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24.07.2020 •
Mathematics
Examine the system of equations. –2x + 3y = 6 –4x + 6y = 12 Answer the questions to determine the number of solutions to the system of equations. What is the slope of the first line? What is the slope of the second line? What is the y-intercept of the first line? What is the y-intercept of the second line? How many solutions does the system have?
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Ответ:
Examine the system of equations.
–2x + 3y = 6
–4x + 6y = 12
Answer the questions to determine the number of solutions to the system of equations.
What is the slope of the first line?
✔ 2/3
What is the slope of the second line?
✔ 2/3
What is the y-intercept of the first line?
✔ 2
What is the y-intercept of the second line?
✔ 2
How many solutions does the system have?
✔ infinitely many
Ответ:
10.6 ft
Step-by-step explanation:
The complete question is:
The area of the triangle is 35 square feet. Use a quadratic equation to find the length of the base. Round your answer to the nearest tenth.Base=x+4 Height=x
SOLUTION:
As you know, Area of triangle 'A' = 1/2 x b x h
Where,
Base 'b' = x+4
Area 'A' = 35 ft²
Height 'h'= x
35 = (1/2)(x+4)x
35 =(x² + 4x)/2
2 * 35 =x² + 4x
70 = x² + 4x
x² + 4x - 70=0
Formula for the quadratic equation is
x = [- b ± √(b² - 4ac)]/2a
Where,
a=1, b= 4, c=-70
Plugging in the values.
x = [- 4 ± √4² - (4 × 1 × - 70)] / (2 × 1 )
x = [- 4 ± √(16 + 280)]/2
x = [- 4 ± √296]/2
x = (- 4 + 17.2)/2 or x = (- 4 - 17.2)/2
x = 13.2/2 or x = - 21.2/2
As, we choose to ignore negative value of 'x'
Therefore, x = 13.2/2 = 6.6
And, Length of the base will be:
x + 4 = 6.6 + 4 => 10.6 ft