Which relationship describes angles 1 and 2?

You are creating a decorated rope that is at least 20 feet long to create a rope you are using beads that are 6 inches long writ

Nitella [24]

Answer:

The number of beads used must be at least 40 to make a decorated rope of at least 20 feet length. The inequality is:

$6n\geq 240\\n\geq 40$

Step-by-step explanation:

Let the number of beads used be 'n'.

Now, length of 1 bead = 6 in

∴ Length of 'n' beads = $6\times n=6n\ in$

Now, minimum length of rope is 20 ft. Converting feet to inches, we get:

$20\ ft =20\times 12=240\ in$

Now, beads are inserted in the rope. So, the length of rope is same as the length of all the beads joined together.

As per question, length must be at least 20 ft or 240 in.

Therefore, the length of all beads joined together must be at least 240 inches. This gives,

$6n\geq 240\\n\geq \frac{240}{6}\\n\geq 40$

Therefore, the number of beads used must be at least 40 to make a decorated rope of at least 20 feet length.

5 0

4 years ago

Determine the values of the unlabeled parts of the triangle.

____ [38]

Answer:

∠Q = 63.4º, PQ = 2, QO = 4.47

Step-by-step explanation:

A triangle is a polygon with three sides and three angles. There are different types of triangles such as the equilateral triangle, isosceles triangle, scalene triangle, right angled triangle.

Triangle POQ is a right angled triangle because ∠P = 90°. Also, ∠O = 26.6°.

Therefore in ΔPOQ: ∠P + ∠O + ∠Q = 180° (sum of angles in a triangle).

90 + 26.6 + ∠Q = 180

∠Q + 116.6 = 180

∠Q = 180 - 116

∠Q = 63.4°

We can find PQ and QO using sine rule. Sine rule for ΔPOQ is given as:

$\frac{PO}{sin Q}= \frac{PQ}{sinO}= \frac{QO}{sin P}\\\\Finding\ PQ :\\\\\frac{PO}{sin Q}= \frac{PQ}{sinO}\\\\\frac{4}{sin(63.4)} =\frac{PQ}{sin(26.6)}\\\\PQ= \frac{4}{sin(63.4)} *sin(26.6)\\\\PQ = 2\\\\Also\ finding\ QO:\\\\\frac{PO}{sin Q}= \frac{QO}{sinP}\\\\\frac{4}{sin(63.4)} =\frac{QO}{sin(90)}\\\\QO=\frac{4}{sin(63.4)} *sin(90)\\\\QO = 4.47$