Mathematics, 04.03.2021 20:40 maddiem5027

State if each triangle is acute, obtuse, or right using Pythagorean theorem converse.

State if each triangle is acute, obtuse,or right using Pythagorean theorem converse.

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Answer from: milkshakegrande101

Right triangle

Step-by-step explanation:

Properties for acute, obtuse or right triangle,

1). Given triangle will be a right triangle if,

Hypotenuse² = (Leg 1)² + (Leg 2)²

2). Triangle will be an acute triangle if,

(Largest side)² < (leg 1)² + (leg 2)²

3). Triangle will be an obtuse triangle if,

(Largest side)² > (leg 1)² + (leg 2)²

Now we apply these properties in the given triangle,

(Largest side)² = (√11105)²

= 11105

(leg 1)² = (76)²

= 5776

(leg 2)² = (73)²

= 5329

Since 11105 = 5776 + 5329 (First Property)

11105 = 11105

Therefore, given triangle is a right triangle.

Answer from: Quest

answer: a and c are correct

step-by-step explanation:

the +5 is the vertical translation

the added negative symbol in front is the reflection over the y-axis

Which statements describe one of the transformations performed on f(x) = x^2 to create g(x) = -(x -

Answer from: Quest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is

$y\leq -x+4$

similarly, check the second related equation.

$3(1)=0$

it is a dashed line, so this statement is true if the sign of inequality is > . the required inequality is

$3y> x$

15 points write a system of inequalities to represent the shaded portion of the graph

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