6
9
×__
54. or u can do 6×9 =54 so u can do it either way or do the 9 trick
and the fact is
Answer:
To find the point of intersection, just solve for x and y in the equations
so since x - y = -5
x = y - 5
now that we have a value of x, we will substitute x with in in the other equation
<em>5x + 3y = -9</em>
<em>5(y-5) + 3y = -9</em>
<em>5y - 25 + 3y = -9</em>
<em>8y = 16 </em>
y = 2
now use this value of y in the equation we made for x
<em>x = y - 5</em>
<em>x = 2 - 5</em>
x = -3
Hence, the point of contact is (-3 , 2)
Answer:
Step-by-step explanation:
If the triangle is equilateral :
2x +y/2 = 5x/3+y + ½ = 2/3x +2y +5/2
so the perimeter is : P = 3(2x +y/2) or 3(5x/3+y + ½) or 3(2/3x +2y +5/2)
the simplest is : P = 3(2x +y/2)
P = 6x + (3y)/2
When ever you have percentages, it should be helpful to bear in mind you can express them as multipliers. In this case, it will be helpful.
So, if we let:
a = test score
b = target score
then, using the information given:
a = 1.1b + 1
a = 1.15b - 3
and we get simultaneous equations.
'1.1' and '1.15' are the multipliers that I got using the percentages. Multiplying a value by 1.1 is the equivalent of increasing the value by 10%. If you multiplied it by 0.1 (which is the same as dividing by 10), you would get just 10% of the value.
Back to the simultaneous equations, we can just solve them now:
There are a number of ways to do this but I will use my preferred method:
Rearrange to express in terms of b:
a = 1.1b + 1
then b = (a - 1)/1.1
a = 1.15b - 3
then b = (a + 3)/1.15
Since they are both equal to b, they are of the same value so we can set them equal to each other and solve for a:
(a - 1)/1.1 = (a + 3)/1.15
1.15 * (a - 1) = 1.1 * (a + 3)
1.15a - 1.15 = 1.1a + 3.3
0.05a = 4.45
a = 89
Answer:
Step-by-step explanation:
The sum of the interior angles of a triangle is 180 degrees. Thus, angle C must be 
.
In any triangle, the Law of Sines is given by 
.
Therefore, we have:
