Ask question

Ask question

All categories

3 years ago

11

A florist is filling a large order for a client. The client wants no more than 300 roses in vases. The smaller vase will contain

8 roses and the larger vase will contain 12 roses. The client requires that there are at least twice as many small vases as large vases. The client requires that there are at least 6 small vases and no more than 12 large vases.
Let x represent the number of small vases and y represent the number of large vases.

What constraints are placed on the variables in this situation?

1 answer:

d1i1m1o1n [39]3 years ago

4 0

Answer:

$8x+12y\leq 300$

$x\geq 6$

$y\leq 12$

$x\geq 2y$

Step-by-step explanation:

We are given that

x=Number of small vases

y=Number of large vases

Total number of roses not more than 300 in vases.

Number of roses in small vase atleast=8

Number of roses in large vase not more than =12

We have to find the constraints are placed on the variables in the given situation.

According to question

$8x+12y\leq 300$

$x\geq 6$

$y\leq 12$

$x\geq 2y$

You might be interested in

What is the quotient of 18/1000?show your work

d1i1m1o1n [39]

Hi there, 18÷1000=.018. Therefore, the answer is .018

4 0

3 years ago

Read 2 more answers

What is the answer to this question algbra

navik [9.2K]

Answer:photo math

Step-by-step explanation:

5 0

3 years ago

Which equation is y = –6x^2 + 3x + 2 rewritten in vertex form? y = negative 6 (x minus 1) squared + 8 y = negative 6 (x + one-fo

mart [117]

Answer:

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

Step-by-step explanation:

Given:

$y = -6x^2 + 3x + 2$

Required

Rewrite in vertex form

The vertex form of an equation is in form of: $y = a(x - h)^2+ k$

Solving: $y = -6x^2 + 3x + 2$

Subtract 2 from both sides

$y - 2 = -6x^2 + 3x + 2 - 2$

$y - 2 = -6x^2 + 3x$

Factorize expression on the right hand side by dividing through by the coefficient of x²

$y - 2 = -6(x^2 + \frac{3x}{-6})$

$y - 2 = -6(x^2 - \frac{3x}{6})$

$y - 2 = -6(x^2 - \frac{x}{2})$

Get a perfect square of coefficient of x; then add to both sides

------------------------------------------------------------------------------------

<em>Rough work</em>

The coefficient of x is $\frac{-1}{2}$

It's square is $(\frac{-1}{2})^2 = \frac{1}{4}$

Adding inside the bracket of $-6(x^2 - \frac{x}{2})$ to give: $-6(x^2 - \frac{x}{2} + \frac{1}{4})$

To balance the equation, the same expression must be added to the other side of the equation;

Equivalent expression is: $-6(\frac{1}{4})$

------------------------------------------------------------------------------------

The expression becomes

$y - 2 -6(\frac{1}{4})= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{6}{4}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

$y - 2 -\frac{3}{2}= -6(x^2 - \frac{x}{2} + \frac{1}{4})$

Factorize the expression on the right hand side

$y - 2 -\frac{3}{2}= -6(x - \frac{1}{2})^2$

$y - (2 +\frac{3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{4+3}{2})= -6(x - \frac{1}{2})^2$

$y - (\frac{7}{2})= -6(x - \frac{1}{2})^2$

$y +\frac{7}{2} = -6(x - \frac{1}{2})^2$

Make y the subject of formula

$y = -6(x - \frac{1}{2})^2 -\frac{7}{2}$

<em>Solved</em>

7 0

3 years ago

Read 2 more answers

Otis measured the heights of several sunflowers. He found that their heights were 4, 6, 7, 9, and 9 feet Otis found that the mea

lana66690 [7]

Answer:

B) 7 feet is the median (center) and 5 is the range (spread)

Step-by-step explanation:

spread is the difference between the largest and smallest numbers in the data set (9 - 4 = 5 in this case)

6 0

3 years ago

3 years ago a father was 3 times as old as his son, in five years time he will be twice as old as his son, what will be the sum

ivolga24 [154]

Answer: 46 years

Step-by-step explanation:

Let the father's age be x and the son's age be y, then 3 years ago:

Father = x - 3

son = y - 3

Then , from the first statement :

x - 3 = 3 ( y - 3 )

x - 3 = 3y - 9

x = 3y - 9 + 3

x = 3y - 6 .......................................... equation 1

In five years time

father = x + 5

son = y + 5

Then , from the second statement

x + 5 = 2 ( y + 5 )

x + 5 = 2y + 10

x = 2y + 10 - 5

x = 2y + 5 ........................ equation 2

Equating equation 1 and 2 , we have

3y -6 = 2y + 5

add 6 to both sides

3y = 2y + 5 + 6

subtract 2y from both sides

3y - 2y = 11

y = 11

substitute y = 11 into equation 1 to find the value of x

x = 3y - 6

x = 3(11) - 6

x = 33 - 6

x = 27

This means that the father is presently 27 years and the son is presently 11 years.

In four years time

father = 27 + 4 = 31

son = 11 + 4 = 15

sum of their ages in four years time will be

31 + 15 = 46 years

5 0

3 years ago

Read 2 more answers