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3 years ago

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Mathematics

1 answer:

bonufazy [111]3 years ago

6 0

Answer:

-23/3

Step-by-step explanation:

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What is the area of triangle DEF?

FrozenT [24]

Answer:

$A=2\sqrt{14}\ units^2$

Step-by-step explanation:

we know that

Heron's Formula is a method for calculating the area of a triangle when you know the lengths of all three sides.

$A=\sqrt{s(s-a)(s-b)(s-c)}$

where

a, b and c are the length sides of triangle

s is the semi-perimeter of triangle

we have

$a=5\ units,b=6\ units,c=3\ units$

<em>Find the semi-perimeter s </em>

s= $\frac{5+6+3}{2}=7\ units$

Find the area of triangle

$A=\sqrt{7(7-5)(7-6)(7-3)}$

$A=\sqrt{7(2)(1)(4)}$

$A=\sqrt{56}\ units^2$

simplify

$A=2\sqrt{14}\ units^2$

3 0

2 years ago

A map is laid out in the standard (x,y) coordinate plane. How long, in units, is an airplane's path on the map as the airplane f

xeze [42]

Answer:

Distance between the points A and B is 15.52 units.

Step-by-step explanation:

It has been given in the question that an airplane flies along a straight line from City A to City B.

Map has been laid out in the (x, y) coordinate plane and the coordinates of these cities are A(20, 14) and B(5, 10).

Distance between two points A'(x, y) and B'(x', y') is represented by the formula,

d = $\sqrt{(x-x')^{2}+(y-y')^{2}}$

So we plug in the values of (x, y) and (x', y') in the formula,

d = $\sqrt{(20-5)^{2}+(14-10)^{2}}$

d = $\sqrt{(15)^{2}+(4)^{2}}$

d = $\sqrt{225+16}$

d = 15.52

Therefore, distance between the points A and B is 15.52 units.

4 0

3 years ago

An angle measures 28º less than the measure of its complementary angle. What is the measure of

GuDViN [60]

Answer:

Let the angle=x

So the other angle will be = y

X-28 +y=90

5 0

2 years ago

Quadrilateral KLMN is a rectangle. The coordinates of L are L(1,-4), and the coordinates of Mare M(3,-2). Find the slopes of sid

lozanna [386]

L(1, -4)=(xL, yL)→xL=1, yL=-4
M(3, -2)=(xM, yM)→xM=3, yM=-2

Slope of side LM: m LM = (yM-yL) / (xM-xL)
m LM = ( -2 - (-4) ) / (3-1)
m LM = ( -2+4) / (2)
m LM = (2) / (2)
m LM = 1

The quadrilateral is the rectangle KLMN
The oposite sides are: LM with NK, and KL with NK
In a rectangle the opposite sides are parallel, and parallel lines have the same slope, then:
Slope of side LM = m LM = 1 = m NK = Slope of side NK
Slope of side NK = m NK = 1

Slope of side KL = m KL = m MN = Slope of side MN

The sides KL and LM (consecutive sides) are perpendicular (form an angle of 90°), then the product of their slopes is equal to -1:
(m KL) (m LM) = -1
Replacing m LM = 1
(m KL) (1) = -1
m KL = -1 = m MN

Answer:
Slope of side LM =1
Slope of side NK =1
Slope of side KL = -1
Slope of side MN = -1

3 0

3 years ago

If Sarah walked 5 kilometers this weekend, about how many miles did she walk

Harrizon [31]

She walked 3.107 miles

4 0

3 years ago