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2 years ago

Fill in the following 5 statements and 5 reasons used to complete this proof.

Mathematics

1 answer:

Allisa [31]2 years ago

5 0

Answer:

AD ≅ CD.

Step-by-step explanation:

Statement : consider triangles ADB and DBC.

1) AB = CD

2) ∠ABD = ∠DBC

3) DB = DB

4) ⇒ ΔADB and ΔDBC are congruent triangles.

5) AD = DC.

Reasons ;

1) given, AB = CB

2) given, DB bisects ∠ ABC

3) common side of both triangles

4) as two sides and one angle are equal in both triangles

5) congruent triangles

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A jacket usually sells for $69.00. If the jacket is 30% off, and sales tax is 8%, what is the total price of the jacket, includi

Ivan

$52.16
30% of 69 is 20.7.
69-20.7= $43.30
8% of 43.3 is 3.864.
43.3+3.864= $52.164
round down due to the 4.
$52.16

7 0

3 years ago

PLEASE help due today Geometry

irina1246 [14]

$\\ \sf\Rrightarrow \dfrac{15}{20}=\dfrac{21}{28}$

$\\ \sf\Rrightarrow \dfrac{1}{4}=\dfrac{1}{4}$

Hence they are similar

<A=<H
And ratio of sides are same

Hence both triangles are similar by SAS property

$\\ \sf\Rrightarrow ∆KDH\sim ∆ABD$

8 0

2 years ago

If 5y = 6x + 16 and 9x = 7y-20, what is the value of 3x - 2y?

Law Incorporation [45]

The value of 3x-2y is -4. From the equation 5y=6x=16 and 9x=7y-20 the values of (x,y) is (4,8).

Step-by-step explanation:

The given equations are,

5y=6x+16.......................(1)

9x=7y-20......................(2)

3x-2y...............................(3)

Step:1

Modify the equations (1) and (2) in (x+y=constant) format,

6x-5y=-16.....................(4)

9x-7y=-20....................(5)

Step:2

Equation (4) is multiplied by 7 ( ∵ 7×Eqn(4))

42x-35y=-112..............(6)

Step:3

Equation (5) is multiplied by 5 (∵ 5×Eqn(5))

45x-35y=-100.............(7)

Step:4

Subtracting Equation (6) and (7)

42x-35y=-112

45x-35y=-100

( - )

(42x-45x)+(35y-35y)=(100-112)

(-3x)+(0)=(-12)

x=4

Step:5

Substitute X value in Equation (1),

5y=6x+16...................(1)

where, x=4,

5y= (6×4)+16

5y=40

y= 8

Step: 6

Check for solution, substitute x and y values in equation (2).

9x=7y-20.......................(2)

(9×4)=(7×8)-20

36=36

Step:7

From given, 3x-2y

where, X=4 and y=8

3x-2y = (3×4)-(2×8)

= 12-16

3x-2y = -4

Result:

The value for 3x-2y is -4. The values of (x,y) are (4,8).

5 0

2 years ago

Read 2 more answers

Given: ∆ABC –iso. ∆, m∠BAC = 120°

lidiya [134]

Answer: $P\triangle ADH = (a+b+\sqrt{a^2+b^2} )$ unit

Step-by-step explanation:

Since Here Δ ABC is a isosceles triangle.

Also, $AH\perp BC$ and $HD\perp AC$

Thus, ∠ ADH = 90°

That is, Δ ADH is the right angle triangle.

In which, AD = a unit and HD = b unit

And, By the definition of Pythagoras theorem,

$AH^2 = HD^2 + AD^2$

⇒ $AH^2 = a^2 +b^2$

⇒ $AH = \sqrt{a^2+b^2}$

Since, the perimeter of a triangle = sum of the all sides of the triangle.

Therefore, perimeter of ΔADH = AD + DH + AH

= $a + b + \sqrt{a^2+b^2}$ unit

4 0

3 years ago

Find the angle between u = (8.- 3) and v = (-3,- 8) Round to the nearest tenth of a degree.

Nimfa-mama [501]

Answer:

Step-by-step explanation:

First you must calculate the module or the magnitude of both vectors

The module of u is:

$|u|=\sqrt{(8)^2 + (-3)^2} \\\\|u|=\sqrt{64 + 9}\\\\|u|=8.544$

The module of v is:

$|v|=\sqrt{(-3)^2 + (-8)^2} \\\\|u|=\sqrt{9 + 64}\\\\|u|=8.544$

Now we calculate the scalar product between both vectors

$u*v = 8*(-3) + (-3)*(-8)\\\\u*v = -24+ 24=0$

Finally we know that the scalar product of two vectors is equal to:

$u*v = |u||v|*cos(\theta)$

Where $\theta$ is the angle between the vectors u and v. Now we solve the equation for $\theta$

$0 = 8.544*8.544*cos(\theta)\\\\0 = cos(\theta)\\\\\theta= arcos(0)\\\\\theta=90\°$

the answer is 90°

Whenever the scalar product of two vectors is equals to zero it means that the angle between them is 90 °

5 0

3 years ago

Read 2 more answers