Pq 2x 1 and qr 5x 44 find pq – Embark on an algebraic adventure with the equation puzzle: pq = 2x + 1 and qr = 5x + 44. Dive into the intriguing world of variables and equations as we unravel the mystery of finding pq.
The given equations hold the key to solving for pq, a variable that plays a crucial role in this mathematical puzzle. Join us as we explore the steps involved in isolating pq and determining its numerical value.
Key Variables and their Values
In the given context, we have two variables: pq and qr. These variables represent the lengths of two line segments in a geometric figure, specifically a parallelogram.
The values for these variables are given as follows:
- pq = 2x + 1
- qr = 5x – 44
These variables are significant because they determine the dimensions of the parallelogram. The length of pq represents the base of the parallelogram, while the length of qr represents the height of the parallelogram.
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Algebraic Equations
Algebraic equations are mathematical expressions that contain variables and constants. They are used to represent relationships between quantities and to solve problems.In this case, we have two algebraic equations: “pq = 2x + 1” and “qr = 5x + 44.” These equations can be used to find the values of the variables p, q, and r.
Solving for pq, Pq 2x 1 and qr 5x 44 find pq
To solve for pq, we can substitute the expression for qr into the equation for pq:“`pq = 2x + 1pq = 2x + 1pq = 2(5x + 44) + 1pq = 10x + 89“`Therefore, the value of pq is 10x + 89.
Solving for ‘pq’
To isolate ‘pq’ from the given equations, we need to manipulate and simplify the equations algebraically.
First, we can substitute the value of ‘qr’ from the second equation into the first equation:
pq = 2x(5x + 44)
Next, we can distribute the ‘2x’ to simplify the expression:
pq = 10x 2+ 88x
Finally, we can divide both sides of the equation by ’10x’ to isolate ‘pq’:
pq/10x = x + 8.8
Therefore, the value of ‘pq’ is 10x(x + 8.8).
Value of ‘pq’: Pq 2x 1 And Qr 5x 44 Find Pq
Based on the given equations and variable values, we can determine the numerical value of ‘pq’.
Substituting the values of ‘qr’ and ‘x’ into the equation ‘pq = 2x + qr’, we get:
pq = 2(1) + 5(4)pq = 2 + 20pq = 22
Therefore, the numerical value of ‘pq’ is 22.
Q&A
What is the significance of the variables pq and qr in these equations?
pq and qr represent unknown values that we aim to determine through the given equations.
How do we isolate pq from the given equations?
We manipulate the equations algebraically to express pq in terms of x and the known values.
What is the numerical value of pq based on the given equations?
The numerical value of pq can be determined by substituting the given values into the isolated equation.
