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harina [27]
3 years ago
8

Triangle ABC has vertices with Alx, 3).

Mathematics
1 answer:
densk [106]3 years ago
5 0

Answer:

x = 3

This triangle ABC will be a right triangle as its sides obey the Pythagoras theorem.

Step-by-step explanation:

Let us assume that the triangle Δ ABC has vertices A(x,3), B(-3,-1) and C(-1,-4) and it is a right triangle.  

We have to determine x.

Applying the Pythagoras Theorem,

AB² + BC² = AC² {If AC is the hypotenuse of the right triangle}

⇒ [(x + 3)² + 4²] + [(- 2)² + 3²} = (x + 1)² + 7²

⇒ x² + 6x + 38 = x² + 2x + 50

⇒ 4x = 12

⇒ x = 3 (Answer)

This triangle ABC will be a right triangle as its sides obey the Pythagoras theorem. (Answer)

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Consider h(x)=x^2+8+15. identify its vertex and y-intercept.
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Answer:

Vertex: (-4, -1)

Y-intercept: (0, 15)

Step-by-step explanation:

Given the quaratic function, h(x) = x² + 8x + 15:

In order to determine the vertex of the given function, we can use the formula, [x = \frac{-b}{2a}, h(\frac{-b}{2a})].

<h3>Use the equation:  [x = \frac{-b}{2a}, h(\frac{-b}{2a})]</h3>

In the quadratic function, h(x) = x² + 8x + 15, where:

a = 1, b = 8, and c = 15:

Substitute the given values for <em>a</em> and <em>b</em> into the equation to solve for the x-coordinate of the vertex.

x = \frac{-b}{2a}

x = \frac{-8}{2(1)}

x = -4

Subsitute the value of the x-coordinate into the given function to solve for the <u>y-coordinate of the vertex</u>:

h(x) = x² + 8x + 15

h(-4) = (-4)² + 8(-4) + 15

h(-4) = 16 - 32 + 15

h(-4) = -1

Therefore, the vertex of the given function is (-4, -1).

<h3>Solve for the Y-intercept:</h3>

The <u>y-intercept</u> is the point on the graph where it crosse the y-axis. In order to find the y-intercept of the function, set x = 0, and solve for the y-intercept:

h(x) = x² + 8x + 15

h(0) = (0)² + 8(0) + 15

h(0) = 0 + 0 + 15

h(0) = 15

Therefore, the y-intercept of the quadratic function is (0, 15).

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2 years ago
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Step-by-step explanation:

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Step-by-step explanation:

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P(x) = 2x3 − x2 + 10x; <br><br> a 1/2 <br><br><br><br> b 5<br><br><br> c 0<br><br><br> d 2
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Answer:

a......5

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Step-by-step explanation:

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