Answer:
16x² − 56x + 49
Step-by-step explanation:
The square of difference of two terms can be expressed as a perfect square trinomial in the following manner:
![(a-b)^{2}=a^{2}-2ab+b^{2}](https://tex.z-dn.net/?f=%28a-b%29%5E%7B2%7D%3Da%5E%7B2%7D-2ab%2Bb%5E%7B2%7D)
The symbol with square terms must be always positive. So this removes the first two options from the given choices. The correct option is either c or d.
Only the option d can be expressed as a perfect square as shown below:
![16x^{2}-56x+49\\\\ = (4x)^{2}-2(4x)(7)+(7)^{2}\\\\ =(4x - 7)^{2}](https://tex.z-dn.net/?f=16x%5E%7B2%7D-56x%2B49%5C%5C%5C%5C%20%3D%20%284x%29%5E%7B2%7D-2%284x%29%287%29%2B%287%29%5E%7B2%7D%5C%5C%5C%5C%20%3D%284x%20-%207%29%5E%7B2%7D)
Option c would have been correct if it was -30b instead of -15b i.e. the middle term is twice the product of first and second term.
So, option D is correct
(1 point) Consider the universal set U={1,2,3,4,5,6,7,8,9,10}, define the set A be the even numbers, the set B be the odd number
Sloan [31]
Answer:
a) AUC = {2,4,6,8,10}
b) BnC = {}
c) AnB = {}
d) B-C = B = {1,3,5,7,9}
Step-by-step explanation:
The set A is the even numbers, those that are divisible by two.
So A = {2,4,6,8,10}
B is the odd numbe.rs. An odd number is a number that is not divisible by two.
So B = {1,3,5,7,9}.
C = {4,5,6}, as the problem states
a) The union of sets is a set containing all elements that are in at least one of the sets. So the union of A and C is a set that contains all elements that are in at least one of A or C.
So AUC = {2,4,6,8,10}.
b) The intersection of two sets consists of all elements that in both sets. So, the intersection of B and C is the set that contains all elements that are in both B and C.
There are no elements that are in both B and C, so the intersection is an empty set
BnC = {}
c) Same explanation as b), there are no elements that are in both A and B, so another empty set.
AnB = {}
d) The difference of sets B and C consists of all elements that are in B and not in C. We already have in b) that BnC = {}, so:
B-C = B = {1,3,5,7,9}
x=smaller number
y=larger number
x+y=12
y=3x-6
Let's begin with the first equation...
x+y=12
Let's substitute...
x+(3x-6)=12
4x-6=12
Let's add 6 to both sides as we proceed to isolate x...
6+4x-6=12+6
4x=18
Let's divide both sides by 4...
(4x)/4=18/4
x=9/2=4.5---smaller number
12-4.5=7.5s larger number
3x + 2 = 2x + 7
Subtract 2 from both sides:
3x = 2x +5
Subtract 2x from both sides:
x = 5
Answer: x = 5
Juan is in the middle
<u>Explanation:</u>
Given:
Five students in total
_ _ _ _ _
Juan is not the shortest. So, Juan can be in 2nd, 3rd, 4th or 5th position.
_ J J J J
Tad is the tallest and not standing next to Juan, So,
_ J J _ T
Caroline is next to Tad. So,
_ J J C T
Juan is not standing next to Pamela. So,
P _ J C T
Marco is taller than Pamela. So,
P M J C T
The height is arranged in increasing order from Pamela to Tad.
Thus, from the series we can see that Juan is in the middle.