10. (04.02 LC)
For the following system, if you isolated x in the second equation to use the substitution method, what expression would you substitute into the first equation? (1 point)
2x+y=8
-x-3y=-12
O 3y + 12
O-3y + 12
O 3y - 12
-3y - 12

Answer:

Box dimensions:

L = 3 ft

D = 6 ft

H = 1 ft

Volume  V = 18 ft³

Step-by-step explanation:

a) Each side of the future box is

L = 5 - 2*x     D = 8 - 2*x  

height of the box is   x

Then the volume of the box as function of x is:

V(x) =  ( 5 - 2*x ) * ( 8  - 2*x ) * x

V(x) = ( 40 - 10*x - 16*x + 4*x² ) * x

V(x) = 40*x - 26*x² + 4*x³

Tacking derivatives on both sides of the equation:

V´(x) = 40 - 52*x + 12x²     or     V´(x) = 20 - 26*x + 6*x²

If V´(x) = 0

6*x² - 26*x + 20  = 0

Solving for x

x₁,₂  = (-b ± √ b² - 4*a*c  ] /2*a

x₁,₂  = ( 26  ±  √ 676  - 480  ) / 12

x₁,₂  =  (26 ± 14 )/ 12

x₁  = 1

x₂ = 3,33        ( we dismiss this solution since is not feasible according to cardboard dimensions )

Then the sides of the box are:

L = 5 -2*x      L  =  5 - 2*1     L = 3 ft

D = 8 - 2*x    D  = 8 - 2*1     D = 6 ft

H = x = 1 ft

And the volume is    V = 6*3*1 = 18 ft³

Answer:

A. Translation

Step-by-step explanation:

Given

Preimage

[tex]J = (-6,9)[/tex]

[tex]K = (-6,4)[/tex]

[tex]L = (-3,4)[/tex]

Image

[tex]J' = (2,9)[/tex]

[tex]K' = (2,4)[/tex]

[tex]L' = (5,4)[/tex]

Required

Which transformation occurred

The transformation that occurs is translation because each of the preimage were translated or shifter right by 8 units.

The rule applied here is:

[tex](x,y)=>(x+8,y)[/tex]

So, we have:

[tex]J = (-6,9)[/tex] [tex]==> (-6+8,9) = (2,9)[/tex]

[tex]K = (-6,4)[/tex] [tex]==> (-6+8,4) = (2,4)[/tex]

[tex]L = (-3,4)[/tex] [tex]==> (-3+8,4) = (5,4)[/tex]

Hence, the transformation is (a) Translation

Answer:

[tex]x = 8[/tex]

Step-by-step explanation:

Set up the proportion

[tex] \frac{3}{6} = \frac{7}{6 + x} [/tex]

[tex]18 + 3x = 42[/tex]

[tex]3x = 24[/tex]

[tex]x = 8[/tex]

Answer:

perimeter = 48 Area = 144

Step-by-step explanation:

was that all?

Answer:

20% of his budget

Step-by-step explanation:

1500 - 100% /10

150 - 10 % ×2

300 - 20%

Answer:

20%

Step-by-step explanation:

The % is 300 / 1500 * 100% = 0.2 * 100% = 20%

Answer:

13

Step-by-step explanation:

Computers=6

Printers=7

Now,

=6+7

=13

Answer:

3x+4

Step-by-step explanation:

It’s D the answer is D

Answer:

5/8 in simplest form is 5/8

Step-by-step explanation:

Answer:

5/8 is in the simplest form already.

Step-by-step explanation:

It cant be lowered anymore, due to 5 not being divisible by 4, 2, or 8, which is what 8 is divisible by.

Answer:

-18, |-17|, |-18|, |19|, 20

Step-by-step explanation:

the absolute value of -17 is 17, the absolute value of -18 is 18, and the absolute value of 19 is just 19. Absolute values are never negative.

Hope this helps!

Answer:

Steps:

V = 5.5 × 3.5 × 9

V = 173.25 in³

Answer:

D

Step-by-step explanation:

2 x 2 = 4 x PI = 12.56

Answer:

rock, pop, metal, country

Step-by-step explanation:

i just took the test :)

On Edmentum and got it right.

9514 1404 393

Answer:

  (d)  new line is less steep

Step-by-step explanation:

Changing the slope from 3 to 1/3 makes the line less steep.

__

In the attachment, the blue line is the new line.

Answer:

4 and 40

Step-by-step explanation:

2/5 of 10 is 4

2/5 of 100 is 40

Answer:

[tex]2\frac{1}{2}[/tex]

Step-by-step explanation:

Answer:

36 Inches

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

it would just be 12×3=36

Answer:

-10m-9

Step-by-step explanation:

-3(4m+3)+2m

combine like terms

-12m-9+2m

-10m-9

Answer:

38.5ft²

Step-by-step explanation:

Triangle area formula = [tex]\frac{1}{2} * b * h[/tex]

Triangle area = [tex]\frac{1}{2} * 11 * 7[/tex]

Triangle area = 0.5 * 11 * 7

Triangle area = 38.5ft²

Answer: GIVE THE GUY BRAILIEST PLEASE

Answer:

36

Step-by-step explanation:

sqrt(36)^2

36

I hope this helps

Answer:

I think that its D

Step-by-step explanation:

..

Answer:

A 2

Step-by-step explanation:

have a good day /night sorry if wrong

Answer:

the measures of the three angles: x=18°, y= 68°, z=. 94°

9514 1404 393

Answer:

Step-by-step explanation:

We're going to say Job A is the charge at Jim's shop. For h hours, that charge will be the sum of the parts cost and the hourly charge:

  j = 25 +55h

Job B is the charge at Myron's shop. Similarly, that charge is ...

  m = 50 +30h

__

The two charges are equal when ...

  j = m

  25 +55h = 50 +30h

  25h = 25 . . . . . . . . . . . subtract 25+30h from both sides of the equation

  h = 1 . . . . . . . . . . divide by 25

The charges are the same at the two shops for 1 hour worked.

_____

Additional comment

You may be expected to write your equations using y for the charge and x for the hours. I like to use variable names that remind me what they stand for.

__

In general, when you have rates that have different fixed fees and different per-quantity costs, the "break even" quantity is the ratio of the difference in fees to the difference in per-quantity costs. Here the parts (fees) differ by $25, and the per-hour cost differs by $25, so the number of hours is 25/25 = 1 to make the charges equal.

Answer:

A = 13

B = 50

C = 22.5

D = 3.5

E = 16.3

Step-by-step explanation:

divide each area by 4

ex: 52 ÷ 4 = 13

Answer:

The nth term is [tex]a_n = 4 - 5(n-1)[/tex]

The 60th term of the sequence is -291.

Step-by-step explanation:

Arithmetic sequence:

In an arithmetic sequence, the difference between consecutive terms is always the same, and it is called common difference.

The nth term is given by:

[tex]a_n = a_1 + (n-1)d[/tex]

In which [tex]a_1[/tex] is the first term and d is the common difference.

4,-1,-6

The common difference is:

[tex]d = -1 - 4 = -5[/tex]

First term [tex]a_1 = 4[/tex]

So

[tex]a_n = a_1 + (n-1)d[/tex]

[tex]a_n = 4 - 5(n-1)[/tex]

60th term:

[tex]a_{60}[/tex]. Si

[tex]a_{60} = 4 - 5(60-1) = -291[/tex]

The 60th term of the sequence is -291.