If a quadratic equation has a discriminant that equals zero, which of the following statements is always true?
1 answer:
Answer:
d. The equation has one solution and there is not enough information to determine the direction of the parabola.
Step-by-step explanation:
For a general quadratic equation
y = ax² +bx +c
the solution is
The discriminant (D) is the part of the quadratic formula underneath the radical: b² - 4ac.
D tells us whether there are
- two different real solutions
- two identical real solutions ("one solution")
- two complex solutions.
If D= 0,
and there are two identical solutions ("one solution").
The direction of the parabola depends on the sign of a.
That information is not given, so we cannot determine the direction of the parabola.
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Answer:
12.53
Step-by-step explanation:
∠BCA = (180°-40°)/2 = 70°
Laws of Sines: CA/sin 40° = AB/sin 70° = 5/sin 70°
CA = 5/sin 70° * sin 40° = 3.40
area of semicircle CA = (3.1416 * 1.70²) / 2 = 4.54
By Heron's Formula, area of triangle ABC:
1/4 √(a+b+c) (a+b-c) (b+c-a) (c+a-b) = 1/4 * √13.4*3.4*3.4*6.6
= 7.99
Entire region area = 4.54 + 7.99 = 12.53
Answer:
d) $128.65
Step-by-step explanation:
The table format from the question can be properly expressed as :
Coefficients Standard Error t Statistic p value
Intercept 39.14942 22.30182 1.755436 0.109712
x 1.792312 0.407507 4.398234 0.001339
Source df SS MS F = 29.51443
Regression 1 16850.99 16850.99 19.34446 = 0.682478
Residual 9 7839.915 871.1017
Total 10 24690.91
For a rural household with $90,000 annual income, Abby's model predicts weekly grocery expenditure of:_________.
The estimated regression equation is as follows:
Expenditure (y) = 39.15 + 1.79 x
For a rural household with $90,000 annual income; the independent variables will assume the following values
x = 50
Thus; the estimated groceries expenditure is computed from the above regression equation by replacing the values of the independent variables;
This can be expressed as:
y = 39.15 + 1.79 (50)
y = 39.15 + 89.5
y = $128.65
Answer:
The degree of the polynomial is 9
Step-by-step explanation:
Recall that the degree of a polynomial is given by the degree of its leading term (the term with largest degree). Recall as well that the degree of a term is the maximum number of variables that appear in it.
So, let's examine each of the terms in the given polynomial, and count the number of variables they contain to find their individual degrees. then pick the one with maximum degree, and that its degree would give the actual degree of the entire polynomial.
1) term contains one variable "x" , one variable "y", and seven variables "z", so a total of nine. Then its degree is: 9
2) term contains three variables "x" , one variable "y", and four variables "z", so a total of eight. Then its degree is: 8
3) term contains three variables "x" and three variables "y", so a total of six variables. Then its degree is : 6
Therefore, the leading term of this polynomial is the first one, and it gives its degree to the entire polynomial. the polynomial is of degree 9.