Solve a quadratic equation using the zero product property

-14x + 15y = 15 -21x - 20y = -10 Use substitution to find the x and y coordinates.

denis-greek [22]

          -14x + 15y = 15
      -14x + 14x + 15y = 14x + 15
         15y = 14x + 15
          15    15
         y = ¹⁴/₁₅x + 1
   -21x - 20y = -10
   -21x - 20(¹⁴/₁₅x + 1) = -10
-21x - 20(¹⁴/₁₅x) - 20(1) = -10
       -21x - 18²/₃x - 20 = -10
      -39²/₃x - 20 = -10
      + 20 + 20
      -39²/₃x = 10
       -39²/₃   -39²/₃
   x = ⁻³⁰/₁₁₉
         y = ¹⁴/₁₅x + 1
   y = ¹⁴/₁₅(⁻³⁰/₁₁₉) + 1
   y = ⁻²⁸/₁₁₉ + 1
   y = ⁹¹/₁₁₉
      (x, y) = (⁻³⁰/₁₁₉, ⁹¹/₁₁₉)

8 0

2 years ago

At the movie theatre, child admission is $5.30 and adult admission is $9.70. On Wednesday, 156 tickets were sold for a total sal

serious [3.7K]

Answer:

The number of adult tickets are 57.

Step-by-step explanation:

Given,

Total number of tickets = 156

Total money = $1077.60

Solution,

Let the number of adult be x and of child be y .

So, Total number of tickets = Number of adults + Number of child

$\therefore x+y = 156\ \ \ \ \ \ equation\ 1$

Now, according to question;

Total money = $Number\ of\ adults\times admission\ fee + Number\ of\ child\times admission\ fee$

$\therefore x\times 9.70+y\times 5.30 = 1077.60\ \ \ \ \ \ equation\ 2$

On multiplying by 10 on both side, we get;

$97x+53y=10776\ \ \ \ \ \ equation\ 3$

Now multiplying equation 1 by 53 then subtract it from equation 3, we get;

$(x+y)\times53 = 156\times53\\53x+53y=8268\\(97x+53y=10776)-(53x+53y=8268)\\44x=2508\\x=\frac{2508}{44} =57$

Since x is the number of adults,

Number of adults=57

Number of child = y = 156-57=99

Thus the number of adult tickets are 57.

7 0

2 years ago

Please help me find the total area of the composite figure below (geometry)

Akimi4 [234]

Answer:

lw + $\frac{1}{2}$ × π × $(\frac{l}{2} )^{2}$ ⇒ Answer D is correct

Step-by-step explanation:

First, let us find the area of the semi-circle.

Area = $\frac{1}{2}$ × π × r²

Given that,

diameter of the semi-circle is ⇒ l

∴ radius ⇒ l / 2

Let us find it now.

Area = $\frac{1}{2}$ × π × r²

Area = $\frac{1}{2}$ × π × $(\frac{l}{2} )^{2}$

Secondly, let us find the area of the rectangle.

Area = length × width

Given that,

length ⇒ l

width ⇒ w

Let us find it now.

Area = length × width

Area = l ×w

Area = lw

And now let us find the total area.

Total area = Area of the rectangle + Area of the semi - circle

Tota area = lw + $\frac{1}{2}$ × π × $(\frac{l}{2} )^{2}$

8 0

2 years ago

Find the value of each expression. -5 -9 -13

Andrei [34K]

Answer:

-27

Step-by-step explanation:

-5-9=-14

-14-13=-27

3 0

3 years ago

Which of the following operations could you perform on both sides of the given equation to solve it? check all that apply. 8x -

antiseptic1488 [7]

8x-2x=24+6
6x=30
6x/6=30/6
x=5

3 0

3 years ago