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2 years ago

Calculate AD and hence BD.

Mathematics

1 answer:

Vilka [71]2 years ago

7 0

Answer:

AD = 15 cm , BD = 3 cm

Step-by-step explanation:

Δ ABC is similar to Δ ADE ( by the AA postulate )

then the ratios of corresponding sides are in proportion, that is

$\frac{AD}{AB}$ = $\frac{DE}{BC}$ ( substitute values )

$\frac{AD}{12}$ = $\frac{10}{8}$ ( cross- multiply )

8 × AD = 12 × 10 = 120 ( divide both sides by 8 )

AD = 15 cm

AB + BD = AD , that is

12 + BD = 15 ( subtract 12 from both sides )

BD = 3 cm

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Select the correct answer.

Lina20 [59]

Based on the SAS congruence criterion, the statement that best describes Angie's statement is:

Two triangles having two pairs of congruent sides and a pair of congruent angles do not necessarily meet the SAS congruence criterion, therefore Angie is incorrect.

<h3 /><h3>What is congruency?</h3>

The Side-Angle-Side Congruence Theorem (SAS) defines two triangles to be congruent to each other if the included angle and two sides of one is congruent to the included angle and corresponding two sides of the other triangle.

An included angle is found between two sides that are under consideration.

See image attached below that demonstrates two triangles that are congruent by the SAS Congruence Theorem.

Thus, two triangles having two pairs of corresponding sides and one pair of corresponding angles that are congruent to each other is not enough justification for proving that the two triangles are congruent based on the SAS Congruence Theorem.

The one pair of corresponding angles that are congruent MUST be "INCLUDED ANGLES".

Therefore, based on the SAS congruence criterion, the statement that best describes Angie's statement is:

Two triangles having two pairs of congruent sides and a pair of congruent angles do not necessarily meet the SAS congruence criterion, therefore Angie is incorrect.

Learn more about congruency at

brainly.com/question/14418374

#SPJ1

5 0

2 years ago

HELP OMG HELP IM SO STUCK

tangare [24]

Answer: -1

Step-by-step explanation:

1 - (-3) - 5 = 1 + 3 - 5

Thats because subtracting by a negative number is the same as adding the negative number's absolute value (Distance away from zero).

(1 + 3) - 5 = -1

PEMDAS Addition and Subtraction from left to right.

7 0

3 years ago

From a practice assignment:<br>solve the following differential equation given initial conditions

hodyreva [135]

If $y' = e^y \sin(x)$ and $y(-\pi)=0$ , separate variables in the differential equation to get

$e^{-y} \, dy = \sin(x) \, dx$

Integrate both sides:

$\displaystyle \int e^{-y} \, dy = \int \sin(x) \, dx \implies -e^{-y} = -\cos(x) + C$

Use the initial condition to solve for $C$ :

$-e^{-0} = -\cos(-\pi) + C \implies -1 = 1 + C \implies C = -2$

Then the particular solution to the initial value problem is

$-e^{-y} = -\cos(x) - 2 \implies e^{-y} = \cos(x) + 2$

(A)

4 0

2 years ago

PLEASE PLEASE PLEASE HELP ME YALL‼️‼️‼️‼️‼️

Inessa [10]

Answer:

Hi .. im happy to help

answer is 0.033

Step-by-step explanation:

P = C(4,4)÷C(10,4)

P = 1 ÷ 30

$p = \frac{1 }{30}$

p = 0.033

3 0

3 years ago

The perimeter of an airplane ticket is 32 centimeters. The area is 60 square centimeters. What are the dimensions of the ticket

victus00 [196]

We model the ticket as a rectangle.
For this case what you should know is that the perimeter of the rectangle is given by:
P = 2w + 2l
The area of the rectangle is given by:
A = w * l
In both cases:
w: width
l: long
We have the following system of equations:
32 = 2w + 2l
60 = w * l
Solving the system we obtain:
The dimensions of the ticket are:
(10 cm) * (6 cm)
Answer:
the dimensions of the ticket are:
(10 cm) * (6 cm)
Note: see attached image for system solution

8 0

3 years ago