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3 years ago

Geometry... Please help and I'll mark brainliest. Triangle proofs & reasons

Mathematics

1 answer:

aliya0001 [1]3 years ago

6 0

Answer:

We are given that,

Polygons ABC and DBC are triangles.

Also, ABC and DBC are Right Triangles as ∠ABC and ∠DBC are 90 respectively.

AB ↔ CD

Now,

From the HL Congruency we know that,

"Two Right triangles are congruent if the Hypotenuses and at least One Side  of both the triangles correspond to each other."

Here,

Triangles ABC and DBC were given to be right triangles.

AB and CD are the hypotenuses of ΔABC and Δ DBC respectively. (From the construction of the figure) and are given equal.
The Side BC of both the triangles correspond as they share the side BC together.

Here, As the three conditions of being congruent through HL Congruency are satisfied, ΔABC & Δ DBC are congruent through the HL Congruency Criterion.

ΔABC ≅ Δ DBC [Hence, Proved]

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alukav5142 [94]

Note: in the 2nd eqn we are given a formula for x: x = 2y-15. Sub this result into the first eqn; doing so will eliminate x:

-5(2y-15)+4y =3

-10y + 75 + 4y = 3, so -6y = -72. Then y = 12. Solution is (9,12).

Check this by subst.:

Is -5(9)+4(12) = 3?
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3 0

3 years ago

I will mark the BRAINIEST Solve for x

Elanso [62]

Answer:

x = 10.5

Step-by-step explanation:

Firstly, in geometry, you may have to prove that the two triangles pictured are similar.

Since the two horizontal lines are marked, they are assumed to be parallel.

Therefore, if the lines are parallel, the two bottom angles of each triangle can be treated as the same due to the [Corresponding Angles Theorem], respectively

As such, the two triangles can be seen as SIMILAR as proven by Angle-Angle Similarity.

Now that we've proven both triangles to be similar, we can then set up ratios for the sides:

$\frac{8}{6}$ = $\frac{8+14}{y}$

Note: we are using y as a measure of the entire right side of the triangle, so

y = 6 + x

Continuing on, if you cross-multiply the fractions to solve for y:

8y = 6 * 22

Simplify.

8y = 132

Simplify again.

y = 16.5

We are not done yet! We are solving for x, so remember y = 6 + x

16.5 = 6 + x

Solve for x.

x = 10.5

6 0

3 years ago

A die is rolled 20 times. given that three of the rolls came up 1, five came up 2, four came up 3, two came up 4, three came up

Serjik [45]

Solution:

Number of times a die is rolled = 20

1 - 3=A

2 - 5=B

3 - 4=C

4 - 2=D

5 - 3=E

6 - 3=F

Total number of arrangements of outcomes , when a dice is rolled 20 times given that 1 appear 3 times, 2 appears 5 times, 3 appear 4 times, 4 appear 2 times , 5 appear three times, and 6 appear 3 times

= Arrangement of 6 numbers (A,B,C,D,E,F) in 6! ways and then arranging outcomes

= 6! × [ 3! × 5! × 4!×2!×3!×3!]

= 720 × 6×120×24×72→→[Keep in Mind →n!= n (n-1)(n-2)(n-3)........1]

= 895795200 Ways

8 0

3 years ago

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Kobotan [32]

Answer:

$39$