Which of these is least likely to describe

Identify the three similar right triangles in the given diagram.

irga5000 [103]

Answer:

B. ΔABD, ΔADC, ΔDBC

Step-by-step explanation

Step -1 In ΔABD and ΔADC (from figure).

∠DAB=∠CAD (common in both triangles) ,

∠DBA=∠CDA =90 degree, and

∠BDA=∠DCA (rest angle of the two triangles).

therefore ΔABD similar to ΔADC (by AAA similarity theorem).

Step -2 In ΔDBC and ΔADC (from figure).

∠DCB=∠ACD (common in both triangles) ,

∠DBC=∠ADC =90 degree, and

∠CDB=∠CAD (rest angle of the two triangles).

therefore ΔDBC similar to ΔADC (by AAA similarity theorem).

Step -3 In ΔABD and ΔDBC (from figure).

∠BDA=∠BCD (because , ∠ACD=ADB from stap-1 and ∠ACD=∠BCD from figure) ,

∠DBA=∠CBD =90 degree, and

∠BAC=∠BDC (rest angle of the two triangles).

therefore ΔABD similar to ΔDBC (by AAA similarity theorem).

In the above step- ΔABD similar to ΔADC, ΔDBC similar to ΔADC and ΔABD similar to ΔDBC.

Hence ΔABD, ΔADC, ΔDBC similar to each other in the given figure.

4 0

3 years ago

Two cars traveled equal distances in different amounts of time. Car A traveled the distance in 2 h, and Car B traveled the dista

Yuki888 [10]

$d=v \cdot t$
d - distance
v - speed
t - time

Car A:
$v_1 \\
t_1=2 \\
d_1=v \cdot 2=2 v$

Car B:
15 mph faster than car A
$v_2=v_1+15 \\ t_2=1.5 \\ d_2= (v_1+15) \cdot 1.5=1.5v_1 + 22.5$

Both cars traveled equal distances:
$d_1=d_2 \\
2v_1 = 1.5v_1+22.5 \\
2v_1-1.5v_1=22.5 \\
0.5v_1=22.5 \\
v_1=45 \\ v_2=45 + 15 =60$

Car B traveled at the speed of 60 mph.

6 0

3 years ago

UITE

max2010maxim [7]

A logical conclusion would say “Kelly is 15 minutes late to school.”

4 0

2 years ago

the formula for the area of a square s to the 2nd power, where s is the side length of the square. What is the area of a square

Helen [10]

The answer to this is 36.

5 0

2 years ago

Let p(x) = x^2 + 8x + 12 and q(x) = x^3 + 5x^2 - 6x. Define r(x) = p(x) \cdot q(x).

Anna [14]

The roots of the entire polynomic expression, that is, the product of p(x) = x^2 + 8x + 12 and q(x) = x^3 + 5x^2 - 6x, are x₁ = 0, x₂ = -2, x₃ = -3 and x₄ = -6.

<h3>How to solve a product of two polynomials </h3>

A value of x is said to be a root of the polynomial if and only if r(x) = 0. Let be r(x) = p(x) · q(x), then we need to find the roots both for p(x) and q(x) by factoring each polynomial, the factoring is based on algebraic properties:

r(x) = (x + 6) · (x + 2) · x · (x² + 5 · x - 6)

r(x) = (x + 6) · (x + 2) · x · (x + 3) · (x + 2)

r(x) = x · (x + 2)² · (x + 3) · (x + 6)

By direct inspection, we conclude that the roots of the entire polynomic expression are x₁ = 0, x₂ = -2, x₃ = -3 and x₄ = -6. $\blacksquare$

To learn more on polynomials, we kindly invite to check this verified question: brainly.com/question/11536910

5 0

2 years ago