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Thepotemich [5.8K]
3 years ago
8

Please help asap 27pts

Mathematics
1 answer:
mart [117]3 years ago
6 0

7x\geq-56\qquad|\text{divide both sides by 7}\\\\x\geq-8\\-------------------------------\\9x < 54\qquad|\text{divide both sides by 9}\\\\x < 6\\\\Answer:\ d)\ -8\leq x < 6

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Determine each of the following.
castortr0y [4]

Answer:

(a) \{1,2,3,4,5,6,7,8,9,10\}

(b) 10

(c) \{\}

(d) 0

(e) 1024

Step-by-step explanation:

(a)

A = {x ∈ Z | 0 < x, x² ≤ 100}

We need to find all the elements of given set.

The given conditions are

0                ... (1)

x^2\leq 100

Taking square root on both sides.

-\sqrt{100}\leq x\leq \sqrt{100}

-10\leq x\leq 10             .... (2)

Using (1) and (2) we get

0

Since x ∈ Z,

A=\{1,2,3,4,5,6,7,8,9,10\}

(b)

We need to find the value of  | {x ∈ Z | 0 < x, x² ≤ 100}| or |A|. It means have to find the number of elements in set A.

|A|=10

| {x ∈ Z | 0 < x, x² ≤ 100}| = 10

(c)

B = {x ∈ Z | x > 10, x² ≤ 100}

We need to find all the elements of given set.

The given conditions are

x>10                ... (3)

x^2\leq 100

It means

-10\leq x\leq 10             .... (4)

Inequality (3) and (4) have no common solution, so B is null set or empty set.

B=\{\}

(d)

We need to find the value of |{x ∈ Z | x > 10, x² ≤ 100}| or |B|. It means have to find the number of elements in set B.

|B|=0

|{x ∈ Z | x > 10, x² ≤ 100}| = 0

(e)

We need to find the value of | P(A) |. P(A) is the power set of set A.

Number of elements of a power set is

N=2^n

where, n is the number of elements of set A.

We know that the number of elements of set is 10. So the value of |P(A)| is

|P(A)|=2^{10}

|P(A)|=1024

Therefore |P(A)|=1024.

7 0
3 years ago
Expand the following 5(2x-4)
Yuliya22 [10]

Answer:

x= 2

Step-by-step explanation:

5*2= 10 then add the x at the end

5*4=20

then you divide both sides by 10

(10x/10)- (20/10)

x= 2

or if your rewriting it then:

(5*2x)- (5*4)=?

Hope this helped :D

8 0
3 years ago
What is the total amount and the amount of interest earned on $5,000 at 8% for 20 years? Total Amount Interest Amount compounded
Lina20 [59]

Answer:

final balance = 24,634.02

compound interest = 19,634.02

Step-by-step explanation:

3 0
3 years ago
Of the dogs at the dog show,
Olin [163]
So, let's say that all the dogs had a number of x.

then 1/12 x were the Hound Group dogs.

then, out of the Hound Group,, that is 1/12 x, 3/10 were English Foxhounds.

For this, we need to multiply the fractions:

\frac{1}{12}x* \frac{3}{10} = \frac{3}{120}x =\frac{1}{40}x

so of all the dogs at the show, the English Foxhunds were a 1/40 fraction,  
5 0
3 years ago
Read 2 more answers
LAM
Serggg [28]

Answer:

gduduufufj jeuyeyrhfi garewhkod ishstdkgo

3 0
2 years ago
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