Remember, you can do anything to an equation as long as you do it to both sides
0.6x-10=1.4x-(-14)
and minusing a negative means adding
0.6x-10=1.4x+14
minus 0.6x from both sides
0.6x-0.6x-10=1.4x-0.6x+14
0-10=0.8x+14
-10=0.8x+14
minus 14 both sides
-14-10=0.8x+14-14
-24=0.8x+0
-24=0.8x
multily both sides by 10
-240=8x
divide both sides by 8
-240/8=(8x/8)
-30=(8/8)x
-30=1x
-30=x
x=-30
Answer:
1) Antonio's statement
2) <A = 123
Step-by-step explanation:
1) Antonio's statement is incorrect. This is because the opposite angles of a quadrilateral add up to 180°. Erin was incorrect because the opposite angles of this quadrilateral are unequal.
2) 2x+7+5x-2 = 180° (opposite angles of quadrilateral)
Now
7x+5 = 180
7x = 175
x = 25
<A = 5x-2
= 5(25)-2
= 125-2
= 123
Answer:
Adjacent, b = 45 units
Step-by-step explanation:
Let the length of sides of the triangle be;
- Opposite side = a
- Adjacent side = b
- Hypotenuse side = c
<u>Given the following data;</u>
Hypotenuse, c = 53 units
Opposite, a = 28 units
To find the missing side (adjacent), we would have to apply Pythagorean' theorem.
From Pythagorean theorem;
c² = a² + b²
Substituting into the formula, we have;
53² = 28² + b²
2809 = 784 + b²
Rearranging the equation (collecting like terms), we have;
b² = 2809 - 784
b² = 2025
Taking the square root of both sides, we have;
b = √2025
<em>Adjacent, b = 45 units</em>
The conclusion is that the system does not have a solution. This is that the equations written do not have an intersection point, they represent parallel lines and, for any x value, one line is always over the other.
In terms of the landscapers charges, it means that the two landscapers have the same hourly rate (the slope of the lines) but different fees..
For example imagine one landscapers charges $0.5 the hour plus a fixed $5 fee
The correspondan equation would be: y = 0.5x + 5
If the other charges $0.5 the hour and a fixed $20 fee. the correspondant equation would be y = 0.5 x + 20
When you try to solve the system you get:
0.5x + 5 = 0.5x + 20
You can remove the 0.5x terms because they appear in the two sides, then
5 = 20.
Which means that the two costs will never be equal.
.
Answer: the maximum number of guests that he can invite would be 9
Step-by-step explanation:
Darnel's retirement party cost $33, plus an additional $1 for each guest he invites. Assuming Darnel wants to invite x guests to his retirement party, the total amount of money that Darnel would spend is
33 + x
if darnel can afford to spend a total of $42 on his retirement party, then
42 = 33 + x
x = 42 - 33 = 9