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3 years ago

In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, BE=2x2−x , and DE=x2+6 .

2 answers:

8 0

<span>The diagonals of a parallelogram bisect each other. So we just equate the two equations BE and DE 2x^2 - x = x^2 + 6 2x^2 - x - x^2 - 6 = 0 x^2 - x - 6 = 0 This is quadratic eqn. So we obtain. (x - 3) ( x + 2) = 0 Setting each to 0 and solving for x, we have that x = 3 and x = -2 So we have two possible values for BD. But Since BE = DE then we can simply double each If x = 3 BD = 2 (2(3)^2 - 3) = 2 ( 18 - 3) = 30 units If x = - 2 BD = 2((-2)^2 -3 ) = 2 (8 - 3) = 10 units</span>

4vir4ik [10]3 years ago

7 0

Answer:

The answer is 30, I took the test

Step-by-step explanation:

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An adventurous dog strays from home, runs three blocks east, two blocks north, one block east, one block north, and two blocks w

Marrrta [24]

<h2>Answer:</h2>

<u>Distance = 360.55 m</u>

<u>Direction = North-East</u>

<h2>Step-by-step explanation:</h2>

In the question,

The adventurous dog starts from O, say.

He moves 3 blocks East = 300 m

then,

2 blocks North = 200 m

1 block East = 100 m

1 block North = 100 m

2 blocks West = 200 m

So,

Distance of the Dog's <u>final position</u> from the <u>initial position</u><u>.</u>

OE is given by,

In triangle OLE, using Pythagoras theorem,

$OE^{2}=OL^{2}+LE^{2}\\OE^{2}=(200)^{2}+(300)^{2}\\OE^{2}=40000+90000\\OE=360.55\,m$

<em><u>Therefore, the distance of Dog from the Home is 360.55 m and the direction of Dog from Home is North-East.</u></em>

8 0

3 years ago

For a certain map, the scale shows that 1 cm on the map equals 2.50 km on earth's surface. two towns on the map are 4.75 cm apar

Julli [10]

<span>In this problem, to find the answer we have to setup a series of ratios that relate the scale to real life distance. We know that 1cm = 2.50km, so that ratio would be 1cm/2.5km. For two towns that are 4.75cm apart on the map, we set a ration of 4.75cm/x km, where x is the actual distance. Now we set the ratios equal to each other and solve for x. 1/2.5=4.75/x where x = 4.75*2.5/1 = 11.875 and rounding up we get 11.88 km. The two towns are actually 11.88 km apart from each other.</span>

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3 years ago

You have $50 to spend at the fair. Admission is $5 and tickets are $0.50 each. How many tickets can you buy? {Write an equation.

anzhelika [568]

Answer:

You can buy 90 tickets

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3 years ago

Help needed ASAP will give BRAINLIEST and 5 Stars rate

garri49 [273]

(-3, 3) because it is the intersection point.

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3 years ago

18) If the straight line y=m X touches the circle (x - 2)^2 + (y - 6)^2 = 4, then m= ......

fenix001 [56]

Answer:

(8) d. 4/3 (9) a. (X - 4)^2 + (y-4)^2= 25

Step-by-step explanation:

8. CENTER OF CIRCLE: O (2,6)

radius of circle : r = √4 = 2

if m = 4/3 line: y = 4/3 x

perpendicular distance (d) from center of circle to line y = 4/3 x is

d = |((4/3 x 2) + (-1) x 6)| / √((4/3)² + (-1)²) = |(-10/3)| / √(25/9) = (10/3) / (5/3) = 2

d = r means line touch with circle

9. center of circle is the intersection of the diagonals of rectangle (4,4) and its radius is 5 (illustrated)

the equation of circle: (X - 4)^2 + (y-4)^2= 25

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3 years ago