A(4,2) to (X + 1, y - 5)
so
A' (5, -3)
then reflected across y-axis
A' (-5, -3)
a)A(4,2), point A is located in quadrant I
b)A'(5,-3), point A' is located in quadrant IV
c)A'(-5,-3), point A' is located in quadrant III
Answer:
599 general admission tickets were sold while 277 reserved seats admission tickets were sold
Step-by-step explanation:
Here, we want to know the number of each types of tickets sold.
Let the number of general admission ticket be x while the number of reserved seats ticket be y
Mathematically since the total of both tickets is 876;
then;
x + y = 876 ••••••••••••(i)
The total amount of money generated from general admission is cost of general admission ticket * the number of general admission tickets sold = $2.50 * x = $2.50x
The total amount of money generated from reserved seat admission tickets sales is cost of reserved seat admission ticket * the number of reserved seats admission ticket sold = $5 * y = $5y
Adding both gives $2882.50
Thus;
2.5x + 5y = 2882.5 •••••••••(ii)
Now, from i, let’s say x = 876 -y
Let’s insert this into ii
2.5(876-y) + 5y = 2882.5
2190 -2.5y + 5y = 2882.5
2190 + 2.5y = 2882.5
2.5y = 2882.5 - 2190
2.5y = 692.5
y = 692.5/2.5
y = 277
Recall;
x = 876 -y
Thus;
x = 876 - 277 = 599
Answer:
x = 3
This triangle ABC will be a right triangle as its sides obey the Pythagoras theorem.
Step-by-step explanation:
Let us assume that the triangle Δ ABC has vertices A(x,3), B(-3,-1) and C(-1,-4) and it is a right triangle.
We have to determine x.
Applying the Pythagoras Theorem,
AB² + BC² = AC² {If AC is the hypotenuse of the right triangle}
⇒ [(x + 3)² + 4²] + [(- 2)² + 3²} = (x + 1)² + 7²
⇒ x² + 6x + 38 = x² + 2x + 50
⇒ 4x = 12
⇒ x = 3 (Answer)
This triangle ABC will be a right triangle as its sides obey the Pythagoras theorem. (Answer)
<h2><u>
Answer with explanation</u>
:</h2>
Let p be the population proportion of parents who had children in grades K-12 were satisfied with the quality of education the students receive.
Set of hypothesis :
Confidence interval for population proportion is given by :-
, where
n= sample size
= sample proportion
and 
is the two-tailed z-value for confidence level (c).
As per given ,
Sample size of parents : n= 1085
Number of parents indicated that they were satisfied= 466
Sample proportion : 
Critical value for 90% confidence interval : 
( by z-value table)
Now, the 90% confidence interval :
Thus , the 90% confidence interval: (0.4043, 0.4537).
Since 0.43 lies in 90% confidence interval , it means we do not have enough evidence to reject the null hypothesis .
i.e. We are have no evidence that parents' attitudes toward the quality of education have changed.
Answer:
30 miles/1 hour is the unit rate.
Step-by-step explanation:
This is the unit rate because unit rates are a number over 1 unit. 30 miles/1 hour fulfills that, and the others are 2 and 3 hours.
