Answer:
a. x = 82 degrees
b. All angles less than 90 degrees are 65 degrees and 33 degrees and 82 degrees in an acute triangle.
Step-by-step explanation:
A triangle has to equal to 180 degrees, add 65 and 33 together to get 98 degrees, subtract 180 from 98 to get 82 degrees. Part B is self explanatory.
This is an Arithmetic Progression with 1st term 11 and common difference d=6
Number of Rows Number of seats Common difference " d"
----------------------- ----------------------- -------------------------------------
1st a₁ = 11
2nd a₁+d =17 d =2nd - 1st = 6
3rd a₁ +2d = 23 d =3rd - 2nd = 6
4th a₁ +3d = 29 d= 4th - 3rd = 6
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nth ROW a(n) = a₁ + (n-1)d
18th ROW a₁₈ = 11 + (18-1).6 = 11+(17)(6) = 113
General equation to predict the number of seat an the nth row:
Number of seats in nth row = a₁ + (n-1).d
Answer:
The solution is (3 , 1)
Step-by-step explanation:
To solve the system of the equation you can use the elimination method or substitution method.
We will use the substitution method
From the first equation x + 2y = 5⇒get x = 5 - 2y
In the second equation 3x + 5y = 14⇒we will substitute x by 5 - 2y
3(5 - 2y) + 5y =14
15 - 6y + 5y = 14
-6y + 5y = 14 - 15
-y = -1
y = 1
Substitute the value of y in x = 5 - 2y
x = 5 - 2(1) = 5 -2 =3
∴ The solution of the system of equations is (3 , 1)
Answer: 
Step-by-step explanation:
Let be "x" the height inches (in the model) of a 84 foot building.
According to the information provided in the exercise, we know that the height of a two-story building is 21 feet and in the scale model its height is 3 inches.
Knowing this, we can set up the following proportion:
The final step is to solve for "x" in order to calculate its value. We get that this is:
Therefore, an 84 foot building will be 12 inches tall in the model.
Consider this option:
1. if the point (4;6) is the centre of the circle and the point (2;5) is the first endpoint of its diameter, then point (4;6) is the middle point of the diameter (it means that is the middle between the 1st and the 2d endpoints of diameter).
2. using the property described above:
for x of the 2d endpoint of the diameter: x=4*2-2=6;
for y of the 2d endpoint of the diameter: y=6*2-5=7.
answer: (6;7)
