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Vesna [10]
3 years ago
15

The five interior angles in a  pentagon are in the ratio 2:3:4:5:6. What is the measure of the pentagon's largest angle?

Mathematics
1 answer:
zmey [24]3 years ago
5 0
Let All angles be x times multiplied to ratio , so we"ll get :-

2x + 3x + 4x + 5x + 6x = 540°

20x = 540

x = 540/20

⇒ x = 27 ,

so angles are :-

⇒ 2x = 2×27 = 54°

⇒ 3x = 3×27 = 81°

⇒ 4x = 4×27 = 108°

⇒ 5x = 5×27 = 135°

⇒ 6x = 6×27 = 162°

Hence 162° is the greatest angle
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Write an equation of the line that passes through a pair of points (-5, -2) (3, -1)
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Answer:

y = 0.125x + -1.375

Step-by-step explanation:

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5 0
3 years ago
Fiona is trying to prove that a pair of expressions are equivalent by using substitution. Which pair of expressions has the same
fiasKO [112]

Missing Part of the Question

  • 3 (4 - y) -7 ; 5 + 3y
  • 9 + y + 4y - 2 - 3y; -2y + 7
  • 5 + y - 2 - 6y + y; 8y + 3
  • 2y + 7 + y - 2 + y; 4y + 5

Answer:

  • 2y + 7 + y - 2 + y; 4y + 5

Step-by-step explanation:

Given

y = 3

Required

Which pair of expression are equal

To get the pair of expression that are equal; we simply substitute 3 for y in each of the expressions

3 (4 - y) -7 and 5 + 3y

<em>Substitute 3 for y in 3 (4 - y) -7</em>

This gives 3(4 - 3) -7

= 3(1) - 7

= 3 - 7

= -4

<em>Then Substitute 3 for y in 5 + 3y</em>

This gives  5 + 3(3)

= 5 + 9

= 14

-4 and 14 are not equal

---------------------------------------------------------------------------------------

9 + y + 4y - 2 - 3y; -2y + 7

<em>Substitute 3 for y in </em>9 + y + 4y - 2 - 3y

This gives 9 + 3 + 4(3) - 2 - 3(3)

= 9 + 3 + 12 - 2 - 9

= 13

<em>Then Substitute 3 for y in -2y + 7</em>

This gives  -2(3) + 7

= -6 + 7

= 1

13 and 1 are not equal

---------------------------------------------------------------------------------------

5 + y - 2 - 6y + y; 8y + 3

<em>Substitute 3 for y in 5 + y - 2 - 6y + y</em>

This gives 5 + 3 - 2 - 6(3) + 3

= 5 + 3 - 2 - 18 + 3

= -9

<em>Then Substitute 3 for y in 8y + 3</em>

This gives  8(3) + 3

= 24 + 3

= 27

-9 and 27 are not equal

---------------------------------------------------------------------------------------

2y + 7 + y - 2 + y; 4y + 5

<em>Substitute 3 for y in 2y + 7 + y - 2 + y</em>

This gives 2(3) + 7 + 3 - 2 + 3

= 6 + 7 + 3 - 2 + 3

= 17

<em>Then Substitute 3 for y in 4y + 5</em>

This gives  4(3) + 5

= 12 + 5

= 17

17 and 17 are equal

Hence, Option D is correct

6 0
3 years ago
Widget Wonders produces widgets. They have found that the cost, c(x), of making x widgets is a quadratic function in terms of x.
AnnyKZ [126]

The total cost of producing 6 widgets is $24 if the company also discovered that it costs $16 to produce 2 widgets, $18 to produce 4 widgets, and $48 to produce 10 widgets.

<h3>What is a quadratic equation?</h3>

Any equation of the form \rm ax^2+bx+c=0  where x is variable and a, b, and c are any real numbers where a ≠ 0 is called a quadratic equation.

As we know, the formula for the roots of the quadratic equation is given by:

\rm x = \dfrac{-b \pm\sqrt{b^2-4ac}}{2a}

Let's suppose the quadratic function is:

c(x) = ax² + bx + c

Plug c(x) = $16

x = 2

16 = 4a + 2b + c ...(1)

Plug c(x) = $18

x = 4

18 = 16a + 4b + c ...(2)

Plug c(x) = $48

x = 10

48 = 100a + 10b + c ...(3)

After solving equations (1), (2), and (3) by substitution method:

a = 0.5

b = -2

c = 18

c(x) = 0.5x² -2x + 18

Plug x = 6 widgets:

c(6) = 0.5(36) - 12 + 18 = $24

Thus, the total cost of producing 6 widgets is $24 if the company also discovered that it costs $16 to produce 2 widgets, $18 to produce 4 widgets, and $48 to produce 10 widgets.

Learn more about quadratic equations here:

brainly.com/question/2263981

#SPJ1

5 0
2 years ago
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