I am stuck with this question can anyone help please 2(3x-5)+3(2x+3)

Help please, due tomorrow morning. (15 points)

Alex Ar [27]

Answer:

7) 29 bottles; $3.19 each; 8 hours 24 minutes

8) 12x^2 +40x +28; 4x^2 +24x +36; d = 4√2(x +2)

Step-by-step explanation:

7)

a) 275 mL = 0.275 L, so the number of small bottles that can be filled is ...

8/0.275 ≈ 29.1

29 fill bottles can be filled

__

b) In order make 175% profit, the revenue from the sale of the 29 bottles must be ...

$33.65 × 275% = $92.54

Then each bottle must be priced at ...

$92.54/29 = $3.19

The price for each bottle must be $3.19.

__

c) The number of staff-hours required for 45 containers is ...

(4)(5 1/4) = 21 . . . . staff-hours

Then the work rate per container is ...

(21 staff·hours)/(45 containers) = 7/15 staff·hours/container

= 28 staff·minutes/container

Then for 3 staff and 54 containers, the time required is ...

(28 staff·minutes/container)(54 containers)/(3 staff) = 504 minutes

= 8 hours, 24 minutes

_____

8)

a) The area is the product of length and width. The 4 rectangles will have an area 4 times the area of one rectangle.

A = 4(3x +7)(x +1) = 4(3x^2 +10x +7) = 12x^2 +40x +28

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b) The edge dimension of the shaded square is ...

(3x +7) -(x +1) = 2x +6

The area of the shaded square is the square of this length, so is ...

A = (2x +6)^2 = 4x^2 +24x +36

__

c) The edge length of the larger square is the sum of the length and width of the surrounding rectangles:

s = (3x +7) +(x +1) = 4x +8 = 4(x +2)

The diagonal length is √2 times this edge length*, so is ...

d = s√2

d = 4√2(x +2)

____

* If you're not allowed to make use of this fact without deriving it, consider the hypotenuse of an isosceles right triangle with side lengths 1. By the Pythagorean theorem, the hypotenuse (c) has length ...

c^2 = 1^2 +1^2

c = √2 . . . . . . . . . take the square root

This ratio of sides and hypotenuse (1:1:√2) applies to any isosceles right triangle, so applies to the diagonal of the square in this problem.

6 0

3 years ago

Hannah has only nickels and dimes in her wallet she has a total of $2.50 and a total of 30 coins how many nickels does she have?

hodyreva [135]

She has 10 nickels
She has 20 dimes

8 0

3 years ago

If north is the direction of the positive y-axis and east is the direction of the positive x-axis, give the unit vector pointing

tatuchka [14]

North is the direction of positive y-axis. East is the direction of positive x-axis. So West will be the direction of negative x-axis.

Northwest will mean, in between north and west i.e. in between y-axis and the negative x-axis which is the mid of the 2nd quadrant. Thus the vector pointing northwest will form an angle of 135 degrees with positive x-axis.

The magnitude of unit vector is 1 and is forming an angle of 135 degrees. In terms of its components, we can write:

x-component = 1 cos (135) = $- \frac{ \sqrt{2} }{2}$
y-component = 1 sin (135) = $\frac{ \sqrt{2} }{2}$

Thus the unit vector will be = $- \frac{ \sqrt{2} }{2}x+ \frac{ \sqrt{2} }{2}y$

In vector form, component form the vector can be written as:

$(- \frac{ \sqrt{2} }{2}, \frac{ \sqrt{2} }{2})$

7 0

3 years ago

Read 2 more answers

Question 17(Multiple Choice Worth 1 points)

Marina86 [1]

Answer:A fine of $0.75 is paid if the book returned by the due date.

No fine is paid if the book is returned 1 day after the due date.

A fine of $0.75 is paid if the book is returned 1 day after the due date.

Bit by bit clarification:

A fine of $0.75 is paid if the book returned by the due date.

No fine is paid if the book is returned 1 day after the due date.

A fine of $0.75 is paid if the book is returned 1 day after the due date.