Answer: The first option.
Step-by-step explanation:
This domain has no domain restrictions. Therefore, it covers all real numbers. x∈R
Answer:
Set builder notation: {a | a ≥ -21}
Interval notation: [-21, ∞)
Step-by-step explanation:
A set represents a collection of things, objects, or numbers. A set builder notation is in the form y = {x | x is an odd number between 8 and 10}, which means y contains all the odd numbers between 8 and 10.
Interval notation is a way to define a set of numbers between a lower limit and an upper limit using end-point values. for example (8, 20) means numbers between 8 and 20.
Given -3a-15≤-2a+6; solving :
-3a - 15 ≤ -2a + 6
-3a + 2a ≤ 6 + 15
-a ≤ 21
dividing through by -1:
a ≥ -21
The solution is:
Set builder notation: {a | a ≥ -21}
Interval notation: [-21, ∞)
Constant terms are just numbers (no x). The answer is 2
Answer:
the dimension of the box is : 8 by 5 by 3
Length = 8
Width = 5
Height = 3
Step-by-step explanation:
Let x,y and z represent the length, width and height of the box.
Given;
The length is 3 inches more than the width
x = y+3 .......1
the width is 2 inches more than the height
y = z + 2
z = y-2 .........2
Volume = length×width×height = xyz = 120 in^3
xyz = 120 ........3
Substituting equation 1 and 2 into 3
(y+3)×y ×(y-2) = 120
y(y^2+y-6) = 120
y^3 + y^2 - 6y - 120 = 0
Solving the polynomial equation we have;
y = 5
From equation 1;
x = y+3 = 5+3
x = 8
From equation 2;
z = y-2 = 5-2
z = 3
Therefore, the dimension of the box is
8 by 5 by 3
Length = 8
Width = 5
Height = 3
Answer:
Number of birds = 13
Explanation:
An animal shelter spends $1.50 per day to care for each bird and $3.50 per day to care for each cat.
Let the number of bird be 'a' and number of cat be 'b'.
Total money spent = 103.5
1.5 a + 3.5 b = 103.5 ------------------------equation 1
Total number of birds and cats = 37
a + b = 37 ------------------------equation 2
1.5 x equation 2
1.5 a + 1.5 b = 55.5 ------------------equation 3
equation 1 - equation 3
2 b = 103.5 - 55.5 = 48
b = 24
Substituting in equation 2
a = 37 - 24 = 13
Number of birds = 13, Number of cats = 24.
