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yKpoI14uk [10]
3 years ago
10

)Consider the following pair of equations: y = −2x + 8 y = x − 1 Explain how you will solve the pair of equations by substitutio

n. Show all the steps and write the solution in (x, y) form.
Mathematics
1 answer:
Ira Lisetskai [31]3 years ago
5 0

Hi there,

Take y from first equation and use it / substitute it into the second equation:

-2x + 8 = x - 1, so 3x = 9, therefore x = 3.

Then y = x - 1 = 3 - 1 => y = 2.

Solution is (3,2).

A quick check: 2 = -2*3 + 8, true, and 3 = 2 - 1, also true.

Green eyes.

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2 years ago
A Rectangle is removed from a right triangle to create the shaded region below. Find the area of the shaded region be sure to in
Scorpion4ik [409]

The given shapes area is found to be 4 square yards.

Step-by-step explanation:

Step 1; To determine the area of an indefinite shape we must divide it into the shapes that we know. The shape that is given can be split into a triangle with a rectangle in it.

Step 2; Any given triangles area is half the multiplication of its base value and its height value. In the given diagram, the base of the triangle measures a length of 5 yards and the length from base to top is 4 yards

Area of the triangle = \frac{1}{2} * base * height = \frac{1}{2} * 5 * 4 = 10 square yards.

The given rectangle measures a length of 3 yards and a width of 2 yards. The area of any given rectangle is the multiplication of its length and width.

Area of the rectangle = Length * Width = 3 yards * 2 yards = 6 square yards.

Step 3; To find the total area of the shape we must subtract the the rectangle's area from the triangle's area.

Area of given shape = Area of the triangle - Area of the rectangle.

Area of given shape = 10 square yards - 6 square yards = 4 square yards.

7 0
3 years ago
Find the standard equation of the parabola that satisfies the given conditions. Also, find the length of the latus rectum of eac
lakkis [162]

Answer:

The standard parabola

                                y² = -18 x +27

Length of Latus rectum = 4 a = 18

                         

Step-by-step explanation:

<u><em>Explanation:-</em></u>

Given focus : (-3 ,0) ,directrix  : x=6

Let P(x₁ , y₁) be the point on parabola

PM perpendicular to the the directrix L

                          SP² = PM²

                (x₁ +3)²+(y₁-0)²  = (\frac{x_{1}-6 }{\sqrt{1} } )^{2}

              x₁²+6 x₁ +9 + y₁² = x₁²-12 x₁ +36

                          y₁² = -18 x₁ +36 -9

                           y₁² = -18 x₁ +27

The standard parabola

                                y² = -18 x +27

    Length of Latus rectum = 4 a = 4 (18/4) = 18

                         

5 0
3 years ago
A rectangle with length 16cm and width 12cm is inscribed in a circle.What is the area of the region inside the circle and outsid
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The area of circle is πr2.
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3 0
3 years ago
IMAX Movie Prices. There were 322 people at a recent showing of the IMAX 3D movie "300". Admission was $8.75 each for adults and
dsp73

Answer:

218 adults and 104 children attended.

Step-by-step explanation:

From the information given, you can write the following equations:

x+y=322 (1)

8.75x+6y=2531.50 (2), where:

x is the number of adults

y is the number of children

First, you can solve for x in (1):

x=322-y (3)

Then, you can replace (3) in (2) and solve for y:

8.75(322-y)+6y=2531.50

2817.5-8.75y+6y=2531.50

2817.5-2531.50=8.75y-6y

286=2.75y

y=286/2.75

y=104

Finally, you can replace the value of y in (3) to find x:

x=322-104

x=218

According to this, the answer is that 218 adults and 104 children attended.

8 0
2 years ago
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