Answer: a = 4
Step-by-step explanation: Area of a triangle is calculated as: 
.
The triangle formed by the parabola has base (b) equal to the distance between the points where the graph touches x-axis and height (h) is the point where graph touches the y-axis.
The points on the x-axis are the roots of the quadratic equation:
a(x-3)(x+2)=0
(x-3)(x+2)=0
x - 3 = 0
x = 3
or
x + 2 = 0
x = -2
So, base is the distance between (-2,0) and (3,0).
Since they are in the same coordinate, distance will be:
b = 3 - (-2)
b = 5
Area of the triangle is 10. So constant a is
5a = 10.2
a = 4
The constant a of the function y = a(x-3)(x+2) is 4.
The number of salads Ishaan and his friends can afford is 6 salads.
<h3>What are Word Problems?</h3>
Word Problems in mathematics involve crucial understanding and the use of variables and arithmetic operations to solve real-life cases.
From the given information;
- The total amount with Ishaan and his friends = $40
- If they decided to spend the money on salad(x) and one salad(x) cost = $6
Thus, the number of salads they can purchase is:
x = 6 salads remaining $4
Therefore, we can conclude that the number of salads they can purchase with $40 is 6 salads with a remaining amount of $4.
Learn more about word problems here:
brainly.com/question/21405634
Answer:
Example: A four-sided shape has two adjacent sides with lengths of 4 meters. You can find the area of this square by multiplying its base times its height: 4 × 4 = 16 square meters. Example: A square's diagonals are both equal to 10 centimeters.
Answer:
The probability that a product is defective is 0.2733.
Step-by-step explanation:
A product consists of 3 parts. If any one of the part is defective the whole product is considered as defective.
The probability of the 3 parts being defective are:
P (Part 1 is defective) = 0.05
P (part 2 is defective) = 0.10 P (part 3 is defective) = 0.15
Compute the probability that a product is defective as follows:
P (Defective product) = 1 - P (non-defective product)
= 1 - P (None of the 3 parts are defective)
= 1 - P (Part 1 not defective) × P (Part 2 not defective) × P (Part 1 not defective)
![=1-[(1-0.05)\times(1-0.10)\times (1-0.15)]\\=1-[0.95\times0.90\times0.85]\\=1-0.72675\\=0.27325\\\approx0.2733](https://tex.z-dn.net/?f=%3D1-%5B%281-0.05%29%5Ctimes%281-0.10%29%5Ctimes%20%281-0.15%29%5D%5C%5C%3D1-%5B0.95%5Ctimes0.90%5Ctimes0.85%5D%5C%5C%3D1-0.72675%5C%5C%3D0.27325%5C%5C%5Capprox0.2733)
Thus, the probability that a product is defective is 0.2733.
Answers:
Functions
- y = -x+11
- y = 2x^2-6x+4
- y = -7
Not functions
- x = 3
- x^2+y^2 = 81
- y^2 = -5x-12
=======================================================
Explanation:
A function is possible if and only if any given x input leads to exactly one y output.
For something like x^2+y^2 = 81, we can see that x = 0 leads to either y = 9 or y = -9. So this would <u>not</u> be a function. We would need x to pair with only y value to have it be a function.
We have the same thing going on with y^2 = -5x-12 as well.
For anything of the form x = k, where k is any real number, this is also not a function. We have one single input only and it leads to infinitely many outputs. So in a sense, this is even worse compared to the other examples.
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In summary, we have these three non-functions:
- x = 3
- x^2+y^2 = 81
- y^2 = -5x-12
Everything else is a function. You can use the vertical line test as a visual way to check.
