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3 years ago

What is the solution to the compound inequality 3x-8 less than or equal to -5 or 2x - 7 > 5

Mathematics

1 answer:

Svetllana [295]3 years ago

7 0

Answer:

The solution for the compound inequality = ∅

Step-by-step explanation:

The given inequality:

3x - 8 ≤ -5 & 2x - 7 > 5

<u>For the inequality 3x - 8 ≤ -5</u>

3x - 8 ≤ -5 add 8 to both sides

3x ≤ 3 divide both side by 3

x ≤ 1

So, the solution of the inequality 3x - 8 ≤ -5 ⇒ x ∈ (-∞ , 1]

<u>For the inequality 2x - 7 > 5</u>

2x - 7 > 5 add 7 to both sides

2x > 12 divide both sides 2

x > 6

So, the solution of the inequality 2x - 7 > 5 ⇒ x ∈ (6 , ∞)

The solution for the compound inequality will be:

(-∞ , 1] ∩ (6 , ∞) = ∅

See the attached figure.

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Verify a÷(b+c)not equal(a÷b)+a÷c for each of the following values of a, b and c

just olya [345]

Answer:

a) and b) satisfied the condition of the given equation.

Step-by-step explanation:

Given: $\frac{a}{(b + c)}$ ≠ $\frac{a}{b}$ + $\frac{a}{c}$

Then,

$\frac{a}{(b + c)}$ ≠ $\frac{(ac + ab)}{bc}$

a) For a = 21, b = 4 and c = -2, then we have;

$\frac{21}{(4 + (-2))}$ ≠ $\frac{(21*-2 + 21*4)}{4*-2}$

$\frac{21}{4 - 2}$ ≠ $\frac{(-42 + 84)}{-8}$

$\frac{21}{2}$ ≠ $\frac{42}{-8}$

$\frac{21}{2}$ ≠ $-\frac{21}{4}$

Therefore the condition of the given equation is satisfied.

b) For a = 1, b = 10 and c = 1, then we have:

$\frac{1}{(10 + 1)}$ ≠ $\frac{(1*1 + 1*10)}{10*1}$

$\frac{1}{11}$ ≠ $\frac{(1 + 10)}{10}$

$\frac{1}{11}$ ≠ $\frac{11}{10}$

Therefore the condition of the given equation is satisfied.

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3 years ago

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3 years ago

carl takes a random sample of 100 students in his school and finds that 72% of the sample prefers pizza over burgers. there are

Sonbull [250]

For every 100 students, 72 prefer pizza.
The are 15 groups of 100 students each amongst 1500 students;
The total number of students preferring pizza then is;
15*72= 1080

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3 years ago

Read 2 more answers

JIM'S BACKYARD IS A RECTANGLE THAT IS 15 5/6 YARDS LONG AND 10 2/5 YARDS WIDE. JIM BUYS SOD IN PIECES THAT ARE 1 1/3 YARDS LONG

Stolb23 [73]

Jim's backyard:
15 5/6 yd long
10 2/5 yd wide

Sod pieced:
1 1/3 yd long
1 1/3 yd wide

Area of backyard:
15 5/6 times 10 2/5 =
164 2/3 yd

Area of Sod Piece:
1 1/3 times 1 1/3 =
1 7/9 yd

Divide area of backyard by area of sod piece :
164 2/3 divided by 1 7/9 =
92 5/8

He will need to buy 93 pieces of sod to cover his backyard.

7 0

3 years ago

Half of the class likes chips 4th of the class likes pennies and the 7kids left want waterfront how many kids are in the class

S_A_V [24]

There are 28 kids in the class

Step-by-step explanation:

If an object is divided into different part, then

The total of all parts is 1
To find a missing part subtract the sum of the other parts from 1

∵ Half of the class likes chips

- Have means $\frac{1}{2}$

- Assume that the number of kids in the class is x

∴ The number of kids likes the chips = $\frac{1}{2}$ × x =

∵ 4th of the class likes pennies

- 4th means $\frac{1}{4}$

∴ The number of kids likes pennies = $\frac{1}{4}$ x

∵ The rest of the class want waterfront

- Find the rest of the class in terms of x by subtracting the sum

of the two given fractions from the number of kids

∴ The number of kids left = $x-(\frac{1}{2}x+\frac{1}{4}x)$

∵ $\frac{1}{2}x+\frac{1}{4}x=\frac{3}{4}x$

∴ The number of kids left = $x-\frac{3}{4}x$

∴ The number of kids left = $\frac{1}{4}$ x

∵ 7 kids left

- Equate $\frac{1}{4}$ x by 7 and find x

∴ $\frac{1}{4}$ x = 7

Multiply both sides by 4

∴ x = 28

There are 28 kids in the class

Learn more:

You can learn more about the fractions in brainly.com/question/1312102

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3 years ago