There are 5 solutions for this system.
x^2 + 4y^2 = 100 ____1
4y - x^2 = -20 ____2
Add both 1 & 2 together. x^2 gets cancelled
4y^2 + 4y = 80 (send 80 to the other side and divide by 4)
Then equation the becomes : y^2 + y -20 =0
Now factorise the equation: (y+5) (y-4) = 0
Solve for y : y = -5 and y = 4
Using the values of y to find the values of x. From equation 1:
x^2 = 100 - 4y^2 x = /100 - 4y^2 (/ means square root) Replace values of y
y = -5, x = /100 - 4(-5)^2 = /100 - 100 = 0
y = 4, x = /100 - 4(4)^2 = / 100 - 64 = /36 = -6 or 6
Thus we have 6 solutions y = -5, 4 and x = -6, 0, 6
Answer:
I think 8
Step-by-step explanation:
9/2 and 5/8
here 8 is the LCM.
so, 9/2 × 4/4
5/8 × 1/1
which gives: 36/8 and 5/8
Answer:
14 glue bottles.
Step-by-step explanation:
Let's use a ratio:
sticks : bottles
5 : 2
35 : 14
There are 14 glue bottles in the classroom.
The domain and the range for the relations are given as follows:
- 13. Domain x ∈ R, range y ∈ R.
- 14. Domain {x ∈ Z| -4 ≤ x ≤ 4 and x is even} , range y ∈ {y ∈ Z| -1 ≤ y ≤ 4}.
- 15. Domain {x ∈ Z| -4 ≤ x ≤ 1} , range y ∈ {y ∈ Z| -4 ≤ y ≤ 1}.
- 16. Domain x ∈ R, range y ∈ R.
<h3>What are the domain and range of a function?</h3>
- The domain of a function is the set that contains all possible input values. Hence, in a graph, the domain is given by the values of x.
- The range of a function is the set that contains all possible output values. Hence, in a graph, the domain is given by the values of y.
For items 13 and 16, the functions are continuous, hence it is over the real numbers, and both the domain and range are all real values.
For items 14 and 15, the functions are discrete, hence it is over the integer numbers, and the domain is composed by the values assumed by x and the range is composed by the values assumed by y.
More can be learned about domain and range at brainly.com/question/10197594
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