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rjkz [21]
3 years ago
8

You have three consecutive odd integers. Four times the smallest decreased by 5 is the same as the largest increased by 12. What

is the smallest of the integers?
Mathematics
1 answer:
vladimir1956 [14]3 years ago
5 0

Answer:

The smallest of the integers is 7

Step-by-step explanation:

Let the integers be x, y and z

From the question, the integers are consecutive odd integers.

Hence,

If the smallest of the integers is x and the largest is z, then we can write that,

x + 2 = y and

y + 2 = z

Then, x + 2 + 2 = z

∴ x + 4 = z ....... (1)

From the question, four times the smallest decreased by 5 is the same as the largest increased by 12, that is

4x -5 = z + 12 ....... (2)

Put the value of z = x + 4 in equation (1) into equation (2),

We then get

4x - 5 = x + 4 + 12

4x - x = 4 + 12 + 5

3x = 21

x = 7

Hence, the smallest of the integers is 7

The other integers are 9 and 11 ( y= 9 and z = 11)

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Solve the following inequality. 21<_-3(x - 4) < 30 A. 28<_x < 37 B. -3 <_ x < 6 C. -6 < x <_ -3 D. -10 &
Aloiza [94]

Answer:

Option C -6

Step-by-step explanation:

we have

21\leq -3(x-4)

The compound inequality can be divided into two inequality

21\leq -3(x-4) -----> inequality A

-3(x-4) ----> inequality B

Solve inequality A

21\leq -3x+12

9\leq -3x

Divide by -3 both sides

when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

-3\geq x

Rewrite

x\leq -3

The solution of the inequality A is the interval (-∞,-3]

Solve the inequality B

-3x+12

-3x

Divide by -3 both sides

when you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality symbol

x>-6

The solution of the inequality B is the interval [-6,∞)

The solution of the compound inequality is

[-6,∞) ∩ (-∞,-3]=(-6,-3]

-6

3 0
3 years ago
Kyle is shopping for his favorite
nalin [4]

Answer:

The 9 ounce box is the better deal, and Kyle will save 2 cents.

Step-by-step explanation:

First, you should find how much 1 once would cost in the 9 ounce box.

Do 2.52 ÷ 9 = x

x = 0.28

This means that in the <u>9 ounce box, one ounce costs 28 cents</u>.

Now, find how much one once would cost in the 12 ounce box.

3.60 ÷ 12 = x

x = 0.30

This means that in the <u>12 ounce box, one ounce costs 30 cents</u>.

This means that the 9 ounce box is a better deal, because it costs less per ounce.

0.30 - 0.28 = 0.02. This means there is a 2 cent difference in their prices per ounce.

So, Kyle should choose the 9 ounce box, and he will save 2 cents per box.

5 0
2 years ago
Select the procedure that can be used to show the converse of the Pythagorean theorem using side links chosen from 3 feet, 4 fee
snow_tiger [21]

Answer:

B

Step-by-step explanation:

B

4 0
3 years ago
Read 2 more answers
TeeVee Electronics, Inc., makes console and wide-
Tom [10]

Answer:

First we need to put all the given information in a table, that way we'll express it better into inequalities.

                                     Cost      Production Max.

Console screen (x)      $600              450

Wide-screen (y)           $900              200

                                 $360,000

We have:

600x+900y \leq 360,000

Because they can't spend more than $360,000 in production.

x\leq 450\\y\leq 200

Because the number of television is restricted.

The profit function is

P(x,y)=125x+200y (this is the function we need to maximize).

First, we need to draw each inequality. The image attached shows the region of solution, which has vertices (0,200), (300,200), (450, 100) and (450,0).

Now, we test each point in the profit function to see which one gives the highest profit.

For (300,200):

P(300,200)=125(300)+200(200)=37,500+40,000=77,500

300 console screen and 200 wide screen give a profit of $77,500.

For (450,100):

P(450,100)=125(450)+200(100)=56,250+20,000=76,250

450 console screen and 100 wide screen give a profit of $76,250.

<h3>Therefore, to reach the maximum profits, TeeVee Electronic, Inc., must produce 300 console screen televisions and 200 wide-screen televisions to profit $77,500,</h3>

4 0
3 years ago
Help me with this please
ElenaW [278]

The greatest common factor is 2z^3.

In order to find the greatest common factor, always start with the coefficient of the lowest term. Let's see what the factors of 14 are.

Factors of 10: 1, 2, 5, 10

Now we look to see which are also factors of the next highest number.

Factors of 14: 1, 2, 7, 14

Only 1 and 2 are similar factors. Since 2 is also a factor of 70, 2 in the coefficient of our greatest common factor.

Next we look for the term with the least number of z's. 14z^3 is the least number of z's. This means we can take out z^3. Giving us the final answer of 2z^3.

5 0
3 years ago
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