<u>4.</u> Since angles 1 and 2 are supplementary, this means they add up to 180 degrees. Make them add up to 180 in an equation and solve for a. Substitute a back into m∠2 to find your answer.
(11a + 19) + (6a - 9) = 180
Combine like terms.
17a + 10 = 180
Subtract 10 from both sides.
17a = 170
Divide both sides by 17 to isolate and solve for the variable a.
a = 10
Substitute 10 for a into m∠2.
6(10) - 9 ==> 60 - 9 = 51
The measure of angle 2 is 51 degrees.
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<u>5.</u> Since Ray BD bisects ∠ABC that means that both the formed angles are equal to each other, so make them equal to each other in an equation.
5y - 3 = 2y + 12
Add 3 to both sides.
5y = 2y + 15
Subtract 2y from both sides.
3y = 15
Divide both sides by 3 to isolate and solve for the variable y.
y = 5
Answer:
1.7 meters?
Step-by-step explanation:
We are given the following information:
the sum of the first number cubed and the second number is 500
their product is a maximum
We are looking for the 2 missing numbers.
To answer this, let's represent the two numbers as x and w.
From the given, we can form the following equation:

We can then express y as:

We can express their product as:

To find the maximum value of x, let's solve for the derivative of -x^4 + 500 x.

Then we solve for the value of x where f'(x) = 0.

Then we use x = 5 to solve for the second number, w.

Therefore, the two numbers are 5 and 375.
Answer:
Let x be the number.
Given the statement: Three sets of a sum of a number and four are added to the sum of seven times the same number and thirteen.
" sum of a number and four" translated to x + 4
"Three sets of a sum of a number and four" translated to 3(x+4)
"sum of seven times the same number and thirteen" translated to 7x + 13
then;
the expression for the given statement become;

Using distributive property: 

Combine like terms;

Therefore, the simplified expression for Three sets of a sum of a number and four are added to the sum of seven times the same number and thirteen. is, 
(4 + 5) is greater than 3·4 + 5 by 8.
Step-by-step explanation:
- Step 1: Value of (4 + 5) = 9
- Step 2: Value of 3·4 + 5 = 12 + 5 = 17 (as per BODMAS rule)
- Step 3: Find the difference between the two.
⇒ 17 - 9 = 8