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3 years ago

Solve the inequality- 5/2(3x+4)<6-3x. Show your work.

Mathematics

1 answer:

DochEvi [55]3 years ago

6 0

Answer:

x < -8/21

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

$(\frac{5}{2} * 3x) + (\frac{5}{2} * 4) < -3x + 6$
$\frac{15}{2}x + 10 < -3x + 6$

Step 2: Add 3x to both sides.

$\frac{15}{2}x + 10 + 3x < -3x + 6 + 3x$
$\frac{21}{2}x + 10 < 6$

Step 3: Subtract 10 from both sides.

$\frac{21}{2}x + 10 - 10 < 6 - 10$
$\frac{21}{2}x < -4$

Step 4: Multiply both sides by 2/21.

$\frac{21}{2}x * \frac{2}{21} < -4 * \frac{2}{21}$ $x < -\frac{8}{21}$

Therefore, the answer is x < -8/21.

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Match the real-world problem to its constant of proportionality.

irakobra [83]

Answer:

a. $18.36 for 3 pizzas : k = 6.12

b. $4.17 for 3 pounds of bananas . k = 1.39

c. $16.48 for 4 pounds of potatoes . k = 4.12

d. 2 cups of flour to make 24 cookie . k = 12

Step-by-step explanation:

PROPORTIONALITY:

Two quantities x and y are said to proportional to each other

if for x ∝ y , x = y k.

Here, k is called the PROPORTIONALITY CONSTANT.

⇒ $x \propto y \implies k = \frac{x}{y}$

Now, for the given quantities:

a. $18.36 for 3 pizzas [box]

Here, $k = \frac{x}{y} = \frac{18.36}{3} = 6.12$

So, the proportionality constant is 6.12.

b. $4.17 for 3 pounds of bananas [box]

Here, $k = \frac{x}{y} = \frac{4.17}{3} = 1.39$

So, the proportionality constant is 1.39.

c. $16.48 for 4 pounds of potatoes [box]

Here, $k = \frac{x}{y} = \frac{16.48}{4} = 4.12$

So, the proportionality constant is 4.12.

d. 2 cups of flour to make 24 cookies

Here, $k = \frac{x}{y} = \frac{24}{2} = 12$

So, the proportionality constant is 12.

7 0

3 years ago

Is y = |x| a function

Doss [256]

Answer:

Yes

Step-by-step explanation:

A function is a relation for which each value from the set of the first components of the ordered pairs is associated with exactly one value from the set of second components of the ordered pair.

Hope this helps!

8 0

3 years ago

Read 2 more answers

A student writes an incorrect step while checking if the sum of the measures of the two remote interior angles of triangle ABC b

rosijanka [135]

Answer:

4.) Step 2; it should be m∠o + m∠p = 180 degrees (supplementary angles)

Step-by-step explanation:

o and p are supplementary angles, and therefore add up to 180 degrees.

5 0

3 years ago

How do you work out the prince of a gallon of gas dropped from the summer high price of $3.50 to the winter low price of $2.87.

seraphim [82]

Answer:

4.50%

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

The ratio of bleach to water in a cleaning solution is 2:18. For every 1 liter of bleach, how many liters of water are in the so

Paha777 [63]

Answer:

For every 1 liter of bleach there are 9 liters of water in the solution

Step-by-step explanation:

∵ The ratio of bleach to water in a cleaning solution is 2 : 18

- That means for every 2 liters of bleach there is 18 liters of water

∵ There is 1 liter of bleach

- Let us use the ratio method

→ bleach : water

→ 2 : 18

→ 1 : x

- By using cross multiplication

∴ x × 2 = 1 × 18

∴ 2 x = 18

- Divide both sides by 2

∴ x = 9

∵ x represents the number of liters of the water in the solution

∴ The number of liters of the water in the solution is 9

For every 1 liter of bleach there are 9 liters of water in the solution

7 0

3 years ago