(3x−9x)+(12+8)
Answer
−6x+20
Answer:
The measures of the three interior angles of the triangle are {40,55,85}.
Step-by-step explanation:
Let a = the measure of the first angle of the triangle.
Let b = the measure of the second angle of the triangle.
Let c = the measure of the third angle of the triangle.
The problem statement tells us that
(1) a = a
(2) b = a + 15 and
(3) c = a + 45
Now we (should) know that the sum of the three angles of a triangle is 180 degrees. Then we get
(4) a + b + c = 180 or by substitution we get
(5) a + (a + 15) + (a + 45) = 180 or
(6) a + a + 15 + a + 45 = 180 or
(7) 3*a + 60 = 180 or
(8) 3*a = 180 - 60 or
(9) 3*a = 120
Now divide both sides of (9) by 3 to get
(10) 3*a/3 = 120/3 or
(11) a = 40
Using (2) and (3) we get
(12) b = 40 + 15 or
(13) b = 55 and
(14) c = 40 + 45 or
(15) c = 55
Always check the answer. Use (4)
Is (40 + 55 + 85 = 180)?
Is (95 + 85 = 180)?
Is (180 = 180)? Yes
Question 1: To find volume the formula is Length× Width × height
So it would be 2 1/2× 6 × 3 1/2= 5 1/2
So the volume is 5 1/2
Question 2: You have to multiply 6 × 4 = 24
9514 1404 393
Answer:
- after 7 minutes
- 19,600 feet
Step-by-step explanation:
Here's the "pencil and paper" solution:
The two altitude equations are ...
- y = 41300 -3100x
- y = 2800x
They can be solved by setting the expressions for y equal to each other.
2800x = 41300 -3100x
5900x = 41300
x = 41300/5900 = 7
y = 2800·7 = 19600
The planes will both be at 19,600 feet after 7 minutes.
_____
Attached are solutions from a graphing calculator, and from a calculator app that is able to solve systems of equations.
I find the graphing calculator the easiest to use. I can enter equations using a keyboard, and the solution is displayed in a form that can be copied and pasted.
The calculator app on my phone requires equation entry using a small on-screen keyboard, with multiple key hits required to access some functions. (y is obtained by hitting the x key twice, for example.)
The "pencil and paper" solution is not so difficult, but requires a certain amount of writing (or good short-term memory). The solutions for x and y require separate calculations, whereas the other methods give both x and y at the same time.