Answer:
x = 136/11
, y = 68/11
Step-by-step explanation:
Solve the following system:
{6 x - y = 68
2 y = x
Hint: | Choose an equation and a variable to solve for.
In the second equation, look to solve for x:
{6 x - y = 68
2 y = x
Hint: | Reverse the equality in 2 y = x in order to isolate x to the left hand side.
2 y = x is equivalent to x = 2 y:
{6 x - y = 68
x = 2 y
Hint: | Perform a substitution.
Substitute x = 2 y into the first equation:
{11 y = 68
x = 2 y
Hint: | Choose an equation and a variable to solve for.
In the first equation, look to solve for y:
{11 y = 68
x = 2 y
Hint: | Solve for y.
Divide both sides by 11:
{y = 68/11
x = 2 y
Hint: | Perform a back substitution.
Substitute y = 68/11 into the second equation:
{y = 68/11
x = 136/11
Hint: | Sort results.
Collect results in alphabetical order:
Answer: {x = 136/11
, y = 68/11
a. Answer: m = 2
<u>Step-by-step explanation:</u>
f(x) = x² - 4x + 1
f(m) = m² - 4m + 1 = -3
m² - 4m + 4 = 0
(m - 2)(m - 2) = 0
m = 2
***************************************************
b. Answer: k = 2 and k = 5
<u>Step-by-step explanation:</u>
f(x) = x² - 7x + 14
f(k) = k² - 7k + 14 = 4
k² - 7k + 10 = 0
(k - 2)(k - 5) = 0
k = 2 k = 5
Answer:
x = - 
, x = 
Step-by-step explanation:
Given
x² - x - 
= 0
Multiply through by 4 to clear the fraction
4x² - 4x - 3 = 0
Consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term
product = 4 × - 3 = - 12 and sum = - 4
The factors are + 2 and - 6
Use these factors to split the x- term
4x² + 2x - 6x - 3 = 0 ( factor the first/second and third/fourth terms )
2x(2x + 1) - 3(2x + 1) = 0 ← factor out (2x + 1) from each term
(2x + 1)(2x - 3) = 0
Equate each factor to zero and solve for x
2x + 1 = 0 ⇒ 2x = - 1 ⇒ x = -
2x - 3 = 0 ⇒ 2x = 3 ⇒ x =
Any line can be expresses as:
y=mx+b where m=slope=(y2-y1)/(x2-x1) and b=y-intercept (value of y when x=0)
First find the slope:
m=(2-0)/(8-0)=2/8=1/4 so we have thus far:
y=0.25x+b, we solve for b using any point on the line, (8,2)
2=0.25(8)+b
2=2+b
0=b
So the line is:
y=.25x which they might also express as y=x/4
The answer is E. (1/4)x
