7. x=3 is the midpoint between the roots. The other root is x = 2*3 -(-5) = 11.
8a) f(x) = (x +3)^2 -49. The vertex is (-3, -49). The roots are -10, 4.
8b) y = (x+4)^2 -1. The vertex is (-4, -1). The roots are -5, -3.
8c) f(x) = 2(x +3)^2 -34. The vertex is (-3, -34). The roots are -3±√17.
Answer:
x=12
Step-by-step explanation:
The right side is a right triangle
The base is 1/2 of the bottom or 5
The height is x and the hypotenuse is 13
We can use the Pythagorean theorem
a^2 +b^2 = c^2
5^2 +x^2=13^2
25+x^2 = 169
Subtract 25 from each side
25-25+x^2 = 169-26
x^2 =144
Take the square root of each side
sqrt(x^2) = sqrt(144)
x= 12
Answer:
x = -.5
Step-by-step explanation:
x - 2.5 = -3
Add 2.5 to each side
x - 2.5+2.5 = -3+2.5
x = -.5
Answer:
8.550
Step-by-step explanation:
Answer: there are 5 more girls than boys.
Step-by-step explanation:
The ratio of boys to girls in a classroom is 5:6. The total ratio is the sum of the proportion. It becomes 5 + 6 = 11
If there are 55 students in total, it means that the number of boys in the class is
5/11 × 55 = 25 boys
Also, the number of girls in the class is
6/11 × 55 = 30 girls
Therefore, the difference between the number of girls and boys in the class is
30 - 25 = 5 girls
