Answer:
30
Step-by-step explanation:
To find the determinant of a 3x3 matrix, you can use this method. (See picture.)
Start with the first number in the top row, and block off the row and column. A 2x2 matrix will be left. Find the determinant of this 2x2 matrix, and multiply it by the number in the top row.
Repeat for the other two numbers in the top row. Add the first result, subtract the second, and add the third.
det A = -2 [(3)(-5) − (a)(0)] − 2 [(0)(-5) − (a)(0)] + b [(0)(0) − (3)(0)]
det A = -2 (3)(-5) − 0 + 0
det A = 30
The probability would be 9/12 or 3/4 in the lowest form
Answer:
134 degrees
Step-by-step explanation:
Line PQS is 180 degrees. That being said, the addition of <PQR and <SQR equal 180 degrees.
Now you need to set up an equation to find out what angle PQR is. Since there is an X, you need to solve for X. The equation looks like this:
<u>Solve for x</u>
Now plug in 43 where you see x. For this question, you only need to focus on (3x+5)
3(43) + 5 = 134
m<PQR = 134°
Do this every, single, time when you see these questions. Remember that line PQS is 180 degrees, and both of those angles are equal to 180 degrees.
If you want to check if this is true, plug in 43 into our equation we made to see if it equals 180 degrees. <em>If it doesn't equal 180, your equation is incorrect.</em>
<em />
3(43)+5+43+3 = 180
134 + 46 = 180
180 = 180 ✅
For starters, create an equation to show David's earnings. We can do this using Danielle's as a basis, which is set up as y=(# of hours)x+(bonus). This gives us y=12x+80. Now, as we need both their ys to be equal, we just set both equations equal to each other, making 15x+50=12x+80. Now, we solve for x, starting with 15x+50=12x+80, subtracting 12x from both sides to get 3x+50=80, subtracting 50 from both sides to get 3x=30, and dividing three from both sides to get x=10. To check, we just plug in our answer to both equations and see if the ys match up. With Danielle's equation, we get y=15(10)+50=150+50=200 and with David's equation, we get y=12(10)+80=120+80=200, proving that our answer is correct.
She received 12 calls from her son and 30 calls in total.
40% of 30 is 12.
