The points R(-4,3), S(1, -3), and T(2, 1) are connected to form ARST.

2. A certain TV can be purchased from the manufacturer for $160. A certain online retailer has a standard markup of 30%, and a c

Vanyuwa [196]

Price, when purchased online: 1.30($160)
Price, when purchased at superstore: 1.40($160)

Difference in prices: 1.40($160) - 1.30($160) = 0.10($160) = $16

A higher markup brings a higher retail price.

8 0

3 years ago

For what value of x is quadrilateral CDEF a parallelogram? x=?

Contact [7]

Answer:

x = 5

Step-by-step explanation:

Since we know that the diagonals bisect each other and divide into equal parts so ➡

x - 2 = 2x -7

2x - x = 7 - 2

x = 5

8 0

2 years ago

1. Based on the information given, can you determine that the quadrilateral must be a

zhenek [66]

Solving Q1: Given BE = ED and AE = EC.

Considering triangles ΔAED and ΔCEB;

1. AE = EC (given)

2. ∠AED = ∠CEB (vertical angles)

3. ED = EB (given)

ΔAED ≡ ΔCEB (Side-Angle-Side congruency of triangles)

∠DAE = ∠BCE and AD = BC (using CPCTC)

⇒ AD║BC (Converse of Alternate Interior angles theorem)

Similarly consider triangles ΔABE and ΔCDE;

1. AE = CE (given)

2. ∠BEA = ∠DEC (vertical angles)

3. BE = DE (given)

ΔABE ≡ ΔCDE (Side-Angle-Side congruency of triangles)

∠ABE = ∠CDE and AB = CD (using CPCTC)

⇒ AB║CD (Converse of Alternate Interior angles theorem)

Since we have AB║CD, AB = CD and AD║BC, AD = BC.

Therefore, quadrilateral ABCD is a parallelogram.

****************************************************************************************************

Solving Q2: The parallelogram has the angle measures shown in the diagram.

It is clearly visible that both the triangles are Isosceles triangles, so opposite sides in each triangle are equal.

Consider two triangles given in the problem, we have two sets of congruent angles and one included side is common in both triangles.

Using Angle-Side-Angle congruence of triangles, both the triangles would be congruent too.

Using CPCTC, we can say opposite sides of quadrilateral would be congruent.

Therefore, all sides in given quadrilateral are equal.

Hence, Given quadrilateral is a Rhombus.

7 0

2 years ago

A fair die is tossed 5 times. Let <img src="https://tex.z-dn.net/?f=%5Cdfrac%7Bm%7D%7Bn%7D" id="TexFormula1" title="\dfrac{m}{n}

Ray Of Light [21]

Answer:

m = 1

Step-by-step explanation:

We can suppose that the number we are looking for is for example 5.

(we can do so because the probability is the same for each number - it'sna fair dice)

For the first toss the probability we have 5 is 1/6 (we have 6 numbers on the dice and number 5 is just one of the possible 6 outcomes).

For the second toss the probability we have 5 is again 1/6.

For the rest of 3 tosses we don'tcare what number we will get( we have our two consecutive 5s), so all of the outcomes for the rest of 3 tosses are good for us (probability is 6/6 = 1)

Threfore, the probability to get two consecutive 5s is 1/6 * 1/6 * 1 * 1 * 1 = 1/36.

We can see that m = 1.

4 0

3 years ago

Which of the following statements are enough to prove that triangles EFI and GFH are similar?

SCORPION-xisa [38]

To Prove: ΔEFI ~ Δ GFH

Proof:

When two triangles are similar, their corresponding sides are Proportional and their corresponding interior angles are equal.

Two Triangles can be proven similar by following Similarity Criterion.

1. AA

2.SSS

3.SAS

→∠EFI=∠GFH-------[Vertically Opposite angles]

The Other statement which is needed to prove that triangles EFI and GFH are similar is

Option C:→ ∠E ≅ ∠G

So, Two triangles ΔEFI and Δ GFH are Similar by Angle-Angle(AA) Criterion.

6 0

3 years ago

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