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1 year ago

How do i solve for x

Mathematics

1 answer:

GarryVolchara [31]1 year ago

7 0

Answer:

X is 36 and y is 48.

Step-by-step explanation:

So a couple of things here: both triangles are equal, and triangles always add up to 180 degrees. If we do some math:

180-108-48=24

This means that 2x-y needs to equal 24. We know what y is, it's 48 since both triangles are equal. Lets do some more math to find x.

48+24=72

72 divided by 2 = 36. 36 is the answer for x.

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3 years ago

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2 years ago

The range of y = - 32x ^ 2 + 90x + 3

mariarad [96]

Given:

The given function is:

$y=-32x^2+90x+3$

To find:

The range of the given function.

Solution:

We have,

$y=-32x^2+90x+3$

It is a quadratic function because the highest power of the variable x is 2.

Here, the leading coefficient is -32 which is negative. So, the graph of the given function is a downward parabola.

If a quadratic function is $f(x)=ax^2+bx+c$ , then the vertex of the quadratic function is:

$Vertex=\left(\dfrac{-b}{2a},f(\dfrac{-b}{2a})\right)$

In the given function, $a=-32,b=90,c=3$ .

$\dfrac{-b}{2a}=\dfrac{-90}{2(-32)}$

$\dfrac{-b}{2a}=\dfrac{-90}{-64}$

$\dfrac{-b}{2a}=\dfrac{45}{32}$

The value of the given function at $x=\dfrac{45}{32}$ is:

$y=-32(\dfrac{45}{32})^2+90(\dfrac{45}{32})+3$

$y=\dfrac{2121}{32}$

The vertex of the given downward parabola is $\left(\dfrac{45}{32},\dfrac{2121}{32}\right)$ . It means the maximum value of the function is $y=\dfrac{2121}{32}$ . So,

$Range=\left\{y|y\leq \dfrac{2121}{32}\right\}$

$Range=\left(-\infty, \dfrac{2121}{32}\right ]$

Therefore, the range of the given function is $\left (-\infty, \dfrac{2121}{32}\right ]$ .

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