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1 year ago

PLEASE HELP ME!!!!!!!!!

Mathematics

1 answer:

Makovka662 [10]1 year ago

6 0

Answer:

(a) (5, -3)

Step-by-step explanation:

The "substitution method" for solving a system of equations requires that you write an expression that can be substituted for a variable in one or more of the other equations in the system.

<h3>Expression to substitute</h3>

The given equations are ...

y = x -8
2x +3y = 1

We notice the first equation gives an expression for y. This is exactly what we want to substitute for y in the second equation.

<h3>Substitution</h3>

When the expression (x-8) is substituted for y in the second equation, you get ...

2x +3(x -8) = 1

This simplifies to ...

5x -24 = 1

<h3>Solution</h3>

This 2-step equation can now be solved in the usual way:

5x = 25 . . . . . . add 24 to isolate the variable term

x = 25/5 = 5 . . . . . divide by the coefficient of x

Note that we now know what the correct answer choice is.

Using the expression for y, we find ...

y = x -8 = 5 -8 = -3

The solution is (x, y) = (5, -3).

The attached graph confirms this solution.

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Read 2 more answers

Calculate this reflection of the triangle:

Mice21 [21]

Answer:

a = 3, b = 0, c = 0, d = -2

Step-by-step explanation:

<em>To find the reflection Multiply the matrices</em>

∵ The dimension of the first matrix is 2 × 2

∵ The dimension of the second matrix is 2 × 3

<em>1. Multiply the first row of the 1st matrix by each column in the second matrix add the products of each column to get the first row in the 3rd matrix.</em>

2. Multiply the second row of the 1st matrix by each column in the second matrix add the products of each column to get the second row of the 3rd matrix

$\left[\begin{array}{ccc}1&0\\0&-1\end{array}\right]$ × $\left[\begin{array}{ccc}0&3&0\\0&0&2\end{array}\right]$ = $\left[\begin{array}{ccc}(1*0+0*0)&(1*3+0*0)&(1*0+0*2)\\(0*0+-1*0)&(0*3+-1*0)&(0*0+-1*2)\end{array}\right]=\left[\begin{array}{ccc}0&3&0\\0&0&-2\end{array}\right]$

Compare the elements in the answer with the third matrix to find the values of a, b, c, and d

∴ a = 3

∴ b = 0

∴ c = 0

∴ d = -2

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3 years ago

Find the height of a triangle that has an area of 54 cm2 with the width 3 cm less than its height.

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<h3>What is Triangle?</h3>

A polygon with three edges and three vertices is called a triangle. It is one of the fundamental geometric shapes. Triangle ABC is the display style for a triangle with vertices A, B, and C.
In Euclidean geometry, any three points that are not collinear produce a singular triangle and a singular plane (i.e. a two-dimensional Euclidean space).
In other words, every triangle is contained in a plane, and there is only one plane that contains that triangle.
All triangles are enclosed in a single plane if all of the geometry is the Euclidean plane, however, this is no longer true in higher-dimensional Euclidean spaces.
Except when otherwise specified, this article discusses triangles in Euclidean geometry, namely the Euclidean plane.

given that

let the height of the triangle be x

then the width is x-3

Area = $\frac{height \times length}{2}$