Answer:
(-1, 5)
Step-by-step explanation:
3 [x + y = 4]
3x + 3y = 12
- 3x + 7y = 32
-4y = -20
y = 5
x + 5 = 4
x = -1
Answer:




Step-by-step explanation:
Given
See attachment for proper format of table
--- Sample
A = Supplier 1
B = Conforms to specification
Solving (a): P(A)
Here, we only consider data in sample 1 row.
In this row:
and 
So, we have:



P(A) is then calculated as:


Solving (b): P(B)
Here, we only consider data in the Yes column.
In this column:
and 
So, we have:



P(B) is then calculated as:


Solving (c): P(A n B)
Here, we only consider the similar cell in the yes column and sample 1 row.
This cell is: [Supplier 1][Yes]
And it is represented with; n(A n B)
So, we have:

The probability is then calculated as:


Solving (d): P(A u B)
This is calculated as:

This gives:

Take LCM


<h3>
Answer: </h3><h3>
Yes, the triangles are similar</h3><h3>
AC = 6</h3>
======================================================
Explanation:
Focus on triangle ABC. Let's find the missing angle
A+B+C = 180
113+B+22 = 180
B+135 = 180
B = 180-135
B = 45
Between the triangles, have two pairs of angles that are congruent
A = D = 113
B = E = 45
Which is enough to prove the triangles are similar through the angle angle (AA) similarity theorem. This must mean that C = F = 22
Since we have A pair with D, and B pair with E, this means that 
The order of the letters is important so we know how the angles pair up. The first letters pair up together, the second letters pair up, and so on.
Consequently, this means sides BC and EF pair up and AC and DF pair up
We can then say...
BC/EF = AC/DF
18/12 = x/4
18*4 = 12*x
72 = 12x
12x = 72
x = 72/12
x = 6
AC = 6
Answer:
Then, a=-1 and b=-1
Step-by-step explanation:
We need to solve the following system of equations using the adition method:
2a+3b=-1 (i)
3a+5b=-2 (ii)
First, we multiply the equation (i) by -3 and the equation (ii) by 2, so we get:
-6a-9b=3
6a+10b=-4
Adding the two equations we have:
-6a-9b=3
6a+10b=-4
--------------------------
0 + b = -1
Then b=-1. Now, let's substitute the value of b into equation (i):
2a+3b=-1
2a + 3(-1) = -1
2a -3 = -1
2a = 2
a = 1
Then, a=-1 and b=-1
Answer:
1=n
Step-by-step explanation:
Step 1- Distribute into the parenthesis.
7(3)+5(3)n= 6n+1(6)+4(6)n
Step 2- Multiply
21+15n= 6n+6+24n
Step 3- Add common variables to simplify.
21+15n= (24n+6n)+6
21+15n= 30n+6
Step 4- Subtract the smallest variable to both sides.
21+15n= 30n+6
-15n -15n
21= 15n+6
Step 5- Subtract 6 to both sides.
21= 15n+6
-6 -6
15= 15n
Step 6- Divide both sides by 15.
<u>15</u>= <u>15n</u>
15 15
1=n