Answer:
Width: 450 feet
Length: 720 feet
Step-by-step explanation:
So we start with the equation to find the perimeter -
2l + 2w = p
l = length
w = width
p = perimeter
We insert the 2,340 ft as the perimeter -
2l + 2w = 2,340 ft
Now we find another equation for the "length is 270 ft greater than width" -
l = 270 ft + w
Using substitution, we substitute the y in the first equation with 270 ft + w -
2 (270 ft + w) + 2w = 2,340 ft
540 ft + 2w + 2w = 2,340 ft
540 ft + 4w = 2,340 ft
4w = 2,340 ft - 540 ft
4w = 1,800 ft
w = 1,800 ft / 4
w = 450 ft
Now to find the width we substitute the w with 450 ft -
l = 270 ft + w
l = 270 ft + 450 ft
l = 720 ft
Check -
2 * 720 ft + 2 * 450 ft = 2,340 ft
1,440 ft + 900 ft = 2,340 ft
2,340 ft = 2,340 ft (Correct)
The linear equation is y = -x - 6
Step-by-step explanation:
To form a linear equation from two points lie on the line which the equation represented it
- Find the slope of the line by using the formula
- Then use the slope-intercept form of the equation y = m x + b
- To find the value of b substitute x and y of the equation by the coordinates of one of the two given points
∵ Points (-2 , -4) and (-3 , -3) lie on the line
∴ 
= -2 and 
= -3
∴ 
= -4 and 
= -3
- Substitute these values in the formula of the slope
∵ 
∴ m = -1
∵ The form of the equation is y = m x + b
∵ m = -1
∴ y = (-1) x + b
∴ y = -x + b
To find b substitute x and y in the equation by the coordinates of
point (-2 , -4) OR (-3 , -3)
∵ x = -3 and y = -3
∴ -3 = -(-3) + b
∴ -3 = 3 + b
- Subtract 3 from both sides
∴ -6 = b
∴ The equation is y = -x + (-6)
∴ y = -x - 6
The linear equation is y = -x - 6
Learn more:
You can learn more about linear equation in brainly.com/question/4326955
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For this case the amplitude is given by:
A = (l-1l + 3) / 2
A = 4/2
A = 2
The middle line is given by:
y = 1
The period of the function is given by:
T = l x2 - x1 l
T = l 0 - 2pi l
T = l - 2pi l
T = 2pi
Answer:
Amplitude: 2; period: 2π; midline: y = 1
Answer:
y = 3x - 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 3x + 2 ← is in slope- intercept form
with slope m = 3
Parallel lines have equal slopes , then
y = 3x + c ← is the partial equation
To find c substitute (3, 8 ) into the partial equation
8 = 9 + c ⇒ c = 8 - 9 = - 1
y = 3x - 1 ← equation of parallel line
Answer:
m∠1=80°
m∠2=112°
m∠3=131°
m∠4=80°
m∠5=37°
Step-by-step explanation:
First you have to find m∠2
To do that find m∠6 (I created this angle shown in pic below)
Find m∠6 by using the sum of all ∠'s in a Δ theorem
m∠6=180°-(63°+49°)
m∠6=68°
Now you can find m∠2 with the supplementary ∠'s theorem
m∠2=180°-68°
m∠2=112°
Then you find m∠5 using the sum of all ∠'s in a Δ theorem
m∠5=180°-(112°+31°)
m∠5=37°
Now you can find m∠1
m∠1=180°-(63°+37°)
m∠1=180°-100°=80°
m∠4 can easily be found too now:
m∠4=180°-(63°+37°)
m∠4=80°
m∠3=180°-49°
m∠3=131°
