Answer:
y = x + 1
Step-by-step explanation:
Step 1: Find the slope.
<u>Parallel lines have the same slope.</u> That means that the line we are seeking is going to have the same slope as line x - y = 7.
To find the slope of the line x - y = 7 let's change it to the slope-intercept form.
<u>Slope-Intercept Form</u>
y = mx + b
m ... slope
b ... y-intercept
Let's change the equation of the parallel line to slope-intercept form (isolate y).
x - y = 7
Add y on both sides.
x - y + y = 7 + y
x = 7 + y
Subtract 7 on both sides.
x - 7 = 7 + y - 7
x - 7 = y
y = x - 7
Let's read the slope from the equation.
Instead of y = x - 7 we can write y = 1x -7.
Now it's obvious that m (slope) is 1.
m = 1
So far, our equation of the line is:
y = 1x + b
which is te same as
y = x + b
Step 2: Find y-intercept.
To find out y-intercept (b), we substitiute the point (-7, -6) in the equation. Points are in form (x, y) so -7 is x and -6 is y.
y = x + b
-6 = -7 + b
Solve for b.
1 = b
Step 3: Substitute slope and y-intercept in general formula for slope-intercept form of the line.
Now substitute m and b in slope-intercept form y = mx + b.
m = 1
b = 1
Equation of the line:
y = x + 1
Answer:
−
7
2
−
9
i
3
x
−
3
sin
(
x
)
⋅
cot
(
x
)
Step-by-step explanation:
Answer:
x = 4.85 feet
Step-by-step explanation:
Original area of the petting farm = 10 × 14
= 140 square feet
.
New area = double the original area = 140 * 2
= 280 square feet
New area of the petting farm =
Width × length
280 = (10+x) × (14+x)
280 = 140 + 10x + 14x + x²
280 - 140 = x² + 24x
140 = x² + 24x
x² + 24x - 140 = 0
Solve the quadratic equation
x = -b ± √b² - 4ac / 2a
= -24 ± √(24)² - 4*1*-140 / 2*1
= -24 ± √ 576 - (-560) / 2
= -24 ± √ 576 + 560 / 2
= -24 ± √1,136 / 2
= -24 ± 4√71 / 2
= -24/2 ± 4√71/2
= -12 ± 2√71
x = 4.8523 or x = -28.8583
x can not be a negative value
Therefore,
x = 4.85 feet to the nearest hundredth
(gºf) means solve f(x) first, then use that for g(x)
In the equation for f(x) replace x with -3:
f(x) = x +4 = -3 +4 = 1
Now replace the x in the equation for g(x) with 1
g(x) = x = 1
