Answer:
x=-19
Step-by-step explanation:
After modelling the mathematical statement and solving its equivalent mathematical relation, we get x = -36.
<h3>What is Equation Modelling?</h3>
Equation modelling is the process of writing a given mathematical statement in the form of a numeric mathematical expression taking into considerations the operations, constants and other variables.
Given in the question is a number such that twice the difference of a number and 9 is equal to three times the sum of the number and 6.
Assume that the number is x. Now, we will model the equation and solve for x. According to the question, the following mathematical relation represents the statement-
2(x - 9) = 3(x + 6)
2x - 18 = 3x + 18
x = - 36
Therefore, the number is -36.
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The answer will be for every x, y will be 1.25
The answer is <span>a.)(x - 4)2 = 3.
(x - a)</span>² = b can be expressed as:
x² - 2ax + a² = b ⇒ x² - 2ax + a² - b = 0
Our equation is x² - 8x + 13 = 0.
The general formula is x² - 2ax + (a² - b) = 0
Thus:
8x = 2ax and a² - b = 13
Divide both sides of the first equation (8x = 2ax) by x:
8 = 2a ⇒ a = 8 ÷ 2 = 4
Replace a in the second equation (a² - b = 13):
4² - b = 13 ⇒ b = 4² - 13 = 16 - 13 = 3
Now when we have a and b, let's just replace them in the general equation:
(x - a)² = b
(x - 4)² = 3
The volume of the rectangular prism can be found with the formula
v= length × width × height
V = 10×10×30 = 3000
the volume of the triangular prism can be found with
v = 1/2(base×width×height)
v=1/2×30×9×10 = 1/2×2700
v = 1350
Now add the two volumes together for the total volume...
3000+1350 = 4,350 in^3
