Give a reason for each step of the proof.
Given: <1 and <2 are complimentary
<1 is congruent to <3,
<2 is congruent to <4
Prove: <3 and <4 are complimentary
Statements: Reasons:
1. <1 and <2 are complimentary 1.Given
2. m<1 + m<2=90* 2.<u>DEFINITION OF COMPLEMENTARY ANGLES</u>
3. <1 is congruent to <3, <2 is congruent to <4 3.__GIVEN______
4. m<1=m<3, m<2=m<4 4.<u>DEFINITION OF CONGRUENT ANGLES_</u>
5. m<3 + m<2=90* 5. <u>SUBSTITUTION PROPERTY (m<1 is replaced by m<3.) </u>
6. m<3 +m<4=90* 6. <u>DEFINITION OF COMPLEMENTARY ANGLES </u>
7. <3 and <4 are complimentary 7.<u> DEFINITION OF COMPLEMENTARY ANGLES</u>
Answer:
36 objects
Step-by-step explanation:
You want the value of x when t=9, so you're solving ...
9 = 0.007x^2 +0.003x
9 = 0.007(x^2 + 3/7x)
From here, we observe that an approximation is probably sufficient.
9/0.007 = x(x +3/7) . . . . . the expression on the right is nearly x^2
x ≈ 3/√.007 ≈ 35.9 ≈ 36
We can check:
.007(36)(36 3/7) = 9.18
.007(35)(35 3/7) = 8.68
To keep the computer busy for 9 seconds, it needs to sort 36 objects.
Answer:
2/3
Step-by-step explanation:
You have 6 possible outcomes. Getting 1 outcome is 1/6. You have 2 possible outcomes. Getting 1 outcome is 1/2.
Add 1/2 and 1/6 to get 2/3
Answer:

Explanation:
You are comparing irrational numbers.
By inspection, i.e. at first sight you can only compare
because they have the same radicand.
You can order: 
You can introduce the 2 inside the radical by squaring it:

Since 5 is between 3 and 12, you can order:
Which is:
You must know that π ≈ 3.14.
5 is less than 9 and the square root of 9 is 3; hence,
and 
Now you must determine whether π is less than or greater than 
Using a calculator or probing numbers between 3 and 4 you get 
Hence, the complete order is:
Answer:
add 5 then multiply by 1/2
Step-by-step explanation:
Twice a number is 2n.
The difference of twice a number and five 2n - 5.
The difference of twice a number and five is three. 2n - 5 = 3
2n - 5 = 3
2n - 5 + 5 = 3 + 5 (1) add 5
2n = 8
1/2*2n = 1/2*8 (2) multiply by 1/2
n = 4