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3 years ago

In the figure, angle D measures 71° and angle G measures 37°. What is the measurement of angle A?

Mathematics

1 answer:

HACTEHA [7]3 years ago

3 0

Answer:

34 °

Step-by-step explanation:

∠D = 71°

∠G = 37°

In ΔGEF

Using angle sum property of triangle : Sum of all angles of triangle is 180°

∠G+∠E+∠F = 180°

Since ΔGEF is right angled triangle at F so, ∠F = 90°

Now, 37°+∠E+90° = 180°

127°+∠E= 180°

∠E= 180°-127° =53°

Now ∠E+∠D = 53°+71° = 124°

Now using exterior angle property in ΔABC

An exterior angle of a triangle is equal to the sum of the opposite interior angles

∠E+∠D is the exterior angle of ΔABC

So, ∠A+∠B = ∠E+∠D

since ΔABC is right angled triangle at B so, ∠B = 90°

∠A+90° = 124°

∠A = 124°-90°

∠A = 34°

Hence the measurement of angle A is 34 °

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3 years ago

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Step-by-step explanation:

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3 years ago

Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an answer does not exist, enter

Lapatulllka [165]

Answer:

Relative minimum: $\left(-\frac{5}{2}, -\frac{33}{4}\right)$ , Relative maximum: $DNE$

Step-by-step explanation:

First, we obtain the First and Second Derivatives of the polynomic function:

First Derivative

$f'(x) = 2\cdot x + 5$ (1)

Second Derivative

$f''(x) = 2$ (2)

Now, we proceed with the First Derivative Test on (1):

$2\cdot x + 5 = 0$

$x = -\frac{5}{2}$

The critical point is $-\frac{5}{2}$ .

As the second derivative is a constant function, we know that critical point leads to a minimum by Second Derivative Test, since $f\left(-\frac{5}{2}\right) > 0$ .