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Misha Larkins [42]

2 years ago

9

Which congruence criteria can be used directly from the information about triangles HIJ and MNO to prove IJ¯¯¯¯¯¯≅MN¯¯¯¯¯¯¯¯¯¯ b

y CPCTC? HI¯¯¯¯¯¯¯≅NO¯¯¯¯¯¯¯¯, ∠I≅∠N, ∠H≅∠O (1 point) ASA congruence AAS congruence SAS congruence HL congruence

1 answer:

skelet666 [1.2K]2 years ago

7 0

Answer: $\overline{IJ}\cong \overline{MN}$

Step-by-step explanation:

Given: In triangle HIJ and triangle MNO we have

$\overline{HI}\cong \overline{NO}, \angle{I}\cong \angle{N} ,\angle{H}\cong \angle{O}$

here, HI and NN are the included side between ∠I & ∠H and ∠N and ∠O.

So , by ASA congruence rule,

ΔHIJ ≅ ΔMNO

So by CPCTC (corresponding parts of the congruent triangles are congruent)

$\overline{IJ}\cong \overline{MN}$

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A N S W E R Q U I C K P L E A S E

chubhunter [2.5K]

Answer:

1. A

2. D

3. D

Step-by-step explanation:

The standard form of a parabola is

$y=\frac{1}{4p}(x-h)^2+k$ ..... (1)

Where, (h,k) is vertex, (h,k+p) is focus and y=k-p is directrix.

1. The directrix of a parabola is y=−8 . The focus of the parabola is (−2,−6) .

$k-p=-8$ ...(a)

$(h,k+p)=(-2,-6)$

$k+p=-6$ .... (b)

$h=-2$

On solving (a) and (b), we get k=-7 and p=1.

Put h=-2, k=-7 and p=1 in equation (1).

$y=\frac{1}{4(1)}(x-(-2))^2+(-7)$

$y=\frac{1}{4}(x+2)^2-7$

Therefore option A is correct.

2 The directrix of a parabola is the line y=5 . The focus of the parabola is (2,1) .

$k-p=5$ ...(c)

$(h,k+p)=(2,1)$

$k+p=1$ .... (d)

$h=2$

On solving (c) and (d), we get k=3 and p=-2.

Put h=2, k=3 and p=-2 in equation (1).

$y=\frac{1}{4(-2)}(x-(2))^2+(3)$

$y=-\frac{1}{8}(x-2)^2+3$

Therefore option D is correct.

3. The focus of a parabola is (0,−2) . The directrix of the parabola is the line y=−3 .

$k-p=-3$ ...(e)

$(h,k+p)=(0,-2)$

$k+p=-2$ .... (f)

$h=0$

On solving (e) and (f), we get k=-2.5 and p=0.5.

Put h=0, k=-2.5 and p=0.5 in equation (1).

$y=\frac{1}{4(0.5)}(x-(0))^2+(-2.5)$

$y=\frac{1}{2}(x)^2-2.5$

$y=\frac{1}{2}(x)^2-\frac{5}{2}$

Therefore option D is correct.

5 0

2 years ago

Find the value of x. 4^3 = x

pshichka [43]

Answer:

x=64

Step-by-step explanation:

3 0

2 years ago

Read 2 more answers

Divide 6x^4+2x^3-6x^2-14x-1 by 3x+1

kolezko [41]

Using synthetic division, we find the result of the division
(6x^4 +2x^3 -6x^2 -14x -1)/(3(x +1/3))
to be ...
(6x^3 -6x -12)/3 +3/(3x +1)

The result is ...
2x^3 -2x -4 +3/(3x+1)

3 0

3 years ago

A department store buys 300 shirts at a cost of $2,400 and sells them at a selling price of $10 each. Find the percent markup.

Solnce55 [7]

Answer:

67%

Step-by-step explanation:

Given : A department store buys 300 shirts at a cost of $1800 .

Then By unitary method , the cost of one shirt = Cost of 300 shirts divided by 300

= $1800 ÷ 300 = $6

i.e. cost of one shirt = $6

Also, Selling price of one shirt = $10

Price mark up = Selling price - Cost price

= $10-$6 = $4

The percent mark up=

(rounded to the nearest percent)

Hence, the percent markup = 67%

4 0

2 years ago

A vacant city lot is being turned into a neighborhood garden. The neighbors want to fence in a triangular section of the lot and

ozzi

9514 1404 393

Answer:

17 ft, 27 ft, 20 ft

Step-by-step explanation:

Let s represent the length of the shortest side. The the longest side is (2s-7) and the third side is (s+3). The perimeter is the sum of the side lengths:

64 = s +(2s -7) +(s +3)

64 = 4s -4 . . . . . . . . . . . collect terms

16 = s -1 . . . . . . . . . . divide by 4

17 = s . . . . . . . . . add 1

2s -7 = 2·17 -7 = 27 . . . . . the length of the longest side

s +3 = 17 +3 = 20 . . . . . . . the length of the third side

The side lengths are 17 feet, 27 feet, and 20 feet.

8 0

2 years ago