Which property is demonstrated by the following statement? 13 + (27 + g) = (13 + 27) + 6 Please help me I am being timed!!!

Mathematics

1 answer:

KIM [24]3 years ago

6 0

Answer:

Associative property of addition

Step-by-step explanation:

Associative property of addition

(a + b) + c = a + (b + c)

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The diagram shows how cos θ, sin θ, and tan θ relate to the unit circle. Copy the diagram and show how sec θ, csc θ, and cot θ r

DIA [1.3K]

Copy the diagram and show how sec θ, csc θ, and cot θ relate to the unit circle.

The representation of the diagram is shown if Figure 1. There's a relationship between sec θ, csc θ, and cot θ related the unit circle. Lines green, blue and pink show the relationship.

a.1 First, find in the diagram a segment whose length is sec θ.

The segment whose length is sec θ is shown in Figure 2, this length is the segment $\overline{OF}$ , that is, the line in green.

a.2 Explain why its length is sec θ.

We know these relationships:

(1) $sin \theta=\frac{\overline{BD}}{\overline{OB}}=\frac{\overline{BD}}{r}=\frac{\overline{BD}}{1}=\overline{BD}$

(2) $cos \theta=\frac{\overline{OD}}{\overline{OB}}=\frac{\overline{OD}}{r}=\frac{\overline{OD}}{1}=\overline{OD}$

(3) $tan \theta=\frac{\overline{FD}}{\overline{OC}}=\frac{\overline{FC}}{r}=\frac{\overline{FC}}{1}=\overline{FC}$

Triangles ΔOFC and ΔOBD are similar, so it is true that:

$\frac{\overline{FC}}{\overline{OF}}= \frac{\overline{BD}}{\overline{OB}}$ 

∴ $\overline{OF}= \frac{\overline{FC}}{\overline{BD}}= \frac{tan \theta}{sin \theta}= \frac{1}{cos \theta} \rightarrow \boxed{sec \theta= \frac{1}{cos \theta}}$ 

b.1 Next, find cot θ

The segment whose length is cot θ is shown in Figure 3, this length is the segment $\overline{AR}$ , that is, the line in pink.

b.2 Use the representation of tangent as a clue for what to show for cotangent.

It's true that:

$\frac{\overline{OS}}{\overline{OC}}= \frac{\overline{SR}}{\overline{FC}}$

But:

$\overline{SR}=\overline{OA}$
$\overline{OS}=\overline{AR}$

Then:

$\overline{AR}= \frac{1}{\overline{FC}}= \frac{1}{tan\theta} \rightarrow \boxed{cot \theta= \frac{1}{tan \theta}}$

b.3 Justify your claim for cot θ.

As shown in Figure 3, θ is an internal angle and ∠A = 90°, therefore ΔOAR is a right angle, so it is true that:

$cot \theta= \frac{\overline{AR}}{\overline{OA}}=\frac{\overline{AR}}{r}=\frac{\overline{AR}}{1} \rightarrow \boxed{cot \theta=\overline{AR}}$

c. find csc θ in your diagram.

The segment whose length is csc θ is shown in Figure 4, this length is the segment $\overline{OR}$ , that is, the line in green.

3 0

4 years ago

How many solutions does the equation have?? 3(d+11)=6(d+33) PLEASE HELP MEEEEEEE

Misha Larkins [42]

A powerful way to find out is to solve the equation. Let's try that.

   3 (d + 11) = 6 (d + 33)

Eliminate the parentheses: 3d + 33 = 6d + 198

Subtract 3d from each side: 33 = 3d + 198

Subtract 198 from each side: -165 = 3d

Divide each side by 3 : - 55 = d

There it is ... the solution to the original equation.
'd' has to be -55, otherwise the original equation isn't a true statement.
-55 is the ONLY number that 'd' can be. If you write in any other number
for 'd', the equation will be false.

For example, less see what the equation says when d=2 :

   3(2 + 11) = 6(2 + 33)

   3( 13 ) = 6( 35 )

   39    = 210

Is that a true statement ? Is 39 equal to 210 ?
No. 39 and 210 are not equal. They are different.
So the equation is not true when d = 2 .
The equation is true ONLY when d = -55 .

The equation has exactly one solution.

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3 years ago

Help please, I don’t understand

frozen [14]

Answer:

Step-by-step explanation:

i dont see anything i can help with

7 0

3 years ago

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