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
It is given in the question that
You are buying a new printer and a new scanner for your computer and you cannot spend over $150. The printer you want costs $80.
Let the price of scanner be $ x .
So we have

Subtracting 80 from both sides

It means , the price should be not more then $70 .
Therefore in case, the price of scanner is $75, then you will not remain within your budget .
Answer:

Step-by-step explanation:

First, we must find the z-scores for each limit
for 54
z = (54 - 58) / 4 = -1
For this z-score, the area under the curve is 0.1587
for 62
z = (62 - 58) / 4 = 1
The area under the curve is 0.8413
Subtracting the two z-scores:
0.8413 - 0.1587 = 0.6825
Multiplying by 150
150 (0.6825) = 102.39
So, the closest answer is
102
Answer:
(x, y, z) = (-4, 29, 17)
Step-by-step explanation:
These three equations have a unique solution. If you want "z arbitrary", you need to write a system of two equations with three variables (or, equivalently, a set of dependent equations).
It is convenient to let a graphing calculator, scientific calculator, or web site solve these.
_____
You can reduce the system to two equations in y and z by ...
subtracting the last equation from the first:
3y -7z = -32
subtracting twice the last equation from the second:
3y -2z = 53
Subtracting the first of these from the second, you get ...
5z = 85
z = 17
The remaining variable values fall out:
y = (53+2z)/3 = 87/3 = 29
x = -9 +2z -y = -9 +2(17) -29 = -4
These equations have the solution (x, y, z) = (-4, 29, 17).