Answer:
12
Step-by-step explanation:
you divide 24 by 2 because it is multiplication, and the opposite is division.
Answer:
(1, 5)
Step-by-step explanation:
The solution to the system of equations is the point of intersection of the two lines. From inspection of the graph, the point of intersection is at (1, 5).
<u>Proof</u>
The solution to a system of equations is the point at which the two lines meet.
⇒ g(x) = f(x)
⇒ 3x + 2 = |x - 4| + 2
⇒ 3x = |x - 4|
⇒ 3x = x - 4 and 3x = -(x - 4)
⇒ 3x = x - 4
⇒ 2x = -4
⇒ x = -2
Inputting x = -2 into the 2 equations:
⇒ g(-2) = 3 · -2 + 2 = -4
⇒ f(-2) = |-2 - 4| + 2 = 8
Therefore, as the y-values are different, x = -2 is NOT a solution
⇒ 3x = -(x - 4)
⇒ 3x = 4 - x
⇒ 4x = 4
⇒ x = 1
Inputting x = 1 into the 2 equations:
⇒ g(1) = 3 · 1 + 2 = 5
⇒ f(1) = |1 - 4| + 2 = 5
Therefore, as the y-values are the same, x = 1 IS a solution
and the solution is (1, 5)
Answer:
39 feet
Step-by-step explanation:
From the question;
let length of ladder =x feet
height of ladder will be=x-3 feet
ground distance of ladder bottom to building=15 feet
Applying Pythagorean relation
a²+b²=c²
where a=15 feet b=x-3 feet and c=x feet thus
x²-15²=(x-3)²
x²-225=x²-6x+9
collect like term
x²-x²-225-9=-6x
-234= -6x
x= 39 feet length of ladder
distance from ground to top of ladder= 39-3=36 feet
An equation which can be used to solve the given system of equations is 3x⁵ - 5x³ + 2x² - 10x + 4 = 4x⁴ + 6x³ - 11.
<u>Given the following data:</u>
y = 3x⁵ - 5x³ + 2x² - 10x + 4
y = 4x⁴ + 6x³ - 11
<h3>What is a system of equations?</h3>
A system of equations can be defined an algebraic equation that only has two (2) variables and can be solved simultaneoulsy.
Equating the given equations, we have:
y = y
3x⁵ - 5x³ + 2x² - 10x + 4 = 4x⁴ + 6x³ - 11
3x⁵ - 5x³ + 2x² - 10x + 4 - (4x⁴ + 6x³ - 11) = 0
3x⁵ - 5x³ + 2x² - 10x + 4 - 4x⁴ - 6x³ + 11 = 0
3x⁵ - 5x³ + 2x² - 10x + 4 - 4x⁴ - 6x³ + 11 = 0
3x⁵ - 4x⁴ - 11x³ + 2x² - 10x + 15 = 0
Read more on equations here: brainly.com/question/13170908
