What is the domain of: -9(x-2)^2+116

Let Q(x, y) be the predicate "If x < y then x2 < y2," with domain for both x and y being R, the set of all real numbers.

Levart [38]

Answer:

a) Q(-2,1) is false

b) Q(-5,2) is false

c)Q(3,8) is true

d)Q(9,10) is true

Step-by-step explanation:

Given data is $Q(x,y)$ is predicate that $x$ then $x^{2}$ . where $x,y$ are rational numbers.

a)

when $x=-2, y=1$

Here $-2$ that is $x$ satisfied. Then

$(-2)^{2}$

$4$ this is wrong. since $4>1$

That is $x^{2}$ $>y^{2}$ Thus $Q(x,y)$ $=Q(-2,1)$ is false.

b)

Assume $Q(x,y)=Q(-5,2)$ .

That is $x=-5, y=2$

Here $-5$ that is $x$ this condition is satisfied.

Then

$(-5)^{2}$

$25$ this is not true. since $25>4$ .

This is similar to the truth value of part (a).

Since in both $x$ satisfied and $x^{2} >y^{2}$ for both the points.

c)

if $Q(x,y)=Q(3,8)$ that is $x=3$ and $y=8$

Here $3$ this satisfies the condition $x$ .

Then $3^{2}$

$9$ This also satisfies the condition $x^{2}$ .

Hence $Q(3,8)$ exists and it is true.

d)

Assume $Q(x,y)=Q(9,10)$

Here $9$ satisfies the condition $x$

Then $9^{2}$

$81$ satisfies the condition $x^{2}$ .

Thus, $Q(9,10)$ point exists and it is true. This satisfies the same values as in part (c)

6 0

2 years ago

Venus Waldo reviewed her account statement and wanted to verify that the interest amount was correct. Her new balance was $12,09

user100 [1]

Answer:

The interest on the savings account is $46.47

Step-by-step explanation:

Here, we want to know the interest earned on the savings account.

The difference between the new and previous balance will be; 12,098.12 - 9,053.20 = $3,044.92

The difference between amount deposited and amount withdrawn is 3,298.45 - 300 = 2,998.45

This is the amount that is supposed to be on the account without interest

So the interest earned would be; 3044.92 - 2,998.45 = $46.47

3 0

2 years ago

Suppose n(x)= 22 and n(y) is 13 what is the maximum number of elements X ∪Y can have ?

Nikolay [14]

The inclusion/exclusion principle states that

$|X\cup Y|=|X|+|Y|-|X\cap Y|$

That is, the union has as many members as the sum of the number of members of the individual sets, minus the number of elements contained in both sets (to avoid double-counting).

Therefore, $|X\cup Y|$ will have the most elements when the sets $X$ and $Y$ are disjoint, i.e. $X\cap Y=\emptyset$ , which would mean the most we can can in this case would be

$|X\cup Y|=|X|+|Y|=22+13=35$

(Note that $n(X)=|X|$ denotes the cardinality of the set $X$ .)

3 0

3 years ago

Which statement can be used to fill in the blank space?

liberstina [14]

If we draw a diagonal which will also be a transversal DB, then we get ∠ADB is congruent to ∠CBD by Alternate interior angles.

It will be the first option.

7 0

2 years ago

Zachary sold 1/2 of a 40-acre lot. He then sold 3/5 of the remaining lot. What fraction of the land did he sell in all? (Write t

Mazyrski [523]

4/5 acres of the land were sold.
40* 1/2 = 20
20* 3/5 = 12
12+20= 32
32/40 = 4/5 simplified

4 0

2 years ago