need help on this

Question

value of x that results in the required y value

5x²=7 

x=1, 1.1 ,1.2 ,1.3, 1.4, 1.5

y=

 

x²-7x+10=5

x=0.5, 0.6, 0.7, 0.8, 0.9, 1

y=

 

3x²-5x=2

x=1, 2, 3, 4, 5, 

y=

 

 

Answer 1

Hello,

 

You can use the quadratic formula to solve all three of these questions. The first thing you need to do for each equation is get the equation to appear in the Ax + By + C = 0 format. To do this, follow the rules of algebra. For instance, in equation #1, simply subtract 7 from both sides. The equation will now become 5x² - 7 = 0. In equation #2, subtract 5 from both sides. The equation will now become x² - 7x + 5 = 0. In equation #3, subtract 2 from both sides. The equation will now become 3x² -5x - 2 = 0.

 

Now, once you have each equation in the form described in the above paragraph, employ the quadratic formula to solve. The quadratic formula is provided below:

 

(-B +/- (SQRT: B² - 4AC))/2A

 

SQRT: Square Root

 

For equation #1, this gives us:

 

(0 +/- (SQRT: 0² - 4(5)(-7))/2(5) =  +/- 1.18. Since your answer choices are all positive, the answer would be 1.2.

 

For equation #2, this gives us:

 

(7 +/- (SQRT: -7² - 4(1)(5))/2(1) = 6.19 or 0.81. Select answer choice 0.8.

 

For equation #3, this gives us:

 

5 +/- (SQRT: -5² - 4(3)(-2))/2(3) = -0.33 or 2. Select answer choice 2.

 

For all of these equations there are two solutions. The quadratic formula provides you with such solutions. You can plug the solutions back into the problem and check your work with a calculator to make sure. For instance, in the third equation 3(2²) - 5(2) does in fact equal 2, since this is the same thing as 12 - 10, following the order of operations, which is essentially PEMDAS.

 

Frank