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liq [111]
3 years ago
8

Kayla wants to find the width, AB, of a river. She walks along the edge of the river 65 ft and marks point C. Then she walks 25

ft further and marks point D. She turns 90° and walks until her location, point A, and point C are collinear. She marks point E at this location, as shown.
(a) Can Kayla conclude that Δ and Δ are similar? Why or why not?

(b) Suppose DE = 15 ft. What can Kayla conclude about the width of the river?

Mathematics
1 answer:
AlladinOne [14]3 years ago
8 0

Answer:

Part A) The triangles ABC and EDC are similar by AAA, because the three internal angles are equal in both triangles

Part B) The width of the river is about 39\ ft

Step-by-step explanation:

we know that

If two triangles are similar, then the ratio of its corresponding sides is equal and its corresponding angles are congruent

Part A) we know that

In this problem , triangles ABC and CDE are similar by AAA, because its corresponding angles are congruent

so

m<DCE=m<ACB -----> by vertical angles  

m<EDC=m<ABC -----> is a right angle

m<DEC=m<CAB -----> the sum of the internal angles must be equal to 180 degrees

Part B) we know that

The triangles ABC and EDC are similar -------> see Part A

therefore

\frac{BC}{DC}=\frac{AB}{DE}

substitute the values and solve for AB

\frac{65}{25}=\frac{AB}{15}

AB=15*(\frac{65}{25})=39\ ft

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NNADVOKAT [17]
I think the answer is B but I am not sure
7 0
3 years ago
Consider the trinomial 6x2 + 13x + 6.
attashe74 [19]
In the given expression 6X² + 13X +6, we can easily identify the values of a, b and c. These values are a=6, b=13 and c=6
For the value of "ac", we have:
ac=6*6
ac=36
For a sum of b are 4, we have
ac+b=36+13=49
Therefore, the answer for the last question "The two numbers that have a product of ac and a sum of b are 4 and 9".
8 0
3 years ago
Read 2 more answers
Jason had $32. He spent all the money on buying 4 CDs for $x each and 2 magazines for $y each. If Jason had bought 5 CDs and 2 m
Leni [432]
You can set up two equations from the information given. I will set them up for you:

32 = 4x + 2y
36 = 5x + 2y

Let's solve the first equation to come up with a value for y.

32 = 4x + 2y
32 - 4x = 2y
16 - 2x = y

Now we plug y into the other equation.

36 = 5x + 2(16-2x)
36 = 5x + 32 - 4x
4 = x

Now we have our real x value and we can plug it into the first equation.

32 = 4(4) + 2y
32 = 16 + 2y
16 = 2y
8 = y

Since x = 4 and y = 8, you get the final coordinates of (4,8).

Your answer is the second statement provided above.
3 0
3 years ago
PLEASE HELP ME!!!!!!!! ASAP
DedPeter [7]
Let's take these one at a time.
A
The A choice is that the y intercept of g(x) < y intercept of f(x). Remember, a y intercept occurs when x = 0
g(x) = 2 * sqrt(x) - 8
g(0) = 2*0 - 8
g(0) = - 8
=======
f(x) = - 4 when x = 0 (you just read it.) - 4 is greater than -8. That's a true statement. Think money. Would you rather be 4 dollars in debt or 8 dollars in debt? 
A: True <<<<<< answer for A.

B
y intercept  occurs when x = 0 The values of f(x) and g(x) have been found in part A.

Are they equal?

The y intercept of g(x) = g(0) = 2*sqrt(0) - 8 = - 8
The y intercept of f(x) = f(x)  = - 4 when x = 0 

Conclusion
They are not equal and B is not the answer.

C
The x intercept occurs when y = 0
g(x) = 0 
0 = 2*sqrt(x) - 8
8 = 2*sqrt(x)
4 = sqrt(x)
x = 16
======
When f(x) = 0, x = 16.

Conclusion
The x intercepts are both 16. This statement is true.
C: True <<<<<< answer.

D
If the condition is anything but equal, the statement is false. g(x) is not greater then f(x).

D <<<<<< False.
3 0
3 years ago
Suppose a certain manufacturing company produces connecting rods for 4- and 6-cylinder automobile engines using the same product
gregori [183]

Answer:

Generally the constraint that sets next week are shown below

Generally the constrain that sets next week maximum production of connecting rod for 4 cylinder  to  W_4 or  0 is  

     x_4 \le W_4 *  s_4

    x_4 \le 5000 *  s_4

Generally the constrain that sets next week maximum production of connecting rod for 6 cylinder  to  W_6 or  0  is  

     x_6 \le W_6 *  s_6

     x_6 \le 8,000 *  s_6

Generally the constrain that limits the production of connecting rods  for both 4 cylinder and 6 cylinders  is

     x_4 \le W_4 *  s_6

=>   x_4 \le 5000 *  s_6

     x_4 \le W_6 *  s_4

=>    x_4 \le 8000 *  s_4

     s_4 + s_6 = 1

The minimum cost of production for next week is  

   U  =  M_4 *  x_4 + M_6 * x_6 + C_4 * s_4 + C_6 * s_6

=>  U  =  13x_4 + 16x_6 + 2000 s_4 + 3500 s_6

Step-by-step explanation:

The cost for the four cylinder production line is  C_4 =  \$2,100

The cost for the six cylinder production line is  C_6 = \$3,500

The manufacturing cost for each four cylinder is  M_4= \$13

 The manufacturing cost for each six cylinder is M_6= \$16

  The weekly production capacity for 4 cylinder connecting rod is W_4 = 5,000

   The weekly production capacity for 6 cylinder connecting rod is W_6 = 8,000

Generally the constraint that sets next week are shown below

Generally the constrain that sets next week maximum production of connecting rod for 4 cylinder  to  W_4 or  0 is  

     x_4 \le W_4 *  s_4

    x_4 \le 5000 *  s_4

Generally the constrain that sets next week maximum production of connecting rod for 6 cylinder  to  W_6 or  0  is  

     x_6 \le W_6 *  s_6

     x_6 \le 8,000 *  s_6

Generally the constrain that limits the production of connecting rods  for both 4 cylinder and 6 cylinders  is

     x_4 \le W_4 *  s_6

=>   x_4 \le 5000 *  s_6

     x_4 \le W_6 *  s_4

=>    x_4 \le 8000 *  s_4

     s_4 + s_6 = 1

The minimum cost of production for next week is  

   U  =  M_4 *  x_4 + M_6 * x_6 + C_4 * s_4 + C_6 * s_6

=>  U  =  13x_4 + 16x_6 + 2000 s_4 + 3500 s_6

3 0
3 years ago
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