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3 years ago

1

Mathematics

1 answer:

Eduardwww [97]3 years ago

7 0

Answer:

Cartesian plane: This is a particular case of a coordinate plane, such that we have two (or more) perpendicular axes, and usually is used for rectangular coordinates.

Two-dimensional: A coordinate plane can be two-dimensional, some examples are polar coordinates, where the coordinates are the radius and the angle, or rectangular coordinates, where the variables are x and y.

Three-dimensional: Similar to before, a coordinate plane can be three-dimensional in several ways, like in spherical coordinates or cylindrical coordinates.

Extends forever: The axes in a rectangular coordinate plane extend forever, so this description also works.

Perpendicular axes: In some cases, like in rectangular coordinates, the axes are perpendicular, (but not always) so this can also be used.

Parallel axes: As each axis is measured along its length, having two parallel axes will be useless (as we could use only one axis instead of two) so this is the only one that would not apply to a coordinate axis.

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Stephen scored 17/20 on his spelling test. What was his percentage score ?

Sergio [31]

Answer:

Step-by-step explanation:

He scored 85%

(17/20)%

85%

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3 years ago

Read 2 more answers

Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6

Reptile [31]

Answer:

a. No solution, parallel lines.

b. One solution.

Step-by-step explanation:

Given the system of equations:

a. $2x-4y=12$

$-3x+6y=-15$

b. $2x-4y=12$

$-5x+3y=10$

To give a geometric description of the given system of equations.

The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.

i.e.

Number of planes = Number of variables

Number of lines = Number of equations in the system.

Here, we are given 2 variables and 2 equation in each system.

So, they can be represented in the xy-coordinates plane.

And the number of solutions to the system depends on the following condition.

Let the system of equations be:

$A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0$

1. One solution:

There will be one solution to the system of equations, If we have:

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

2. Infinitely Many Solutions: (Identical lines in the system)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}= \dfrac{C_1}{C_2}$

3. No Solution:(Parallel lines)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Now, let us discuss the system of equations one by one:

a. $2x-4y=12$ OR $2x-4y-12=0$

$-3x+6y=-15$ OR $-3x+6y+15=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -3, B_2 = 6, C_2= 15$

Here, the ratio:

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2} = -\dfrac{2}{3}\\\dfrac{C_1}{C_2} = -\dfrac{4}{5}$

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Therefore, no solution i.e. parallel lines.

b. $2x-4y=12$ OR $2x-4y-12=0$

$-5x+3y=10$ OR $-5x+3y-10=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -5, B_2 = 3, C_2 = -10$

$\dfrac{A_1}{A_2}= -\dfrac{2}{5}\\\dfrac{B_1}{B_2} = -\dfrac{4}{3}\\\dfrac{C_1}{C_2} = -\dfrac{6}{5}$

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

So, one solution.

Kindly refer to the images attached for the graphical representation of the given system of equations.

6 0

3 years ago

Use repeated addition to find the solution to each multiplication problem. Change any improper fractions to mixed numbers. 4x1/3

Nata [24]

Answer:

$1\frac{1}{3}$

Step-by-step explanation:

Given the following question:

$4\times\frac{1}{3}$

To find the answer simply multiply the numerators and the denominators by each other.

$4\times\frac{1}{3}$
$4=\frac{4}{1}$
$\frac{4}{1} \times\frac{1}{3}$
$4\times1=4$
$1\times3=3$
$=\frac{4}{3}$
$\frac{4}{3} =4\div3=1\frac{1}{3}$
$1\frac{1}{3}$

Hope this helps.

7 0

2 years ago

Tell whether the ordered pair is a solution of the given system. (-2,-4) {y=1/2x -3, y=-2x-8}

kompoz [17]

Answer:

The ordered pair $(-2,\, -4)$ is indeed a solution to the system:

$\left\lbrace\begin{aligned} & y = \frac{1}{2}\, x - 3 \\ & y = -2\, x - 8\end{aligned}\right.$ .

Step-by-step explanation:

Consider a system of equations about variables $x$ and $y$ . An ordered pair $(x_{0},\, y_{0})$ (where $x_{0}$ and $y_{0}$ are constant) is a solution to that system if and only if all equations in that system hold after substituting in $x = x_{0}$ and $y = y_{0}$ .

For the system in this question, $(-2,\, -4)$ would be a solution only if both equations in the system hold after replacing all $x$ in equations of the system with $(-2)$ and all $y$ with $(-4)$ .

The $\texttt{LHS}$ of the equation $y = (1/2)\, x - 3$ would become $(-4)$ . The $\texttt{RHS}$ of that equation would become $(1/2) \, (-2) - 3$ . The two sides are indeed equal.

Similarly, the $\texttt{LHS}$ of the equation $y = -2\, x - 8$ would become $(-4)$ . The $\texttt{RHS}$ of that equation would become $(-2)\, (-2) - 8$ . The two sides are indeed equal.

Thus, $x = (-2)$ and $y = (-4)$ simultaneously satisfy both equations of the given system. Therefore, the ordered pair $(-2,\, -4)$ would indeed be a solution to that system.

8 0

2 years ago

Can u help me answer dis

gavmur [86]

Answer:

the base is 10 and the height is 6.4

3 0

3 years ago