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skad [1K]
3 years ago
9

Ben uses a compass and a straightedge to construct ∠DEF ≅ ∠ABC, as shown below:

Mathematics
1 answer:
Len [333]3 years ago
5 0

Answer: Choice D

∠DEF ≅ ∠ABC when BH = EJ, BI = EK, and HI = JK.

======================================================

Explanation:

Effectively what Ben is doing is ensuring that

  • BH = EJ
  • BI = EK
  • HI = JK

are the three congruent corresponding sides. This is by construction. After those constructions, he would use SSS to prove the triangles congruent. Lastly, he can then say angle DEF is congruent to angle ABC due to CPCTC.

CPCTC = corresponding parts of congruent triangles are congruent.

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Rectangle R has varying length l and width w but a constant perimeter of 4 ft. A. Express the area A as a function of l. What do
ivanzaharov [21]
Given:
l = length of the rectangle
w = width of the rectangle
P = 4 ft, constant perimeter

Because the given perimeter is constant,
2(w + l) = 4
w + l = 2
w = 2 - l            (1)

Part A.
The area is
A = w*l 
   = (2 - l)*l
 A  = 2l - l²
This is a quadratic function or a parabola.

Part B.
Write the parabola in standard form.
A = -[l² - 2l]
   = -[ (l -1)² - 1]
   = -(l -1)² + 1
This is a parabola with vertex at (1, 1). Because the leading coefficient is negative the curve is downward, as shown below.

The maximum value occurs at the vertex, so the maximum value of A = 1.
From equation (1), obtain
w = 2 - l = 2 - 1 = 1.
The maximum value of the area occurs when w=1 and l=1 (a square).

Answer:
The area is maximum when l=1 and w=1.
The geometric argument is based on the vertex of the parabola denoting maximum area.

4 0
3 years ago
A rectangular garden has length and width as given by the expressions below.
Tom [10]

Answer:

P = -12xy - 56y - 42x + 8

Step-by-step explanation:

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P = 2(4 - 7(3x + 4y)) + 2(3x(-2y))

P = 8 - 14(3x + 4y) + 6x(-2y)

P = 8 - 42x - 56y - 12xy

                              P = -12xy - 56y - 42x + 8

3 0
3 years ago
Read 2 more answers
Will give brainliest.
lesya692 [45]

Answer:

1. y = \frac{-A}{By}x + \frac{C}{By}

2. Divide the Opposite of A and B

3. Doesn't make sense the y-intercept is C/By sry I can't help that one

Step-by-step explanation:

1. Ax + By = C

By = -Ax + C

y = \frac{-A}{By}x + \frac{C}{By}

2. No explanation

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3 years ago
A well pump pumps at a rate of 40 gallons per minute. you want to fill a 1,000-gallon tank. the tank already has 80 gallons. you
Vlad [161]
Possibly 230 minutes?? dont quote me on that lol
6 0
3 years ago
How many one-thirds are there in three-fourths?
kumpel [21]

Answer:

there are 2.25 one-thirds in a three-fourth.

Hope this helps you out!

7 0
3 years ago
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