Answer:
Yes, twice
Step-by-step explanation:
The equation will intersect the x-axis when y = 0, so we have
x² - 4x = -3 now solve this quadratic for x...
x² - 4x + 3 = 0
factor...
(x - 3)(x - 1) = 0,
so at x = 1 and x = 3, the function crosses the x-axis
See the graph below
Answer:
Step-by-step explanation:
<u>Quadratic Function</u>
Standard Form of Quadratic Function
The standard representation of a quadratic function is:
where a,b, and c are constants.
When the zeros of f (x1 and x2) are given, it can be written as:
f(x)=a(x-x1)(x-x2)
Where a is a constant called the leading coefficient.
We are given the two roots of f: x1=-3 and x2=4, thus:
f(x)=a(x+3)(x-4)
We also know that f(5)=8, thus:
f(5)=a(5+3)(5-4)=8
Operating:
a(8)(1)=8
Solving:
a=1
The function is:
f(x)=1(x+3)(x-4)
Operating:
Answer:
Step-by-step explanation:
Given: ∠N≅∠S, line l bisects TR at Q.
To prove: ΔNQT≅ΔSQR
Proof:
From ΔNQT and ΔSQR
It is given that:
∠N≅∠S (Given)
∠NQT≅∠SQR(Vertical opposite angles)
and TQ≅QR ( Definition of segment bisector)
Thus, by AAS rule,
ΔNQT≅ΔSQR
Hence proved.
Statement Reason
1. ∠N≅∠S given
2. ∠NQT≅∠SQR Vertical angles are congruent
3. line l bisects TR at Q. given
4. TQ≅QR Definition of segment bisector
5. ΔNQT≅ΔSQR AAS theorem
Hence proved.
Thus, option D is correct.
Answer:
Measure of CIO = 30°
Measure of MAP = 150°
Complement of smaller angle = 60°
Step-by-step explanation:
Given that <CIO and <MAP are supplementary, therefore:
m<CIO + m<MAP = 180°
Let x be m<CIO
m<MAP = 5x
Thus:
x + 5x = 180
Solve for x
6x = 180
Divide both sides by 6
x = 30°
The smaller angle = m<CIO = x = 30°
The bigger angle = m<MAP) = 5x = 5(30) = 150°
Complement of the smaller angle = 90 - 30 = 60°
