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AleksAgata [21]
3 years ago
12

The perimeter of △CDE is 55 cm. A rhombus DMFN is inscribed in this triangle so that vertices M, F, and N lie on the sides CD ,

CE , and DE respectively. Find CD and DE if CF=8 cm and EF=12 cm.
Mathematics
1 answer:
ivanzaharov [21]3 years ago
7 0

Answer:

  CD = 14 cm; DE = 21 cm

Step-by-step explanation:

The perimeter is the sum of side lengths (in centimeters), so ...

  CD + DE + CF + EF = 55

  CD + DE + 8 + 12 = 55 . . . . . . . substittute for CF and EF

  CD + DE = 35 . . . . . . . . . . . . . . subtract 20

___

The segment DF is a diagonal of the rhombus, so bisects angle D. That angle bisector divides ΔCDE into segments that are proportional. That is, ...

  CD/DE = CF/EF = 8/12 = 2/3

___

So, we have two segments whose sum is 35 (cm) and whose ratio is 2 : 3. The total of "ratio units is 2+3=5, so each must stand for a length unit of 35/5 = 7 (cm). The sides are ...

  CD = 2·7 cm = 14 cm

  DE = 3·7 cm = 21 cm

<em>Check</em>

  CD + DE = (14 +21) cm = 35 cm . . . . . matches requirements

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Translate the following words into an algebraic expression.
olganol [36]

Answer:

You've learned how to work with variables and how to evaluate algebra expressions, now we are going to translate words into algebraic expressions.

This skill will come in handy when working with word problems or real life situations. Pay close attention to the "key words" that represent mathematical operations.

You are probably very used to translating words into numerical expressions. Think about this...

We are used to seeing the words, plus, sum, difference, minus, product ...

The good news is that these very same words that we use to write numerical expressions are going to be used to write algebra expressions.

The difference between a numerical expression and an algebra expression is that we will be using variables when writing an algebraic expression. Instead of "8 plus 9" (with two given numbers), you would see, "a number plus 9".

We don't know exactly "what number", so we would use a variable to indicate that it can be any number.

Key words for each operation are indicated in bold. This will help you to easily translate the expression.

As, you can see from the red, bold words, the key words for addition are: sum, more than, plus, increase, add, older than.

Please also remember that addition is commutative; therefore, you can reverse the digits and you will end up with the same answer.

Now, let's take a look at the key words for subtraction.

5 0
3 years ago
Read 2 more answers
Which equation should be used to solve this problem?
dolphi86 [110]
Equation:

55 = x + (x+15)
6 0
3 years ago
Choose the equation that represents the graph below: (1 point) Graph of a line passing through points 0 comma 6 and 9 comma 0 y
aleksklad [387]

Answer:

Option C is correct.

Equation of a line y=\frac{-2}{3}x+6 passing through (0,6) and (9,0).

Explanation:

Given the two points (0, 6) and (9 ,0).

To find the equation for the given two points (x_{1},y_{1}) and (x_{2},y_{2}) is,

y-y_{1}=m(x-x_{1}); where m is the slope and is given by:

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

First find the slope m:

m=\frac{0-6}{9-0} =\frac{-6}{9} =\frac{-2}{3}

Substitute this value in equation of line:

y-6=\frac{-2}{3} (x-0) or

y-6=\frac{-2}{3} x

⇒ y=\frac{-2}{3}x+6

Therefore, the equation for the given point is:  y=\frac{-2}{3}x+6


7 0
3 years ago
Plz help me NOW I will mark you brainliest
puteri [66]
  • Let x be the percentage of p.
  • Therefore,
  • m\% \:  \: of \:  \: n = x\% \:  \: of \:  \: p \\  =  >  \frac{mn}{100}  =  \frac{px}{100}  \\  =  > mn =  \frac{px}{100}  \times 100 \\  =  > mn = px \\  =  >  \frac{mn}{p}  = x

<u>Answer:</u>

<u>\frac{mn}{p}</u>

Hope you could get an idea from here.

Doubt clarification - use comment section.

8 0
2 years ago
2 Points
Leviafan [203]

Answer:

C

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3 years ago
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