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Aleks [24]
3 years ago
8

A system of equations is given below:

Mathematics
1 answer:
algol [13]3 years ago
4 0

The given system of equations is:

y = 4x − 3 ...(1)

2x + 7y = 41 ...(2)

Notice that the first equation is a solved equation for y. So, we can simply substitute 4x-3 for y in equation (2) to solve. This method is also knwon as substitution method by which we can plug in one equation into other equation.

So, if we will substitute y=4x-3 in equation (2) then we will get,

2x+7(4x-3)=41

Hence, third choice 2x + 7(4x − 3) = 41 is the correct answer.

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Find the length of the radius of the circle, which is inscribed into a right trapezoid with lengths of bases a and b.
egoroff_w [7]

Answer:

  r = (ab)/(a+b)

Step-by-step explanation:

Consider the attached sketch. The diagram shows base b at the bottom and base a at the top. The height of the trapezoid must be twice the radius. The point where the slant side of the trapezoid is tangent to the inscribed circle divides that slant side into two parts: lengths (a-r) and (b-r). The sum of these lengths is the length of the slant side, which is the hypotenuse of a right triangle with one leg equal to 2r and the other leg equal to (b-a).

Using the Pythagorean theorem, we can write the relation ...

  ((a-r) +(b-r))^2 = (2r)^2 +(b -a)^2

  a^2 +2ab +b^2 -4r(a+b) +4r^2 = 4r^2 +b^2 -2ab +a^2

  -4r(a+b) = -4ab . . . . . . . . subtract common terms from both sides, also -2ab

  r = ab/(a+b) . . . . . . . . . divide by the coefficient of r

The radius of the inscribed circle in a right trapezoid is r = ab/(a+b).

_____

The graph in the second attachment shows a trapezoid with the radius calculated as above.

6 0
3 years ago
Why wasn't i doing this sooner :)
Licemer1 [7]

Step-by-step explanation:

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7 0
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Which value is included in the solution set for the inequality graphed on the number line? –5 –2 0 3
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Step-by-step explanation:

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Read 2 more answers
What is the simplified value of the expression below? 8.5 + (12 + 4) times 2 minus 7
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Answer:

33.5  

-by-step explanation:

8.5 + (12 + 4) × 2 - 7

Use PEMDAS ( I think this is right hope it helps!)

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Seven cereal bars are shared equally by 3 students. How many does each student receive?I really need help and my teacher won't h
Katarina [22]

Answer:

Each student gets 2 1/3

Step-by-step explanation:

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7 0
3 years ago
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