2. WXZ=YXZ
3. Reflexive property of equality
(if they are angles)-
4. WXZ=YXZ ~~Reason- Congruent angles have equal number of degrees
(if they are triangles-more likely judging by the problem)-
4. Triangle WXZ=YXZ ~ Reason- SAS Congruence Postulate

5 0

3 years ago

An isosceles right-angled triangle is shown.

Bad White [126]

Answer:

$\boxed{x=4}$

Step-by-step explanation:

Area of triangle = 0.5 × Base × Height

→ Substitute in the values

200 = 0.5 × 5x × 5x

→ Simplify

200 = 12.5x²

→ Divide both sides by 12.5

16 = x²

→ Square root both sides

4 = x ∴ x = 4

6 0

3 years ago

The diameter of a circle has length 12. The center is at*(-5, 2). Give the equation

labwork [276]

Answer:

Equation of the circle is : $x^{2} + 10x + y^{2} -4y -7 =0$

Step-by-step explanation:

Let us consider the image attached in the answer area.

The center O has the co-ordinates i.e. (-5,2) and the diameter given is 12 units.

We know that radius is half of diameter.

$\text{Radius = }\dfrac{\text{Diameter}}{2}$

$\text{Radius = }\dfrac{12}{2}\\\Rightarrow \text{Radius = 6units}$

The equation for circle given the center and radius, can be represented as:

$(x-a)^{2}+ (y-b)^{2} = r^{2}$

Where (a,b) is the co-ordinate of center and r is the radius.

Let us consider the following formula:

$(p+q)^2 = p^{2}+ q^{2} +2pq\\(p-q)^2 = p^{2}+ q^{2} -2pq$

$(x-(-5))^{2}+ (y-2)^{2} = 6^{2}\\\Rightarrow (x+5)^{2}+ (y-2)^{2} = 36\\\Rightarrow x^{2} + 25 + 10x +y^{2} + 4-4y=36\\\Rightarrow x^{2} + 10x +y^{2} -4y-7=0$

Hence, Equation of the circle is : $x^{2} + 10x + y^{2} -4y -7 =0$

4 0

3 years ago