Answer:
The solution of the equation are x = - 1 , y = 0 and z = 3
Step-by-step explanation:
Given three linear equation as :
6 x - y + z = - 3 ......A
4 x - 3 z = - 13 ......B
2 y + 5 z = 15 ......C
Solving eq A and C
I.e 2× (6 x - y + z ) = -3 ×2
or, 12 x - 2 y + 2 z = - 6
So, ( 12 x - 2 y + 2 z ) + ( 2 y + 5 z) = - 6 + 15
Or, 12 x + 7 z = 9 ......D
Solving eq B and D
I.e 3 × ( 4 x - 3 z ) = - 13 × 3
or, 12 x - 9 z = - 39
So, ( 12 x + 7 z ) - ( 12 x - 9 z ) = 9 + 39
or, 16 z = 48
∴ z = 
i.e z = 3
put the value of z in eq D
So, 12 x + 7×3 = 9
Or, 12 x = 9 - 21
or, 12 x = - 12
∴ x = - 
I.e x = - 1
Now, Put The value of z in eq C
or, 2 y + 5 z = 15
or, 2 y + 5 × 3 = 15
Or, 2 y = 15 - 15
or, 2 y = 0
∴ y = 0
Hence The solution of the equation are x = - 1 , y = 0 and z = 3 Answer
The area of triangle EFG with a base of 2 feet and height of 8 feet is 8 ft².
<h3>What is an
equation?</h3>
An equation is an expression that shows the relationship between two or more numbers and variables.
Let h represent the height of triangle ABC, hence:
18 ft² = (1/2) * 3 * h
h = 12 ft
Let x represent the height of triangle EFG, hence:
x/12 = 2/3
x = 8 feet
Area of EFG = (1/2) * 2 * 8 = 8 ft²
The area of triangle EFG with a base of 2 feet and height of 8 feet is 8 ft².
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Answer:
-15a^2+20ab
Step-by-step explanation:
Given data
We are given the expression
(-3a + 4b) to be multiplied by 5a
hence we have
(-3a + 4b)*5a
open bracket
-15a^2+20ab
Hence the answer is
-15a^2+20ab
The equation in which b varies directly as the <em>square</em> root of c is b = 50 · √c. (Correct choice: B)
<h3>What is the equation of the direct variation between two variables?</h3>
In this problem we have a case of <em>direct</em> variation between two variables, which is mathematically described by a <em>direct proportionality</em> model, whose form and characteristics are shown below:
b ∝ √c
b = k · √c (1)
Where k is the <em>proportionality</em> constant.
First, we determine the value of the constant of proportionality by substituting on b and c and clearing the variable: (b = 100, c = 4)
k = b / √c
k = 100 / √4
k = 100 / 2
k = 50
Then, the equation in which b varies directly as the <em>square</em> root of c is b = 50 · √c. (Correct choice: B)
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