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pishuonlain [190]
2 years ago
15

State what additional information is required in order to know that the triangles are congruent for the reason given.

Mathematics
2 answers:
STALIN [3.7K]2 years ago
4 0
I believe that would be B! Good luck I hope this helps
Amiraneli [1.4K]2 years ago
4 0

Answer:

  • B) PQ ≅ VR

Step-by-step explanation:

<u>Reason given:</u>

  • SAS, side-angle-side

<u>Required information:</u>

  • Two sides and the included angle

<u>Information given:</u>

  • ∠RQP ≅ ∠QRV
  • QR ≅ RQ, same side

<u>Addition information needed, the other side, adjacent to given angle:</u>

  • PQ ≅ VR

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Given a = 4 and b = -2, evaluate -|b - a|. Please help!
Sergeeva-Olga [200]
The answer is:  - 6 .
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Evaluate the value INSIDE the "bars". 
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6 0
3 years ago
Write 2 numbers that round to 480 when rounded to the nearest 10.
OLga [1]

Step-by-step explanation:

First, 480 rounded to the nearest ten is:

480

second 480 rounded to the nearest ten is 481

6 0
3 years ago
Find x so that the points (x,x+1), (x+2,x+3) and (x+3,2x+4) form a right-angled triangle.
azamat

Let <em>a</em>, <em>b</em>, and <em>c</em> be vectors each starting at the origin and terminating at the points (<em>x</em>, <em>x</em> + 1), (<em>x</em> + 2, <em>x</em> + 3), and (<em>x</em> + 3, 2<em>x</em> + 4), respectively.

Then the vectors <em>a</em> - <em>b</em>, <em>a</em> - <em>c</em>, and <em>b</em> - <em>c</em> are vectors that point in directions parallel to each of the legs formed by the triangle with these points as its vertices.

If this triangle is to contain a right angle, then exactly one of these pairs of vectors must be orthogonal. In other words, one of the following must be true:

(<em>a</em> - <em>b</em>) • (<em>a</em> - <em>c</em>) = 0

<em>or</em>

(<em>a</em> - <em>b</em>) • (<em>b</em> - <em>c</em>) = 0

<em>or</em>

(<em>a</em> - <em>c</em>) • (<em>b</em> - <em>c</em>) = 0

We have

<em>a</em> - <em>b</em> = (<em>x</em>, <em>x</em> + 1) - (<em>x</em> + 2, <em>x</em> + 3) = (-2, -2)

<em>a</em> - <em>c</em> = (<em>x</em>, <em>x</em> + 1) - (<em>x</em> + 3, 2<em>x</em> + 4) = (-3, -<em>x</em> - 3)

<em>b</em> - <em>c</em> = (<em>x</em> + 2, <em>x</em> + 3) - (<em>x</em> + 3, 2<em>x</em> + 4) = (-1, -<em>x</em> - 1)

Case 1: If (<em>a</em> - <em>b</em>) • (<em>a</em> - <em>c</em>) = 0, then

(-2, -2) • (-3, -<em>x</em> - 3) = (-2)×(-3) + (-2)×(-<em>x</em> - 3) = 2<em>x</em> + 12 = 0   ==>   <em>x</em> = -6

which would make <em>a</em> - <em>c</em> = (-3, 3) and <em>b</em> - <em>c</em> = (-1, 5), and their dot product is not zero. Then the triangles vertices are at the points (-6, -5), (-4, -3), and (-3, -8).

Case 2: If (<em>a</em> - <em>b</em>) • (<em>b</em> - <em>c</em>) = 0, then

(-2, -2) • (-1, -<em>x</em> - 1) = (-2)×(-1) + (-2)×(-<em>x</em> - 1) = 2<em>x</em> + 4 = 0   ==>   <em>x</em> = -2

which would make <em>a</em> - <em>c</em> = (-3, -1) and <em>b</em> = (-1, 1), and their dot product is also not zero. The vertices are the points (-2, -1), (0, 1), and (1, 0).

Case 3: If (<em>a</em> - <em>c</em>) • (<em>b</em> - <em>c</em>) = 0, then

(-3, -<em>x</em> - 3) • (-1, -<em>x</em> - 1) = (-3)×(-1) + (-<em>x</em> - 3)×(-<em>x</em> - 1) = <em>x</em> ² + 4<em>x</em> + 6 = 0

but the solutions to <em>x</em> here are non-real, so we throw out this case.

So there are two possible values of <em>x</em> that make a right triangle, <em>x</em> = -6 and <em>x</em> = -2.

3 0
3 years ago
At the local store, the cost of 1 pair of jeans is $24 and the cost of 3 pairs is $24 × 3 = $72. At the online store, the cost o
Juli2301 [7.4K]

Complete question :

Complete the tables to relate the numbers of pairs of jeans to the cost of the jeans at each store. Assume that Tim is placing a single order, and

ignore any taxes.

Answer:

$24, $72

$50

Step-by-step explanation:

From the table :

At local store :

2 pair of jeans cost $48

Cost of a pair :

Cost of 2 pairs / number of pairs

$48 / 2 = $24

Cost of 3 pairs :

Cost per pair * number of pairs :

$24 * 3 = $72

At online store :

Cost of Jean include a fixed fee of $6

Cost of one pair of Jean = $28

Actual cost of Jean :

$28 - $6 = $22

Hence, cost of 2 pair of jeans:

($22*2) + $6

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2 years ago
What is the function to use in excel when you want to find the cost times the number of units?
Brrunno [24]
I think its unit price
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3 years ago
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