For the first line we have a slope of (y2-y1)/(x2-x1)
(2--2)/(1--1)=4/2=2 so we have:
y=2x+b, now solve for b with either of the points, I'll use: (1,2)
2=2(1)+b
b=0 so the first line is:
y=2x
Now the second line:
(1-10)/(4--2)=-9/6=-3/2 so far then we have:
y=-3x/2+b, using point (4,1) we solve for b...
1=-3(4)/2+b
1=-6+b
b=7 so
y=-3x/2+7 or more neatly...
y=(-3x+14)/2
...
The solution occurs when both the x and y coordinates for each are equal, so we can say y=y, and use our two line equations...
2x=(-3x+14)/2
4x=-3x+14
7x=14
x=2, and using y=2x we see that:
y=2(2)=4, so the solution occurs at the point:
(2,4)
Answer:
Dimensions = 21 centimeters by 4.2 centimeters.
Step-by-step explanation:
Let the length of the rectangle be L.
Let the width of the rectangle be W.
Given the following data;
Perimeter of rectangle = 50cm
Translating the word problem into an algebraic expression, we have;
L = 5W
To find the dimensions of the rectangle;
Perimeter of rectangle = 2L + 2W
50 = 2L + 2W
50 = 2(5W) + 2W
50 = 10W + 2W
50 = 12W
W = 50/12
W = 4.2 cm.
To find the length;
L = 5W
L = 5*4.2
L = 21 cm.
Answer:
1. A = 59
2. A = 43
Step-by-step explanation:
If we have a right triangle we can use sin, cos and tan.
sin = opp/ hypotenuse
cos= adjacent/ hypotenuse
tan = opposite/ adjacent
For the first problem, we know the opposite and adjacent sides to angle A
tan A = opposite/ adjacent
tan A = 8.8 / 5.2
Take the inverse of each side
tan ^-1 tan A = tan ^-1 (8.8/5.2)
A = 59.42077313
To the nearest degree
A = 59 degrees
For the second problem, we know the adjacent side and the hypotenuse to angle A
cos A = adjacent/hypotenuse
cos A = 15.3/21
Take the inverse of each side
cos ^-1 cos A = cos ^-1 (15.3/21)
A = 43.23323481
To the nearest degree
A = 43 degrees
Answer:
speed of James is: 3.75 miles/hour.
Step-by-step explanation:
We need to find the speed of James in miles per hour(mi/hr)
we know that 1 mile=5280 feet
James takes 120 steps in 1 minute so he will cover 120×60 steps in 1 hour.
i.e. he takes 7200 steps in 1 hour.
also each step of James=2.75 feet
total distance covered by James in 1 hour=2.75×7200 feet=19800 feet
hence speed of James= (distance covered by james in 1 hour)/1 hour
speed of James=3.75 miles/hour.
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The error in the steps is that In step 1, she should have also distributed -3/8 over –16d, to get 3 + 6 d + 2 d = 24
<h3>Simplifying linear equations</h3>
Given the following equation as shown below
-3/8(-8-16d)+2d = 24
Step 1 Distribute -3/8 over the expression in parentheses
3 + 6d + 2d = 24
Simply the like terms
3 + 8d = 24
Subtract 3 from both sides of the equation.
8d = 24 - 3
8d = 21
d = 21/8
Hence the error in the steps is that In step 1, she should have also distributed -3/8 over –16d, to get 3 + 6 d + 2 d = 24
Learn more on linear equation here: brainly.com/question/1884491
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