By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
<h3>How to determine the missing coefficients of a quartic equation</h3>
A value x is a root of a polynomial if and only if p(x) = 0. We must replace the given equation with the given roots and solve the resulting system of <em>linear</em> equations:
(- 1)⁴ - 5 · (- 1)³ - 7 · (- 1)² + (- 1) · c + d = 0
- c + d = 1 (1)
3⁴ - 5 · 3³ - 7 · 3² + 3 · c + d = 0
3 · c + d = 117 (2)
The solution of this system is c = 29 and d = 30.
By concepts of polynomials and systems of linear equations, the constants c and d of the expression p(x) = x⁴ - 5 · x³ - 7 · x² + c · x + d are 29 and 30.
To learn more on polynomials: brainly.com/question/11536910
#SPJ1
The sine has a range -1 to +1 so y goes from 1+2(-1) to 1+2(1) = -1 to 3
Range: -1 ≤ y ≤ 3
Answer:
The correct options are;
D. Triangles ABC and A'B'C' are congruent
E. Angle ABC is congruent to angle A'B'C'
F. Segment BC is congruent to segment B'C'
H. Segment AQ is congruent to segment A'Q'
Step-by-step explanation:
The given information are;
The angle of rotation of triangle ABC = 60°
Therefore, given that a rotation of a geometric figure about a point on the coordinate plane is a form of rigid transformation, we have;
1) The length of the sides of the figure of the preimage and the image are congruent
Therefore;
BC ≅ B'C'
2) The angles formed by the sides of the preimage are congruent to the angles formed by the corresponding sides of the image
Therefore;
∠ABC ≅ ∠A'B'C'
3) The distances of the points on the figure of the preimage from the coordinates of the point of rotation are equal to the distances of the points on the figure of the image from the coordinates of the point of rotation
Therefore;
Segment AQ ≅ A'Q'.
Answer:
I(x)=x+1
Step-by-step explanation:
Answer:
160 Seconds or 2 minutes and 45 seconds
Step-by-step explanation: So 6.4x25=160 seconds or 2 min 45 sec
