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Alik [6]
3 years ago
6

Im struggling on this can someone explain it to me

Mathematics
1 answer:
AleksandrR [38]3 years ago
6 0

Answer:

B. 31°; 106° and 43°.

Step-by-step explanation:

1) the rule is:

(5x-7)+(3x+1)+(11x-4)=180°;

2) if to solve this equation, then x=10°;

3) if x=10, then after the substitution the answer is 43;31;106.

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A rectangular package sent by a postal service can have a maximum combined length and girth (perimeter of a cross sectio) of 108
Morgarella [4.7K]

Answer:

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

Step-by-step explanation:

This is a optimization with restrictions problem.

The restriction is that the perimeter of the square cross section plus the length is equal to 108 inches (as we will maximize the volume, we wil use the maximum of length and cross section perimeter).

This restriction can be expressed as:

4x+L=108

being x: the side of the square of the cross section and L: length of the package.

The volume, that we want to maximize, is:

V=x^2L

If we express L in function of x using the restriction equation, we get:

4x+L=108\\\\L=108-4x

We replace L in the volume formula and we get

V=x^2L=x^2*(108-4x)=-4x^3+108x^2

To maximize the volume we derive and equal to 0

\dfrac{dV}{dx}=-4*3x^2+108*2x=0\\\\\\-12x^2+216x=0\\\\-12x+216=0\\\\12x=216\\\\x=216/12=18

We can replace x to calculate L:

L=108-4x=108-4*18=108-72=36

The maximum volume of the package is obtained with a cross section of side 18 inches and a length of 36 inches.

4 0
3 years ago
Read 2 more answers
What number is 40% of 720
Zarrin [17]
You would have to set you problem up like
   x         40
____=_____
 720     100

you would multiply 40 by 720 then you would divide 28,800 by 100 your answer will be 288.
3 0
3 years ago
Solve the equation. \dfrac{11}6 =n+\dfrac79 6 11 ​ =n+ 9 7 ​ start fraction, 11, divided by, 6, end fraction, equals, n, plus, s
kvasek [131]
11/6 = n + 7/9
11/6 - 7/9 = n = 19/18
5 0
3 years ago
Find the value of X. Write your answer in simplest form.<br>What does X equal? ​
drek231 [11]

<u>Given</u>:

Given that the figure of similar triangles.

The altitude of the triangle is x.

The length of the left part is 30.

The length of the right part is 15.

We need to determine the value of x.

<u>Value of x:</u>

The value of x can be determined using the geometric mean theorem.

Thus, we have;

\frac{\text { left }}{\text { altitude }}=\frac{\text { altitude }}{\text { right }}

Substituting the values, we have;

\frac{30}{x}=\frac{x}{15}

Cross multiplying, we get;

30 \times 15= x^2

     450=x^2

Taking square root on both sides, we have;

15 \sqrt{2}=x

Thus, the value of x is 15√2

7 0
3 years ago
Sarah is 13 years older than Mike. The sum of their ages is 37. How old is Sarah and how old is Mike? Enter your answer as on or
Blizzard [7]

Answer:

(24,13)

Step-by-step explanation:

24 is Sarah's age.

13 is Mike's age.

System:

\left \{24+13=37

I hope this helped!

3 0
3 years ago
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