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3 years ago

Which graph represents the solution set of the compound inequality? −5 < a − 4 < 2

Mathematics

2 answers:

never [62]3 years ago

8 0

$-5 < a - 4 < 2\\\\ -1$

the 3rd one

jeyben [28]3 years ago

3 0

Answer:

Correct graph is:

Third

Step-by-step explanation:

we have to determine the graph of the inequality:

−5 < a − 4 < 2

Adding 4 on each side of the above inequality:

-5+4 < a-4+4 < 2+4

i.e. -1 < a < 6

Hence, graph of the inequality −5 < a − 4 < 2 is the set of all values between -1 and 6 and excluding -1 and 6

Correct graph is:

Third

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A restaurant owner was experimenting with the taste of her homestyle lemon drink. She started with 60 litres of water. She remov

Burka [1]

Answer:

ratio of pure lemon juice to water in the homestyle lemon drink is 5 : 19.

Step-by-step explanation:

In order to solve the final ratio of lemon juice to water, let us start by determining the initial ratio of pure lemon juice to water in the first mix. This is done as follows:

Total volume of mixture = 60 liters

initial volume of water = 60 liters

initial volume of lemon juice = 0 liters

1) She removed 15 liters of the water and replaced it with 15 liters of pure lemon juice.

Volume of water = 60 - 15 = 45 liters

Volume of lemon juice = 15 liters

$\therefore \frac{15}{60}\ = \frac{1}{4}\ of\ the\ first\ mix\ is\ lemon\ juice\\\frac{45}{60}\ = \frac{3}{4}\ of\ the\ first\ mix\ is\ pure\ water$

2) She removed 10 liters of the new mixture

Let us convert this amount removed into ratio:

$lemon\ juice\ = \frac{1}{4}\ \times 10 = \frac{10}{4} = \frac{5}{2}\ liters.\\ \therefore the\ owner\ removes\ \frac{5}{2}\ liters\ of\ pure\ lemon\ juice\\pure\ water\ = \frac{3}{4}\ \times 10 = \frac{30}{4} = \frac{15}{2}\ liters\\ \therefore\ the\ owner\ removes\ \frac{15}{2}\ liters\ of\ water\ from\ the\ first\ mix.$

New volumes of water and lemon juice after removing the 10 liters of mixture is calculated as follows:

$lemon\ juice\ = 15 - \frac{5}{2} = \frac{30-5}{2} = \frac{25}{2}\ liters\ of\ lemon\ juice\\pure\ water\ = 45 - \frac{15}{2} = \frac{90-15}{2} = \frac{75}{2}\ liters\ of\ pure\ water$

3) and replaced it with 10 liters of water.

$New\ volume\ of\ water\ = 10 + \frac{75}{2} = \frac{20+ 75}{2} = \frac{95}{2}\ liters$

The final ratio of lemon juice to water:

$\frac{25}{2} : \frac{95}{2}\\= 25 : 95\\= 5 : 19$

Therefore, the final ratio of pure lemon juice to water in the homestyle lemon drink is 5 : 19.

4 0

3 years ago

What is the y-intercept of the quadratic function

Masja [62]

Answer:

(0,12) are the correct y-intercepts.

7 0

2 years ago

Read 2 more answers

Larry claims that (14 + 12) × (8 + 12) and (14 × 12) + (8 × 12) are equivalent because they have the same digits and the same op

FromTheMoon [43]

Answer:

$(14+12)\times (8+12) > (14\times 12)+(8\times 12)$

Step-by-step explanation:

First let us evaluate the value of both the expressions.

$(14+12)\times (8+12) = 26\times 20 = 520$

$(14\times 12)+(8\times 12) = 168 + 96 = 264$

a) Hence, Larry's claim that both the expressions are equivalent is wrong.

The evaluation of the expressions have been shown above. The second expression was obtained by swapping the addition and multiplication order and that created the difference.

b) Clearly,

520 > 264

Therefore,

$(14+12)\times (8+12) > (14\times 12)+(8\times 12)$

$(14+12)\times (8+12)$ is greater by the expression $(14\times 12)+(8\times 12)$ by a value of 520 - 264 = 256.

7 0

3 years ago

Last week Mark ran 31 miles more than Jack. Mark ran 46 miles .How many miles did Jack run

Levart [38]

You take what Mark ran, 46 miles, and you see that Mark ran 31 more miles than Jack, so the equation would be 46-31, which would be 15 miles. So, Jack ran 15 miles.

8 0

3 years ago

Read 2 more answers

What is the answer to this question?

katen-ka-za [31]

Answer:

10 in., 18.5 in., 31.5 in.

Step-by-step explanation:

Ask me if you need step-by-step, since the problem seems to be multiple choice.

8 0

3 years ago