A
Given a quadratic in standard form : y = ax² + bx + c ( a ≠ 0 ), then
The x-coordinate of the vertex is
= - 
y = - 3x² + 2x - 7 is in standard form
with a = - 3, b = 2 and c = - 7, hence
= - 
= 
Substitute this value into the equation for y-coordinate
y = - 3 ()² + 2 ( ) - 7
= - + 
- 
= - 
vertex = ( , - ) → A
Answer:
They buy 6 hotdogs and 5 popcorn
Step-by-step explanation:
Assume that they buy x hotdogs and y popcorn
∵ They buy a total of 11 hotdogs and popcorn
∵ The number of hotdogs is x and the number of popcorn is y
∴ x + y = 11 ⇒ (1)
∵ Hot dogs cost $2.50 each
∵ Popcorn costs $1.00 each
∵ They spend $20 on hot dogs and popcorn
→ Multiply x by 2.5 and y by 1, add the products and equate the sum by 20
∴ 2.5(x) + 1(y) = 20
∴ 2.5x + y = 20 ⇒ (2)
Now we have a system of equations to solve it
→ Subtract equation (1) from equation (2)
∵ (2.5x - x) + (y - y) = (20 - 11)
∴ 1.5x + 0 = 9
∴ 1.5x = 9
→ Divide both sides by 1.5 to find x
∴ x = 6
→ Substitute the value of x in equation (1) to find y
∵ 6 + y = 11
→ Subtract 6 from both sides
∴ 6 - 6 + y = 11 - 6
∴ y = 5
∴ They buy 6 hotdogs and 5 popcorn
Answer:
1 < x < 7.5
Step-by-step explanation:
This problem can be solved using given below property of triangle.
Sum of two sides is always greater than third side of triangle.
Difference of two sides is always lesser than third side of triangle.
_______________________________________________
Given
sides length
6.5 units
3.5 units
Third side is 2.5 + x
using the property, Sum of two sides is always greater than third side of triangle.
6.5 + 3.5 > 2.5 +x
=>10 >2.5 + x
=>2.5 + x< 10
=> x< 10 -2.5
=> x < 7.5
using the property, Difference of two sides is always lesser than third side of triangle.
6.5 - 3.5 > 2.5 +x
=>3.5 > 2.5 +x
=> 2.5 +x > 3.5
=> x > 3.5 - 2.5
=> x > 1
combining both we have
1 < x < 7.5
out of the given option none is 1 < x < 7.5
hence, correct answer will be 1 < x < 7.5 and wrong option can be claimed by student.
Answer: i guess the problem is with P(x) => "x = 
", then P(x) is true if that equality is true, and is false if the equality is false.
so lets see case for case.
a) x = 0, and 
= 0. So p(0) is true.
b) x = 1 and 
= 1, so P(1) is true.
c) x = 2, and 
= 4, and 2 ≠ 4, then P(2) is false.
d) x= -1 and = 1, and 1 ≠ -1, so P(-1) is false.
Answer:
root 25
Step-by-step explanation:
root 25 is 5, and every other number may not be able to be written as a whole number (please give brainliest)
