A carpenter makes bookcases in 2 sizes, large and small. It takes 4 hours to make a
large bookcase and 2 hours to make a small one. The profit on a large bookcase is
$35 and on a small bookcase is $20. The carpenter can spend only 32 hours per
week making bookcases and must make at least 2 of the large and at least 4 of the
small each week. How many small and large bookcases should the carpenter make
to maximize his profit? What is his profit?

Answer:

Step-by-step explanation:

An absolute value of |x| {modulus of x} is the value of a real number x. The given equation is not true.

An absolute value of |x| {modulus of x} is the value of a real number x, the value we get is always a non-negative number, for example, |-5| will give 5, and also, |5| will give 5 as well.

A hypothesis is a speculative conclusion or assertion that is made without proof. Now, to prove that the given equation is not true substitute the value of both the variables as -1. Therefore,

x = y = -1

Substitute the value on the left side of the equation,

|x - y|

= |-1 - (-1)|

= |-1 + 1|

= |0|

= 0

Substitute the value on the right side of the equation,

|x| - |y|

= |-1| - |-1|

= 1 + 1  

= 2

Since the left and the right side of the equation is not satisfied, therefore, it can be concluded that the given equation is not true.

Learn more about Absolute value here:

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Answer:

16

Step-by-step explanation:

Given the definitions of f(x) and g(x) below,

f(x) = x^2+ x + 10

g(x) = -5x-3

f(g(x)) = f(-5x-3)

f(-5x-3) = (-5x-3)²+((-5x-3)+10

f(-5x-3) = 25x²+30x+9-5x-3+10

f(-5x-3) = 25x² +25x+16

f(g(x)) = 25x² +25x+16

f(g(-1)) = 25(-1)² +25(-1)+16

f(g(-1)) = 25-25 + 16

f(g(-1)) = 16

Hence f(g(-1)) is 16

Answer:

3a-2a+7-4

a+3

Step-by-step explanation:

like and unlike terms arranging

and add and subtraction

Answer:

11 maybe???

Step-by-step explanation:

Answer:

c y=6x+4

Step-by-step explanation:

Answer:

it is 1000x+2000

Step-by-step explanation:

Answer:

c because 3.3.3.3 is 3 to the 4th power expanded

Answer:

2.2

Step-by-step explanation:

Answer:

11/5

Step-by-step explanation:

The last one as we can see that as the wight increases, the miles per gallon decreases.

Step-by-step explanation:

[tex]5x - 2[/tex]

...........

Answer:

2-5x

Step-by-step explanation:

let the number be x, 5 *x = 5x.

2 less means ,2 minus,

>> 2-5x.

Answer:

20,19,18

Step-by-step explanation:

because you have to go backwards

Answer:

The answer is G. 5/3

Step-by-step explanation:

I used the elimination process and multiplied the second equation by three which allowed me to cancel out the positive and negative three y's.

6x+3y=13

(3x-y=4)*3

6x+3y=13

9x-3y=12

6x+9x=15x

13+12=25

15x=25

15x/15=25/15

By dividing, the fifteens on the left cancel out leaving:

x=1.66667 or 1 2/3 = 5/3

I hope this helps. :)

Answer: b im pretty sure hope this helps :)

Step-by-step explanation:

Answer:

A: x = -4

B: a = -7 (I'm assuming the '-' in front of 49 was supposed to be an '=')

Step-by-step explanation:

A: You need to group the like terms together, and isolate the variable, which in this case is x.

Take the 7 over to the other side, so the equation looks a little bit like this.

3-7 = x.

3-7 is -4, so we've gotten our answer.

x = -4.

B: -7a = 49.

When two negative numbers are multiplied together, the product becomes positive.

49 is 7x7.

-7 times -7 would be 49.

So, in this situation, a would be -7.

a = -7.

Answer:

− 3 = − 14

Step-by-step explanation:

Hope this helps !

Answer:

x = 5°

EF = 58°

GH = 55°

Step-by-step explanation:

From The diagram :

Recall ; Angle on a straight line = 180°

This means :

EF + FG + GH = 180

EF = (10x + 8)°

GH = (11x)°

FG = 67°

HENCE;

10x + 8 + 11x + 67 = 180

21x + 75° = 180°

21x = 180 - 75

21x = 105

x = 105 / 21

x = 5

EF = 10x + 8 = 50 + 8 = 58°

GH = 11x = 11 * 5 = 55°

Answer:

C. 1 13/18

Explanation:

Answer:

12y2

Step-by-step explanation:

Answer: x= 12/103

alternate form x =0.116505

Step-by-step explanation:

Try Photo math! It explains step by step!

Hope this helps!!!!

Answer:

Its cost about 1.5625

if you rounded its 1.56 :)

Step-by-step explanation:

Answer:

Each litters can be represented as; x and y respectively to the 7% and the 28%

x + y =1

7x + 28y =19.6

This a simultaneous equation and can either be solved by using elimination or substitution method

Using the substitution method

eqn1, x=1-y

putting into eqn2

7(1-y)+28y =19.6

7-7y+28y=19.6

21y=12.6

y=3/5

but x=1-y

so

x=1-3/5

x=2/5

Answer:

12.054 < 12.54

Step-by-step explanation:

12.054 is less than 12.54 because it has a zero in the tenths place, and 12.54 has a five in the tenths place! Always check the first spot after the decimal first. Best of luck<3

Answer:

12.054 < 12.54

Step-by-step explanation:

Answer:

In the graph, we can see that the relation between length and weight is given by the adjusted line, which passes through the points (24, 16) and (28, 25)

Remember that a linear relation can be written as:

y = a*x + b

Where a is the slope and b is the y-intercept.

If this line passes through the points (x₁, y₁) and (x₂, y₂) the slope can be calculated as:

a = (y₂ - y₁)/(x₂ - x₁)

Then in our case, the slope will be:

a = (25 - 16)/(28 - 24) = 9/4

y = (9/4)*x + b

Knowing that this line passes through (24, 16), we know that when x = 24, y must be equal to 16.

If we replace these in the equation, we can find the value of b.

16 = (9/4)*24 + b

16 = 54 + b

16 - 54 = b - 38

Then the equation is:

y = (9/4)*x - 38

Now that we know the equation, we can simply replace y by 34 pounds to find the value of x.

34 = (9/4)*x - 38

34 + 38 = (9/4)*x

72*(4/9) = x = 32

So we can estimate that the length of a fish that weighs 34 pounds is 32 (I do not know the unit of length, I can't see the horizontal axis on the image)

Answer:

(D) 3/10

Step-by-step explanation:

So its split into 10 different rates each and its on the third split So 3/10.

Answer:

the answer is B.........................

I would say its the second one.

the student shouldve distributed the 2^3x+3 into 2^3x+9

Answer:

The age of paintings is - 26,601 years .

Step-by-step explanation:

Lets calculate-

A= [tex]0.25 A[/tex]o

Therefore ,

[tex]A= A[/tex]o [tex]e^-^0^.^0^0^0^1^2^1^t[/tex]

[tex]ln0.25=-0.000121t[/tex]

[tex]-3.2188=-0.000121t[/tex]

[tex]t=\frac{-3.2188}{-0.000121}[/tex]

  t= 26,601.65

Therefore , the age of paintings is 26,601 years old.

Answer:

m = - 6 :)

Step-by-step explanation:

Answer:

I think the answer is A 64cm cubed