The rule of the function g (x) will be;
⇒ g (x) = - x + 3
What is mean by Translation?
A transformation that occurs when a figure is moved from one location to another location without changing its size or shape is called translation.
Given that;
g (x) is the indicated transformation of f (x).
The rule of f (x) is,
f (x) = - x + 5 ; horizontally translation 2 units left.
Now,
The rule of f (x) is,
f (x) = - x + 5 ; horizontally translation 2 units left.
Since, g (x) is the indicated transformation of f (x).
So, g (x) = f (x + 2)
Hence, We get;
g (x) = - (x + 2) + 5
= - x - 2 + 5
= - x + 3
Thus, The rule of the function g (x) will be;
⇒ g (x) = - x + 3
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<h3><u>The value of the greater number is 15.</u></h3><h3><u>The value of the smaller number is 7.</u></h3>
x = 2y + 1
3x = 5y + 10
Because we have a value for x we can plug this value in to find the value of y.
3(2y + 1) = 5y + 10
Distributive property.
6y + 3 = 5y + 10
Subtract 5y from both sides.
y + 3 = 10
Subtract 3 from both sides.
y = 7
We can plug this value back into the original equation to find the value of x.
x = 2(7) + 1
x = 15
If x^2+bx+16 has at least one real root, then the equation x^2+bx+16=0 has at least one solution. The discriminant of a quadratic equation is b^2-4ac and it determines the nature of the roots. If the discriminant is zero, there is exactly one distinct real root. If the discriminant is positive, there are exactly two roots. The discriminant of <span>x^2+bx+16=0 is b^2-4(1)(16). The inequality here gives the values of b where the discriminant will be positive or zero:
b^2-4(1)(16) ≥ 0
</span><span>b^2-64 ≥ 0
(b+8)(b-8) </span><span>≥ 0
The answer is that all possible values of b are in the interval (-inf, -8]∪[8,inf) because those are the intervals where </span>(b+8)(b-8) is positive.
