Let
x-------> the length side of the original cube
we have

Divide by
both sides

The system of equations is equal to
--------> equation 
--------> equation 
using a graphing tool
see the attached figure
we know that
the solution of the system of equations is the intersection both graphs
therefore
the solution is

therefore
<u>the answer is</u>

A complex mathematical topic, the asymptotic behavior of sequences of random variables, or the behavior of indefinitely long sequences of random variables, has significant ramifications for the statistical analysis of data from large samples.
The asymptotic behavior of the sample estimators of the eigenvalues and eigenvectors of covariance matrices is examined in this claim. This work focuses on limited sample size scenarios where the number of accessible observations is comparable in magnitude to the observation dimension rather than usual high sample-size asymptotic .
Under the presumption that both the sample size and the observation dimension go to infinity while their quotient converges to a positive value, the asymptotic behavior of the conventional sample estimates is examined using methods from random matrix theory.
Closed form asymptotic expressions of these estimators are obtained, demonstrating the inconsistency of the conventional sample estimators in these asymptotic conditions, assuming that an asymptotic eigenvalue splitting condition is satisfied.
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You need to isolate x, which means you need to get it alone. 16x and 11x are like terms because they both have an x, do subtract them. 16-11=5. So 15 = 5x
Then to turn 5x into x, divide by five. This is because 5/5 is 1, and 1x is x. Divide both sides, so
X = 3
Juanita and Keenan ordered 85 flashlights and 17 sleeping bags.
Step-by-step explanation:
Given,
Cost of each flashlight = $12
Cost of each sleeping bag = $45
Total cost = $1785
Let,
x represent the number of flashlights ordered
y represent the number of sleeping bags ordered
According to given statement;
12x+45y=1785 Eqn 1
x = 5y Eqn 2
Putting value of x from Eqn 2 in Eqn 1

Dividing both sides by 105

Putting y=17 in Eqn 1

Juanita and Keenan ordered 85 flashlights and 17 sleeping bags.
Keywords: linear equation, substitution method
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Answer:
y = -x - 8
Step-by-step explanation:
Slope intercept form is y = mx + b, so subtract x from both sides to convert the equation to slope-intercept form.