\\2JAF = 180-108\\\\2JAF = 72\\\\JAF = 36^0\\\\BAJ = 120 - JAF\\\\BAJ = 120 - 36\\\\BAJ = 84^0](https://tex.z-dn.net/?f=JAF%20%2B%20BAJ%20%3D%20120%20%5C%20%5C%20-----%20%281%29%5C%5C%5C%5CJAF%20%2B%20JFA%20%2B%20108%20%3D%20180%20%5C%20%20%28sum%20%5C%20of%20%5C%20angles%5C%20%20in%20%5C%20%5CDelta%5C%20AJF%29%5C%5C%5C%5C%7CAJ%7C%20%3D%20%7CJF%7C%20%5C%5C%5C%5C2JAF%20%3D%20180-108%5C%5C%5C%5C2JAF%20%3D%2072%5C%5C%5C%5CJAF%20%3D%2036%5E0%5C%5C%5C%5CBAJ%20%3D%20120%20-%20JAF%5C%5C%5C%5CBAJ%20%3D%20120%20-%2036%5C%5C%5C%5CBAJ%20%3D%2084%5E0)
Thus, the size of angle BAJ in the given regular polygons is 84⁰.
Learn more here: brainly.com/question/18565704
Answer:
![2(z+3)](https://tex.z-dn.net/?f=2%28z%2B3%29)
Step-by-step explanation:
We are given that the expression
![z+(z+6)](https://tex.z-dn.net/?f=z%2B%28z%2B6%29)
We have to find the expression which is equivalent to given expression.
![z+z+6](https://tex.z-dn.net/?f=z%2Bz%2B6)
To find the equivalent expression we will combine like terms
Now, combine like terms we get
![(z+z)+6](https://tex.z-dn.net/?f=%28z%2Bz%29%2B6)
By using the property
![a+a+..+a(n times)=na](https://tex.z-dn.net/?f=a%2Ba%2B..%2Ba%28n%20times%29%3Dna)
Therefore, the expression we get
![2z+6](https://tex.z-dn.net/?f=2z%2B6)
Now, taking common 2
![2(z+3)](https://tex.z-dn.net/?f=2%28z%2B3%29)
Hence, the expression which is equivalent to given expression is given by
![2(z+3)](https://tex.z-dn.net/?f=2%28z%2B3%29)