Step-by-step explanation:
Hey there!!!
Here,
Given, A line passes through point (2,-2) and is perpendicular to the y= 5x+2.
The equation of a straight line passing through point is,
![(y - y1) = m1(x - x1)](https://tex.z-dn.net/?f=%28y%20-%20y1%29%20%3D%20m1%28x%20-%20x1%29)
Now, put all values.
![(y + 2) = m1(x - 2)](https://tex.z-dn.net/?f=%28y%20%20%2B%202%29%20%3D%20m1%28x%20-%202%29)
It is the 1st equation.
Another equation is;
y = 5x +2........(2nd equation).
Now, Comparing it with y = mx + c, we get;
m2=5
As per the condition of perpendicular lines,
m1×m2= -1
m1 × 5 = -1
Therefore, m2= -1/5.
Keeping the value of m1 in 1st equation.
![(y + 2) = \frac{ - 1}{5} (x - 2)](https://tex.z-dn.net/?f=%28y%20%2B%202%29%20%3D%20%20%5Cfrac%7B%20-%201%7D%7B5%7D%20%28x%20-%202%29)
Simplify them.
![5(y + 2) = - x + 2](https://tex.z-dn.net/?f=5%28y%20%2B%202%29%20%3D%20%20-%20x%20%2B%202)
![5y + 10 = - x + 2](https://tex.z-dn.net/?f=5y%20%2B%2010%20%3D%20%20-%20x%20%2B%202)
![x + 5y + 8 = 0](https://tex.z-dn.net/?f=x%20%2B%205y%20%2B%208%20%3D%200)
Therefore the required equation is x+5y+8= 0.
<em><u>Hope it helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>
Answer:
55.5 left over.
Step-by-step explanation:
128/2 = 64
half each week so;
1 whole = two weeks
8 weeks = 8
+ 1 = 8 1/2
so, 64/8.5
is going to be 55.5 left.
Answer:
51
Step-by-step explanation:
5*5=25
5/5=1
5+25+1-5+25
30+1-5+25
31-5+25
26+25
51
Answer:
![1 \frac{1}{6}](https://tex.z-dn.net/?f=1%20%5Cfrac%7B1%7D%7B6%7D)
Step-by-step explanation:
![\frac{3}{4}+ \frac{5}{12} =?\\](https://tex.z-dn.net/?f=%5Cfrac%7B3%7D%7B4%7D%2B%20%5Cfrac%7B5%7D%7B12%7D%20%3D%3F%5C%5C)
The fractions have unlike denominators. First, find the Least Common Denominator and rewrite the fractions with the common denominator.
×
+
×![\frac{1}{1})=?](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B1%7D%29%3D%3F)
Complete the multiplication and the equation becomes
![\frac{9}{12} + \frac{5}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B9%7D%7B12%7D%20%2B%20%5Cfrac%7B5%7D%7B12%7D)
The two fractions now have like denominators so you can add the numerators.
![\frac{9+5}{12} = \frac{14}{12}](https://tex.z-dn.net/?f=%5Cfrac%7B9%2B5%7D%7B12%7D%20%3D%20%5Cfrac%7B14%7D%7B12%7D)
This fraction can be reduced by dividing both the numerator and denominator by the Greatest Common Factor of 14 and 12 using
GCF(14,12) = 2
14÷2 / 12÷2 =7/6
The fraction
7/6
is the same as
7÷6
Convert to a mixed number using
long division for 7 ÷ 6 = 1R1, so
7/6= ![1 \frac{1}{6}](https://tex.z-dn.net/?f=1%20%5Cfrac%7B1%7D%7B6%7D)
Therefore:
3/4 − (−5/12) = ![1 \frac{1}{6}](https://tex.z-dn.net/?f=1%20%5Cfrac%7B1%7D%7B6%7D)
Solution by Formulas
Apply the fractions formula for subtraction, to
3/4 − (−5/12)
and solve
(3×12) − (−5×4) 4×12
=3/6− (−20/48)
=56/48
Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF( 56,48) = 8
56÷8 / 48÷8 =7/6
Convert to a mixed number using
long division for 7 ÷ 6 = 1R1, so
7/6= ![1 \frac{1}{6}](https://tex.z-dn.net/?f=1%20%5Cfrac%7B1%7D%7B6%7D)
Therefore:
3/4 − (-5/12) = ![1 \frac{1}{6}](https://tex.z-dn.net/?f=1%20%5Cfrac%7B1%7D%7B6%7D)