Answer:
<em>102°</em>
Step-by-step explanation:
(3x - 12)° + (2x + 2)° = 180°
5x - 10 = 180 ⇒ x = 38
m∠A = (3x - 12)°
<em>m∠A</em> = (3×38 - 12)° = <em>102°</em>
Answer:
Step-by-step explanation:
Given:
12 meters longer than his throw
To translate the word phrase into math expression.
Solution:
let represents the throw by him.
Now according to given data his throw is 12 meters longer
So equation now becomes as
<u>2x + 3y = 1</u>
<u>y = 3x + 15</u>
There's not much you can do with the first equation, because it has
two variables in it ... 'x' and 'y' . No matter how much you move them
around, you'll never be able to get either one equal to just a number.
Is there any way you could get rid of one of the variables in the first
equation, and have just 1 letter in it to solve for ?
Absolutely ! The second equation tells you something that 'y' is <u>equal</u> to,
(3x + 15). "EQUAL" is very powerful. It means that wherever you see 'y',
you can put (3x + 15) in its place, and you won't change anything or
upset anything. One thing you can do is take that (3x + 15) from the <span>
2nd</span> equation, and put it right into the first equation in place of 'y'.
You'll see how that helps as soon as you do it.
First equation: <u>2x + 3y = 1</u>
Substitute for 'y' : 2x + 3(<em>3x + 15</em>) = 1
Remove parentheses: 2x + 3(3x) + 3(15) = 1
2x + 9x + 45 = 1
Combine the terms with 'x' in them: 11x + 45 = 1
Look what you have now ! An equation with only one variable in it !
Subtract 45 from each side: 11x = -44
Divide each side by 11 : <em> x = -4</em>
You're more than halfway there. Now you know what 'x' is,
and you can use it with either equation to find what 'y' is.
-- If you use it with the first equation: <u> 2x + 3y = 1</u>
Put in the value of 'x': 2(<em>-4</em>) + 3y = 1
Remove the parentheses: -8 + 3y = 1
Add 8 to each side: 3y = 9
Divide each side by 3 : <em> y = 3</em>
-- If you use it with the 2nd equation: <u>y = 3x + 15</u>
Put in the value of 'x' : y = 3(<em>-4</em>) + 15
Remove the parentheses: y = -12 + 15
Add numbers on the right side: <em> y = 3</em> (same as the other way)
So there's your solution for the system of two equations:
<em> x = -4</em>
<em> y = 3</em>
Answer: y= x-2
To draw this on the graph use the y-intercept to count the number of units you need to move up or down along the y axis. Then to plot the second point using the slope value to determine how many units to move up or down from the y-intercept point in this case it is 1. join the points to draw the line of slope intercept on the graph
Solution:
Find the slope in order to find the line of equation
m= y2-y1/x2-x1
Take both the coordinates and name it A (4,2) B(3,1) for convenience
m= 1-2/3-4
m=-1/-1
m=1 (slope)
Now find the y intercept using the equation below
y=mx+ b
where
y = y coordinate
m= slope
x= x coordinate
b= y intercept
SO
Note: use any of the coordinate the answer would be the same in either case
I will be using the coordinate (4,2)
y=mx+b
2=(1)(4)+b
2-4=b
-2=b
So the equation is
y= x-2
Hi there!
To find equivalent fractions, we need to multiply both the numerator and the denominator by the same number.
These equivalent fractions are the original fractions multiplied by 2/2:
2/3 = 4/6
1/2 = 2/4
5/12 = 10/24
Hope this helps!