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pentagon [3]
3 years ago
14

In triangle $DEF,$ $\angle D = 30^\circ,$ $\angle F = 60^\circ,$ and $EF = 6.$ Find $DE + DF.$ [asy] unitsize(2 cm); pair D, E,

F; D = (0,sqrt(3)); E = (0,0); F = (1,0); draw(D--E--F--cycle); label("$D$", D, N); label("$E$", E, SW); label("$F$", F, SE); label("$6$", (E + F)/2, S); [/asy]
Mathematics
1 answer:
sergey [27]3 years ago
5 0

Answer:

Step-by-step explanation:

The answer to this question is 12+6sqrt3.

This is because of the 30, 60, and 90 degree rule. The rule states that the hypotenuse is equal to twice the length of the shorter leg, which is the side across from the 30 degree angle.

Using the rule you now know that DF is 12. Then use the Pythagorean Theorem to find the length of DE. 12^2=144, and 6^2=36. 144-36=108.

The square root of 108 simplified=6sqrt3.

Then you add them together and get 12+6sqrt3.

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49°<br> Solve for 42.<br> 2 = [?]<br> 44/62
Brrunno [24]

Answer:

∠2 = 41°

Step-by-step explanation:

∠2 + 49° + 90° = 180°

∠2 + 139° = 180°

∠2 = 180° - 139°

∠2 = 41°

5 0
3 years ago
Read 2 more answers
He radius of a circle is 2 kilometers. What is the area of a sector bounded by a 45° arc?
faust18 [17]
We know that
area of a circle=pi*r²
for r=2 km
area of a circle=pi*2²-----> 12.56 km²

if 360° (full circle) has an area of---------> 12.56 km²
 45°---------------------------------> x
x=45*12.56/360-----> x=1.57 km²

the answer is
1.57 km²
7 0
3 years ago
Latrell has $8 to spend on postcards. He wants to buy one large postcard and some small ones. Write and solve an inequality to d
fgiga [73]
I have had this worksheet

8 0
4 years ago
Is the expression a polynomial? If yes, write in standardform, if not state why not
Studentka2010 [4]

Answer:

Step-by-step explanation:

1) Not a polynomial. Because x² is in the denominator.

2) Yes, it is a polynomial.

Standard form: 5x² + 2x - 99

3) Not a polynomial.

\sqrt{8x^{3}} = (8x^{3})^{\frac{1}{2}} = 8^{\frac{1}{2}}x^{\frac{3}{2}} .

Power of x is a fraction. so , it is not a polynomial.

4) Power of x is (-2). Power of x should not be a negative integer. SO, it is not a polynomial.

5) Yes:

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6 0
2 years ago
2.) Find the circumference of a circle if the area of the circle is 379.94 in? Use 3.14 as an
dybincka [34]

Answer:

c = 69.1

Step-by-step explanation:

which equals it to 379.94

hope it helps

7 0
3 years ago
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