Given the function f(x) = x3 − 18x2 + 107x − 210, what are the y-intercept and x-intercepts? Show the work steps to find these intercepts
Answers
Answer:
The y-intercept of the function is -210 and the x-intercepts of the function are 5,6,7.
Step-by-step explanation:
The given function is
To find y-intercept put x=0.
The y-intercept of the function is -210.
To find the x intercepts put f(x)=0.
For x=5, the above equation is true, therefore (x-5) is factor of the equation.
Use synthetic method to find the factors.
Use zero product property and equate each factor equal to zero.
Therefore the x-intercepts are 5, 6 and 7.
Related Questions
Work out the value of x in this quadrilateral.
If you pay $8.50 per square yard of carpeting, what is your total cost for 27.5 square yards?a. $233.75 b. $223.75 c. $228.75 d. $232.75
What is -4x+8=48 what is x
If g(x) is the inverse of f(x)=4x+12 and f(x)=, what is g(x)
Answers
g(f(x))
= 6((x^2) - 5)
= (6x^2) - 30
so its equal to
(6x^2) - 30
Answers
Answers
Answer:
Step-by-step explanation:
As a rule, the "simplified form" means there are no fractions under a radical.
Answer:
D on Edge
Step By Step Explination:
I did the test
Answers
Answer:
Alaina got 4, Miguel got 2(4) = 8 while Kira got 2(8) = 16
Step-by-step explanation:
Let the number he gave to Alaina be x. Now, we know he gave twice as many to Miguel. Amount received by Miguel is 2x.
He gave Kira 2 times what he gave Miguel, that is 2x * 2 = 4x
Addition of all these equals 28. We now get x
4x + 2x + x = 28
7x = 28
X = 28/7
x = 4
Alaina got 4, Miguel got 2(4) = 8 while Kira got 2(8) = 16
The average rate of change of f(t) from t = 2 to t = 6 is ______ thousand owners per year
Answers
f(6) = 0.25*(6^2) -.5*(6) +3.5 = 9-3+3.5 = 9.5
average rate of change = [f(6) - f(2)]/ (6-2)
= (9.5-3.5)/4 = 6/4 = 1.5
Answer:
it would be 1.5
Step-by-step explanation:
Answers
Answer: The option is D.
Step-by-step explanation:
A line that intersects another line segment and separates it into two equal parts is called a bisector.
In a quadrangle, the line connecting two opposite corners is called a diagonal. We will show that in a parallelogram, each diagonal bisects the other diagonal.
Problem
ABCD is a parallelogram, and AC and BD are its two diagonals. Show that AO = OC and that BO = OD
Strategy
Once again, since we are trying to show line segments are equal, we will use congruent triangles. And here, the triangles practically present themselves. Let’s start with showing that AO is equal in length to OC, by using the two triangles in which AO and OC are sides: ΔAOD and ΔCOB.
There are all sorts of equal angles here that we can use. Several pairs of (equal) vertical angles, and several pairs of alternating angles created by a transversal line intersecting two parallel lines. So finding equal angles is not a problem. But we need at least one side, in addition to the angles, to show congruency.
As we have already proven, the opposite sides of a parallelogram are equal in size, giving us our needed side.
Once we show that ΔAOD and ΔCOB are congruent, we will have the proof needed, not just for AO=OC, but for both diagonals, since BO and OD are alsocorresponding sides of these same congruent triangles.
ABCD is a parallelogram
Given
AD || BC
From the definition of a parallelogram
AD = BC Opposite sides of a parallelogram are equal in size
∠OBC ≅ ∠ODA Alternate Interior Angles Theorem, ∠OCB ≅ ∠OAD Alternate Interior Angles Theorem,
ΔOBC ≅ ΔODA
Angle-Side-Angle
BO=OD Corresponding sides in congruent triangles AO=OC Corresponding sides in congruent triangles.
Final answer:
The correct statement about parallelograms is that their diagonals always bisect each other. Opposite angles in a parallelogram are congruent and, while a parallelogram has two pairs of parallel sides, these sides are not necessarily congruent.
Explanation:
In answering your question, which of the following is true about a parallelogram? It's important to understand some key properties of parallelograms. The statement 'D. The diagonals of a parallelogram always bisect each other' is the correct one. In simple terms, this means that the diagonals of a parallelogram always cut each other exactly in half. By contrast, 'A. Opposite angles of a parallelogram are not congruent' is incorrect, because in a parallelogram, opposite angles are indeed congruent. 'B. Parallelograms always have four congruent sides' and 'C. Only two sides of a parallelogram are parallel' are also incorrect, because while a parallelogram does have two pairs of parallel sides, these sides are not necessarily congruent.
Learn more about Parallelogram Properties here:
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