Write an equation for the line on the graph below:

Mathematics

1 answer:

wolverine [178]3 years ago

7 0

Answer:

This line is a horizontal line, so it has an equation y=n, where n is a number.

In this case, because the y intercept is (0,2) the equation is y=2.

Let me know if this helps!

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Find the length of the line PA.

Diano4ka-milaya [45]

RO divides the rectangle into two congruent right triangles.

The area of the one triangle is equal half area of the rectangle.

Calculate the area of rectangle:

$A_R=lw\\l=12,\ w=5\\\\A_R=12\cdot5=60$

The area of right triangle:

$A_T=\dfrac{1}{2}A_R\to A_T=\dfrac{1}{2}\cdot60=30$

Use the Pythagorean theorem to calculate the length of RO:

$|RO|^2=5^2+12^2\\\\|RO|^2=25+144\\\\|RO|^2=169\to|RO|=\sqrt{169}\to|RO|=13$

The formula of an area of this right triangle is:

$A_T=\dfrac{1}{2}|RO||PA|$

Therefore we have the equation:

$\dfrac{1}{2}(13)|PA|=30\qquad|\cdot2\\\\13|PA|=60\quad|:13\\\\|PA|=\dfrac{60}{13}\\\\|PA|\approx4.62$

8 0

3 years ago

Explain why it is possible to draw more than two different rectangles with an area of 36 square units, but it is not possible to

Inessa05 [86]

Answer:

Step-by-step explanation

you are able to make two squares because you can use the square root of 36 and that twill give you 6 not a decimal.

in comparison if you do the square root of 15 it will give you 3.87298335

7 0

3 years ago

What is the product in simplest form x^2+9x+18/x+2 times x^2-3x-10/x^2+2x-24

german

$\dfrac{x^2+9x+18}{x+2}\cdot\dfrac{x^2-3x-10}{x^2+2x-24}=\dfrac{x^2+6x+3x+18}{x+2}\cdot\dfrac{x^2-5x+2x-10}{x^2+6x-4x-24}\\\\=\dfrac{x(x+6)+3(x+6)}{x+2}\cdot\dfrac{x(x-5)+2(x-5)}{x(x+6)-4(x+6)}$

$=\dfrac{(x+6)(x+3)}{x+2}\cdot\dfrac{(x-5)(x+2)}{(x+6)(x-4)}=\dfrac{(x+3)(x-5)}{x-4}\\\\=\dfrac{x^2-5x+3x-15}{x-4}=\dfrac{x^2-2x-15}{x-4}$