Answer:
SSS Theorem
Step-by-step explanation:
All the corresponding sides of these two triangles are of equal length, proving their congruency. Although it can be assumed that they also share the same angles, no angle information is directly given to prove the fact.
The solution to the equation is x = 4
<h3>What are linear equations?</h3>
Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient
<h3>How to determine the solution to the system?</h3>
A system of linear equations is a collection of at least two linear equations.
In this case, the equation is given as
(x + 20)/2 = 3x
Multiply both sides of the equation by 2
x + 20 = 6x
Subtract x from both sides of the equation
5x = 20
Divide both sides of the equation by 5
x = 4
hence, the solution to the equation is x = 4
Read more about equations at:
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Answer:
Step-by-step explanation:
Hello,
<em>"Ray says the third-degree polynomial has four intercepts. Kelsey argues the function can have as many as three zeros only."</em>
We know that Kelsey is right, a polynomial of degree 3 has maximum 3 zeroes, so it means that the graph of this polynomial has maximum 3 x-intercepts.
<u>So how Ray can be right too?</u>
we need to think of y-intercept, if we add the y-intercept then Ray can be right too,
as you can see in one example below
there are 3 x-intercepts and 1 y-intercept.
This being said, Ray is not always right. For instance 
has only 1 zero (multiplicity 3) its graph has only 1 intercept in the point (0,0)
hope this helps
For this case, what we must do is fill squares in all the expressions until we find the correct result.
We have then:
x2 + y2 − 4x + 12y − 20 = 0 x2 + y2 − 4x + 12y = 20
x2 − 4x + y2 + 12y = 20
x2 − 4x + (12/2)^2 + y2 + 12y + (-4/2)^2 = 20 + (12/2)^2 + (-4/2)^2
x2 − 4x + (6)^2 + y2 + 12y + (-2)^2 = 20 + (6)^2 + (-2)^2
x2 − 4x + 36 + y2 + 12y + 4 = 20 + 36 + 4
(x − 2)2 + (y + 6)2 = 60
3x2 + 3y2 + 12x + 18y − 15 = 0
x2 + y2 + 4x + 6y − 5 = 0
x2 + y2 + 4x + 6y = 5
x2 + 4x + (4/2)^2 + y2 + 6y + (6/2)^2 = 5 + (4/2)^2 + (6/2)^2
x2 + 4x + (2)^2 + y2 + 6y + (3)^2 = 5 + (2)^2 + (3)^2
x2 + 4x + 4 + y2 + 6y + 9 = 5 + 4 + 9
(x + 2)2 + (y + 3)2 = 18
2x2 + 2y2 − 24x − 16y − 8 = 0
x2 + y2 − 12x − 8y − 4 = 0
x2 + y2 − 12x − 8y = 4
x2 − 12x + (-12/2)^2 + y2 − 8y + (-8/2)^2 = 4 + (-12/2)^2 + (-8/2)^2
x2 − 12x + (-6)^2 + y2 − 8y + (-4)^2 = 4 + (-6)^2 + (-4)^2
x2 − 12x + 36 + y2 − 8y + 16 = 4 + 36 + 16
(x − 6)2 + (y − 4)2 = 56
x2 + y2 + 2x − 12y − 9 = 0
x2 + y2 + 2x - 12y = 9
x2 + 2x + y2 - 12y = 9
x2 + 2x + (2/2)^2 + y2 - 12y + (-12/2)^2 = 9 + (2/2)^2 + (-12/2)^2
x2 + 2x + (1)^2 + y2 - 12y + (-6)^2 = 9 + (1)^2 + (-6)^2
x2 + 2x + 1 + y2 - 12y + 36 = 9 + 1 + 36
(x + 1)2 + (y − 6)2 = 46
Answer:
4,500 items are made every 4 hours.
5,625 items are made every 5 hours.
Step-by-step explanation:
when you multiply 1125 by for it will equal 4500 and when you multiply 1125 by 5 it will equal 5625