5x+3y=15 <br> solve for y

Suppose that X is a subset of Y. Let p be the proposition ‘x is an element ofX’ and let q be the proposition ‘x is an element of

Genrish500 [490]

Answer:

See answer below

Step-by-step explanation:

The statement ‘x is an element of Y \X’ means, by definition of set difference, that "x is and element of Y and x is not an element of X", WIth the propositions given, we can rewrite this as "p∧¬q". Let us prove the identities given using the definitions of intersection, union, difference and complement. We will prove them by showing that the sets in both sides of the equation have the same elements.

i) x∈AnB if and only (if and only if means that both implications hold) x∈A and x∈B if and only if x∈A and x∉B^c (because B^c is the set of all elements that do not belong to X) if and only if x∈A\B^c. Then, if x∈AnB then x∈A\B^c, and if x∈A\B^c then x∈AnB. Thus both sets are equal.

ii) (I will abbreviate "if and only if" as "iff")

x∈A∪(B\A) iff x∈A or x∈B\A iff x∈A or x∈B and x∉A iff x∈A or x∈B (this is because if x∈B and x∈A then x∈A, so no elements are lost when we forget about the condition x∉A) iff x∈A∪B.

iii) x∈A\(B U C) iff x∈A and x∉B∪C iff x∈A and x∉B and x∉C (if x∈B or x∈C then x∈B∪C thus we cannot have any of those two options). iff x∈A and x∉B and x∈A and x∉C iff x∈(A\B) and x∈(A\B) iff x∈ (A\B) n (A\C).

iv) x∈A\(B ∩ C) iff x∈A and x∉B∩C iff x∈A and x∉B or x∉C (if x∈B and x∈C then x∈B∩C thus one of these two must be false) iff x∈A and x∉B or x∈A and x∉C iff x∈(A\B) or x∈(A\B) iff x∈ (A\B) ∪ (A\C).

8 0

3 years ago

Solve the system of linear equations below. Enter your solution as an ordered pair (x,y). Do not include spaces in your answer..

kotykmax [81]

Y=3
4x+y=19
4x+3=19
4x=19-3
4x=16
x=4

pair is 4,3

5 0

3 years ago

Read 2 more answers

What are the solutions to the nonlinear system of equations below?

Sonbull [250]

Substitute y=4x to the second equation:

x^2 + (4x)^2 = 17
x^2 + 16x^2 = 17
17x^2 = 17
x^2 = 17/17
x^2 = 1
x = 1 and -1

When x=1, y=4(1) = 4
When x=-1, y=4(-1) = -4

Thus the solutions would be (1,4) and (-1,-4). That would correspond to D. and A.

5 0

3 years ago

Ilona is at a friend's home that is several miles from her home. She starts walking at a constant rate in a straight line toward

larisa [96]

Complete question is;

Ilona is at a friends home that is several miles from her home. She starts walking at a constant rate in a straight line toward her home.

The expression -2t + 10 gives the distance, in miles, that Ilona is from her home after t hours. Select True or False for each of the following.

1. The friends home is 10 miles from Ilonas home

2. The distance Ilona has walked away from her friends home after t hours is given by the absolute value of -2t

3.The negative sign in the term indicates that Ilona is walking toward her home

4. Ilona is walking at a rate of 10 miles per hour

Answer:

Statements 1 & 2 are correct.

Step-by-step explanation:

We are told that the expression -2t + 10 gives the distance, in miles, that Ilona is from her home after t hours.

Now, we know that distance = speed x time

Now, from the expression -2t + 10

It's clear that 2t is a distance value.

This means that the speed used in going home is 2 miles/hr

This means that at t hours, she has walked 2t miles from her friends home.

Thus, statement 2 is true because an absolute value of -2t will be 2t.

Since 2t is subtracted from 10 in the expression and 2t is the distance she has walked from her friends house at Time, t. It means that 10 miles is the distance from her friends house to her house.

Thus, statement 1 is also true

7 0

2 years ago

PLEASE ANSWER ASAP! 25 POINTS!

Bess [88]

Answer:

Burgers: 12

French Fries: 34

Step-by-step explanation:

6 0

3 years ago

5x+3y=15 solve for y