Answer:
Step-by-step explanation:
Given:
[∵ ]
Squaring both sides.
[∵ ]
Adding 1 to both sides.
[Taking LCD=9 and adding fractions ]
Taking square root both sides.
∴
<span>The exponential notation
greatly simplifies calculations, especially with very large and very small
numbers. It uses positive and negative exponents to write multiples and sub-multiples of 10. i hope this helps! </span>
<u>Given:</u>
A square pyramid with a base edge length of 8 m and a slant height of 12 m.
<u>To find:</u>
The height of the pyramid.
<u>Solution:</u>
A right-angled triangle can be formed with the slant height, the height, and half the length of the base edge.
The slant height of the pyramid is 12 m long and is the hypotenuse of the right-angled triangle.
Assume the height of the pyramid is x and half the length of the base edge is m.
According to the Pythagorean theorem, the square of the hypotenuse will be equal to the sum of the squares of the other two sides.
The hypotenuse measures 12 m while the other two sides measure 4 m and x m each.
m.
The height of the square-based pyramid is 11.313 m.
Answer:
106 degrees
Step-by-step explanation:
Sides AB and CD are equal in length and sides AD and BC are parallel to each other. This tells us that angles B and C are equivalent. Knowing this, we can set up the following equation to solve for x:
Subtract both sides by 42
Subtract both sides by 2x
Divide both sides by 2
Now, to find angle ABC, or angle B, we can plug x back into its expression:
Therefore, the measure of angle ABC is 106 degrees.
I hope this helps!
Answer:
Austin paid 9 bucks more
Step-by-step explanation:
Zach : original cost is 60 bucks.....on sale for 35% off....means he paid (100% - 35%) = 65%.
65% of 60 = 0.65(60) = 39 <=== what Zach paid
Austin : original price 60 bucks...on sale for 20% off...so he paid 80%
80% of 60 = 0.8(60) = $ 48 <=== what Austin paid
Austin paid (48 - 39) = $ 9 more then Zach