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sertanlavr [38]
3 years ago
10

If DE = 37 cm and EF = 16 cm, then what are the possible lengths for DF so that DE,EF, and DF can form a triangle? Explain your

reasoning.
Mathematics
1 answer:
notsponge [240]3 years ago
8 0

Answer:

The length of DF must be between 21 and 53.

Step-by-step explanation:

In a triangle, the length of two sides added together must exceed the length of the 3rd side. So, since EF is the shortest of the two givens, we know that EF + DF must be greater than DE. So we can plug in these numbers to find the minimum.

EF + DF > DE

16 + DF > 37

DF > 21

Now, for the upper maximum, we know that the two given lengths must be greater than the length of DF. So again, we can solve for the maximum using the amounts.

DE + EF > DF

37 + 16 > DF

53 > DF

With these two in mind, we know that DF must be between 21 and 53

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G(x)=−4x+4, find g(3)
Igoryamba

»»————- ★ ————-««

I believe your answer is:  

g(3) = -8

»»————- ★ ————-««  

Here’s why:  

⸻⸻⸻⸻

\boxed{\text{Evaluating the function...}}\\\\g(x)=-4x+4; g(3)\\\\--------------\\\rightarrow g(3)=-4(3)+4\\\\\rightarrow g(3) = -12  + 4\\\\\rightarrow \boxed{g(3)=-8}

⸻⸻⸻⸻

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

7 0
3 years ago
A triangle has two sides measuring 16 and 21. The included angle is 116°. What is the length of the side opposite the 116° angle
lutik1710 [3]

Answer:

h =26.4

C is correct Option

Step-by-step explanation:

Let,

Base of the triangle = b = 16  

Perpendicular of the triangle = p = 21

Hypotenuse of the triangle= h = ?

According to Pythagoras theorem;

 h^{2} = b^{2} +p^{2}

 h^{2} = 21^{2} +16^{2}

 h^{2} =441+256

 h^{2} =697

 h =\sqrt{697}

h =26.4

 

 

3 0
4 years ago
Which equation results from adding the equations in this system?
Diano4ka-milaya [45]

Answer:

  • D. - 5x = - 10

Step-by-step explanation:

<u>Given equations:</u>

  • -8x+8y = 8
  • 3x-8y=-18

<u>Add together:</u>

  • -8x + 8y + 3x - 8y = 8 - 18
  • - 5x = - 10

Correct option is D

7 0
3 years ago
What's the slope of a line that passes through (-12,15) and (0,4)​
Ierofanga [76]

Answer:

D. -11/12

Step-by-step explanation:

Slope Formula: m = \frac{y2-y1}{x2-x1}

Simply plug in our coordinates:

m = (4 - 15)/(0 + 12)

m = -11/12

3 0
3 years ago
1. The total area within any continuous probability distribution is equal to 1.00.
olchik [2.2K]

Answer:

1. True

2. False.

3. True.

Step-by-step explanation:

1. The total area within any continuous probability distribution is equal to 1.00: it is true because the maximum probability (value) is one (1), therefore, the total (maximum) area is also one (1).

<em>Hence, for continuous probability distribution: probability = area</em>.

2. For any continuous probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: False because it has an infinite number of possible values, which can not be counted or uncountable.

<em>Hence, it cannot be computed. </em>

3. For any discrete probability distribution, the probability, P(x), of any value of the random variable, X, can be computed: True because it has a finite number of possible values, which are countable or can be counted.

<em>Hence, it can be computed. </em>

5 0
4 years ago
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