What are the x-intercepts of the parabola represented by the equation y = 3x2 + 6x − 10
Answers
Answer:
x ≈ {-3.082, 1.082}
Step-by-step explanation:
I find the easiest way to answer such a question (with medium accuracy) is to use a graphing calculator. The graph shown in the attachment gives the answers listed above.
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From vertex form
The graphing calculator also makes it easy to find the vertex of the parabola. If we divide by 3 so the scale factor is 1, then the y-value of the vertex is -13/3 and the vertex form of the equation can be written ...
... y = (x +1)² -13/3
This has x-intercepts easily found.
... 0 = (x +1)² -13/3 . . . . x-intercepts are where y=0
... (x +1)² = 13/3 . . . . . . . add 13/3
... x +1 = ±√(13/3) . . . . . take the square root
... x = -1 ±√(13/3) . . . . . subtract 1
... x ≈ {-3.0816660, 1.0816660}
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Using the quadratic formula
This equation has a=3, b=6, c=-10, so we can put these values into the quadratic formula to find the x-interecepts.
... x = (-b±√(b²-4ac))/(2a)
... x = (-6 ±√(6² -4(3)(-10)))/(2(3))
... x = (-6 ±√156)/6 = -1 ±√(13/3) . . . or . . . -1 ±(√39)/3
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Which number(s) below belong to the solution set of the inequality? Check all that apply. 9x 117A. 12 B. 14 C. 19 D. 13 E. 6 F. 8
B. All real numbers
C. All real numbers between -6 and -1 & -1 and 2
D. All real numbers between -8 and 4
Answers
I think that it's D because the y-values go from 4 and end at -8
Answers
Answer:
0.6%
Step-by-step explanation:
We have a standard deck of 52 playing cards, which is made up of 13 cards of each type (hearts, diamonds, spades, clubs)
Therefore there are one nine hearts, one nine diamonds, one nine spades and one nine clubs, that is to say that in total there are 4. Therefore the probability of drawing a nine is:
4/52
In the second card it is the same, an eight, that is, there are 4 eight cards, but there is already one less card in the whole deck, since it is not replaced, therefore the probability is:
4/51
So the final probability would be:
(4/52) * (4/51) = 0.006
Which means that the probability of the event is 0.6%
Answers
Let's solve the inequality
Therefore the solution of the inequality is the set:
Solve for t: 5t - 4 = 11
Answers
Answer:
t=3
Step-by-step explanation:
5t-4=|11
+4 |+4
5t= | 15
÷5 | ÷5
t = 3
Answers
Answer:
Positive 233
Step-by-step explanation:
7300-3280-2620-1167(14000/12)=233.
39.25 square inches
314 square inches
157 square inches
Answers
274.75 square inches of pizza are remaining. Option A is the correct option.
What is π in math?
The ratio of a circle's diameter to its circumference, or "pi," is a mathematical constant that is roughly equal to 3.14159 (/pa/; also written as "pi"). Numerous mathematical and physics formulas contain the number. It is an irrational number, meaning that although fractions like 22/7 are frequently used to approximate it, it cannot be expressed exactly as a ratio of two integers.
Given that, the diameter of large pizza is 20 inches.
The radius of a circular shape is half of the diameter.
The radius of the pizza is (20 inches)/2 = 10 inches.
Area of a circular shape is ∏r² .
The area of the pizza is 3.14×10² = 314 in²
The total part of the pizza is considered as 1.
One-eighth of the pizza is eaten, and the remaining portion is (1-1/8) = 7/8.
The area of remaining pizza is
314 in² × (7/8)
= 274.75 square inches
To learn more about area of a circular shape click on the below link:
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