Answer:
4y = 6x + 40
Step-by-step explanation:
The general equation of a straight line is y = mx + b
m is the slope and b is the y-intercept
let us write both equations in this form;
we have this as;
6y = -4x + 1
y = -4x/6 + 1/6
and;
2x + 3y = 18
3y = -2x + 18
y = -2x/3 + 6
So firstly we want to find an equation that is perpendicular to the first
When two lines are perpendicular, their slopes has a product of -1
The slope of the first line is -4/6
let the slope of the line we want be m
As per they are perpendicular;
-4/6 * m = -1
-4m/6 = -1
-4m = -6
m = 6/4
So now, we want the y-intercept greater than that of the second equation which is a y-intercept of 6
we can choose 10
and we have the equation as:
y = 6x/4 + 10
multiply through by 4
4y = 6x + 40
Answer:
98$ in savings
Step-by-step explanation:
If you do all the spending combined you would do $700+$325=$1025 $420+$182=$602 add those = $1627+$300=$1927 if his monthly take-home pay is $2025 you would have to do $2025-$1927=$98 remanding.
<u>Answer:</u>
The total number of whole cups that we can fit in the dispenser is 25
<u>Solution:</u>
It is given that the height of each cup is 20 cm.
But when we stack them one on top of the other, they only add a height of 0.8 to the stack.
The stack of cups has to be put in a dispenser of height 30 cm.
So we need o find out how many cups can fit in the dispenser.
Since the first cup is 20 cm high, the height cannot be reduced. So the space to fit in the remaining cups in the stack is only 30-20 cm as that’s the remaining space in the dispenser
So,
30 - 20 = 10 cm
To stack the other cups we have 10 cm of height remaining
As we know that addition of each adds 0.8 cm to the stack, the total number of cups that can be fit in the dispenser can be calculated by the following equation. Let the number of cups other than the first cup be denoted by ‘x’.
10 + 0.8x = 30
0.8x = 20
x = 25
The total number of cups that we can fit in dispenser is 25
Answer:
![L(f(t)) = \dfrac{6}{S^2+1} [\sqrt{3} \ S +1 ]](https://tex.z-dn.net/?f=L%28f%28t%29%29%20%3D%20%5Cdfrac%7B6%7D%7BS%5E2%2B1%7D%20%5B%5Csqrt%7B3%7D%20%5C%20S%20%2B1%20%5D)
Step-by-step explanation:
Given that:
recall that:
cos (A-B) = cos AcosB + sin A sin B
∴
![f(t) = 12 [cos\ t \ cos \dfrac{\pi}{6}+ sin \ t \ sin \dfrac{\pi}{6}]](https://tex.z-dn.net/?f=f%28t%29%20%3D%2012%20%5Bcos%5C%20%20t%20%5C%20%20cos%20%5Cdfrac%7B%5Cpi%7D%7B6%7D%2B%20sin%20%5C%20t%20%20%5C%20sin%20%5Cdfrac%7B%5Cpi%7D%7B6%7D%5D)
![f(t) = 12 [cos \ t \ \dfrac{3}{2}+ sin \ t \ sin \dfrac{1}{2}]](https://tex.z-dn.net/?f=f%28t%29%20%3D%2012%20%5Bcos%20%5C%20%20t%20%5C%20%5Cdfrac%7B3%7D%7B2%7D%2B%20sin%20%20%5C%20t%20%20%5C%20sin%20%5Cdfrac%7B1%7D%7B2%7D%5D)
![L(f(t)) = L ( 6 \sqrt{3} \ cos \ (t) + 6 \ sin \ (t) ]](https://tex.z-dn.net/?f=L%28f%28t%29%29%20%3D%20L%20%28%206%20%5Csqrt%7B3%7D%20%5C%20cos%20%5C%20%28t%29%20%2B%206%20%5C%20sin%20%5C%20%28t%29%20%5D)
![L(f(t)) = 6 \sqrt{3} \ L [cos \ (t) ] + 6\ L [ sin \ (t) ]](https://tex.z-dn.net/?f=L%28f%28t%29%29%20%3D%206%20%5Csqrt%7B3%7D%20%5C%20L%20%5Bcos%20%5C%20%28t%29%20%5D%20%2B%206%5C%20L%20%5B%20sin%20%5C%20%28t%29%20%5D)
Answer:
90
Step-by-step explanation:
they are vertical angles
