In ΔOPQ, o = 6.6 inches, p = 2.1 inches and q=6 inches. Find the measure of ∠O to the nearest 10th of a degree.

The measure of ∠O is 97.2° to the nearest tenth

Step-by-step explanation:

To solve this question, we will use the cosine rule

In Δ OPQ

Side o is opposite to ∠O

Side p is opposite to ∠P

Side q is opposite to ∠Q

By using the cosine rule

∵ o² = p² + q² - 2(p)(q)cos∠O

∵ o = 6.6 inches

∵ p = 2.1 inches

∵ q = 6 inches

→ Substitute them in the rule above

∴ (6.6)² = (2.1)² + (6)² - 2(2.1)(6)cos∠O

∴ 43.56 = 4.41 + 36 - 25.2cos∠O

→ Add the like terms in the right side

∴ 43.56 = 40.41 - 25.2cos∠O

→ Subtract 40.41 from both sides

∵ 3.15 = -25.2cos∠O

→ Divide both sides by -25.2 to find cos∠O

∴ -0.125 = cos∠O

→ Use your calculator to find ∠O

∵ m∠O =

∴ m∠O = 97.18075578

→ Round it to the nearest tenth ⇒ 2d.p.

∴ m∠O = 97.2°

first option

a function is a relation in which an input is paired with exactly one output.

so, let's find the right answer.

in our first option, our inputs are january, february, and march. the outputs are 30, 28, and 25. each input has it's own output. this is correct!

our second option we know is incorrect, because ms. valverade has two outputs, dogs and cats. this is not a function.

our third option is incorrect as well. the yellow square has two ouputs, the square and the triangle.

lastly, in our fourth option, we see the number 7 two times with a different output. therefore, this is not a function.

remember: each input must be paired with only one output!

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.