MATHEMATICS HIGH SCHOOL

Given: ABCD ∥gram, BK ⊥ AD , AB ⊥ BD AB=6, AK=3 Find: m∠A, BK, Area of ABCD

Answers

Answer 1

Answer:

1. Consider right triangle ABK. In this triangle AB is the hypotenuse, BK and AK are legs. By the Pythagorean theorem,

$AB^2=AK^2+BK^2,\n\n6^2=3^2+BK^2,\n\nBK^2=36-9=27,\n\nBK=3√(3)\ un.$

2. Use the definition of $\cos \angle A:$

$\cos \angle A=\frac{\text{adjacent leg}}{\text{hypotenuse}}=(AK)/(AB)=(3)/(6)=(1)/(2).$

Then $m\angle A=60^(\circ).$

3. Consider right triangle ABD. In this triangle AD is the hypotenuse, AB and BD are legs. Since $m\angle A=60^(\circ),$ then

$m\angle BDA=180^(\circ)-90^(\circ)-60^(\circ)=30^(\circ).$

The leg that is opposite to the angle of 30° is half of the hypotenuse, so

$AD=2AB=12\ un.$

4. The area of parallelogram aBCD is

$A_(ABCD)=AD\cdot BK=12\cdot 3√(3)=36√(3)\ sq. un.$

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Y is equal to 21 and x is equal to 10

How do I solve this?

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Work is attached..

:D

What is 70/x = 15/21?

Answers

Answer:

Step-by-step explanation:

cross multiply

70×21÷15

1470/15=98

What is the length of the radius of a circle with a center at 2 + 3i and a point on the circle at 7 + 2i?

Answers

Hello,

A=2+3i
B=7+2i
AB=B-A=7+2i-(2+3i)=5-i

Radius=√(5²+1²)=√26

Answer:

b. squareroot 26

Step-by-step explanation:

what is the solution to the system of equations? y =1/3 x – 10 2x y = 4 (–8, 6) (–6, 16) (6, –8) (16, –6)

Answers

Answer:

Option C is correct.

Solution to the given system of equation is (6 , -8)

Step-by-step explanation:

Given the system of equation:

$y= (1)/(3) x-10$ ......[1]

$2x+y =4$ .....[2]

Substitute the equation [1] in [2] we get;

$2x +(1)/(3)x -10 =4$

Combine like terms;

$(7)/(3)x -10 =4$

Add 10 to both side of an equation:

$(7)/(3)x -10 +10=4+10$

Simplify:

$(7)/(3)x =14$

Divide both sides by $(3)/(7)$ we get;

$(3)/(7) * (7)/(3)x = 14 * (3)/(7)$

Simplify:

x = 6

Substitute the value of x =6 in equation [1] we get;

$y= (1)/(3)(6)-10$

$y= 2-10$

Simplify:

y = - 8

therefore, the solution to the given system of equation is; (6 , -8)

You can also see in the graph as shown below:

y = 1/3 x - 10
2x + y = 4
2x + 1/3 x - 10 = 4
7/3 x = 14
x = 6
y = 1/3(6) - 10 = 2 - 10 = -8
Therefore solution is (6, -8)

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